BY AUGUSTUS DE MORGAN: A BUDGET OF PARADOXES, Volume I

This is a digest of the original available at https://www.gutenberg.org/ebooks/23100
If you see anything in this that is interesting to you, you should not quote this digest, you should go to the original and track down what interests you.  I have made many changes, in language and in the order of subjects, that would be severely embarrassing if passed off as the real thing.  --  MPJ, 4/24/20. 


INTRODUCTORY.
    If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, he might use such arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject.  But if there were a thousand flies, all buzzing about the great creature, and each declaring that he was bigger than the quadruped; each giving different and frequently contradictory reasons; and each despising and opposing the reasons of the others — I should feel quite at ease.  The case of each would be destroyed by the rest.
    I use "paradox" in the old sense: something apart from general opinion, either in subject matter, method, or conclusion.
    Many such things would now be called crotchets, except that to call a thing a crotchet is to speak lightly of it, which was not the old necessary sense of paradox.  Thus in the sixteenth century many spoke of the earth's motion as the paradox of Copernicus.  In the seventeenth century, the depravation of meaning took place, in England at least; Phillips says paradox is "a thing which seemeth strange and absurd, and contrary to common opinion."
    During recent centuries, physical knowledge has come to rest upon a basis it did not have before: mathematics.  Now the question is not whether some hypothesis is better or worse according to pure thought, but whether it accords with observed phenomena.  Even in sciences not yet under the dominion of mathematics, and perhaps never to be, a working copy of the mathematical process has been made.  This is not known to the followers of those sciences who are not themselves mathematicians and therefore very often exalt their horns against mathematics.  They might as well be squaring the circle, for any sense they show in this particular.
    A great many individuals, ever since the rise of the mathematical method, have attacked its direct and indirect consequences.  I shall not here stop to point out how the very accuracy of exact science gives better aim than the preceding state of things could give.  I shall call each of these persons a paradoxer, and his system a paradox.
    That a little knowledge is a dangerous thing is one of the most fallacious of proverbs.  A person of small knowledge is in danger of trying to make his little do the work of more; but a person without any is in more danger of making his no knowledge do the work of some.
    The manner in which a paradoxer will show himself will not depend on what he maintains, but on whether he has sufficient knowledge of what has been done by others, especially as to the mode of doing it, a preliminary to inventing knowledge for himself.  Most persons have an immense variety of opinions on an immense variety of subjects, and all persons must be their own guides in many things.  But many do not reflect that they have ceased to stand on ground on which their process is defensible.  Aspiring to lead others, they have never given themselves the fair chance of being first led by others into something better than they can start for themselves.
    That they should first do this is what others have a fair right to expect.  New knowledge, when to any purpose, must come by contemplation of old knowledge in every matter which concerns thought; mechanical contrivance sometimes, not very often, escapes this rule.  All the men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned in what had been before them.  I do not say that every man has made direct acquaintance with the whole of his mental ancestry; many have, I may say, only known their grandfathers by the report of their fathers.  But even on this point it is remarkable how many of the greatest names in all departments of knowledge have been real antiquaries in their several subjects.
    Upon meeting those who plague others with their great discoveries, the first demand should be: Mr. Moses, before I allow you to lead me over the Red Sea, you must show me that you are learned in all the wisdom of the Egyptians upon your own subject.  The demand for previous knowledge disposes of twenty-nine cases out of thirty; the thirtieth is worth listening to.
    I have talked to more than a hundred and fifty paradoxers; it is not my own fault if they have not been a thousand.  Nobody knows how they swarm, except those to whom they naturally resort.  They are in all ranks and occupations, all ages and characters.  They are very earnest, and their purpose is the dissemination of their paradoxes.  The mass are illiterate, and a great many waste their means, and are in or approaching penury.  They despise one another.
    I select, to the mystic number seven, instances of my personal knowledge of paradoxers, in illustration of as many misconceptions.
        1.    Attempt by help of the old philosophy, the discoverer not possessing modern knowledge.  A poor schoolmaster, in rags, introduced himself to a scientific friend with whom I was talking, and announced that he had found out the composition of the sun.  "How was that done?" — "By consideration of the four elements." — "What are they?" — "Of course, fire, air, earth, and water." — "Did you not know that air, earth, and water, have long been known to be no elements at all, but compounds?" — "What do you mean, sir?  Who ever heard of such a thing?"
        2.    The notion that difficulties are enigmas, to be overcome in a moment by a lucky thought.  A nobleman of very high rank, now long dead, read an article by me on the quadrature, in an early number of the Penny Magazine.  He had, I suppose, school recollections of geometry.  He put pencil to paper, drew a circle, and constructed what seemed likely to answer, and, indeed, was — as he said — certain, if only this bit were equal to that; which of course it was not.
        3.    Discovery at all hazards, to get on in the world.  Thirty years ago, an officer of rank, trying for a decoration from the Crown, found that his claims were of doubtful amount.  Now this officer had bethought himself one day that there could be no difficulty in finding the circumference of a circle: if a circle were rolled upon a straight line until the undermost point came undermost again, there would be the straight line equal to the circle.  He came to me, saying that he did not feel equal to the statement of his claim in this respect, but that if some clever fellow would put the thing in a proper light, he thought his affair might be managed.
        4.    The notion that mathematicians cannot find the circle for common purposes.  A working man measured the altitude of a cylinder accurately, found its bulk, calculated the ratio of the circumference to the diameter, and found it answered very well on other modes of trial; his result was about 3.14.  Somebody sent him to me.  Like many paradoxers, he seemed to have turned the whole force of his mind upon one of his points, on which alone he would be open to refutation.  He had read some of Kater's experiments, and had got the Act of 1825 on weights and measures.  Say what I would, he had but one answer — "Sir! I go upon Captain Kater and the Act of Parliament."  Finally, I produced the table the Astronomical Memoirs, in which were a large number of observed places of the planets compared with prediction, and asked him whether it could be possible that persons who did not know the circle better than he could make the calculations so accurately?  He was perfectly astonished, and took the titles of some books which he said he would read.
        5.    Application for the reward from abroad.
        6.    Application for the reward at home.  An agricultural laborer squared the circle, and brought the proceeds to London.  He left his papers with me, one of which was the copy of a letter to the Lord Chancellor, desiring his Lordship to hand over forthwith 100,000 pounds, the amount of the alleged offer of reward.  I returned the papers, with a note stating that he had not the knowledge requisite to see in what the problem consisted.  I got for answer a letter in which I was told that a person who could not see that he had done the thing should "change his business, and appropriate his time and attention to a Sunday school, to learn what he could, and keep the litle children from durting their close."  I also received a letter from a friend of the quadrator, informing me that I knew his friend had succeeded, and had been heard to say so.  There are many who have such deep respect for any attempt at thought that they are shocked at ridicule even of those who have made themselves conspicuous by pretending to lead the world in matters which they have not studied.
        7.    An elderly man came to me to show me how the universe was created: there was one molecule, which by vibration became — Heaven knows how! — the Sun.  Further vibration produced Mercury, and so on.  Some modifications of vibration gave heat, electricity, etc.  I listened until my informant ceased to vibrate — which is always the shortest way — and then said, "Our knowledge of elastic fluids is imperfect."  "Sir!" said he, "I see you perceive the truth of what I have said, and I will reward your attention by telling you what I seldom disclose, never, except to those who can receive my theory — the little molecule whose vibrations have given rise to our solar system is the Logos of St. John's Gospel!"  He went away to Dr. Lardner, who would not go into the solar system at all — the first molecule ended the question.  So hard on poor discoverers are men of science who are not antiquaries in their subject!  On leaving, he said, "Sir, Mr. De Morgan received me in a very different way!  He heard me attentively, and I left him perfectly satisfied of the truth of my system."  Many paradoxers, of all classes, believe they have convinced everyone who is not peremptory to the verge of incivility.
    There may be paradox upon paradox.  There is a good instance in the eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and afterwards Saint, and his quarrels with Boniface, an Englishman, Archbishop of Mentz, also afterwards Saint.  All we know about the matter is that there exists a letter of 748 from Pope Zachary, citing Virgil, then a simple priest, to Rome to answer the charge of maintaining that there is another world under our earth, with another sun and moon.  The letter contains threats in the event of the charge being true.  There history drops the matter.  On so small a basis has been constructed a companion case to the persecution of Galileo.  On one side the positive assertion, with indignant comment, that Virgil was deposed for antipodal heresy; on the other, serious attempts at justification, palliation, or mystification.  Some have maintained that the antipodist was a different person from the canonized bishop; there is a second Virgil, made to order.
    When your shoes pinch and will not stretch, always throw them away and get another pair; the same with your facts.

DR. MILNER'S PARADOXES.
    By "rational paradoxers" I include all who, in private life, and in matters which concern themselves, take their own course, and suit their own notions, no matter what other people may think of them.  These men will put things to uses they were never intended for, to the great distress and disgust of their gregarious friends.  I am one of the class, and I could write a little book of cases in which I have incurred absolute reproach for not "doing as other people do."  Three of my atrocities:
        I took one of those butter dishes which have for a top a dome with holes in it, which is turned inward, out of reach of accident, when not in use.  Turning the dome inwards, I filled the dish with water, and put a sponge in the dome; the holes let it fill with water, and I had a penwiper, always moist, worth its price five times over.  "Why!  What do you mean?  It was made to hold butter.  You are always at some queer thing or other!"
        I bought a lead-pencil comb intended to dye the hair, it being supposed that the application of pencil lead will have this effect.  I did not try that, but I divided the comb into two, separated the part of closed prongs from the other; and thus I had two ruling machines.  By drawing the end of one of the machines along a ruler, I could rule twenty pencil lines at a time.  I thought I should have killed a friend to whom I explained it; he could not for the life of him understand how pencil lines on paper would dye the hair.
        Two persons in conversation agreed that it was often a nuisance not to be able to lay hands on a bit of paper to mark the place in a book, every bit of paper on the table was sure to contain something not to be spared.  I very quietly said that I always had a stock of bookmarkers ready cut, with a proper place for them; my readers owe many of my anecdotes to this absurd practice.  My two colloquials burst into a fit of laughter — about what?  There could be nothing foolish in my taking measures to avoid what they knew was an inconvenience.  I was in this matter obviously their superior, and so they laughed at me.
    Much more candid was the Royal Duke of the last century, who was noted for slow ideas.  "The rain comes into my mouth," said he, while riding.  "Had not your Royal Highness better shut your mouth?" said the equerry.  The Prince did so, and ought, by rule, to have laughed heartily at his adviser; instead of this, he said quietly, "It doesn't come in now."

THE STORY OF BURIDAN'S ASS.
Questiones Morales, by T. Buridan.
    Buridan (died about 1358) is the creator of the famous ass which was, perhaps is, a vulgar proverb in Burgundy.  The argument is that Buridan was for free will — that is, will which determines conduct, let motives be ever so evenly balanced.  An ass is equally pressed by hunger and by thirst; a bundle of hay is on one side, a pail of water on the other.  Surely, you will say, he will not be ass enough to die for want of food or drink; he will then make a choice — that is, will choose between alternatives of equal force.  The problem became famous in the schools; some allowed the poor donkey to die of indecision; some denied the possibility of the balance, which was no answer at all.

A STORY ABOUT THE ROYAL SOCIETY.
    Fifteen or sixteen years ago the Royal Society determined to restrict the number of yearly admissions to fifteen men of science, and noblemen ad libitum; the men of science being selected and recommended by the Council, with a power, since practically surrendered, to the Society to elect more.
    This plan appears to me to be directly against the spirit of their charter, whose true intent was that all who are fit should be allowed to promote natural knowledge in association, from and after the time at which they are both fit and willing.
    It is also working more absurdly from year to year; the tariff of fifteen per annum will soon amount to the practical exclusion of many who would be very useful.  This begins to be felt already, I suspect.
    But the body of the Society has the remedy in its own hands.  When the alteration was discussed by the Council, my friend the late Mr. Galloway, then one of the body, opposed it strongly, and inquired particularly into the reason why fifteen, of all numbers, was the one to be selected.  Was it because fifteen is seven and eight, typifying the Old Testament Sabbath, and the New Testament day of the resurrection following?  Because Paul strove fifteen days against Peter, proving that he was a doctor both of the Old and New Testament?  Because the prophet Hosea bought a lady for fifteen pieces of silver?  Because according to Micah seven shepherds and eight chiefs should waste the Assyrians?  Because Ecclesiastes commands equal reverence to be given to both Testaments in the words "Give a portion to seven, and also to eight"?  Because the waters of the Deluge rose fifteen cubits above the mountains?  Because they lasted fifteen decades of days?  Because Ezekiel's temple had fifteen steps?  Because Jacob's ladder has been supposed to have had fifteen steps?  Because fifteen years were added to the life of Hezekiah?  Because the feast of unleavened bread was on the fifteenth day of the month?  Because the scene of the Ascension was fifteen stadia from Jerusalem?  Because the stonemasons and porters employed in Solomon's temple amounted to fifteen myriads? etc.  The Council were amused and astounded by the volley of fifteens fired at them.

GIORDANO BRUNO AND HIS PARADOXES.
Jordani Bruni Nolani de Monade, Numero et Figura ...  item de Innumerabilibus, Immenso, et Infigurabili ...  Frankfort, 1591.
    I cannot imagine how I came to omit a writer whom I have known so many years, unless the following story will explain it.  The officer reproved the boatswain for perpetual swearing; the boatswain answered that he heard the officers swear.  "Only in an emergency," said the officer.  "That's just it," replied the other; "a boatswain's life is a life of 'mergency."  Bruno was all paradox; and my mind was not alive to his paradoxes, just as my ears might have become dead to the boatswain's oaths.
    He was a vorticist before Descartes, an optimist before Leibnitz, a Copernican before Galileo.  It would be easy to collect a hundred paradoxes of his.  He was born about 1550, and was roasted alive at Rome in 1600, for the maintenance and defence of the holy Church and its rights and liberties.  These last words are from the writ of our own good James I, under which Leggatt was roasted at Smithfield in 1612.

THE CHURCH QUESTION.
    The Satanic doctrine that a church may employ force in aid of its dogma is supposed to be obsolete in England, except as an individual paradox; but this is difficult to settle.  Opinions are much divided as to what the Roman Church would do in England, if she could; any one who doubts that she claims the right does not deserve an answer.
    When the hopes of the Tractarian section of the High Church were in bloom, before the most conspicuous intellects among them had transgressed their ministry that they might go to their own place, I had the curiosity to see how far it could be ascertained whether they held the only doctrine which makes me the personal enemy of a sect: the assumption of a right to persecute.
    I found this in one tract, modified by an assertion that force was not efficient.  I cannot now say that this tract was one of the celebrated ninety.  In these volumes I find, augmenting as we go on, declarations about the character and power of "the Church" which have a suspicious appearance.  The suspicion is increased by that curious piece of sophistry, No. 87, on religious reserve.  The queer paradoxes of that tract leave us in doubt as to everything but this: that the church(man) is not bound to give his whole counsel in all things, and not bound to say what the things are in which he does not give it.  There is now no fear; but the time was when, if not fear, there might be a looking for of fear to come; nobody could then be so sure as we now are that the lion was only asleep.
    Among other exquisite quirks of interpretation in No. 87 is the following.  God himself employs reserve; he is said to be decked with light as with a garment (the old or prayer-book version of Psalm civ. 2).  To an ordinary apprehension this would be a strong image of display, manifestation, revelation; but there is something more.  "Does not a garment veil in some measure that which it clothes?  Is not that very light concealment?"  No. 87, admitted into a series, fixes upon the managers of the series, who permitted its introduction, a strong presumption of that underhand intent with which they were charged.  At the same time it is honorable to our liberty that this series could be published; though its promoters were greatly shocked when the Essayists and Bishop Colenso took a swing on the other side.
    The Tractarian mania has now (October 1866) settled down into a chronic vestment disease, complicated with fits of transubstantiation, which has taken the name of Ritualism.  The common sense of our national character will not put up with a continuance of this grotesque folly; millinery in all its branches will at last be advertised only over the proper shops.  I am told that the Ritualists give short and practical sermons; if so, they may do good in the end.  The English Establishment has always contained those who want an excitement; the New Testament, in its plain meaning, can do little for them.  Since the Revolution, Jacobitism, Wesleyanism, Evangelicism, Puseyism, and Ritualism, have come on in turn, and have furnished hot water for those who could not wash without it.

NAPIER ON REVELATIONS.
A plain discoverie of the whole Revelation of St. John ...  whereunto are annexed certain oracles of Sibylla....  Set Foorth by John Napier L. of Marchiston.  London, 1611.  The first edition was Edinburgh, 1593.
    Napier always believed that his great mission was to upset the Pope, and that logarithms and such were merely episodes and relaxations.  It is a pity that Napier is forgotten and unread.  He is one of the first who gave us the six thousand years.  "There is a sentence of the house of Elias reserved in all ages, bearing these words: The world shall stand six thousand years, and then it shall be consumed by fire; two thousand yeares voide or without lawe, two thousand yeares under the law, and two thousand yeares shall be the daies of the Messias...."

ON BACON'S NOVUM ORGANUM.
    1620.  In this year, Francis Bacon published his Novum Organum, which, starting in the last century, was long held in England to be the work which taught Newton and all his successors how to philosophize.  That Newton never mentions Bacon, nor alludes in any way to his works, passed for nothing.  In our day it begins to be seen that, great as Bacon was, and great as his book really is, he is not the philosophical father of modern discovery.

The Works of Francis Bacon.  Edited by James Spedding, R. Leslie Ellis, and Douglas D. Heath.
    No knowledge of nature without experiment and observation; so said Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé, Gilbert, Kepler, Galileo, Harvey, etc., before Bacon wrote.
    No derived knowledge until experiment and observation are concluded; so said Bacon, and no one else.
    We do not mean to say that he laid down his principle in these words, or that he carried it to the utmost extreme; we mean that Bacon's ruling idea was the collection of enormous masses of facts, and then digested processes of arrangement and elimination, so artistically contrived, that a man of common intelligence, without any unusual sagacity, should be able to announce the truth sought for.
    Bacon did not live to mature the whole of this plan.  Are we really to believe that if he had completed the Instauratio we who write this should have been on a level with Newton in physical discovery?  Bacon asks this belief of us, and does not get it.  But it may be said, Your business is with what he did leave, and with its consequences.  Be it so.  Mr. Ellis says "That his method is impracticable cannot, I think, be denied, if we reflect not only that it never has produced any result, but also that the process by which scientific truths have been established cannot be so presented as even to appear to be in accordance with it."
    That this is true is well known to all who have studied the history of discovery.  Those who deny it are bound to establish either that some great discovery has been made by Bacon's method — we mean by the part peculiar to Bacon — or better still, by making some new discovery can be made by his method.
    The immortal Harvey, who was discovering the circulation of the blood, while Bacon was in the full flow of thought upon his system, may be trusted to say whether he found any likeness in Bacon's system to his own processes, or what would have been any help to him, if he had waited for the Novum Organum.  He said of Bacon, "He writes philosophy like a Lord Chancellor."
    To us, Bacon is eminently the philosopher of error prevented, not of progress facilitated.  The part of Aristotle's logic of which Bacon saw the value was the book on refutation of fallacies.  Is this not the notion of things to which the bias of a practised lawyer might lead him?  In the case before the Court, generally speaking, truth lurks somewhere about the facts, and the elimination of all error will show it in the residuum.  The two senses of the word law come in so as to look almost like a play upon words.  The judge can apply the law so soon as the facts are settled; the physical philosopher has to deduce the law from the facts.  Wait, says the judge, until the facts are determined: did the prisoner take the goods with felonious intent -- did the defendant give what amounts to a warranty -- or the like.  Wait, says Bacon, until all the obtainable facts are brought in; apply my rules of separation to the facts, and the result shall come out as easily as by ruler and compasses.  Bacon's argument is, there can be nothing of law but what must be either perceptible, or mechanically deducible, when all the results of law, as exhibited in phenomena, are before us.  But the truth is, the physical philosopher must frequently conceive law which never was in his previous thought — must educe the unknown, not choose among the known.
    Bacon never included any deduction under observation.  To mathematics he had a dislike.  He averred that logic and mathematics should be the handmaids, not the mistresses, of philosophy; that they should play a subordinate and subsequent part in the dressing of the vast mass of facts by which discovery was to be rendered equally accessible to Newton and to us.  Bacon was very ignorant of all that had been done by mathematics; and he especially objected to astronomy being handed over to the mathematicians.  Leverrier and Adams, calculating an unknown planet into visible existence by enormous heaps of algebra, furnish the last comment of note on this specimen of the goodness of Bacon's views.  Here is Mr. Spedding's collection of casual remarks in Mr. Ellis's several prefaces: Bacon "appears to have been utterly ignorant of the discoveries which had just been made by Kepler's calculations.  Though he complained in 1623 of the want of compendious methods for facilitating arithmetical computations, especially with regard to the doctrine of Series, and fully recognized the importance of them as an aid to physical inquiries — he does not say a word about Napier's Logarithms, which had been published only nine years before and reprinted more than once in the interval.  He complained that no considerable advance had made in geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius.  He saw the importance of determining accurately the specific gravity of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus, and Porta.  He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly apprehend either the nature of the problem or the principles of the solution....  He makes no mention of Archimedes himself, or of Stevinus, Galileo, Guldinus, or Ghetaldus.  He makes no allusion to the theory of equilibrium.  He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of the acceleration of falling bodies, which had been made known by Galileo more than thirty years before.  He proposes an inquiry with regard to the lever — namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination, — though the theory of the lever was as well understood in his own time as it is now....  He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south."
    Much of this was known, but such a summary of Bacon's want of knowledge of the science of his own time was never before collected in one place.  We add that Bacon seems to have been as ignorant of Wright's memorable addition to the resources of navigation as of Napier's addition to the means of calculation.  Mathematics was beginning to be the great instrument of exact inquiry: Bacon threw the science aside, from ignorance, just at the time when his enormous sagacity, applied to knowledge, would have made him see the part it was to play.
    If Newton had taken Bacon for his master, not he, but somebody else, would have been Newton.

BASIS OF MODERN DISCOVERY.
    Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible.  A few facts have suggested an hypothesis, which means a supposition, proper to explain them.  The necessary results of this supposition are worked out, and not until then are other facts examined to see if these ulterior results are found in nature.
    The trial of the hypothesis is the special object: prior to which, hypothesis must have been started, not by rule, but by that sagacity of which no description can be given, precisely because the very owners of it do not act under laws perceptible to themselves.  The inventor of hypothesis, if pressed to explain his method, must answer as did Zerah Colburn, when asked for his mode of instantaneous calculation.  When the poor boy had been bothered for some time in this manner, he cried out in a huff, "God put it into my head, and I can't put it into yours."
    Wrong hypotheses, rightly worked from, have produced more useful results than unguided observation.  Charles the Second founded a Baconian observatory at Greenwich, to observe, observe, observe away at the moon, until her motions were known sufficiently well to render her useful in guiding the seaman.  And no doubt Flamsteed's observations, twenty or thirty of them at least, were of signal use.  But how?  A somewhat fanciful thinker, one Kepler, had hit upon the approximate orbits of the planets by trying one hypothesis after another; he found the ellipse.  The sun in the focus, the motions of the planet more and more rapid as they approach the sun, led Kepler to imagine that a force residing in the sun might move the planets, a force inversely as the distance.  Bouillaud, upon a fanciful analogy, rejected the inverse distance, and, rejecting the force altogether, declared that if such a thing there were, it would be as the inverse square of the distance.  Newton, ready prepared with the mathematics of the subject, tried the fall of the moon towards the earth, away from her tangent, and found that, as compared with the fall of a stone, the law of the inverse square did hold for the moon.  He deduced the ellipse, he proceeded to deduce the effect of the disturbance of the sun upon the moon, upon the assumed theory of universal gravitation.  He found result after result of his theory in conformity with observed fact; and by aid of Flamsteed's observations, which amended what mathematicians call his constants, he constructed his lunar theory.  Had it not been for Newton, the whole dynasty of Greenwich astronomers might have worked away at nightly observation and daily reduction, without any remarkable result; looking forward, as to a millennium, to the time when any man of moderate intelligence was to see the whole explanation.
    What are large collections of facts for?  To make theories from, says Bacon; to try ready-made theories by, says the history of discovery.  It's all the same, says the idolater;  nonsense, say we!

THE REAL VALUE OF BACON'S WORKS.
    Passing over the success of Bacon's own endeavors to improve the details of physical science, which was next to nothing, and of his method as a whole, which has never been practiced, we might say much of the good influence of his writings.
    Sound wisdom, set in sparkling wit, must instruct and amuse to the end of time; and, as against error, we repeat that Bacon is soundly wise, so far as he goes.  There is hardly a form of human error within his scope which he did not detect, expose, and attach to a satirical metaphor which never ceases to sting.  He is largely indebted to a very extensive reading; but the thoughts of others fall into his text with such a close-fitting compactness that he can make even the words of the Sacred Writers pass for his own.  When the truth of the matter as to Bacon's system is fully recognized, we have little fear that there will be a reaction against the man; first because Bacon will always live to speak for himself, for he will not cease to be read; second because those who seek the truth will find it in the best edition of his works, and will be most ably led to know what Bacon was, in the very books which first showed at large what he was not.

THE CONVOCATION AT OXFORD EQUALLY AT FAULT.
    1622.  In the case of Galileo, the absurdity was the act of the Italian Inquisition — for the private and personal pleasure of the Pope — and not of the body which calls itself the Church.  Let the dirty proceeding have its right name.
    The Jesuit Riccioli, the stoutest and most learned Anti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican and Pope-hater, are equally positive that the Roman Church never pronounced any decision; and this in the time immediately following the ridiculous proceeding of the Inquisition.  In like manner a decision of the Convocation of Oxford is not a law of the English Church; which is fortunate, for that Convocation, in 1622, came to a decision quite as absurd, and a great deal more wicked than the declaration against the motion of the earth.  The second was a foolish mistake; the first was a disgusting surrender of right feeling.
    In 1622, one William Knight put forward in a sermon preached before the University certain theses which, looking at the state of the times, may have been improper and possibly of seditious intent.  Knight declared that a man may defend his purse or a woman her honor, against the personal attack of a king, or a private person, if no other means of safety can be found.  The Convocation sent Knight to prison, declared the proposition "falsa, periculosa, et impia," and enacted that all applicants for degrees should subscribe this censure, and make oath that they would neither hold, teach, nor defend Knight's opinions.
    The thesis, in the form given, was unnecessary and improper.  Though strong opinions of the king's rights were advanced at the time, yet no one ventured to say that, ministers and advisers apart, the king might personally break the law; and we know that the first and only attempt which his successor made brought on the crisis which cost him his throne and his head.
    But the declaration that the proposition was false far exceeds in all that is disreputable the decision of the Inquisition against the earth's motion.  We do not mention this little matter in England.  The theses, as given at trial, were not Knight's words, but the digest which it was customary to make in criminal proceedings against opinion.  This heightens the joke, for it appears that the qualifiers of the Convocation took pains to present their condemnation of Knight in the terms which would most unequivocally make their censure condemn themselves.

ON INHABITABLE PLANETS.
A discourse concerning a new world and another planet, in two books.  London, 1640.
Cosmotheoros: or conjectures concerning the planetary worlds and their inhabitants.  Written in Latin, by Christianus Huyghens.  This translation was first published in 1698.  Glasgow, 1757.
    The works propose "That the Moon may be a Planet."  Whether other planets be crowded with organisations some of them having consciousness, is not for me to decide; but I should be much surprised if, on going to one of them, I should find it otherwise.
    The whole dispute tacitly assumes that, if the stars and planets be inhabited, it must be by things of which we can form some idea.  But for aught we know, so many such bodies as there are, so many organisms may there be, of which we have no way of thinking nor of speaking.

INHABITED PLANETS IN FICTION.
    There is a class of hypothetical creations which do not belong to my subject, because they are acknowledged to be fictions, as those of Lucian, Rabelais, Swift, Francis Godwin, Voltaire, etc.  All who have more positive notions as to the composition or organization of other worlds, other than the reasonable conclusion that our Architect must be quite able to construct millions of other buildings on millions of other plans, ought to rank with the writers just mentioned, in all but self-knowledge.  Of every one of their systems I say, as the Irish Bishop said of Gulliver's book, "I don't believe half of it."
    The question of the inhabitants of a particular planet is one which has truth on one side or the other: either there are some inhabitants, or there are none.  Fortunately, it is of no consequence which is true.
    But there are many cases where the balance is equally one of truth and falsehood, in which the choice is a matter of importance.  The world is full of questions of fact or opinion, in which a struggling minority will become a majority, or else will be gradually annihilated; and each of the cases subdivides into results of good, and results of evil.

THE SYMPATHETIC POWDER.
A late discourse ...  by Sir Kenelme Digby....  Rendered into English by R.  White.  London, 1658, 12mo.
    The celebrated sympathetic powder cured by anointing with salve the weapon instead of the wound.  I have long been convinced that it was efficacious.  The directions were to keep the wound clean and cool, and to take care of diet, rubbing the salve on the knife or sword.  If we remember the dreadful notions upon drugs which prevailed, we readily see that any way of not dressing the wound would have been useful.  If the physicians had taken the hint, been careful of diet etc., and poured the little barrels of medicine down the throat of a practicable doll, they would have had their magical cures as well as the surgeons.
    Matters are much improved now; the quantity of medicine given, even by orthodox physicians, would have been called infinitesimal by their professional ancestors.  Accordingly, the College of Physicians has a right to abandon its motto, which is Ars longa, vita brevis, meaning Practice is long, so life is short.

MANKIND A GULLIBLE LOT.
De Cometis: or a discourse of the natures and effects of Comets, as they are philosophically, historically, and astrologically considered.  With a brief (yet full) account of the III late Comets, or blazing stars, visible to all Europe.  And what (in a natural way of judicature) they portend.  Together with some observations on the nativity of the Grand Seignior.  By John Gadbury.  London, 1665.
    D'Israeli sets down Gadbury, Lilly, Wharton, Booker, etc., as rank rogues; I think him quite wrong.  The easy belief in roguery and intentional imposture which prevails in educated society is, to my mind, a greater presumption against the honesty of mankind than all the roguery and imposture itself.  Putting aside mere swindling for the sake of gain, and looking at speculation and paradox, I find very little reason to suspect wilful deceit.
    My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in, judging by experience.

A FORERUNNER OF A WRITTEN ESPERANTO.
An essay towards a real character and a philosophical language.  By John Wilkins (Dean of Ripon, afterwards Bishop of Chester). London, 1668.
    This work is celebrated, but little known.  Its object gives it a right to a place among paradoxes.  It proposes a "language" in which things and their relations shall be denoted by signs, not words, so that any person, whatever his mother tongue, may read it in his own words.  This is an obvious possibility, and, I am afraid, an obvious impracticability.  One man may construct such a system — Bishop Wilkins has done it — but where is the man who will learn it?  The second tongue makes a language, as the second blow makes a fray.

RENE DE SLUSE.
Renati Francisci Slusii Mesolabum.  Liège, 1668.
    The Mesolabum is the solution of the problem of finding two mean proportionals, which Euclid's geometry does not attain.  This is the preliminary to the famous old problem of the duplication of the cube.
    D'Israeli speaks of the "six follies of science" — quadrature, duplication, perpetual motion, philosopher's stone, magic, and astrology.  He might as well have added the trisection, to make the mystic number seven, but had he done so, he would still have been very lenient; only seven follies in all science, from mathematics to chemistry!  Science might have said to such a judge — as convicts used to say who got seven years, expecting it for life — "Thank you, my Lord, and may you sit there till they are over" — may the Curiosities of Literature outlive the Follies of Science!

BEAULIEU'S QUADRATURE.
La Géométrie Françoise, ou la Pratique aisée....  La quadracture du cercle.  Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ...  Paris, 1676. (not Pontault de Beaulieu, the topographer, who died in 1674).
    Beaulieu was attached to the Royal Household, and throughout the century it may be suspected that the household forced a royal road to geometry.  Fifty years before, the king's secretary made a fool of himself, and (so?) contrived to pass for a geometer.  Beaulieu's quadrature amounts to a geometrical construction which gives π = √10.  He had interest enough to get Desargues, the most powerful geometer of his time, the teacher and friend of Pascal, prohibited from lecturing.
    Though our quadrators, etc., very often, and our historians sometimes, assert that men of the character of Copernicus, etc., were treated with contempt and abuse until their day of ascendancy came, nothing can be more incorrect.  From Tycho Brahé to Beaulieu, there is but one expression of admiration for the genius of Copernicus.

MATHEMATICAL THEOLOGY.
Theologiæ Christianæ Principia Mathematica.  Auctore Johanne Craig.  London, 1699.
    This is a celebrated speculation, and has been reprinted abroad, and seriously answered.  Craig is known in the early history of fluxions, and was a good mathematician.  He professed to calculate, on the hypothesis that suspicions against historical evidence increase with the square of the time, how long it will take the evidence of Christianity to die out.  He finds that had the evidence been oral only, Christianity would have gone out AD 800; but, by aid of the written evidence, it will last till AD 3150.  At this period he places the second coming, which is deferred until the extinction of evidence, on the authority of the question "When the Son of Man cometh, shall he find faith on the earth?"
    In order rightly to judge Craig, who added speculations on the variations of pleasure and pain treated as functions of time, it is necessary to remember that in Newton's day the idea of force, as a quantity to be measured, and as following a law of variation, was very new; so likewise was that of probability as an object of measurement.  The success of the Principia of Newton put it into many heads to speculate about applying notions of quantity to other things not then brought under measurement.  Craig imitated Newton's title, and evidently thought he was making a step in advance; but it is not every one who can plough with Samson's heifer.
    It is likely enough that Craig took a hint, directly or indirectly, from Moslem writers who reply to the argument that the Koran has not the evidence derived from miracles.  They say that, as evidence of Christian miracles is daily becoming weaker, a time must at last arrive when it will fail of affording assurance that they were miracles at all; whence would arise the necessity of another prophet and other miracles.

THE LONGITUDE PROBLEM.
A new method for discovering the longitude both at sea and land, humbly proposed to the consideration of the public.  By Wm.  Whiston and Humphry Ditton.  London, 1714.
    This is the celebrated tract written by the two Arian heretics.  Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it the epigram mentioning "Wicked Will Whiston."
    Some readers may think that Swift cared little for Whiston and Ditton, except as a chance hearing of their plan pointed them out as good marks.  But it was not so; the clique had their eye on the guilty pair before the publication of the tract.  The preface is dated July 7; and ten days afterwards Arbuthnot writes to Swift "Whiston has at last published his project of the longitude; the most ridiculous thing that ever was thought on.  But a pox on him!  He has spoiled one of my papers of Scriblerus, which was a proposition for the longitude not very unlike his, to this purpose; that since there was no pole for east and west, that all the princes of Europe should join and build two prodigious poles, upon high mountains, with a vast lighthouse to serve for a polestar.  I was thinking of a calculation of the time, charges, and dimensions.  Now you must understand his project is by lighthouses, and explosion of bombs at a certain hour."
    The plan was certainly impracticable; but Whiston and Ditton might have retorted that they were nearer to the longitude than Swift to the kingdom of heaven, or even to a bishopric.  Arbuthnot here and elsewhere reveals himself as the calculator who kept Swift right in his proportions in the matter of the Lilliputians, Brobdingnagians, etc.  Swift was very ignorant about things connected with number.  He writes to Stella that he has discovered that leap year comes every four years, and that all his life he had thought it came every three years.  When I find the person who did not understand leap-year inventing satellites of Mars in correct accordance with Kepler's third law, I feel sure he must have had help.

The principles of the Philosophy of the Expansive and Contractive Forces ...  By Robert Greene, M.A., Fellow of Clare Hall.  Cambridge, 1727.
    It is the weakness of the orthodox follower of any received system to impute insanity to the solitary dissentient; which is voted (in due time) a very wrong opinion about Copernicus, Columbus, or Galileo -- but quite right about Robert Greene.  If misconceptions, acted on by too much self-opinion, be sufficient evidence of madness, it would be a curious inquiry what is the least percentage of the reigning school which has been insane at any one time.

MATHEMATICAL THEOLOGY.
Mathematical principles of theology, or the existence of God geometrically demonstrated.  By Richard Jack, teacher of Mathematics.  London, 1747.
    Propositions arranged after the manner of Euclid, with beings represented by circles and squares.  But these circles and squares are logical symbols, not geometrical ones.  Some of the houses which Jack built were destroyed by the fortune of war in 1745, at Edinburgh; who will say the rebels did no good whatever?

TWO MODEL INDORSEMENTS.
Dissertation, découverte, et démonstrations de la quadrature mathématique du cercle.  Par M. de Fauré, géomètre.  (s. l., probably Geneva) 1747.
Analyse de la Quadrature du Cercle.  Par M. de Fauré, Gentilhomme Suisse.  Hague, 1749.
    According to this gentleman, a diameter of 81 gives a circumference of 256.
    There is an amusing circumstance about the quarto which has been overlooked, if indeed the book has ever been examined.  John Bernoulli (the one of the day) and Koenig have both given an attestation.  There is reason to think the two sly Swiss played their countryman the same trick as the medical man played Miss Pickle, in the novel of that name.  The lady only wanted to get his authority against sousing her little nephew, and said, "Pray, doctor, is it not both dangerous and cruel to be the means of letting a poor tender infant perish by sousing it in water as cold as ice?" — "Downright murder, I affirm," said the doctor; and certified accordingly.
    De Fauré had built a tremendous scaffolding of equations, quite out of place, and feeling cocksure that his solutions, if correct, would square the circle, applied to Bernoulli and Koenig — who after his tract of two years before, must have known what he was at — for their approbation of the solutions.  And he got it, as follows, well guarded: "Suivant les suppositions posées dans ce Mémoire, il est si évident que t doit être = 34, y = 1, et z = 1, que cela n'a besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.  -- à Basle le 7e Mai 1749.  Jean Bernoulli."
    "Je souscris au jugement de Mr. Bernoulli, en conséquence de ces suppositions. -- à la Haye le 21 Juin 1749.  S. Koenig."
    On which de Fauré remarks with triumph — as I have no doubt it was intended he should do — "il conste clairement par ma présente Analyse et Démonstration, qu'ils y ont déja reconnu et approuvé parfaitement que la quadrature du cercle est mathématiquement démontrée."
    It should seem that it is easier to square the circle than to get round a mathematician.

BISHOP HORNE ON NEWTON.
The theology and philosophy in Cicero's Somnium Scipionis explained.  Or, a brief attempt to demonstrate, that the Newtonian system is perfectly agreeable to the notions of the wisest ancients: and that mathematical principles are the only sure ones.  London, 1751.
    This boyish satire on Newton, written when Horne was nineteen, is amusing.  Speaking of old Benjamin Martin, he goes on as follows: "But the most elegant account of (attraction) is by that hominiform animal, Mr. Benjamin Martin, who having attended Dr. Desaguliers' fine, raree, gallanty shew for some years in the capacity of a turnspit, has, it seems, taken it into his head to set up for a philosopher."
    Thus is preserved the fact, unknown to his biographers, that Benj. Martin was an assistant to Desaguliers in his lectures.  Hutton says of him, that "he was well skilled in the whole circle of the mathematical and philosophical sciences, and wrote useful books on every one of them."  This is quite true, and even at this day he is read by twenty where Horne is read by one.  All that I say of him is due to this contemptuous mention of a more durable man than himself, "Old Ben Martin."
    Old Ben could not be a Fellow of the Royal Society, because he kept a shop — even though the shop sold nothing but philosophical instruments.  Thomas Wright, similarly situated as to shop and goods, never was a Fellow.  The Society of our day has greatly degenerated; those of the old time would be pleased, no doubt, that the glories of their day should be commemorated.  In the early days of the Society, there was a similar difficulty about Graunt, the author of the celebrated work on mortality.  But their royal patron, "who never said a foolish thing," sent them a sharp message, and charged them if they found any more such tradesmen, they should "elect them without more ado."
    The successors of Newton were very apt to declare that he had demonstrated attraction as a physical cause.  However, Newton himself had taken reasonable pains to show that he did not pretend to this.  If any one had said to Newton, I hold that every particle of matter is a responsible being of vast intellect, ordered by the Creator to move as it would do if every other particle attracted it, and gifted with power to make its way in true accordance with that law; what have you to say against it? — Newton must have replied, "Sir!  If you really undertake to maintain this as demonstrable, your soul had better borrow a little power from the particles of which your body is made.  if you merely ask me to refute it, I tell you that I neither can nor need do it; for whether attraction comes in this way or in any other, it comes, and that is all I have to do with it."
    The word attraction, as used by Newton and the best of his followers, only meant a drawing towards, without any implication as to the cause.  Thus whether they said that matter attracts matter, or that young lady attracts young gentleman, they were using one word in one sense.  In this point young Horne made a hit.  He justly censures those who fixed upon Newton a more positive knowledge of what attraction is than he pretended to have.
    Horne quotes Rowning as follows: "Mr. Rowning has a very pretty conceit upon this same subject of attraction, about every particle of a fluid being intrenched in three spheres of attraction and repulsion, one within another, 'the innermost of which is a sphere of repulsion, which keeps them from approaching into contact; the next, a sphere of attraction, diffused around this of repulsion, by which the particles are disposed to run together into drops; and the outermost of all, a sphere of repulsion, whereby they repel each other, when removed out of the attraction.'  So that between the urgings and solicitations of one and t'other, a poor unhappy particle must ever be at his wit's end, not knowing which way to turn, or whom to obey first."

FALLACIES IN A THEORY OF ANNUITIES.
An Essay to ascertain the value of leases, and annuities for years and lives.  By W[eyman] L[ee].  London, 1737.
A valuation of Annuities and Leases certain, for a single life.  By Weyman Lee, Esq. of the Inner Temple.  London, 1751.  Third edition, 1773.
    Every branch of exact science has its paradoxer.  Mr. Weyman Lee was the assailant of what all who had studied called demonstration in the question of annuities.  His error rose out of his not being able to see that the whole is the sum of all its parts.
    By "an annuity of £100" is meant that the buyer is to have for his money £100 in a year if he be then alive, another £100 at the end of two years if then alive, and so on.
    Mr. Lee contended that the way to value an annuity is to find out the term of years which the individual has an even chance of surviving, and to charge for the life annuity the value of an annuity certain for that term.  If of a thousand persons, 500 be sure to die within a year, and the other 500 be immortal, one year is the term which each one has an even chance of surviving, so Lee's rule would set the price of an annuity at one year's payment.  But the true value is obviously half that of a perpetual annuity; so at 5 percent Lee's rule would give less than the tenth of the true value.
    Lee would have said, if alive, that I have put an extreme case: but any universal truth is true in its extreme cases.
    It is not fair to bring forward an extreme case against a person who is speaking as of usual occurrences, but it is quite fair when, as frequently happens, the proposer insists upon a perfectly general acceptance of his assertion.  And yet many who go the whole hog protest against being tickled with the tail.
    Counsel in court are good instances: they are paradoxers by trade.  June 13, 1849, at Hertford, there was an action about a ship insured against a total loss; some planks were saved, and the underwriters refused to pay.  Mr. Z. (for deft.) "There can be no degrees of totality; and some timbers were saved." — L. C. B. "Then if the vessel were burned to the water's edge, and some rope saved in the boat, there would be no total loss." — Mr. Z. "This is putting a very extreme case." — L. C. B. "The argument would go that length."  What would Z. say to the extreme case beginning somewhere between six planks and a bit of rope?

MONTUCLA'S WORK ON THE QUADRATURE.
Histoire des recherches sur la quadrature du cercle ...  avec une addition concernant les problèmes de la duplication du cube et de la trisection de l'angle.  Paris, 1754.  By Montucla.
    Montucla is an admirable historian when he is writing from his own direct knowledge; it is a sad pity that he did not tell us when he was depending on others.  We are not to trust a quarter of his book, and we must read many other books to know which quarter.  The fault is common enough, but Montucla's good three-quarters is so good that the fault is greater in him than in most others; I mean the fault of not acknowledging; for an historian cannot read everything.  But it must be said that mankind give little encouragement to candor on this point.
    Hallam, in his History of Literature, states with his own usual instinct of honesty every case in which he depends upon others; Montucla does not.  And what is the consequence? — Montucla is trusted, and believed in, and cried up; while the smallest talker can lament that Hallam should be so unequal and apt to depend on others, without remembering to mention that Hallam himself gives the information.  As to a universal history of any great subject being written entirely upon primary knowledge, it is a thing of which the possibility is not yet proved by an example.
    Montucla says, speaking of France, that he finds three notions prevalent among the cyclometers: (1) that there is a large reward offered for success; (2) that the longitude problem depends on that success; (3) that the solution is the great end and object of geometry.  The same three notions are equally prevalent among the same class in England.  No reward has ever been offered by the government of either country.  The longitude problem in no way depends upon perfect solution; existing approximations are sufficient to a point of accuracy far beyond what can be wanted.  And geometry, content with what exists, has long passed on to other matters.

Philosophical Essays, in three parts.  By R. Lovett, Lay Clerk of the Cathedral Church of Worcester.  Worcester, 1766.
The Electrical Philosopher: containing a new system of physics founded upon the principle of an universal Plenum of elementary fire....  By R. Lovett, Worcester, 1774.
    Mr. Lovett was one of those ether philosophers who bring in elastic fluid as an explanation by imposition of words, without deducing any one phenomenon from what we know of it.  And yet he says that attraction has received no support from geometry; though geometry, applied to a particular law of attraction, had shown how to predict the motions of the bodies of the solar system.  He, and many of his stamp, have not the least idea of the confirmation of a theory by accordance of deduced results with observation posterior to the theory.

SAINT-MARTIN ON ERRORS AND TRUTH.
Des Erreurs et de la Vérité, ou les hommes rappelés au principe universel de la science; ouvrage dans lequel, en faisant remarquer aux observateurs l'incertitude de leurs recherches, et leurs méprises continuelles, on leur indique la route qu'ils auroient dû suivre, pour acquérir l'évidence physique sur l'origine du bien et du mal, sur l'homme, sur la nature matérielle, et la nature sacrée; sur la base des gouvernements politiques, sur l'autorité des souverains, sur la justice civile et criminelle, sur les sciences, les langues, et les arts.  Par un Ph.... Inc....  A Edimbourg.  1782.  Two vols.
    This is the famous work of Louis Claude de Saint-Martin (1743-1803).  The title promises much, and the writer has smart thoughts now and then; but the whole is the wearisome omniscience of the author's day and country, which no reader of our time can tolerate.  Not that we dislike omniscience, but we have it of our own country, both homemade and imported; and fashions vary.  But surely there can be but one omniscience?  Must a man have but one wife?
    Nay, may not a man have a new wife while the old one is living?  There was a famous instrumental professor forty years ago, who presented a friend to Madame — — .  The friend was startled, and looked surprised, for not many weeks before, he had been presented to another lady, with the same title, at Paris.  The musician observed his surprise, and quietly said, "Celle-ci est Madame — — de Londres."
    The book was printed at Lyons, but it was a trick of French authors to pretend to be afraid of prosecution; it made a book look wicked-like to have a feigned place of printing, and stimulated readers.  A Government which had undergone Voltaire would never have drawn its sword upon quiet Saint-Martin.  To make himself look still worse, he was only philosophe Inc. ..., which is generally read Inconnu but sometimes Incrédule; most likely the ambiguity was intended.  There is an awful paradox about the book, which explains, in part, its leaden sameness.  It is all about l'homme, l'homme, l'homme, except as much as treats of les hommes, les hommes, les hommes; but not one single man is mentioned by name in its 500 pages.  It reminds one of "Water, water everywhere, And not a drop to drink."  Not one opinion of any other man is referred to, either for agreement or opposition.  Not even a town is mentioned.  There is nothing which brings a capital letter into the middle of a sentence, except, by the rarest accident, such a personification as Justice.
    Saint-Martin is great in mathematics.  The number four essentially belongs to straight lines, and nine to curves.  The object of a straight line is to perpetuate ad infinitum the production of a point from which it emanates.  A circle bounds the production of all its radii, tends to destroy them, and is in some sort their enemy.  How is it possible that things so distinct should not be distinguished in their number as well as in their action?  If this important observation had been made earlier, immense trouble would have been saved to the mathematicians, who would have been prevented from searching for a common measure to lines which have nothing in common.  But, though all straight lines have the number four, it must not be supposed that they are all equal, for a line is the result of its law and its number; but though both are the same for all lines of a sort, they act differently, as to force, energy, and duration, in different individuals; which explains all differences of length, etc.  I congratulate the reader who understands this; and I do not pity the one who does not.

A FORERUNNER OF THE METRIC SYSTEM.
Method to discover the difference of the earth's diameters; proving its true ratio to be not less variable than as 45 is to 46, and shortest in its pole's axis 174 miles....  likewise a method for fixing an universal standard for weights and measures.  By Thomas Williams.  London, 1788.
    Mr. Williams was a paradoxer in his day, and proposed what was no doubt laughed at by some.  He proposed the sort of plan which the French — independently of course — carried into effect a few years after.  He would have the 52d degree of latitude divided into 100,000 parts and each part a geographical yard.  The geographical ton was to be the cube of a geographical yard filled with sea-water taken some leagues from land.  All multiples and sub-divisions were to be decimal.

THOMAS PAINE'S RIGHTS OF MAN.
The rights of Man, being an answer to Mr. Burke's attack on the French Revolution.  By Thomas Paine.  In two parts.  1791-1792.
A vindication of the rights of Woman, with strictures on political and moral subjects.  By Mary Wollstonecraft. 1792.
A sketch of the rights of Boys and Girls.  By Launcelot Light, of Westminster School; and Lætitia Lookabout, of Queen's Square, Bloomsbury.  By the Rev. Samuel Parr, LL.D.  1792.
    When did we three meet before?  The first work has sunk into oblivion; had it merited its title, it might have lived.  It is what the French call a pièce de circonstance; it belongs in time to the French Revolution, and in matter to Burke's opinion of that movement.  Those who only know its name think it was really an attempt to write a philosophical treatise on what we now call socialism.  Silly government prosecutions gave it what it never could have got for itself.
    Mary Wollstonecraft's title of was an act of discipleship to Paine's Rights of Man, but is very badly chosen.  The book was marred by the title, especially when the authoress and her husband assumed the right of dispensing with legal sanction until the approach of offspring brought them to a sense of their child's interest.  The right claimed for woman is to have the education of a rational human being, and not to be considered as nothing but woman throughout youthful training.  The maxims of Mary Wollstonecraft are now, though not derived from her, largely followed in the education of girls, especially in home education: just as many of the political principles of Tom Paine, again not derived from him, are the guides of our actual legislation.  I remember, forty years ago, an old lady used to declare that she disliked girls from the age of sixteen to five-and-twenty.  "They are full," said she, "of femalities."  She spoke of their behavior to women as well as to men.  She would have been shocked to know that she was a follower of Mary Wollstonecraft, and had packed half her book into one sentence.
    The third work is a satirical attack on Mary Wollstonecraft and Tom Paine.  The details of the attack would convince any one that neither has anything which would now excite reprobation.

ATTACKS ON RELIGIOUS CUSTOMS.
    Days of political paradox were coming, at which we now stare.  Cobbett said, about 1830, in earnest, that in the country every man who did not take off his hat to the clergyman was suspected, and ran a fair chance of having something brought against him.  I heard this assertion canvassed, when it was made, in a party of elderly persons.  The Radicals backed it, the old Tories rather denied it, but in a way which satisfied me they ought to have denied it less if they could not deny it more.
    But it must be said that the Governments stopped far short of what their partisans would have had them do.  All who know Robert Robinson's very quiet assault on church-made festivals in his History and Mystery of Good Friday (1777) will hear or remember with surprise that the British Critic pronounced it a direct, unprovoked, and malicious libel on the most sacred institutions of the national Church.  It was reprinted again and again.  When the Jacobin day came, the State was really in a fright; people thought twice before they published what would now be quite disregarded.

HONE'S FAMOUS TRIALS.
    The results of Hone's trials (William Hone, 1779-1842) are among the important constitutional victories of our century.
    He published parodies on the Creeds, the Lord's Prayer, the Catechism, etc., with intent to bring the Ministry into contempt: everybody knew that was his purpose.  The Government indicted him for impious, profane, blasphemous intent, but not for seditious intent.
    They hoped to wear him out by proceeding day by day.  December 18, 1817, they hid themselves under the Lord's Prayer, the Creed, and the Commandments; December 19, under the Litany; December 20, under the Athanasian Creed, an odd place for shelter when they could not find it in the previous places.  Hone defended himself for six, seven, and eight hours on the several days; and the jury acquitted him in 15, 105, and 20 minutes.
    In the second trial the offense was laid both as profanity and as sedition, which seems to have made the jury hesitate.  And they probably came to think that the second count was false pretense; but the length of their deliberation is a satisfactory addition to the value of the whole.
    In the first trial the Attorney General (Shepherd) had the impudence to say that the libel had nothing of a political tendency about it, but was avowedly set off against the religion and worship of the Church of England.  The whole is political in every sentence; neither more nor less political than the following, which is part of the parody on the Catechism: "What is thy duty towards the Minister?  My duty towards the Minister is, to trust him as much as I can; to honor him with all my words, with all my bows, with all my scrapes, and with all my cringes; to flatter him; to give him thanks; to give up my whole soul to him; to idolize his name, and obey his word, and serve him blindly all the days of his political life."  And the parody on the Creed begins, "I believe in George, the Regent almighty, maker of new streets and Knights of the Bath."  This is what the Attorney-General said had nothing of a political tendency about it.  But this was on the first trial: Hone was not known.
    The first day's trial was under Justice Abbott (afterwards C. J. Tenterden). It was perfectly understood, when Chief Justice Ellenborough appeared in Court on the second day, that he was very angry at the first result, and put his junior aside to try his own rougher dealing.  But Hone tamed the lion.  An eye witness told me that when he implored of Hone not to detail his own father Bishop Law's views on the Athanasian Creed, which humble petition Hone kindly granted, he held by the desk for support.  And the same when — which is not reported — the Attorney-General appealed to the Court for protection against a stinging attack which Hone made on the Bar: he held on, and said, "Mr. Attorney, what can I do!"
    I was a boy of twelve years old, but so strong was the feeling of exultation at the verdicts that boys at school were not prohibited from seeing the parodies, which would have been held at any other time quite unfit to meet their eyes.  I was not able to comprehend all about the Lord Chief Justice until I read and heard again in after years.  In the meantime, Joe Miller had given me the story of the leopard which was sent home on board a ship of war, and was in two days made as docile as a cat by the sailors.  "You have got that fellow well under," said an officer.  "Lord bless your Honor!" said Jack, "if the Emperor of Marocky would send us a cock rhinoceros, we'd bring him to his bearings in no time!"  When I came to the subject again, it pleased me to entertain the question whether, if the Emperor had sent a cock rhinoceros to preside on the third day in the King's Bench, Hone would have mastered him.
    A large subscription was raised for Hone, headed by the Duke of Bedford for £105.  Many of the leading anti-ministerialists joined, but there were many of the other side who avowed their disapprobation of the false pretense.  Many could not venture their names.  The subscription was very large and would have bought a handsome annuity, but Hone employed it in the bookselling trade, and did not thrive.  His Everyday Book and his Apocryphal New Testament are useful books.  On an annuity he would have thriven as an antiquarian writer and collector.
    It is well that the attack on the right to ridicule Ministers roused a dormant power which was equal to the occasion.  Hone declared, on his honor, that he had never addressed a meeting in his life, nor spoken a word before more than twelve persons.  Had he — which however could not then be done — employed counsel and had a guilty defense made for him, he would very likely have been convicted, and the work would have been left to be done by another.  No question that the parodies disgusted all who reverenced Christianity, and who could not separate the serious and the ludicrous, and prevent their existence in combination.
    The spirit which was roused against the false dealing of the Government in pretending to prosecute for impiety when all the world knew the real offense was, if anything, sedition, was not got up at the moment; there had been previous exhibitions of it.  For example, in the spring of 1818 Mr. Russell, a little printer in Birmingham, was indicted for publishing the Political Litany on which Hone was afterwards tried.  He took his witnesses to the summer Warwick assizes, and was told that the indictment had been removed by certiorari into the King's Bench.  He had notice of trial for the spring assizes at Warwick; he took his witnesses there, and the trial was postponed by the Crown.  He then had notice for the summer assizes at Warwick; and so on.  The policy seems to have been to wear out the obnoxious parties, either by delays or by heaping on trials.  The Government was odious, and knew it could not get verdicts against ridicule, and could get verdicts against impiety.  No difficulty was found in convicting the sellers of Paine's works, and the like.  When Hone was held to bail it was seen that a crisis was at hand.  All parties in politics furnished him with parodies in proof of religious persons having made instruments of them.
    Hone had published, in 1817, tracts of purely political ridicule: Official Account of the Noble Lord's Bite, Trial of the Dog for Biting the Noble Lord, etc.  These were not touched.  After the trials, it is manifest that Hone was to be unassailed, do what he might.  The Political House that Jack built, in 1819; The Man in the Moon, 1820; The Queen's Matrimonial Ladder, Non mi ricordo, The R---l Fowls, 1820; The Political Showman at Home, with plates by G. Cruickshank, 1821; The Spirit of Despotism, 1821 — all would have been legitimate marks for prosecution in previous years.  The biting caricature of several of these works is remembered to this day.  The Spirit of Despotism was a tract of 1795, of which a few copies had been privately circulated with great secrecy.  Hone reprinted it, and prefixed the following address to "Robert Stewart, alias Lord Castlereagh:"  "It appears to me that if, unhappily, your counsels are allowed much longer to prevail in the Brunswick Cabinet, they will bring on a crisis, in which the king may be dethroned or the people enslaved.  Experience has shown that the people will not be enslaved — the alternative is the affair of your employers."  Hone might say this without notice.
    In 1819 Mr. Murray published Lord Byron's Don Juan, and Hone followed it with Don John, or Don Juan Unmasked, a little account of what the publisher to the Admiralty was allowed to issue without prosecution.  The parody on the Commandments was a case very much in point; and Hone makes a stinging allusion to the use of the "unutterable Name, with a profane levity unsurpassed by any other two lines in the English language."  The lines are
    "'Tis strange — the Hebrew noun which means 'I am,'
    The English always use to govern d — — n."
Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord Castlereagh was suppressed by Mr. Murray from delicacy to Ministers.  Q. Why did not Mr. Murray suppress Lord Byron's parody on the Ten Commandments?  A. Because it contains nothing in ridicule of Ministers, and therefore nothing that they could suppose would lead to the displeasure of Almighty God."
    The little matters on which I have dwelt will never appear in history from their political importance, except in a few words of result.  As a mode of thought, silly evasions of all kinds belong to such a work as the present.  Ignorance which seats itself in the chair of knowledge is a mother of revolutions in politics, and of unread pamphlets in circle-squaring.
    From 1815 to 1830 the question of revolution or no revolution lurked in all our English discussions.  The high classes must govern — the high classes shall not govern — and thereupon issue was to be joined.  In 1828-33 the question came to issue, and it was, Revolution with or without civil war; choose.  The choice was wisely made; and the Reform Bill started a new system so well dovetailed into the old that the joinings are hardly visible.  And now, in 1867, the thing is repeated with a marked subsidence of symptoms; and the party which has taken the place of the extinct Tories is carrying through Parliament a wider extension of the franchise than their opponents would have ventured.
    Napoleon used to say that a decided nose was a sign of power; on which it has been remarked that he had good reason to say so before the play was done.  And so had our country; it was saved from a religious war, and a civil war, by the power of that nose over its colleagues.

THOMAS TAYLOR, THE PLATONIST.
The Commentaries of Proclus.  Translated by Thomas Taylor.  London, 1792, 2 vols.
    The reputation of "the Platonist" begins to grow, and will continue to grow.  At page lvi of the Introduction is Taylor's notion of the way to find the circumference.  It is not geometrical, for it proceeds on the motion of a point; the words "on account of the simplicity of the impulsive motion, such a line must be either straight or circular" will suffice to show how Platonic it is.  Taylor certainly professed a kind of heathenism.  D'Israeli said, "Mr. T. Taylor, the Platonic philosopher and the modern Plethon, consonant to that philosophy, professes polytheism."  Taylor printed this in large type, in a page by itself after the dedication, without any disavowal.  I have seen the following, Greek and translation both, in his handwriting: "Every good man, so far as he is a good man, is a heathen; and every Christian, so far as he is a Christian, is a bad man."  Whether Taylor had in his head the Christian of the New Testament, or whether he drew from those members of the "religious world" who make manifest the religious flesh and the religious devil, cannot be decided by us, and perhaps was not known to himself.  If a heathen, he was a virtuous one.

A NEW ERA IN FICTION.
    1795.  This is the date of a very remarkable paradox.  The religious world — to use a name claimed by a doctrinal sect — had long set its face against amusing literature and works of imagination.  Bunyan, Milton, and a few others were irresistible; but a long face was pulled at every attempt to produce something readable for poor people and poor children.  In 1795, a benevolent association began to circulate the works of a lady who had been herself a dramatist, and had nourished a pleasant vein of satire in the society of Garrick and his friends; all of which is carefully suppressed in some biographies.  Hannah More's Cheap Repository Tracts, which were bought by millions of copies, destroyed the vicious publications with which the hawkers deluged the country, by the simple process of furnishing the hawkers with something more saleable.
    Dramatic fiction, in which the characters are drawn by themselves, was, at the middle of the last century, the monopoly of writers who required indecorum, such as Fielding and Smollett.  All, or nearly all, which could be permitted to the young was dry narrative, written by people who could not make their personages talk character; they all spoke alike.  The author of the Rambler is ridiculed, because his young ladies talk Johnsonese; but the satirists forget that all the presentable novel-writers were equally incompetent.
    I make no exception in favor of Miss Burney, though she was the forerunner of a new era.  Suppose a country in which dress is always of one color; then an importer brings in cargoes of blue stuff, red stuff, green stuff, etc., and exhibits dresses of these several colors.  That person is the similitude of Miss Burney.  It would be a delightful change from a universal dull brown, to see one person all red, another all blue, etc.; but the real inventor of pleasant dress would be the one who could mix his colors and keep down the bright and gaudy.  Miss Burney's introduction was so charming, by contrast, that she nailed such men as Johnson, Burke, Garrick, etc., to her books.  But when a person who has read them with keen pleasure in boyhood, as I did, comes back to them after a long period, during which he has made acquaintance with the great novelists of our century, three quarters of the pleasure is replaced by wonder that he had not seen he was at a puppet show, not at a drama.
    Maria Edgeworth, Sydney Owenson (Lady Morgan), Jane Austen, Walter Scott, etc., are all of our century; as are, I believe, all the Minerva Press novels, as they were called, which show some of the power in question.  Perhaps dramatic talent found its best encouragement in the drama itself.  But I cannot ascertain that any such power was directed at the multitude, whether educated or uneducated, with natural mixture of character, under the restraints of decorum, until the use of it by two religious writers of the school called "evangelical," Hannah More and Rowland Hill.  The Village Dialogues, though not equal to the Repository Tracts, are in many parts an approach, and perhaps a copy; there is frequently humorous satire in that most effective form, self-display.  They were published in 1800, and, partly at least, by the Religious Tract Society, the lineal successor of the Repository association, though knowing nothing about its predecessor.

THE RELIGIOUS TRACT SOCIETY.
    After the Religious Tract Society had existed more than fifty years, a friend presented it with a copy of the original prospectus of the Repository, whose existence was not known.  In this prospectus it is announced that from the plan "will be carefully excluded whatever is enthusiastic, absurd, or superstitious."  The "evangelical" party had, from the foundation of the Religious Tract Society, regretted that the Repository Tracts "did not contain a fuller statement of the great evangelical principles;" while in the prospectus it is also stated that "no cause of any particular party is intended to be served by it, but general Christianity will be promoted upon practical principles."  This explains what has often been noticed, that the tracts contain a mild form of "evangelical" doctrine, free from that more fervid dogmatism which appears in the Village Dialogues.
    The Religious Tract Society, in 1863, republished some of H. More's tracts, with alterations, additions, and omissions ad libitum.  This is an improper way of dealing with the works of the dead; especially when the reprints are of popular works.  A small type addition to the preface contains: "Some alterations and abridgements have been made to adapt them to the present times and the aim of the Religious Tract Society."  I think every publicity ought to be given to the existence of such a practice.
    Alterations in works which the Society republishes are a necessary part of their plan, but the fact of alteration should be very distinctly announced on the title of the work itself, not left to a little bit of small type at the end of the preface.  And the places in which alteration has been made should be pointed out, either by marks of omission or by putting altered sentences in brackets.
    May anyone alter the works of the dead at his own discretion?  Readers in general will take each sentence to be that of the author whose name is on the title; so that a correcting republisher makes use of his author's name to teach his own variation.  The tortuous logic of "the trade," which is content when "the world" is satisfied, is not easily answered, any more than an eel is easily caught; but the Religious Tract Society may be convinced in a sentence.  On which course would they feel most safe in giving their account to the God of truth?  "In your own conscience, now?"
    The Society cuts a poor figure before a literary tribunal.  Nothing was wanted except an admission that the remarks made by me were unanswerable, and this was immediately furnished by the Secretary.  In a reply of which six parts out of seven are a very amplified statement that the Society did not intend to reprint all Hannah More's tracts, the remaining seventh is: "I am not careful (perhaps this should be careful not) to notice Professor De Morgan's objections to the changes in 'Mary Wood' or 'Parley the Porter,' but would merely reiterate that the tracts were neither designed nor announced to be 'reprints' of the originals; and much less (this must be careful not; further removed from answer than not careful) can I occupy your space by a treatise on the Professor's question: 'May any one alter the works of the dead at his own discretion?'"
    To which I say: Thanks for help!
    I predict that Hannah More's Cheap Repository Tracts will somewhat resemble the Pilgrim's Progress in their fate: they will become classical works of their kind.  Most assuredly this will happen if my assertion cannot be upset, namely, that they contain the first specimens of fiction addressed to the world at large, and widely circulated, in which dramatic — as distinguished from puppet — power is shown, and without indecorum.

A TRIBUTE TO WILLIAM FREND.
The principles of Algebra.  By William Frend.  London, 1796.  Second Part, 1799.
    This Algebra shows "great distrust of the results of algebraical science which were in existence at the time when it was written."  It makes war of extermination upon all that distinguishes algebra from arithmetic.
    The genuine respect which I entertained for my father-in-law did not prevent my canvassing with perfect freedom his anti-algebraical and anti-Newtonian opinions.  If the manner in which algebra was presented to the learner had been true algebra, he would have been right; and if he had confined himself to protesting against the imposition of attraction as a fundamental part of the existence of matter, he would have been in unity with a great many, including Newton himself.  I wish he had preferred amendment to rejection when he was a college tutor; he wrote and spoke English with a clearness which is seldom equaled.
    It is constantly said that, at his celebrated trial in 1792 for sedition and opposition to the Liturgy, etc., he was expelled from the University.  Actually, he was banished.  People cannot see the difference, but it made all the difference to Mr. Frend.  He held his fellowship and its profits till his marriage in 1808, and was a member of the University and of its Senate till his death in 1841.
    That they would have expelled him if they could, is perfectly true; and there is a funny story — also perfectly true — about their first proceedings being under a statute which would have given the power, had it not been discovered during the proceedings that the statute did not exist. It had come so near to existence as to be entered into the Vice-Chancellor's book for his signature, which it wanted, as was not seen till Mr. Frend exposed it; in fact, the statute had never actually passed.
    I once had a conversation with a very remarkable man, who was generally called "Place, the tailor," but who was politician, political economist, etc.  He sat in the room above his shop — he was then a thriving master tailor at Charing Cross — surrounded by books enough for nine, to shame a proverb.  The blue books alone, cut up into strips, would have measured Great Britain for oh-no-we-never-mention-'ems, the Highlands included.  I cannot find a biography of this worthy and able man.  I happened to mention William Frend, and he said, "Ah!  My old master, as I always call him.  Many and many a time, and year after year, did he come in every now and then to give me instruction, while I was sitting on the board, working for my living, you know."
    Place, who really was a sound economist, is joined with Cobbett, because they were together at one time, and because he was, in 1800, etc., a great Radical.  But for Cobbett, Place had a great contempt.  He told me the following story.  He and others were advising with Cobbett about the defense he was to make on a trial for seditious libel which was coming on.  Said Place, "You must put in the letters you have received from Ministers, members of the Commons from the Speaker downwards, etc., about your Register, and their wish to have subjects noted.  You must then ask the jury whether a person so addressed must be considered as a common sower of sedition, etc.  You will be acquitted; nay, if your intention should get about, very likely they will manage to stop proceedings."  Cobbett was too much disturbed to listen; he walked about the room exclaiming "D — — the prison!" and the like.  He had not the sense to follow the advice, and was convicted.

A STORY ON SIMSON.
    Robert Simson used to sit at his open window on the ground floor, deep in geometry.  Here he would be accosted by beggars, to whom he generally gave a trifle, he roused himself to hear a few words of the story, made his donation, and instantly dropped down into his depths.  Some wags one day stopped a mendicant who was on his way to the window with "Now, my man, do as we tell you, and you will get something from that gentleman, and a shilling from us besides.  You will go and say you are in distress, he will ask you who you are, and you will say you are Robert Simson, son of John Simson of Kirktonhill."  The man did as he was told; Simson quietly gave him a coin, and dropped off.  The wags watched a little, and saw him rouse himself again, and exclaim "Robert Simson, son of John Simson of Kirktonhill!  Why, that is myself.  That man must be an impostor."  Lord Brougham tells the same story, with some difference of details.

BARON MASERES.
    Baron Maseres was, as a writer, dry; those who knew his writings will feel that he seldom could have taken in a joke or issued a pun.  Maseres was the fourth wrangler of 1752, and highest in classics; yet his tutor could not get through the second page of a first book on algebra; a negative quantity stood like a lion in the way.
    The great difficulty of the opponents of algebra lay in want of power or will to see extension of terms.  Maseres implies that extension, accompanied by its refusal, makes jargon.  One of my paradoxers was present at a meeting of the Royal Society in 1864 and asked permission to make some remarks upon a paper.  He rambled into other things, and, naming me, said that I had written a book in which two sides of a triangle are pronounced equal to the third.  So they are, in the sense in which the word is used in complete algebra; in which A + B = C makes A, B, C, three sides of a triangle, and declares that going over A and B, one after the other, is equivalent, in change of place, to going over C at once.  My critic, who might have objected to extension, insisted upon reading me in unextended meaning.

The Doctrine of Life Annuities (726 pages, 1783).
    A strange paradox.  Its size, the heavy dissertations on the national debt, and the depth of algebra supposed known, put it out of the question as an elementary work, and it is unfitted for the higher student.  It is a climax of unsaleability, unreadability, and inutility.  For intrinsic nullity of interest, and dilution of little matter with much ink, I can compare this book to nothing but that of Claude de St. Martin, elsewhere mentioned, or the lectures On the Nature and Properties of Logarithms, by James Little, Dublin, 1830, 8vo.  (254 heavy pages of many words and few symbols), a wonderful weight of weariness.

Origin of the English Language, related by a Swede.
    Some months ago in a party in Holland, consisting of natives of various countries, the merit of their respective languages became a topic of conversation.  A Swede, who had been a great traveler and could converse in most of the modern languages of Europe, laughed very heartily at an Englishman who had ventured to speak in praise of the tongue of his dear country.  I never had any trouble, says he, in learning English.  To my very great surprise, the moment I sat foot on shore at Gravesend, I found out, that I could understand, with very little trouble, every word that was said.  It was a mere jargon, made up of German, French, and Italian, with now and then a word from the Spanish, Latin or Greek.  I had only to bring my mouth to their mode of speaking, which was done with ease in less than a week, and I was everywhere taken for a true-born Englishman; a privilege of no small importance in a country, where each man, God knows why, thinks his foggy island superior to any other part of the world; and though his door is never free from some dun or other coming for a tax, and if he steps out of it he is sure to be knocked down or to have his pocket picked, yet he has the insolence to think every foreigner a miserable slave, and his country the seat of everything wretched.  They may talk of liberty as they please, but Spain or Turkey for my money; barring the bowstring and the inquisition, they are the most comfortable countries under heaven, and you need not be afraid of either if you do not talk of religion and politics.  I do not see much difference too in this respect in England, for when I was there, one of their most eminent men for learning was put in prison for a couple of years, and got his death for translating one of Æsop's fables into English, which every child in Spain and Turkey is taught, as soon as he comes out of his leading strings.
    Here all the company unanimously cried out against the Swede, that it was impossible; for in England, the land of liberty, the only thing its worst enemies could say against it was that they paid for their liberty a much greater price than it was worth.  Every man there had a fair trial according to laws, which everybody could understand; and the judges were cool, patient, discerning men, who never took the part of the crown against the prisoner, but gave him every assistance possible for his defense.
    The Swede was borne down, but not convinced; and he seemed determined to spit out all his venom.  Well, says he, at any rate you will not deny that the English have not got a language of their own, and that they came by it in a very odd way.  Of this at least I am certain, for the whole history was related to me by a witch in Lapland, whilst I was bargaining for a wind.  Here the company were all in unison again for the story.
    "In ancient times, said the old hag, the English occupied a spot in Tartary where they lived sulkily by themselves, unknowing and unknown.  By a great convulsion that took place in China, the inhabitants of that and the adjoining parts of Tartary were driven from their seats, and after various wanderings took up their abode in Germany.  During this time nobody could understand the English, for they did not talk, but hissed like so many snakes.  The poor people felt uneasy under this circumstance, and in one of their hissing meetings, it was determined to seek a remedy, and an embassy was sent to some of our sisterhood then living on Mount Hecla.  They summoned the Devil to their relief.  To him the English presented their petitions, and explained their sad case; and he, upon certain conditions, promised to befriend them, and to give them a language.
    "The poor Devil was little aware of what he had promised; but he is, as all the world knows, a man of too much honor to break his word.  Up and down the world he went in quest of this new language; visited all the universities, and all the schools, and all the courts of law, and all the playhouses, and all the prisons; never was poor devil so fagged.  It would have made your heart bleed to see him.  Thrice did he go round the earth in every parallel of latitude; and at last, wearied and jaded out, back came he to Hecla in despair, and would have thrown himself into the volcano, if he had been made of combustible materials.  Luckily at that time our sisters were engaged in settling the balance of Europe; and whilst they were looking over projects, and counter-projects, and ultimatums, and post ultimatums, the poor Devil, unable to assist them was groaning in a corner and ruminating over his sad condition.
    "On a sudden, a hellish joy overspread his countenance; up he jumped, and, like Archimedes of old, ran like a madman amongst the throng, turning over tables, and papers, and witches, roaring out for a full hour together nothing else but 'Tis found, 'Tis found!'  Away were sent the sisterhood in every direction, some to traverse all the corners of the earth, and others to prepare a larger caldron than had ever yet been set upon Hecla.  The affairs of Europe were at a stand; its balance was thrown aside; prime ministers and ambassadors were everywhere in the utmost confusion; and,by the way, they have never been able to find the balance since that time, and all the fine speeches upon the subject, with which your newspapers are every now and then filled, are all mere hocus pocus and rhodomontade.
    "However, the caldron was soon set on, and the air was darkened by witches riding on broomsticks, bringing a couple of folios under each arm, and across each shoulder.  I remember the time exactly: it was just as the council of Nice had broken up, so that they got books and papers there dog cheap; but it was a bad thing for the poor English, as these were the worst materials that entered into the caldron.  Besides, as the Devil wanted some amusement, and had not seen an account of the transactions of this famous council, he had all the books brought from it laid before him, and split his sides almost with laughing, whilst he was reading the speeches and decrees of so many of his old friends and acquaintances.  All this while the witches were depositing their loads in the great caldron.  There were books from the Dalai Lama, and from China; there were books from the Hindus, and tallies from the Caffres; there were paintings from Mexico, and rocks of hieroglyphics from Egypt; the last country supplied besides the swathings of two thousand mummies, and four-fifths of the famed library of Alexandria.  Bubble! bubble! toil and trouble!  Never was a day of more labor and anxiety; and if our good master had but flung in the Greek books at the proper time, they would have made a complete job of it.  He was a little too impatient: as the caldron frothed up, he skimmed it off with a great ladle, and filled some thousands of our wind-bags with the froth, which the English with great joy carried back to their own country.  These bags were sent to every district: the chiefs first took their fill, and then the common people; hence they now speak a language which no foreigner can understand, unless he has learned half a dozen other languages; and the poor people, not one in ten, understand a third part of what is said to them.  The hissing, however, they have not entirely got rid of, and every seven years, when the Devil, according to agreement, pays them a visit, they entertain him at their common halls and county meetings with their original language.
    "The good-natured old hag told me several other circumstances relative to this curious transaction, which, as there is an Englishman in company, it will be prudent to pass over in silence; but I cannot help mentioning one thing which she told me as a very great secret.  You know, says she to me, that the English have more religions among them than any other nation in Europe, and that there is more teaching and sermonizing with them than in any other country.  The fact is, it matters not who gets up to teach them, the hard words of the Greek were not sufficiently boiled, and whenever they get into a sentence, the poor people's brains are turned, and they know no more what the preacher is talking about, than if he harangued them in Arabic.  Take my word for it if you please; but if not, when you get to England, desire the bettermost sort of people that you are acquainted with to read to you an act of parliament, which of course is written in the clearest and plainest style in which anything can be written, and you will find that not one in ten will be able to make tolerable sense of it.  The language would have been an excellent language, if it had not been for the council of Nice, and the words had been well boiled."
    Here the company burst out into a fit of laughter.  The Englishman got up and shook hands with the Swede: si non è vero, said he, è ben trovato.  But however I may laugh at it here, I would not advise you to tell this story on the other side of the water.  So here's a bumper to Old England for ever, and God save the king.

NEWTON AGAIN OVERTHROWN.
A treatise on the sublime science of heliography, satisfactorily demonstrating our great orb of light, the sun, to be absolutely no other than a body of ice!  Overturning all the received systems of the universe hitherto extant; proving the celebrated and indefatigable Sir Isaac Newton, in his theory of the solar system, to be as far distant from the truth, as many of the heathen authors of Greece and Rome.  By Charles Palmer, Gent.  London, 1798.
    Mr. Palmer burned some tobacco with a burning glass, saw that a lens of ice would do as well, and then says: "If we admit that the sun could be removed, and a terrestrial body of ice placed in its stead, it would produce the same effect.  The sun is a crystaline body receiving the radiance of God, and operates on this earth in a similar manner as the light of the sun does when applied to a convex mirror or glass."

Nov. 10, 1801.  The Rev. Thomas Cormouls, minister of Tettenhall, addressed a letter to Sir Wm. Herschel, including that Newton "certainly wrought the principles he made use of into strict analogy with the real Phenomina of the heavens, and that the rules and results arizing from them agree with them and resolve accurately all questions concerning them.  Though they are not fact and true, or nature, but analogous to it, in the manner of the artificial numbers of logarithms, sines, &c.  A very important question arises, Did Newton mean to impose upon the world?  By no means; he received and used the doctrines reddy formed; he did a little extend and contract his principles when wanted, and commit a few oversights of consequences.  But when he was very much advanced in life, he suspected the fundamental nullity of them; but I have from a certain anecdote strong ground to believe that he knew it before his decease and intended to have retracted his error."
    That Newton wanted to retract before his death, is a notion not uncommon among paradoxers.  Nevertheless, there is no retraction in the third edition of the Principia, published when Newton was eighty-four years old!  The moral of the above is, that a gentleman who prefers instructing William Herschel to learning how to spell, may find a proper niche as a warning to others.  It seems that gravitation is not truth, but only the logarithm of it.

1810.  In this year Jean Wood, Professor of Mathematics in the University of Virginia (Richmond), addressed a printed circular to "Dr. Herschel, Astronomer, Greenwich Observatory."  No mistake was more common than the natural one of imagining that the Private Astronomer of the king was the Astronomer Royal.  The letter was on the difference of velocities of the two sides of the earth, arising from the composition of the rotation and the orbital motion.  The paradox is a fair one, and deserving of investigation; but, perhaps it would not be easy to deduce from it tides, trade winds, aeroliths, &c., as Mr. Wood thought he had done in a work from which he gives an extract, and which he describes as published.  The composition of rotations, &c., is not for the world at large; the paradox of the non-rotation of the moon about her axis is an instance.  How many persons know that when a wheel rolls on the ground, the lowest point is moving upwards, the highest point forwards, and the intermediate points in all degrees of betwixt and between?  This is too short an explanation, with some good difficulties.

The Elements of Geometry.  In 2 vols.  (By the Rev. J. Dobson, B.D.)  Cambridge, 1815.
    Of this unpunctuating paradoxer I shall give an account in his own way: he would not stop for any one; why should I stop for him?  It is worth while to try how unpunctuated sentences will read.
    The reverend J Dobson BD late fellow of saint Johns college Cambridge was rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 and died in 1847 he was of that sort of eccentricity which permits account of his private life if we may not rather say that in such cases private life becomes public there is a tradition that he was called Death Dobson on account of his head and aspect of countenance being not very unlike the ordinary pictures of a human skull his mode of life is reported to have been very singular whenever he visited Cambridge he was never known to go twice to the same inn he never would sleep at the rectory with another person in the house some ancient charwoman used to attend to the house but never slept in it he has been known in the time of coach travelling to have deferred his return to Yorkshire on account of his disinclination to travel with a lady in the coach he continued his mathematical studies until his death and till his executors sold the type all his tracts to the number of five were kept in type at the university press none of these tracts had any stops except full stops at the end of paragraphs only neither had they capitals except one at the beginning of a paragraph so that a full stop was generally followed by some white as there is not a single proper name in the whole of the book I have I am not able to say whether he would have used capitals before proper names I have inserted them as usual for which I hope his spirit will forgive me if I be wrong he also published the elements of geometry in two volumes quarto Cambridge 1815 this book had also no stops except when a comma was wanted between letters as in the straight lines AB, BC I should also say that though the title is unpunctuated in the author's part it seems the publishers would not stand it in their imprint this imprint is punctuated as usual and Deighton and Sons to prove the completeness of their allegiance have managed that comma semicolon and period shall all appear in it why could they not have contrived interrogation and exclamation this is a good precedent to establish the separate right of the publisher over the imprint it is said that only twenty of the tracts were printed and very few indeed of the book on geometry it is doubtful whether any were sold there is a copy of the geometry in the university library at Cambridge and I have one myself the matter of the geometry differs entirely from Euclid and is so fearfully prolix that I am sure no mortal except the author ever read it the man went on without stops and without stop save for a period at the end of a paragraph this is the unpunctuated account of the unpunctuating geometer suum cuique tribuito Mrs Thrale would have been amused at a Dobson who managed to come to a full stop without either of the three warnings.

A RELIGIOUS PARADOX.
Philosophia Sacra, or the principles of natural Philosophy.  Extracted from Divine Revelation.  By the Rev. Samuel Pike. Edited by the Rev. Samuel Kittle.  Edinburgh, 1815.
    The Rev. William Jones is best known as William Jones of Nayland, who (1757) published the Catholic Doctrine of the Trinity; he was also strong for the Hutchinsonian physical trinity of fire, light, and spirit.  This well-known work was generally recommended as the defense of the orthodox system, to those who could not go into the learning of the subject.
    There is now a work more suited to our time: The Rock of Ages, by the Rev. E. H. Bickersteth, now published by the Religious Tract Society, without date, answered by the Rev. Dr. Sadler, in a work (1859) entitled Gloria Patri, in which, says Mr. Bickersteth, "the author has not even attempted to grapple with my main propositions."  I have read largely on the controversy, and I think I know what this means.
    Moreover, when I see the note "There are two other passages to which Unitarians sometimes refer, but the deduction they draw from them is, in each case, refuted by the context" — I think I see why the two texts are not named.  Nevertheless, the author is a little more disposed to yield to criticism than his foregoers; he does not insist on texts and readings which the greatest editors have rejected.  And he writes with courtesy, both direct and oblique, towards his antagonists; which, on his side of this subject, is like letting in fresh air.  So that I suspect the two books will together make a tolerably good introduction to the subject for those who cannot go deep.
    There is a point which I should gravely recommend to writers on the orthodox side: the Unitarians in England have frequently contended that the method of proving the divinity of Jesus Christ from the New Testament would equally prove the divinity of Moses.
    Perhaps Mr. B. has his own meaning of logical terms, such as "proposition;" he certainly has his own meaning of "cumulative." He says his evidence is cumulative; not a chain, the strength of which is in its weakest part, but distinct and independent lines, each of which corroborates the other.  This is the very opposite of cumulative: it is distributive.  When different arguments are each necessary to a conclusion, the evidence is cumulative; when any one will do, even though they strengthen each other, it is distributive.  The word "cumulative" is a synonym of the law word "constructive;" a whole which will do made out of parts which separately will not.  In conclusion, Mr. B. is a Cambridge man; the Oxford men do not confuse the elementary terms of logic.  O dear old Cambridge!  When the New Zealander comes let him find among the relics of your later sons some proof of attention to the elementary laws of thought.  A little-go of logic, please!
    This book is very bad physics.  The sun, apart from its light, evident to the eye!  Heat more self-demonstrating than light, because felt!  Heat only manifested by the life it diffuses!  Light implied not necessary to life!  But the theology is worse than Sabellianism.  To adumbrate — i.e., make a picture of — the orthodox doctrine, the sun must be heavenly body, the light heavenly body, the heat heavenly body; and yet, not three heavenly bodies, but one heavenly body.  The truth is, that this illustration and many others most strikingly illustrate the Trinity of fundamental doctrine held by the Unitarians, in all its differences from the Trinity of persons held by the Orthodox.  Be right which may, the right or wrong of the Unitarians shines out in the comparison.  Dr. Sadler confirms me — by which I mean that I wrote the above before I saw what he says — in the following words: "The sun is one object with two properties, and these properties have a parallel not in the second and third persons of the Trinity, but in the attributes of Deity."
    The letting light alone, as self-evident, and making heat self-demonstrating, because felt — i.e., perceptible now and then — has the character of the Irishman's astronomy:
        "Long life to the moon, for a dear noble cratur,
        Which serves us for lamplight all night in the dark,
        While the sun only shines in the day, which by natur,
        Wants no light at all, as ye all may remark."

SIR RICHARD PHILLIPS.
    Sir Richard Phillips (born 1768) was conspicuous in 1793, when he was sentenced to a year's imprisonment for selling Paine's Rights of Man; and again in 1807, when he was knighted as Sheriff of London.  He was not only an anti-Newtonian, but carried to a fearful excess the notion that statesmen and Newtonians were in league to deceive the world.
    In 1836, he did me the honor to attempt my conversion.  In his first letter he says: "Sir Richard Phillips has an inveterate abhorrence of all the pretended wisdom of philosophy derived from the monks and doctors of the middle ages, and not less of those of higher name who merely sought to make the monkish philosophy more plausible, or so to disguise it as to mystify the mob of small thinkers."  So little did his writings show any knowledge of antiquity that I strongly suspect, if required to name one of the monkish doctors, he would have answered — Aristotle.  These schoolmen, and the "philosophical trinity of gravitating force, projectile force, and void space," were the bogies of his life.
    I think he began to publish speculations in the Monthly Magazine (of which he was editor) in July 1817.  In the Preface, perhaps judging the feelings of others by his own, he says that he "fully expects to be vilified, reviled, and anathematized, for many years to come."  Poor man!  He was let alone.  He appeals with confidence to the "impartial decision of posterity"; but posterity does not appoint a hearing for one per cent of the appeals which are made; and it is much to be feared that an article in such a work of reference as this will furnish nearly all her materials fifty years hence.
    The following, addressed to M. Arago in 1835, will give posterity as good a notion as she will probably need: "Even the present year has afforded EVER-MEMORABLE examples, paralleled only by that of the Romish Conclave which persecuted Galileo.  Policy has adopted that maxim of Machiavel which teaches that it is more prudent to reward partisans than to persecute opponents.  Hence, a bigoted party had influence enough with the late short-lived administration to confer munificent royal pensions on three writers whose sole distinction was their advocacy of the Newtonian philosophy.  A Cambridge professor last year published an elaborate volume in illustration of Gravitation, and on him has been conferred a pension of 300 l. per annum.  A lady has written a light popular view of the Newtonian Dogmas, and she has been complimented by a pension of 200 l. per annum.  And another writer, who has recently published a volume to prove that the only true philosophy is that of Moses, has been endowed with a pension of 200 l. per annum.  Neither of them were needy persons, and the political and ecclesiastical bearing of the whole was indicated by another pension of 300 l. bestowed on a political writer, the advocate of all abuses and prejudices.
    "Whether the conduct of the Romish Conclave was more base for visiting with legal penalties the promulgation of the doctrines that the Earth turns on its axis and revolves around the Sun; or that of the British Court, for its craft in conferring pensions on the opponents of the plain corollary, that all the motions of the Earth are 'part and parcel' of these great motions, and those again and all like them consecutive displays of still greater motions in equality of action and reaction, is A QUESTION which must be reserved for the casuists of other generations....  I cannot expect that on a sudden you and your friends will come to my conclusion, that the present philosophy of the Schools and Universities of Europe, based on faith in witchcraft, magic, &c., is a system of execrable nonsense, by which quacks live on the faith of fools; but I desire a free and fair examination of my Aphorisms, and if a few are admitted to be true, merely as courteous concessions to arithmetic, my purpose will be effected, for men will thus be led to think; and if they think, then the fabric of false assumptions, and degrading superstitions will soon tumble in ruins."
    This for posterity.  For the present time I ground the fame of Sir R. Phillips on his having squared the circle without knowing it, or intending to do it.  In the Protest presently noted he discovered that "the force taken as 1 is equal to the sum of all its fractions ...  thus 1 = 1/4 + 1/9 + 1/16 + 1/25, &c., carried to infinity."  This the mathematician instantly sees is equivalent to the theorem that the circumference of any circle is double of the diagonal of the cube on its diameter.
    Sir R. Phillips had four valuable qualities; honesty, zeal, ability, and courage.  He applied them all to teaching matters about which he knew nothing; and gained himself an uncomfortable life and a ridiculous memory.

WHATELY'S FAMOUS PARADOX.
Historic doubts relative to Napoleon Buonaparte.  London, 1819.
    This tract has since been acknowledged by Archbishop Whately and reprinted.  It is certainly a paradox, but differs from most as being a joke, and a satire upon the reasoning of those who cannot receive narrative, no matter what the evidence, which is to them utterly improbable a priori.

VOLTAIRE A CHRISTIAN.
Voltaire Chrétien; preuves tirées de ses ouvrages.  Paris, 1820.
    If Voltaire have not succeeded in proving himself a strong theist and anti-revelationist, who is to succeed in proving himself one thing or the other in any matter whatsoever? By occasional confusion between theism and Christianity; by taking advantage of the formal phrases of adhesion to the Roman Church, which very often occur, and are often the happiest bits of irony in an ironical production; by citations of his morality, which is decidedly Christian, though often attributed to Brahmins; and so on — the author makes a fair case for his paradox, in the eyes of those who know no more than he tells them.
    Christian!  The word has degenerated into a synonym of man, in what are called Christian countries.  We have the parrot who "swore for all the world like a Christian," and the two dogs who "hated each other just like Christians."  When the Irish duellist of the last century, whose name may be spared in consideration of its historic fame and the worthy people who bear it, was (June 12, 1786) about to take the consequence of his last brutal murder, the rope broke, and the criminal got up, and exclaimed, "By — — Mr. Sheriff, you ought to be ashamed of yourself! this rope is not strong enough to hang a dog, far less a Christian!"
    As to a word so defiled by usage, it is well to know that there is a way of escape from it, without renouncing the New Testament.  I suppose any one may assume for himself what I have sometimes heard contended for, that no New Testament word is to be used in religion in any sense except that of the New Testament.  This granted, the question is settled.  The word Christian, which occurs three times, is always a term of contempt from those without the pale to those within.  Herod Agrippa says to Paul (Acts xxvi. 28), "Almost thou persuadest me to be (what I and other followers of the state religion despise under the name) a Christian."  And (Acts xi. 26) "The disciples (as they called themselves) were called (by the surrounding heathens) Christians first in Antioch."  And (1 Peter iv. 16), "Let none of you suffer as a murderer....  But if as a Christian (as the heathen call it by whom the suffering comes), let him not be ashamed."
    That is, no disciple ever called himself a Christian, or applied the name, as from himself, to another disciple, from one end of the New Testament to the other; and no disciple need apply that name to himself in our day, if he dislike the associations with which the conduct of Christians has clothed it.

WRONSKI ON THE LONGITUDE PROBLEM.
Address of M. Hoene-Wronski to the British Board of Longitude, upon the actual state of the mathematics, their reform, and upon the new celestial mechanics, giving the definitive solution of the problem of longitude. London, 1820.
    The tract above is an attack on modern mathematicians in general, and on the Board of Longitude, and Dr. Young.  M. Wronski was the author of seven quartos on mathematics, showing very great power of generalization.  He was also deep in the transcendental philosophy, and had the Absolute at his fingers' ends.  All this knowledge was rendered useless by a persuasion that he had greatly advanced beyond the whole world, with many hints that the Absolute would not be forthcoming, unless prepaid.
    He was a man of the widest extremes.  At one time he desired people to see all possible mathematics in
    Fx = A0Ω0 + A1Ω1 + A2Ω2 + A3Ω3 + &c.
which he did not explain, though there is meaning to it in the quartos.  At another time he was proposing the general solution of the fifth degree by help of 625 independent equations of one form and 125 of another.

HERBART'S MATHEMATICAL PSYCHOLOGY.
De Attentionis mensura causisque primariis.  By J. F. Herbart. Kœnigsberg, 1822.
    This celebrated philosopher maintained that mathematics ought to be applied to psychology.  For example, let t be the time elapsed since the consideration began, β the whole perceptive intensity of the individual, φ the whole of his mental force, and z the force given to a notion by attention during the time t.  Then,
    z = φ (1 - ε-βt)
Now for a test. There is a jactura, v, the meaning of which I do not comprehend.  If there be anything in it, my mathematical readers ought to interpret it from the formula
    v = πφβ/(1 - β)ε-βt + Cε-t
and to this task I leave them, wishing them better luck than mine.  The time may come when other manifestations of mind, besides belief, shall be submitted to calculation; at that time, should it arrive, a final decision may be passed upon Herbart.

The Mythological Astronomy of the Ancients; part the second: or the key of Urania, the words of which will unlock all the mysteries of antiquity.  Norwich, 1823.
A Companion to the Mythological Astronomy, &c., containing remarks on recent publications....  Norwich, 1824, 12mo.
A new Theory of the Earth and of planetary motion; in which it is demonstrated that the Sun is vicegerent of his own system.  Norwich, 1825.
The analyzation of the writings of the Jews, so far as they are found to have any connection with the sublime science of astronomy.
    These works are all by Sampson Arnold Mackey.  An extraordinary man he certainly was; not one illiterate shoemaker in a thousand could work upon such a singular mass of Sanskrit and Greek words, without showing evidence of being able to read a line in any language but his own, or to spell that correctly.  He was an uneducated Godfrey Higgins.  A few extracts will put this in a strong light: one for history of science, one for astronomy, and one for philology:
    "Sir Isaac Newton was of opinion that 'the atmosphere of the earth was the sensory of God; by which he was enabled to see quite round the earth:' which proves that Sir Isaac had no idea that God could see through the earth."
    "Sir Richard (Phillips) has given the most rational explanation of the cause of the earth's elliptical orbit that I have ever seen in print.  It is because the earth presents its watery hemisphere to the sun at one time and that of solid land the other; but why has he made his Oxonian astonished at the coincidence?  It is what I taught in my attic twelve years before."
    "Admitting that the Eloim were powerful and intelligent beings that managed these things, we would accuse them of being the authors of all the sufferings of Chrisna.  And as they and the constellation of Leo were below the horizon, and consequently cut off from the end of the zodiac, there were but eleven constellations of the zodiac to be seen; the three at the end were wanted, but those three would be accused of bringing Chrisna into the troubles which at last ended in his death.  All this would be expressed in the Eastern language by saying that Chrisna was persecuted by those Judoth Ishcarioth!!!!! (the five notes of exclamation are the author's).  But the astronomy of those distant ages, when the sun was at the south pole in winter, would leave five of those Decans cut off from our view, in the latitude of twenty-eight degrees; hence Chrisna died of wounds from five Decans, but the whole five may be included in Judoth Ishcarioth! for the phrase means 'the men that are wanted at the extreme parts.'  Ishcarioth is a compound of ish, a man, and carat wanted or taken away, and oth the plural termination, more ancient than im...."
    I might show how Michael is the sun, and the D'-ev-'l in French Di-ob-al, also 'L-evi-ath-an — the evi being the radical part both of devil and leviathan — is the Nile, which the sun dried up for Moses to pass.  Also how Moses, the same name as Muses, is from mesha, drawn out of the water, "hence we called our land which is saved from the water by the name of marsh."  Great astronomical and philological attainments, much ability and learning; had evidently read and studied deeply; remarkable for the originality of his views upon the very abstruse subject of mythological astronomy, in which he exhibited great sagacity.  Certainly his views were original; but their sagacity, if it be allowable to copy his own mode of etymologizing, is of an ori-gin-ale cast, resembling that of a person who puts to his mouth liquors both distilled and fermented.

A KANTESIAN JEWELER.
Principles of the Kantesian, or transcendental philosophy.  By Thomas Wirgman. London, 1824.
    Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky and vagarious.  He had been a fashionable jeweler in St. James's Street; he old snuff-boxes, among other things, and fifty years ago a fashionable snuff-boxer would be under inducement, if not positively obliged, to have a stock with very objectionable pictures.  So Wirgman, by this trifling excess of candor, came under the notice of the Suppression Society, and ran considerable risk.  Mr. Brougham was his counsel, and managed to get him acquitted.
    Years and years after this, when Mr. Brougham was deep in the formation of the London University (now University College), Mr. Wirgman called on him.  "What now?" said Mr. B. with his most sarcastic look — a very perfect thing of its kind — "you're in a scrape again, I suppose!"  "No! indeed!" said W., "my present object is to ask your interest for the chair of Moral Philosophy in the new University!"  He had taken up Kant!
    Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to convert me.  "I assure you," said he, "I am nothing but an old brute of a jeweler;" and his eye and manner were of the extreme of jocosity, as good in their way as the satire of his former counsel.  I mention him as one of that class who go away quite satisfied that they have wrought conviction.  "Now," said he, "I'll make it clear to you!  Suppose a number of goldfish in a glass bowl, — you understand?  Well!  I come with my cigar and go puff, puff, puff, over the bowl, until there is a little cloud of smoke: now, tell me, what will the goldfish say to that?"  "I should imagine," said I, "That they would not know what to make of it."  "By Jove! you're a Kantian;" said he, and with this and the like, he left me, vowing that it was delightful to talk to so intelligent a person.  The greatest compliment Wirgman ever received was from James Mill, who used to say he did not understand Kant.  That such a man as Mill should think this worth saying is a feather in the cap of the jocose jeweler.

WALSH'S DELUSIONS.
    John Walsh, of Cork (1786-1847).  This discoverer has had the honor of a biography from Professor Boole, in the Philosophical Magazine for November, 1851.  Mr. Walsh introduced himself to me, as he did to many others, in the ante-Rowlandian days of the Post Office; his unpaid letters were double, treble, &c.  They contained his pamphlets, and cost their weight in silver.
    Mr. Boole, who has taken the moral and social features of Walsh's delusions from the commiserating point of view, which makes ridicule out of place, has been obliged to treat Walsh as Scott's Alan Fairford treated his client Peter Peebles; namely, keep the scarecrow out of court while the case was argued.  My plan requires me to bring him in; and when he comes in at the door, pity and sympathy fly out at the window.
    Let the reader remember that he was not an ignoramus in mathematics; he might have won his spurs if he could have first served as an esquire.  Though so illiterate that even in Ireland he never picked up anything more Latin than Irelandus, he was a very pretty mathematician spoiled in the making by intense self-opinion.  This is part of a private letter to me at the back of a page of print; I had never addressed a word to him:
    "There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards.  There is no differential calculus, no Taylor's theorem, no calculus of variations, &c.  in mathematics.  There is no quackery whatever in mathematics; no % equal to anything.  What sheer ignorant blackguardism that!  In mechanics the parallelogram of forces is quackery, and is dangerous; for nothing is at rest, or in uniform, or in rectilinear motion, in the universe.  Variable motion is an essential property of matter.  Laplace's demonstration of the parallelogram of forces is a begging of the question; and the attempts of them all to show that the difference of twenty minutes between the sidereal and actual revolution of the earth round the sun arises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfect quackery.  The said difference arising from and demonstrating the revolution of the Sun itself round some distant center."
    In the letter to Lord Brougham we read as follows: "I ask the Royal Society of London, I ask the Saxon crew of that crazy hulk, where is the dogma of their philosophic god now?...  When the Royal Society of London and the Academy of Sciences of Paris shall have read this memorandum, how will they appear?  Like two cur dogs in the paws of the noblest beast of the forest....  Just as this note was going to press, a volume lately published by you was put into my hands, wherein you attempt to defend the fluxions and Principia of Newton.  Man!  What are you about?  You come forward now with your special pleading, and fraught with national prejudice, to defend, like the philosopher Grassi, the persecutor of Galileo, principles and reasoning which, unless you are actually insane, or an ignorant quack in mathematics, you know are mathematically false.  What a moral lesson this for the students of the University of London from its head!  Man!  Demonstrate corollary 3, in this note, by the lying dogma of Newton, or turn your thoughts to something you understand.  "Walsh Irelandus."
    Once Mr. Walsh — honor to his memory — had the consideration to save me postage by addressing a pamphlet under cover to a Member of Parliament, with an explanatory letter.  In that letter he gives a candid opinion of himself: "Mr. Walsh takes leave to send the enclosed corrected copy to Mr. Hutton as one of the Council of the University of London, and to save postage for the Professor of Mathematics there.  He will find in it geometry more deep and subtle, and at the same time more simple and elegant, than it was ever contemplated human genius could invent."
    He then proceeds to set forth that a certain "tomfoolery lemma," with its "tomfoolery" superstructure, "never had existence outside the shallow brains of its inventor," Euclid.  He then proceeds thus: "The same spirit that animated those philosophers who sent Galileo to the Inquisition animates all the philosophers of the present day without exception.  If anything can free them from the yoke of error, it is the (Walsh) problem of double tangence.  But free them it will, how deeply soever they may be sunk into mental slavery — and God knows that is deeply enough; and they bear it with an admirable grace; for none bear slavery with a better grace than tyrants.  The lads must adopt my theory....  It will be a sad reverse for all our great professors to be compelled to become schoolboys in their gray years.  But the sore scratch is to be compelled, as they had before been compelled one thousand years ago, to have recourse to Ireland for instruction."
    Walsh's system is, that all mathematics and physics are wrong: there is hardly one proposition in Euclid which is demonstrated.  His example ought to warn all who rely on their own evidence to their own success.  He was not, properly speaking, insane; he only spoke his mind more freely than many others of his class.  He lived a happy life contemplating his own perfections, like Brahma on the lotus-leaf.

GROWTH OF FREEDOM OF OPINION.
    Freedom of opinion, beyond doubt, is gaining ground, for good or for evil according to what the speaker happens to think: admission of authority is no longer made in the old way.  If we take divinity and medicine, it is manifest that a change has come over us.  Once it was enough that dose or dogma should be certified by "Il a été ordonné, Monsieur, il a été ordonné."  Very much changed, but whether for good or for evil does not now matter; the question is, whether paradoxers' contempt of demonstration has augmented with the rejection of dogmatic authority.  It ought to be the other way: for the worship of reason is the system on which, if we trust them, the deniers of guidance ground their plan of life.

THE STATUS OF MEDICINE.
    I have known a medical man — a young one — who was seriously of the opinion that the country ought to be divided into medical parishes, with a practitioner appointed to each, and a penalty for calling in any but the incumbent curer.  How should people know how to choose?  The hair-dressers once petitioned Parliament for an act to compel people to wear wigs.  My own opinion is of the opposite extreme, as in the following letter (Examiner, April 5, 1856); which, to my surprise, I saw reprinted in a medical journal, as a plan not absolutely to be rejected.  I am perfectly satisfied that it would greatly promote true medical orthodoxy, the predominance of well educated thinkers, and the development of their desirable differences.
    "Let every man who chooses — subject to one common law of manslaughter for all the crass cases — doctor the bodies of all who choose to trust him, and recover payment according to agreement in the courts of law.  Provided always that every person practising should be registered at a moderate fee in a register to be republished every six months.
    "Let the register give the name, address, and asserted qualification of each candidate — as licentiate, or doctor, or what not, of this or that college, hall, university, &c., home or foreign.  Let it be competent to any man to describe himself as qualified by study in public schools without a diploma, or by private study, or even by intuition or divine inspiration, if he please.  But whatever he holds his qualification to be, that let him declare.  Let all qualification [269]which of its own nature admits of proof be proved, as by the diploma or certificate, &c., leaving things which cannot be proved, as asserted private study, intuition, inspiration, &c., to work their own way.
    "Let it be highly penal to assert to the patient any qualification which is not in the register, and let the register be sold very cheap.  Let the registrar give each registered practitioner a copy of the register in his own case; let any patient have the power to demand a sight of this copy; and let no money for attendance be recoverable in any case in which there has been false representation.
    "Let any party in any suit have a right to produce what medical testimony he pleases.  Let the medical witness produce his register, and let his evidence be for the jury, as is that of an engineer or a practitioner of any art which is not attested by diplomas.
    "Let any man who practises without venturing to put his name on the register be liable to fine and imprisonment.
    "Every man who practices would be obliged to tell the whole world what his claim is, and would run a great risk if he dared to tell his patient in private anything different from what he had told the whole world.  The consequence would be that a real education in anatomy, physiology, chemistry, surgery, and what is known of the thing called medicine, would acquire more importance than it now has.
    "Heteropath."

THE CHRISTIAN EVIDENCE SOCIETY.
Manifesto of the Christian Evidence Society, established Nov.  12, 1824.  Twenty-four plain questions to honest men.
    These are two broadsides of August and November, 1826, signed by Robert Taylor, A.B., Orator of the Christian Evidence Society.  This gentleman was a clergyman, and was convicted of blasphemy in 1827, for which he suffered imprisonment, and got the name of the Devil's Chaplain.
    The following are quotations: "For the book of Revelation, there was no original Greek at all, but Erasmus wrote it himself in Switzerland, in the year 1516.  Bishop Marsh, vol. i. p. 320." — "Is not God the author of your reason?  Can he then be the author of anything which is contrary to your reason?  If reason be a sufficient guide, why should God give you any other?  If it be not a sufficient guide, why has he given you that?"
    I remember a votary of the Society being asked to substitute for reason "the right leg," and for guide "support," and to answer the two last questions.  He said there must be a quibble, but he did not see what.
    It is pleasant to reflect that the argumentum à carcere is obsolete.  One great defect of it was that it did not go far enough: there should have been laws against subscriptions for blasphemers, against dealing at their shops, and against rich widows marrying them.
    Had I taken in theology, I must have entered books against Christianity.  I mention the above, and Paine's Age of Reason, simply because they are the only English modern works that ever came in my way without my asking for them.  The three parts of the Age of Reason were published in Paris 1793, Paris 1795, and New York 1807.  Carlile's edition is of London, 1818.  It must be republished when the time comes, to show what stuff governments and clergy were afraid of at the beginning of this century.  I should never have seen the book, if it had not been prohibited; a bookseller put it under my nose with a fearful look round him; and I could do no less, in common curiosity, than buy a work which had been so complimented by church and state.  And when I had read it, I said in my mind to church and state, — Confound you!  You have taken me in worse than any reviewer I ever met with.  I forget what I gave for the book, but I ought to have been able to claim compensation somewhere.

ON GODFREY HIGGINS.
The Celtic Druids.  By Godfrey Higgins, Esq. of Skellow Grange, near Doncaster.  London, 1827.
Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis: or an inquiry into the origin of languages, nations, and religions.  By Godfrey Higgins, &c..., London, 1836, 2 vols.
    The system of these works is that "The Buddhists of Upper India (of whom the Phenician Canaanite Melchizedek was a priest), who built the Pyramids, Stonehenge, Carnac, &c. will be shown to have founded all the ancient mythologies of the world, which, however varied and corrupted in recent times, were originally one, and that one founded on principles sublime, beautiful, and true."
    These works contain an immense quantity of learning, very honestly put together.  I presume the enormous number of facts, and the goodness of the index, to be the reasons why the Anacalypsis found a permanent place in the old reading room of the British Museum.
    Mr. Higgins was thoroughly and completely the man of a system.  He was very sure of any fact which he got from any of his authorities; nothing could shake him.  Imagine a conversation between him and an Indian officer who had paid long attention to Hindu antiquities and their remains; a third person was present, ego qui scribo.  G. H. "You know that in the temples of I-forget-who the Ceres is always sculptured precisely as in Greece."  Col. — — , "I really do not remember it, and I have seen most of these temples."  G. H. "It is so, I assure you, especially at I-forget-where."  Col. — — , "Well, I am sure! I was encamped for six weeks at the gate of that very temple, and, except a little shooting, had nothing to do but to examine its details, which I did, day after day, and I found nothing of the kind."  It was of no use at all.
    Higgins began life by exposing and conquering, at the expense of two years of his studies, some shocking abuses which existed in the York Lunatic Asylum.  This was a proceeding which called much attention to the treatment of the insane, and produced much good effect.  He was very resolute and energetic.  The magistracy of his time had such scruples about using the severity of law to people of such station as well-to-do farmers, &c.  They would allow a great deal of resistance, and endeavor to mollify the rebels into obedience.  A young farmer flatly refused to pay under an order of affiliation made upon him by Godfrey Higgins.  He was duly warned; he persisted and shortly found himself in jail.  He went there sure to conquer the Justice, and the first thing he did was to demand to see his lawyer.  He was told, to his horror, that as soon as he had been cropped and prison-dressed, he might see as many lawyers as he pleased, to be looked at, laughed at, and advised that there was but one way out of the scrape.
    There are two works of his by which he was known, apart from his paradoxes.  First, An apology for the life and character of the celebrated prophet of Arabia, called Mohamed, or the Illustrious.  The reader will look at this writing of our English Buddhist with suspicious eye, but he will not be able to avoid confessing that the Arabian prophet has some reparation to demand at the hands of Christians.  Next, Horæ Sabaticæ; or an attempt to correct certain superstitions and vulgar errors respecting the Sabbath.  This book was very heterodox at the time, but it has furnished material for some of the clergy of our day.
    I never could quite make out whether Godfrey took that system which he traced to the Buddhists to have a Divine origin, or to be the result of good men's meditations.  Himself a strong theist, and believer in a future state, one would suppose that he would refer a universal religion, spread in different forms over the whole earth from one source, directly to the universal Parent.  And this I suspect he did, whether he knew it or not.  The external evidence is balanced.  In his preface he says: "I cannot help smiling when I consider that priests have objected to admit my former book, The Celtic Druids, into libraries, because it was antichristian; and it has been attacked by Deists, because it was superfluously religious.  The learned Deist, the Rev. R. Taylor, has designated me as the religious Mr. Higgins."
    The time will come when some profound historian of literature will make himself much clearer on the point than I am.

ON POPE'S DIPPING NEEDLE.
The triumphal Chariot of Friction: or a familiar elucidation of the origin of magnetic attraction, &c. &c.  By William Pope. London, 1829.
    Part of this work is on a dipping-needle of the author's construction.  It must have been under the impression that a book of naval magnetism was proposed, that a great many officers, the Royal Naval Club, etc. lent their names to the subscription list.  How must they have been surprised to find set forth that if a square be inscribed in a circle, a circle within that, then a square again, &c., it is impossible to have more than fourteen circles, let the first circle be as large as you please.  From this the seven attributes of God are unfolded; and further, that all matter was moral, until Lucifer churned it into physical "as far as the third circle in Deity;" this Lucifer, called Leviathan in Job, being thus the moving cause of chaos.  I shall say no more, except that the friction of the air is the cause of magnetism.

THE JACOTOT METHOD.
Epitomé de mathématiques.  Par F. Jacotot, Avocat.  3ième edition, Paris, 1830.
Méthode Jacotot.  Choix de propositions mathématiques.  Par P.  Y. Séprés. 2nde édition.  Paris, 1830.
    Of Jacotot's method, which had some vogue in Paris, the principle was Tout est dans tout, and the process was Apprendre quelque chose, et à y rapporter tout le reste.  The first tract has a proposition in conic sections and its preliminaries; the second has twenty exercises, of which the first is finding the greatest common measure of two numbers, and the last is the motion of a point on a surface, acted on by given forces.  This is topped up with the problem of sound in a tube, and a slice of Laplace's theory of the tides.  All to be studied until known by heart, and all the rest will come, or at least join on easily when it comes.  There is much truth in the assertion that new knowledge hooks on easily to a little of the old, thoroughly mastered.  The day is coming when it will be found out that crammed erudition, got up for examinations, does not cast out any hooks for more.

A DISCOURSE ON PROBABILITY.
    My friend Sir J. L., with a large cluster of intellectual qualities, and another of social qualities, had one point of character which I will not call bad and cannot call good; he never used a slang expression.  To such a length did he carry his dislike, that he could not bear head and tail, even in a work on games of chance, so he used obverse and reverse; but to my delight I found that the force of circumstances beat him at last.  He was obliged to take an example from the race-course, and the name of one of the horses was Bessy Bedlam!  And he did not put her down as Elizabeth Bethlehem, but forced himself to follow the jockeys.

Almanach Romain sur la Loterie Royale de France, ou les Etrennes nécessaires aux Actionnaires et Receveurs de la dite Loterie.  Par M. Menut de St.-Mesmin.  Paris, 1830.
    This book contains all the drawings of the French lottery (two or three, each month) from 1758 to 1830.  It is intended for those who thought they could predict the future drawings from the past; various sets of sympathetic numbers are given to help them.  The principle is, that anything which has not happened for a long time must be soon to come.  The gambling reasoner is incorrigible; if he would but take to squaring the circle, what a load of misery would be saved.
    A writer of 1823, who appeared to be thoroughly acquainted with the gambling of Paris and London, says that the gamesters by profession are haunted by a secret foreboding of their future destruction, and seem as if they said to the banker at the table, as the gladiators said to the emperor, Morituri te salutant.
    The paradoxes of what is called chance, or hazard, might themselves make a small volume.  All the world understands that there is a long run, a general average; but much of the world is surprised that this general average should be computed and predicted.  There are many remarkable cases of verification; and one of them relates to the quadrature of the circle.  Suppose a planked floor of the usual kind, with thin visible seams between the planks.  Let there be a thin straight rod, or wire, not so long as the width of the plank.  This rod, being tossed up at hazard, will either land clear of the seams, or will lay across one seam.  Buffon, and after him Laplace, proved that in the long run the fraction of the whole number of trials in which a seam is intersected will be twice the length of the rod, divided by the circumference of the circle with the width of a plank for its diameter.  This will hardly be believed until it has been tested so often that "there never could have been any doubt about it."

ON CURIOSITIES OF π
    1830.  The celebrated interminable fraction 3.14159..., which the mathematician calls π, is the ratio of the circumference to the diameter.  But it is thousands of things besides.  It is constantly turning up in mathematics; and if arithmetic and algebra had been studied without geometry, π must have come in somehow, though at what stage or under what name must have depended upon the casualties of algebraical invention.  This will readily be seen when it is stated that π is nothing but four times the series
    1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...
It would be wonderful if so simple a series had but one kind of occurrence.  As it is, our trigonometry being founded on the circle, π first appears as the ratio stated.  If, say, a deep study of probable fluctuation from average had preceded, π might have emerged as a number perfectly indispensable in such problems as: What is the chance of the number of aces lying between a million + x and a million - x, when six million throws are made with a die?
    More than thirty years ago I had a friend, now long gone, who was a mathematician, but not of the higher branches; he was, inter alia, thoroughly up in all that relates to mortality, life assurance, &c.  One day, explaining to him how to find the chance is of the survivors of a large number of persons now alive lying between given limits of number at the end of a certain time, I came, of course upon the introduction of π, which I could only describe as the ratio of the circumference of a circle to its diameter.  "Oh, my dear friend! that must be a delusion; what can the circle have to do with the numbers alive at the end of a given time?" — "I cannot demonstrate it to you; but it is demonstrated." — "Oh! stuff! I think you can prove anything with your differential calculus: figment, depend upon it."  I said no more; but, a few days afterwards, I went to him and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly.  I told him that the law was involved in this circumstance.  Take the table of expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come.  "You don't mean that this always happens?" — "Try it."  He did try, again and again; and found it as I said.  "This is, indeed, a curious thing; this is a discovery."

EUCLID WITHOUT AXIOMS.
    The first book of Euclid's Elements.  With alterations and familiar notes.  Being an attempt to get rid of axioms altogether; and to establish the theory of parallel lines, without the introduction of any principle not common to other parts of the elements.  By a member of the University of Cambridge.  Third edition.  London, 1830.
    The author was Lieut. Col. (now General) Perronet Thompson.  Some more attempts upon the problem are of acute and legitimate speculation, but they do not conquer the difficulty in the manner demanded by the conditions of the problem.  The paradox of parallels does not contribute much to my pages; its cases are to be found for the most part in geometrical systems, or in notes to them.  Most of them consist in the proposal of additional postulates; some are attempts to do without any new postulate.
    Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty.  He went so far as to write a paper, which he took with him to the Institute, and began to read it.  But in the first paragraph something struck him which he had not observed: he muttered "Il faut que j'y songe encore," and put the paper in his pocket.

ON M. DEMONVILLE.
    Demonville. — A Frenchman's Christian name is his own secret, unless there be two of the surname.  M. Demonville is a very good instance of the difference between a French and English discoverer.
    In England there is a public to listen to discoveries in mathematical subjects made without mathematics; a public which will hear, and wonder, and think it possible that the pretensions of the discoverer have some foundation.  The unnoticed man may possibly be right; and the old country-town reputation which I once heard of, attaching to a man who "had written a book about the signs of the zodiac which all the philosophers in London could not answer," is fame as far as it goes.  Accordingly, we have plenty of discoverers who, even in astronomy, pronounce the learned in error because of mathematics.
    In France, beyond the sphere of influence of the Academy of Sciences, there is no one to cast a thought upon the matter; all who take the least interest repose entire faith in the Institute.  Hence the French discoverer turns all his thoughts to the Institute, and looks for his only hearing in that quarter.  He therefore throws no slur upon the means of knowledge, but would say, with M. Demonville: "A l'égard de M. Poisson, j'envie loyalement la millième partie de ses connaissances mathématiques, pour prouver mon systême d'astronomie aux plus incrédules."
    This system is that the only bodies of our system are the earth, the sun, and the moon; all the others being illusions, caused by reflection of the sun and moon from the ice of the polar regions.  In mathematics, addition and subtraction are for men; multiplication and division, which are in truth creation and destruction, are prerogatives of deity.  But nothing multiplied by nothing is one.

PARSEY'S PARADOX.
The quadrature of the circle discovered, by Arthur Parsey, author of the 'art of miniature painting.'  Submitted to the consideration of the Royal Society, on whose protection the author humbly throws himself.  London, 1832.
    Mr. Parsey was an artist who also made himself conspicuous by a new view of perspective.  Seeing that the sides of a tower, for instance, would appear to meet in a point if the tower were high enough, he thought that these sides ought to slope to one another in the picture.  On this theory he published a small work, of which I have not the title, with a Grecian temple in the frontispiece, stated, if I remember rightly, to be the first picture which had ever been drawn in true perspective.  Of course the building looked very Egyptian, with its sloping sides.
    In July 1831, reading an article on squaring the circle, and finding that there was a difficulty, he set to work, got a light denied to all mathematicians in — some would say through — a crack, and advertised in the Times that he had done the trick.  He then prepared this work, in which, those who read it will see how, he showed that 3.14159...  should be 3.0625.  He might have found out his error by stepping a draftsman's circle with the compasses.
    Perspective has not had many paradoxes.  The only other one I remember is that of a writer on perspective, whose name I forget, and whose four pages I do not possess.  He circulated remarks on my notes on the subject, published in the Athenæum, in which he denies that the stereographic projection is a case of perspective, because the whole hemisphere makes too large a picture for the eye conveniently to grasp at once.  That is to say, it is no perspective because there is too much perspective.

ON A COUPLE OF GEOMETRIES.
Principles of Geometry familiarly illustrated.  By the Rev. W.  Ritchie, LL.D. London, 1833.
A new Exposition of the system of Euclid's Elements, being an attempt to establish his work on a different basis.  By Alfred Day, LL.D. London, 1839.
    These works belong to a small class which have the peculiarity of insisting that in the general propositions of geometry a proposition gives its converse: that "Every B is A" follows from "Every A is B."  On this I cannot help transferring to my reader the words of the Pasha when he orders the bastinado, — May it do you good!
    A rational study of logic is much wanted to show many mathematicians, of all degrees of proficiency, that there is nothing in the reasoning of mathematics which differs from other reasoning.

NEWTON AGAIN OBLITERATED.
Letter to the Royal Astronomical Society in refutation of Mistaken Notions held in common, by the Society, and by all the Newtonian philosophers.  By Capt. Forman, R.N.  Shepton-Mallet, 1833.
    Capt. Forman wrote against the whole system of gravitation, and got no notice.  He then wrote to Lord Brougham, Sir J.  Herschel, and others I suppose, desiring them to procure notice of his books in the reviews; this not being acceded to, he wrote (in print) to Lord John Russell to complain of their "dishonest" conduct.  He then sent a manuscript letter to the Astronomical Society, inviting controversy; he was answered by a recommendation to study dynamics.  The above pamphlet was the consequence, in which, calling the Council of the Society "craven dunghill cocks," he set them right about their doctrines.
    From all I can learn, the life of a worthy man and a creditable officer was completely embittered by his want of power to see that no person is bound in reason to enter into controversy with every one who chooses to invite him to the field.
    This mistake is not peculiar to philosophers, whether of orthodoxy or paradoxy; a majority of educated persons imply, by their modes of proceeding, that no one has a right to any opinion which he is not prepared to defend against all comers.

SIR JOHN HERSCHEL.
    1834.  In this year Sir John Herschel set up his telescope at Feldhausen, Cape of Good Hope.  He showed a resident a remarkable blood-red star, and some little time after he heard of a sermon preached in those parts in which it was asserted that the statements of the Bible must be true, for that Sir J. H. had seen in his telescope "the very place where wicked people go."
    But red is not always the color.  Sir J. Herschel has in his possession a letter written to his father, Sir W. H., dated April 3, 1787, and signed "Eliza Cumyns," begging to know if any of the stars be indigo in color, "because, if there be, I think it may be deemed a strong conjectural illustration of the expression, so often used by our Saviour in the Holy Gospels, that 'the disobedient shall be cast into outer darkness'; for as the Almighty Being can doubtless confine any of his creatures, whether corporeal or spiritual, to what part of his creation He pleases, if therefore any of the stars (which are beyond all doubt so many suns to other systems) be of so dark a color as that above mentioned, they may be calculated to give the most insufferable heat to those dolorous systems dependent upon them (and to reprobate spirits placed there), without one ray of cheerful light; and may therefore be the scenes of future punishments."
    Some have placed the infernal regions inside the earth, but others have filled this internal cavity — for cavity they will have — with refulgent light, and made it the abode of the blessed.
    It is difficult to build without knowing the number to be provided for.  A friend of mine heard the following (part) dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thank there are of the alact on the arth at this moment? — Eh! mabbee a doozen — Hoot! mon! nae so mony as thot!"

WOODLEY'S DIVINE SYSTEM.
A Treatise on the Divine System of the Universe, by Captain Woodley, R.N., and as demonstrated by his Universal Time-piece, and universal method of determining a ship's longitude by the apparent true place of the moon; with an introduction refuting the solar system of Copernicus, the Newtonian philosophy, and mathematics.  1834.
Description of the Universal Time-piece.
    I think this divine system was published several years before, and was republished with an introduction in 1834.  Capt. Woodley was very sure that the earth does not move; he pointed out to me, in a conversation I had with him, something — I forget what — in the motion of the Great Bear, visible to any eye, which could not possibly be if the earth moved.  He was exceedingly ignorant, as the following quotation from his account of the usual opinion will show: "The north pole of the Earth's axis deserts, they say, the north star or pole of the Heavens, at the rate of 1° in 71¾ years....  The fact is, nothing can be more certain than that the Stars have not changed their latitudes or declinations one degree in the last 71¾ years."
    This is a strong specimen of a class of men by whom all accessible persons who have made any name in science are hunted.  It is a pity that they cannot be admitted into scientific societies, and allowed fairly to state their cases, and stand quiet cross-examination, being kept in their answers very close to the questions, and the answers written down.
    I am perfectly satisfied that if one meeting in the year were devoted to the hearing of those who chose to come forward on such conditions, much good would be done.  But I strongly suspect few would come forward at first, and none in a little while; and I have had some experience of the method I recommend, privately tried.

De la formation des Corps.  Par Paul Laurent. Nancy, 1834.
    Atoms, and ether, and ovules or eggs, which are planets, and their eggs, which are satellites.  These speculators can create worlds, in which they cannot be refuted; but none of them dare attack the problem of a grain of wheat, and its passage from a seed to a plant, bearing scores of seeds like what it was itself.

ON JOHN FLAMSTEED.
An account of the Rev. John Flamsteed, the First Astronomer-Royal....  By Francis Baily, Esq.  London, 1835.  Supplement, London, 1837.
    My friend Francis Baily was a paradoxer: he brought forward things counter to universal opinion.  That Newton was impeccable in every point was the national creed; and failings of temper and conduct would have been utterly disbelieved, if the paradox had not come supported by very unusual evidence.  Anybody who impeached Newton on existing evidence might as well have been squaring the circle, for any attention he would have got.
    This book was published by the Admiralty for distribution, and the distribution was entrusted to Mr. Baily.  On the eve of its appearance, rumors of its extraordinary revelations got about, and persons of influence applied to the Admiralty for copies.  The Lords were in a difficulty: but on looking at the list they saw names, as they thought, which were so obscure that they had a right to assume Mr. Baily had included persons who had no claim to such a compliment as presentation from the Admiralty.  The Secretary requested Mr. Baily to call upon him.  "Mr. Baily, my Lords are inclined to think that some of the persons in this list are perhaps not of that note which would justify their Lordships in presenting this work." — "To whom does your observation apply, Mr. Secretary?" — "Well, now, let us examine the list; let me see; now, — now, — now, — come! — here's Gauss — who's Gauss?" — "Gauss, Mr. Secretary, is the oldest mathematician now living, and is generally thought to be the greatest." — "O-o-oh! Well, Mr. Baily, we will see about it, and I will write you a letter."  The letter expressed their Lordships' perfect satisfaction with the list.
    There was a controversy about the revelations made in this work; but as the eccentric anomalies took no part in it, there is nothing for my purpose.  The following valentine from Mrs.  Flamsteed, which I found among Baily's papers, illustrates some of the points:
        "3 Astronomers' Row, Paradise: February 14, 1836.
        "Dear Sir, — I suppose you hardly expected to receive a letter from me, dated from this place; but the truth is, a gentleman from our street was appointed guardian angel to the American Treaty, in which there is some astronomical question about boundaries.  He has got leave to go back to fetch some instruments which he left behind, and I take this opportunity of making your acquaintance.  That America has become a wonderful place since I was down among you; you have no idea how grand the fire at New York looked up here.  Poor dear Mr. Flamsteed does not know I am writing a letter to a gentleman on Valentine's day; he is walked out with Sir Isaac Newton (they are pretty good friends now, though they do squabble a little sometimes) and Sir William Herschel, to see a new nebula.  Sir Isaac says he can't make out at all how it is managed; and I am sure I cannot help him.  I never bothered my head about those things down below, and I don't intend to begin here.
        "I have just received the news of your having written a book about my poor dear man.  It's a chance that I heard it at all; for the truth is, the scientific gentlemen are somehow or other become so wicked, and go so little to church, that very few of them are considered fit company for this place.  If it had not been for Dr. Brinkley, who came here of course, I should not have heard about it.  He seems a nice man, but is not yet used to our ways.  As to Mr. Halley, he is of course not here; which is lucky for him, for Mr. Flamsteed swore the moment he caught him in a place where there are no magistrates, he would make a sacrifice of him to heavenly truth.  It was very generous in Mr. F.  not appearing against Sir Isaac when he came up, for I am told that if he had, Sir Isaac would not have been allowed to come in at all.  I should have been sorry for that, for he is a companionable man enough, only holds his head rather higher than he should do.  I met him the other day walking with Mr. Whiston, and disputing about the deluge.  'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars understand gravitation yet?'  Now you must know that is rather a sore point with poor dear Mr. Flamsteed.  He says that Sir Isaac is as crochetty about the moon as ever; and as to what some people say about what has been done since his time, he says he should like to see somebody who knows something about it of himself.  For it is very singular that none of the people who have carried on Sir Isaac's notions have been allowed to come here.
        "I hope you have not forgotten to tell how badly Sir Isaac used Mr. Flamsteed about that book.  I have never quite forgiven him; as for Mr. Flamsteed, he says that as long as he does not come for observations, he does not care about it, and that he will never trust him with any papers again as long as he lives.  I shall never forget what a rage he came home in when Sir Isaac had called him a puppy.  He struck the stairs all the way up with his crutch, and said puppy at every step, and all the evening, as soon as ever a star appeared in the telescope, he called it puppy.  I could not think what was the matter, and when I asked, he only called me puppy.
        "I shall be very glad to see you if you come our way.  Pray keep up some appearances, and go to church a little.  St. Peter is always uncommonly civil to astronomers, and indeed to all scientific persons, and never bothers them with many questions.  If they can make anything out of the case, he is sure to let them in.  Indeed, he says, it is perfectly out of the question expecting a mathematician to be as religious as an apostle, but that it is as much as his place is worth to let in the greater number of those who come.  So try if you cannot manage it, for I am very curious to know whether you found all the letters.  I remain, dear sir, your faithful servant,
        "Margaret Flamsteed.
        Francis Baily, Esq.
        "P.S.  Mr. Flamsteed has come in, and says he left Sir Isaac riding cockhorse upon the nebula, and poring over it as if it were a book.  He has brought in his old acquaintance Ozanam, who says that it was always his maxim on earth, that 'il appartient aux docteurs de Sorbonne de disputer, au Pape de prononcer, et au mathématicien d'aller en Paradis en ligne perpendiculaire.'"

FINLEYSON AS A PARADOXER.
God's Creation of the Universe as it is, in support of the Scriptures.  By Mr. Finleyson.  Sixth Edition, 1835.
    This writer, by his own account, succeeded in delivering the famous Lieut. Richard Brothers from the lunatic asylum, and tending him, not as a keeper but as a disciple, till he died.  Brothers was, by his own account, the nephew of the Almighty, and Finleyson ought to have been the nephew of Brothers.  For Napoleon came to him in a vision, with a broken sword and an arrow in his side, beseeching help; Finleyson pulled out the arrow, but refused to give a new sword; whereby poor Napoleon, though he got off with life, lost the battle of Waterloo.  This story was written to the Duke of Wellington, ending with "I pulled out the arrow, but left the broken sword.  Your Grace can supply the rest, and what followed is amply recorded in history." The book contains a long account of applications to Government to do three things: to pay 2,000 l. for care taken of Brothers, to pay 10,000 l. for discovery of the longitude, and to prohibit the teaching of the Newtonian system, which makes God a liar.  The successive administrations were threatened that they would have to turn out if they refused, which, it is remarked, came to pass in every case.
    I have heard of a joke of Lord Macaulay, that the House of Commons must be the Beast of the Revelations, since 658 members, with the officers necessary for the action of the House, make 666.  Macaulay read most things, and the greater part of the rest; so he might be suspected of having appropriated as a joke one of Finleyson's serious points — "I wrote Earl Grey upon the 13th of July, 1831, informing him that his Reform Bill could not be carried, as it reduced the members below the present amount of 658, which, with the eight principal clerks or officers of the House, make the number 666."  But a witness has informed me that Macaulay's joke was made in his hearing a great many years before the Reform Bill was proposed; in fact, when both were students at Cambridge.  Earl Grey was, according to Finleyson, a descendant of Uriah the Hittite.

ON THEOLOGICAL PARADOXERS.
    Among the paradoxers are some of the theologians who in their own organs of the press venture to criticise science.  These may hold their ground when they confine themselves to the geology of long past periods and to general cosmogony, for that is the tug of Greek against Greek; and both sides deal much in what is grand when called hypothesis, petty when called supposition.  And very often they are not conspicuous when they venture upon things within knowledge; wrong, but not quite wrong enough for a Budget of Paradoxes.
    One case, however, is destined to live.  The double stars have been seen from the seventeenth century, and diligently observed by many from the time of Wm. Herschel, who first devoted continuous attention to them.  The year 1836 was that of a remarkable triumph of astronomical prediction.  The theory of gravitation had been applied to the motion of binary stars about each other, in elliptic orbits, and in that year the two stars of γ Virginis, as had been predicted should happen within a few years of that time — for years are small quantities in such long revolutions — the two stars came to their nearest; in fact, they appeared to be one as much with the telescope as without it.  This remarkable turning-point of the history of a long and widely-known branch of astronomy was followed by an article in the Church of England Quarterly Review for April 1837, written against the Useful Knowledge Society.  The notion that there are any such things as double stars is implied to be imposture or delusion, as in the following extract.  I suspect that I myself am the Sidrophel, and that my companion to the maps of the stars, written for the Society and published in 1836, is the work to which the writer refers: "We have forgotten the name of that Sidrophel who lately discovered that the fixed stars were not single stars, but appear in the heavens like soles at Billingsgate, in pairs; while a second astronomer, under the influence of that competition in trade which the political economists tell us is so advantageous to the public, professes to show us, through his superior telescope, that the apparently single stars are really three.  Before such wondrous mandarins of science, how continually must homunculi like ourselves keep in the background, lest we come between the wind and their nobility."
    If the homunculus who wrote this be still above ground, how devoutly must he hope he may be able to keep in the background! But the chief blame falls on the editor.  The title of the article is: "The new school of superficial pantology; a speech intended to be delivered before a defunct Mechanics' Institute.  By Swallow Swift, late M.P. for the Borough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year, month Ventose.  Long live Charlatan!"
    As a rule, orthodox theologians should avoid humor, a weapon very difficult to employ in favor of establishment, and which, nine times out of ten, leaves its wielder fighting on the side of heterodoxy.  Theological argument, when not enlivened by bigotry, is seldom worse than narcotic; but theological fun, when not covert heresy, is almost always sialagogue.
    The article in question is a freak, which no editor should have admitted, except after severe inspection by qualified persons.  The author of this wit committed a mistake which occurs now and then in old satire, the confusion between himself and the party aimed at.  He ought to be reviewing this fictitious book, but every now and then the article becomes the book itself; not by quotation, but by the writer forgetting that he is not Mr. Swallow Swift, but his reviewer.  In fact he and Mr. S. Swift had each had a dose of the Devil's Elixir.
    A novel called the Devil's Elixir, published about forty years ago, proceeds upon a legend of this kind.  If two parties both drink of the elixir, their identities get curiously intermingled; each turns up in the character of the other throughout the three volumes, without having his ideas clear as to whether he be himself or the other.
    I myself have employed such humor as I can command "in favor of establishment."  What it is worth I am not to judge; as usual in such cases, those who are of my cabal pronounce it good, but paradoxers either call it very poor, or commend it as sheer buffoonery.  Be it one or the other, I observe that all the effective ridicule is, in this subject, on the side of establishment.  This is partly due to the difficulty of quizzing plain and sober demonstration; but so much, if not more, to the ignorance of the paradoxers.  For that which cannot be ridiculed, can be turned into ridicule by those who know how.  But by the time a person is deep enough in negative quantities and impossible quantities to be able to satirize them, he is inclined to become a user, and shrinks from being an abuser.
    Imagine a person with a gift of ridicule, and knowledge enough, trying his hand on the junction of the assertions which he will find in various books of algebra.  First, that a negative quantity has no logarithm; secondly, that a negative quantity has no square root; thirdly, that the first non-existent is to the second as the circumference of a circle to its diameter.  One great reason of the allowance of such unsound modes of expression is the confidence felt by the writers that √-1 and log(-1) will make their way, however inaccurately described.  I heartily wish that the cyclometers had knowledge enough to attack the weak points of algebraical diction; they would soon work a beneficial change.

AN EARLY METEOROLOGIST.
Recueil de ma vie, mes ouvrages et mes pensées.  Par Thomas Ignace Marie Forster.  Brussels, 1836.
    Mr. Forster, an Englishman settled at Bruges, was an observer in many subjects, but especially in meteorology.  He communicated to the Astronomical Society, in 1848, the information that, in the registers kept by his grandfather, his father, and himself, beginning in 1767, new moon on Saturday was followed, nineteen times out of twenty, by twenty days of rain and wind.  This statement being published in the Athenæum, a cluster of correspondents averred that the belief is common among seamen, in all parts of the world, and among landsmen too.  Some one quoted a distich:
        "Saturday's moon and Sunday's full
        Never were fine and never wull."
Another brought forward:
        "If a Saturday's moon
        Comes once in seven years it comes too soon."
Mr. Forster did not say he was aware of the proverbial character of the phenomenon.  He was a very eccentric man.  He treated his dogs as friends, and buried them with ceremony.  He quarrelled with the curé of his parish, who remarked that he could not take his dogs to heaven with him.  I will go nowhere, said he, where I cannot take my dog.
    A test:  after a tolerable course of dry weather, there was some snow, accompanied by wind on Saturday last, here in London; there were also heavy louring clouds.  Sunday was cloudy and cold, with a little rain; Monday was louring, Tuesday unsettled; Wednesday quite overclouded, with rain in the morning.  This test shows only a general change of weather with a tendency towards rain.  If Dr. Forster's theory be true, it is decidedly one of the minor instances, as far as London weather is concerned.
    How many coincidences are required to establish a law of connection? It depends how the mind views the matter in question.  Many of the paradoxers are quite set up by a very few instances.  I will now tell a story about myself, then ask them a question.
    So far as instances can prove a law, the following is proved: no failure has occurred.  Let a clergyman be known to me, whether by personal acquaintance or correspondence, or by being frequently brought before me by those with whom I am connected in private life: if that clergyman become a bishop, he is sure, first or last, to become an arch-bishop.  This has happened in every case.  As follows:
        1.  My last schoolmaster was a very intimate college friend of Richard Whately.  Struck by his friend's talents, he used to talk of him perpetually, and predict his future eminence.  Before I was sixteen, and before Whately had even given his Bampton Lectures, I was very familiar with his name, and some of his sayings.  I need not say that he became Archbishop of Dublin.
        2.  When I was a child, a first cousin of John Bird Sumner married a sister of my mother.  In time he became Bishop of Chester, then Archbishop of Canterbury.
        3.  Thomas Musgrave, Fellow of Trinity College, Cambridge, was Dean of the college when I was an undergraduate: this brought me into connection with him, he giving impositions for not going to chapel, I writing them out according.  We had also friendly intercourse in after life; I forgiving, he probably forgetting.  Honest Tom Musgrave, as he used to be called, became Bishop of Hereford, and Archbishop of York.
        4.  About the time when I went to Cambridge, I heard a great deal about Mr. C. T. Longley of Christchurch, from a cousin of mine who spoke of him much, and most affectionately.  Dr. Longley passed from Durham to York, thence to Canterbury.  I cannot quite make out the two Archbishoprics; I do not remember any other private channel through which the name came to me: perhaps Dr. Longley, having two strings to his bow, would have been one archbishop if I had never heard of him.
        5.  When Dr. Wm. Thomson was appointed to the see of Gloucester in 1861, he and I had been correspondents on the subject of logic — on which we had both written — for about fourteen years.  On his elevation I wrote to him, giving the preceding instances, and informing him that he would certainly be an Archbishop.  The the law acted rapidly; for Dr. Thomson's elevation to the see of York took place in 1862.
    Here are five cases; and there is no opposing instance.  I have searched the almanacs since 1828, and can find no instance of a Bishop not finally Archbishop of whom I had known through private sources, direct or indirect.  Now what do my paradoxers say?  Is this a pre-established harmony, or a chain of coincidences? And how many instances will it require to establish a law?

THE HERSCHEL HOAX.
Some account of the great astronomical discoveries lately made by Sir John Herschel at the Cape of Good Hope.  Second Edition.  London.  1836.
    This is a curious hoax, evidently written by a person versed in astronomy, and clever at introducing probable circumstances and undesigned coincidences.  It first appeared in a newspaper.  It makes Sir J. Herschel discover men, animals, etc. in the moon, of which much detail is given.  There seems to have been a French edition, the original, and English editions in America, whence the work came into Britain.  It was produced in the United States by M. Nicollet, an astronomer, once of Paris, and a fugitive of some kind.  About him I have heard two stories.  First that he fled to America with funds not his own, and that this book was a mere device to raise the wind.  Secondly, that he was a protégé of Laplace and the Polignac party, and outspoken.  That after the revolution he was so obnoxious to the republican party that he judged it prudent to quit France; which he did in debt, leaving money for his creditors, but not enough, with M. Bouvard.  In America he connected himself with an assurance office.  The moon-story was written, and sent to France, chiefly to trap M. Arago, Nicollet's special foe, into belief.  And those who narrate this version of the story say that M. Arago was entrapped, and circulated the wonders through Paris, until a letter from Nicollet to M. Bouvard explained the hoax.  I have no personal knowledge of either story, but as the poor man had to endure the first, it is but right that the second should be told with it.

THE MATHEMATICS OF A CREED.
The creed of St. Athanasius proved by a mathematical parallel.  Before you censure, condemn, or approve; read, examine, and understand.  E. B. Revilo.  London, 1839.
    This author really believed himself, and was in earnest.  This tract is worth preserving, as the extreme case of a particular kind.  The following is a specimen.  Infinity being represented by ∞, as usual, and f, s, g, being finite integers, the three Persons are denoted by ∞f, (m ∞)s, ∞g, the finite fraction m representing human nature, as opposed to ∞.  The clauses of the Creed are then given with their mathematical parallels.  I extract:
        "But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one: the glory equal, the Majesty co-eternal.        "It has been shown that ∞f, ∞g, and (m ∞)s, together, are but ∞, and that each is ∞, and any magnitude in existence represented by ∞ always was and always will be, for it cannot be made, or destroyed, and yet exists.
        "Equal to the Father, as touching his Godhead: and inferior to the Father, touching his Manhood."
        "(m ∞)s is equal to ∞f as touching ∞, but inferior to ∞f as touching m: because m is not infinite."
    I might have passed this over, as beneath even my present subject, but for the way in which I became acquainted with it.  A bookseller, not the publisher, handed it to me over his counter: one who had published mathematical works.  He said, with an air of important communication, Have you seen this, Sir!  Educated men, used to books and to the converse of learned men, look with mysterious wonder on such productions as this, for which reason I have made a quotation which many will judge had better have been omitted.  But it would have been an imposition on the public if I were, omitting this and some other uses of the Bible and Common Prayer, to pretend that I had given a true picture of my school.

LOGIC HAS NO PARADOXERS.
Old and new logic contrasted: being an attempt to elucidate, for ordinary comprehension, how Lord Bacon delivered the human mind from its 2,000 years' enslavement under Aristotle.  By Justin Brenan.  London, 1839.
    Logic, though the other exact science, has not had the sort of assailants who have clustered about mathematics.  There is a sect which disputes the utility of logic, but there are no special points which excite dispute among those who admit other things.
    The old story about Aristotle having one logic to trammel us, and Bacon another to set us free — always laughed at by those who really knew either Aristotle or Bacon — now begins to be understood by a large section of the educated world.  The author of this tract connects the old logic with the indecencies of the classical writers, and the new with moral purity; he appeals to women, who "when they see plainly the demoralizing tendency of syllogistic logic, they will no doubt exert their powerful influence against it, and support the Baconian method."  This is the only work against logic which I can introduce.
    I quote the author's idea of a syllogism: "This is a form of couching the substance of your argument or investigation into one short line or sentence — then corroborating or supporting it in another, and drawing your conclusion or proof in a third."
    On this definition he gives an example: "Every sin deserves death," the substance of the "argument or investigation."  Then comes, "Every unlawful wish is a sin," which "corroborates or supports" the preceding.  And lastly, "therefore every unlawful wish deserves death," which is the "conclusion or proof." We learn, also, that "sometimes the first is called the premises (sic), and sometimes the first premiss"; as also that "the first is sometimes called the proposition, or subject, or affirmative, and the next the predicate, and sometimes the middle term."  To which is added, with a mark of exclamation at the end, "but in analyzing the syllogism, there is a middle term, and a predicate too, in each of the lines!"  It is clear that Aristotle never enslaved this mind.
    I have said that logic has no paradoxers, but I was speaking of old time.  In our time, logical paradoxers have appeared.  I do not refer to Prof. Boole, who is not a paradoxer, but a discoverer; his system could neither oppose nor support common opinion, for its grounds were not in the conception of anyone.
    I speak specially of two others, who fought like cat and dog; one was dogmatical, the other categorical. The first was Sir William Hamilton of Edinburgh the metaphysician (not Sir William Rowan Hamilton of Dublin the mathematician), a combination of peculiar genius with unprecedented learning, erudite in all he could want except mathematics, for which he had no turn, and in which he had not even a schoolboy's knowledge, thanks to the Oxford of his younger day.  The other was the author of this work, so fully described in Hamilton's writings that there is no occasion to describe him here.  I shall try to say a few words in common language about the paradoxers.
    Hamilton's great paradox was the quantification of the predicate — a fearful phrase, easily explained.  We all know that when we say "Men are animals," a form wholly unquantified in phrase, we speak of all men, but not of all animals: it is some or all, some may be all for aught the proposition says.  This some-may-be-all-for-aught-we-say, or not-none, is the logician's some.
    One would suppose that "all men are some animals," would have been the logical phrase in all time; but the predicate never was quantified.  The few who alluded to the possibility of such a thing found reasons for not adopting it over and above the great reason, that Aristotle did not adopt it.  Aristotle never ruled in physics or metaphysics in the old time with near so much of absolute sway as he has ruled in logic down to our own time.  The logicians knew that in the proposition "all men are animals" the "animal" is not universal but particular, yet no one dared to say that all men are some animals, and to invent the phrase, "some animals are all men" until Hamilton leaped the ditch, and not only completed a system of enunciation, but applied it to syllogism.
    My own case is as peculiar as his: I have proposed to introduce mathematical thought into logic.  The question is not about absolute truth or falsehood; no one denies that anything I call an inference is an inference.  They say that my alterations are extra-logical; that they are material, not formal; and that logic is a formal science.
    The distinction between material and formal is easily made, where the usual perversions are not required.  A form is an empty machine, such as "Every X is Y"; it may be supplied with matter, as in "Every man is animal."  The logicians will not see that their formal proposition, "Every X is Y," is material in three points, the degree of assertion, the quantity of the proposition, and the copula.  The purely formal proposition is "There is the probability α that X stands in the relation L to Y."
    Sir William Hamilton of Edinburgh was one of the best friends and allies I ever had.  When I first began to publish speculation on this subject, he introduced me to the logical world as having plagiarized from him.  This drew their attention.  He retracted his accusation of wilful theft in a manly way when he found it untenable; but on this point he wavered a little, and was convinced to the last that I had taken his principle unconsciously.  It was his pet notion that I did not understand the commonest principles of logic, that I did not always know the difference between the middle term of a syllogism and its conclusion.  It went against his grain to imagine that a mathematician could be a logician.
    Our first controversy was in 1846.  In 1847, in my Formal Logic, I gave him back a little satire for satire, just to show, as I stated, that I could employ ridicule if I pleased.  He was so offended that he would not accept the copy of the book I sent him, but returned it.  Copies of controversial works, sent from opponent to opponent, are not presents in the usual sense; it was a marked success to make him angry enough to forget this.  It had some effect, however: during the rest of his life I wished to avoid provocation, for I could not feel sure that excitement might not produce consequences.  I allowed his slashing account of me in the Discussions to pass unanswered, and I merely deferred the dispute.  I cannot expect the account in the Discussions to amuse an unconcerned reader as much as it amused myself; but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs assault, I can particularly recommend it.  I never knew until I read it how much I should enjoy a thundering onslought on myself, done with racy insolence by a master hand, to whom my good genius had whispered Ita feri ut se sentiat emori.
    Since that time I have, as the Irishman said, become "dry molded for want of a bating."  Some of my paradoxers have done their best: but theirs is mere twopenny — "small swipes," as Peter Peebles said.  Brandy for heroes!  I hope a reviewer or two will have mercy on me, and give me as good discipline as Strafford would have given Hampden and his set: "much beholden," said he, "should they be to any one that should thoroughly take pains with them in that kind" — meaning objective flagellation.  I shall be the same to anyone who serves me so — in a literary and periodical sense; my corporeal cuticle is as thin as my neighbors'.
    Sir W. H. was suffering under local paralysis before our controversy commenced; and though his mind was quite unaffected, a retort of as downright a character as the attack might have produced serious effect upon a person who had shown himself sensible of ridicule.  Had a second attack of his disorder followed an answer from me, I should have been held to have caused it; though, looking at Hamilton's genial love of combat, I strongly suspected that a retort in kind
        "Would cheer his heart, and warm his blood,
        And make him fight, and do him good."
But I could not venture to risk it.  So all I did, in reply to the article in the Discussions, was to write to him the following note, illustrating an etiquette of controversy: "I beg to acknowledge and thank you ....  It is necessary that I should say a word on my retention of this work, with reference to your return of the copy of my Formal Logic, which I presented to you on its publication: a return made on the ground of your disapproval of the account of our controversy which that work contained.  According to my view of the subject, anyone whose dealing with the author of a book is specially attacked in it, has a right to expect from the author that part of the book in which the attack is made, together with so much of the remaining part as is fairly context.  And I hold that the acceptance by the party assailed of such work or part of a work does not imply any amount of approval of the contents, or of want of disapproval.  On this principle (though I am not prepared to add the word alone) I forwarded to you the whole of my work on Formal Logic and my second Cambridge Memoir.  And on this principle I should have held you wanting in due regard to my literary rights if you had not forwarded to me your asterisked pages, with all else that was necessary to a full understanding of their scope and meaning, so far as the contents of the book would furnish it.  For the remaining portion, which it would be a hundred pities to separate from the pages in which I am directly concerned, I am your debtor on another principle; and shall be glad to remain so if you will allow me to make a feint of balancing the account by the offer of two small works on subjects as little connected with our discussion as the Epistolæ Obscurorum Virorum, or the Lutheran dispute.  I trust that by accepting my Opuscula you will enable me to avoid the use of the knife, and leave me to cut you up with the pen as occasion shall serve, I remain, etc.  (April 21, 1852)."
    I received polite thanks, but not a word about the body of the letter: my argument, I suppose, was admitted.

SOME PRIMITIVE DARWINISM.
Vestiges of the Natural History of Creation.  London, 1840.
    The work is described by its author as "the first attempt to connect the natural sciences into a history of creation."  The attempt was commenced and has been carried on with marked talent, and will be continued.
    I met long ago with a splendid player on the guitar, who assured me, and was confirmed by his friends, that he never practiced except in thought, and did not possess an instrument: he kept his fingers acting in his mind, until they got their habits; thus he learned the most difficult novelties of execution.
    Now what if this should be a minor segment of a higher law?  What if, by constantly thinking of ourselves as descended from primeval monkeys, we should — if it be true — actually get our tails again?  What if the first man who was detected with such an appendage should be obliged to confess himself the author of the Vestiges — a person yet unknown — who would naturally get the start of his species by having had the earliest habit of thinking on the matter?  I confess I never hear a man of note talk fluently about it without a curious glance at his proportions, to see whether there may be ground to conjecture that he may have more of "mortal coil" than others, in anaxyridical concealment.  I do not feel sure that even a paternal love for his theory would induce him, in the case I am supposing, to exhibit himself at the British Association, "With a hole behind which his tail peeped through."
    The first sentence of this book (1840) is a cast of the log, which shows our rate of progress.  "It is familiar knowledge that the earth which we inhabit is a globe of somewhat less than 8,000 miles in diameter, being one of a series of eleven which revolve at different distances around the sun."  The eleven!  Not to mention the Iscariot which Le Verrier and Adams calculated into existence, there is more than a septuagint of new planetoids.

An Exposition of the Nature, Force, Action, and other properties of Gravitation on the Planets.  London, 1842.
An Investigation of the principles of the Rules for determining the Measures of the Areas and Circumferences of Circular Plane Surfaces ....  London, 1844.
    These are anonymous, but the author (whom I believe to be Mr. Denison) is described as author of a new system of mathematics, and also of mechanics.  He had need have both, for he shows that the line which has a square equal to a given circle, has a cube equal to the sphere on the same diameter; that is, in old mathematics, the diameter is to the circumference as 9 to 16!  Again, admitting that the velocities of planets in circular orbits are inversely as the square roots of their distances, that is, admitting Kepler's law, he manages to prove that gravitation is inversely as the square root of the distance: and suspects magnetism of doing the difference between this and Newton's law.
    The above is an outrageous quadrature.  In the preceding year, 1841, was published what I suppose at first to be a Maori quadrature, by Maccook.  But I get it from a cutting out of some French periodical, and I incline to think that it must be by a Mr. McCook.  He makes π to be 2 + 2√(8√2 - 11).

THE DUPLICATION PROBLEM.
Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P., entitled "A method of making a cube double of a cube, founded on the principles of elementary geometry," wherein his principles are proved erroneous, and the required solution not yet obtained.  By Robert Murphy.  Mallow, 1824.
    This refutation was the production of an Irish boy of eighteen years old, self-educated in mathematics, the son of a shoemaker at Mallow.  He died in 1843, leaving a name well known among mathematicians.  His works on the theory of equations and on electricity, and his papers in the Cambridge Transactions, are all of high genius.  The only account of him which I know of is that which I wrote for the Supplement of the Penny Cyclopædia.  He was thrown by his talents into a good income at Cambridge, with no social training except penury, and very little intellectual training except mathematics.  He fell into dissipation, and his scientific career was almost arrested: but he had great good in him.  A sentence in a letter from the late Dean Peacock to me — giving some advice about the means of serving Murphy — sets out the old case: "Murphy is a man whose special education is in advance of his general; and such men are almost always difficult subjects to manage."

A NEW VALUE OF π.
The Invisible Universe disclosed; or, the real Plan and Government of the Universe.  By Henry Coleman Johnson, Esq.  London, 1843.
    The book opens abruptly with: "First demonstration.  Concerning the center: showing that, because the center is an innermost point at an equal distance between two extreme points of a right line, and from every two relative and opposite intermediate points, it is composed of the two extreme internal points of each half of the line; each extreme internal point attracting towards itself all parts of that half to which it belongs...."
    Of course the circle is squared; and the circumference is 3-1/21 diameters.

SOME MODERN ASTROLOGY.
Combination of the Zodiacal and Cometical Systems.  Printed for the London Society, Exeter Hall.  1843.
    What this London Society was, or the "combination," did not appear.  There was a remarkable comet in 1843, the tail of which was at first confounded with what is called the zodiacal light.  This nicely printed little tract, evidently got up with less care for expense than is usual in such works, brings together all the announcements of the astronomers, and adds a short head and tail piece, which I shall quote entire.  As the announcements are very ordinary astronomy, the reader will be able to detect, if such be possible, what is the meaning and force of the "Combination of the Zodiacal and Cometical Systems": "Premonition.  It has pleased the Author of Creation to cause (to His human and reasoning Creatures of this generation, by a 'combined' appearance in His Zodiacal and Cometical system) a 'warning Crisis' of universal concernment to this our Globe.  It is this 'Crisis' that has so generally 'ROUSED' at this moment the 'nations throughout the Earth' that no equal interest has ever before been excited by Man; unless it be in that caused by the 'Pagan-Temple in Rome,' which is recorded by the elder Pliny, 'Nat. Hist.' i. 23. iii. 3. Hardouin."
    This shows the awful threats published at a time of some excitement about the phenomenon, under the name of the London Society.  The assumption of a corporate appearance is a very unfair trick, and there are junctures at which harm might be done by it.

Elective Polarity the Universal Agent.  By Frances Barbara Burton, authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c.  London, 1845.
    The title gives a notion of the theory.  The first sentence states, that 12,500 years ago α Lyræ was the pole star, and attributes the immense magnitude of the now fossil animals to a star of such "polaric intensity as Vega pouring its magnetic streams through our planet."  Miss Burton was a lady of property, and of very respectable acquirements, especially in Hebrew; she was eccentric in all things.

SPECULATIVE THOUGHT IN ENGLAND.
    In the year 1845 the old Mathematical Society was merged in the Astronomical Society.  The circle-squarers, etc., thrive more in England than in any other country; there are most weeds where there is the largest crop.  Speculation, though not encouraged by our Government so much as by those of the Continent, has had not such forcing, but much wider diffusion: few tanks, but many rivulets.
    On this point I quote from the preface to the reprint of the work of Ramchundra, which I superintended for the late Court of Directors of the East India Company: "That sound judgment which gives men well to know what is best for them, as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, perhaps cannot rapidly be advanced without, a great taste for pure speculation among the general mass of the people, down to the lowest of those who can read and write.
    "England is a marked example.  Many persons imagine that our country is the great instance of the refusal of all unpractical knowledge in favor of what is useful.  On the contrary, there is no country in Europe in which there has been so wide a diffusion of speculation, theory, or what other unpractical word the reader pleases.  In our country, the scientific society is always formed and maintained by the people; in every other, the scientific academy — most aptly named — has been the creation of the government, of which it has never ceased to be the nursling.  In all the parts of England in which manufacturing pursuits have given the artisan some command of time, the cultivation of mathematics and other speculative studies has been a very frequent occupation.  In no other country has the weaver at his loom bent over the Principia of Newton,or has the man of weekly wages maintained his own scientific periodical.  With us, since the beginning of the last century, scores upon scores — perhaps hundreds — of annuals have run, some their ten years, some their half-century, some their century and a half, containing questions to be answered, from which many of our examiners in the universities have culled materials for the academical contests.
    "And these questions have always been answered, and in cases without number by the lower order of purchasers, the mechanics, the weavers, and the printers' workmen.  I cannot here digress to point out the manner in which the concentration of manufactures, and the general diffusion of education, have affected the state of things; I speak of the time during which the present system took its rise, and of the circumstances under which many of its most effective promoters were trained.  In all this there is nothing which stands out, like the state-nourished academy, with its few great names and brilliant single achievements.  This country has differed from all others in the wide diffusion of the disposition to speculate, which disposition has found its place among the ordinary habits of life, moderate in its action, healthy in its amount."

THE OLD MATHEMATICAL SOCIETY.
    Among the most remarkable proofs of the diffusion of speculation was the Mathematical Society, which flourished from 1717 to 1845.  Its habitat was Spitalfields, and I think most of its existence was passed in Crispin Street.  It was originally a plain society, belonging to the studious artisan.  The members met for discussion once a week; and I believe I am correct in saying that each man had his pipe, his pot, and his problem.  One of their rules was that "If any member shall so far forget himself and the respect due to the Society as in the warmth of debate to threaten or offer personal violence to any other member, he shall be liable to immediate expulsion, or to pay such fine as the majority of the members present shall decide."  But their great rule, printed large on the back of the title page of their last book of regulations, was "By the constitution of the Society, it is the duty of every member, if he be asked any mathematical or philosophical question by another member, to instruct him in the plainest and easiest manner he is able."  We shall presently see that, in old time, the rule had a more homely form.
    The Society gradually declined, and in 1845 was reduced to nineteen members.  An arrangement was made by which sixteen members, who if not already in the Astronomical Society, became Fellows without contribution, all the books and other property of the old Society being transferred to the new one.  I was on the committee which made the preliminary inquiries, and the reason of the decline was soon manifest. The only question which could arise was whether the members of the society of working men — for this repute still continued — were of that class of educated men who could associate with the Fellows of the Astronomical Society on terms agreeable to all parties.  We found that the artisan element had been extinct for many years; there was not a man but might, as to education, manners, and position, have become a Fellow in the usual way.  Life in Spitalfields had become harder, and the weaver could only live from hand to mouth, and not up to the brain.  The material of the old Society no longer existed.
    In 1798, experimental lectures were given, a small charge for admission being taken at the door.  By this hangs a tale.  Many years ago, I found among papers of a deceased friend, who certainly never had anything to do with the Society, and who passed all his life far from London, a song, headed "Song sung by the Mathematical Society in London, at a dinner given Mr. Fletcher, a solicitor, who had defended the Society gratis."  Some years elapsed before it struck me that my old friend Benjamin Gompertz, who had long been a member, might have some recollection of the matter.  The following is an extract of a letter from him (July 9, 1861): "As to the Mathematical Society, I was a member when only 18 years of age, (Mr. G. was born in 1779), having been, contrary to the rules, elected under the age of 21.  How I came to be a member of that Society — and continued so until it joined the Astronomical Society, and was then the President — was: I happened to pass a bookseller's small shop, of second hand books, kept by a poor tailor but a good mathematician, John Griffiths.  I was very pleased to meet a mathematician, and I asked him if he would give me some lessons; and his reply was that I was more capable to teach him, but he belonged to a society of mathematicians, and he would introduce me.  I accepted the offer, and I was elected, and had many scholars then to teach, as one of the rules was, if a member asked for information, and applied to any one who could give it, he was obliged to give it, or fine one penny.  Though I might say much with respect to the Society which would be interesting, I will for the present reply only to your question.  I well knew Mr. Fletcher, who was a very clever and very scientific person.  He did, as solicitor, defend an action brought by an informer against the Society — I think for 5,000 l. — for giving lectures to the public in philosophical subjects (i.e., for unlicensed public exhibition with money taken at the doors).  I think the price for admission was one shilling, and we used to have, if I rightly recollect, from two to three hundred visitors.  Mr. Fletcher was successful in his defence, and we got out of our trouble.  There was a collection made to reward his services, but he did not accept any reward; and I think we gave him a dinner, as you state, and enjoyed ourselves; no doubt with astronomical songs and other songs; but my recollection does not enable me to say if the astronomical song was a drinking song.  I think the anxiety caused by that action was the cause of some of the members' death.

A NEW THEORY OF TIDES.
A new theory of the tides: in which the errors of the usual theory are demonstrated; and proof shewn that the full moon is not the cause of a concomitant spring tide, but actually the cause of the neaps....  By Commr. Debenham, R.N.  London, 1846.
    The author replied to a criticism in the Athenæum, and in a very few words showed that he had read nothing on the subject.  The reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr. Critic."  Had he read any actual investigations on the usual theory, he would have known that to this day the sun and moon continue to be called planets — though the phrase is disappearing — in speaking of the tides; the sense, of course, being the old one, wandering bodies.
    A large class of the paradoxers, when they meet with something which taken in their sense is absurd, do not take the trouble to find out the intended meaning, but walk off with the words laden with their own first construction.  Such men are hardly fit to walk the streets without an interpreter.
    I was startled for a moment, at the time when a recent happy — and more recently happier — marriage occupied the public thoughts, by seeing in a haberdasher's window, in staring large letters, an unpunctuated sentence which read itself to me as "Princess Alexandra! collar and cuff!"  It immediately occurred to me that had I been any one of some scores of my paradoxers, I should, no doubt, have proceeded to raise the mob against the unscrupulous person who dared to hint to a young bride such conduct towards her new lord.  But certain material contexts in the shop window suggested a less savage explanation.  A paradoxer should not stop at reading the advertisements of Newton or Laplace; he should learn to look at the stock of goods.

AN ASTRONOMICAL PARADOXER.
    Two systems of astronomy.  First, the Newtonian system, showing the rise and progress thereof, with a short historical account; the general theory with a variety of remarks thereon.  Second, the system in accordance with the Holy Scriptures, showing the rise and progress from Enoch, the seventh from Adam, the prophets, Moses, and others, in the first Testament; our Lord Jesus Christ, and his apostles, in the new or second Testament; Reeve and Muggleton, in the third and last Testament; with a variety of remarks thereon.  By Isaac Frost. London, 1846.
    A very handsomely printed volume, with beautiful plates.  Many readers who have heard of Muggletonians have never had any distinct idea of Lodowick Muggleton, the inspired tailor (1608-1698), who about 1650 received his commission from heaven, wrote a Testament, founded a sect, and descended to posterity.  Of Reeve less is usually said; according to Mr. Frost, he and Muggleton are the two "witnesses."
    I content myself with one specimen of Mr. Frost's science: "I was once invited to hear read over 'Guthrie on Astronomy,' and when the reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs in support of his theory of the earth revolving round the sun; all the rest is assertion without any proofs.'  'What are they?' inquired the Doctor.  'Well,' I said, 'they are, first, the power of attraction to keep the earth to the sun; the second is the power of repulsion, by virtue of the centrifugal motion of the earth; all the rest appears to me assertion without proof.'  The Doctor considered a short time and then said, 'It certainly did appear so.'  I said, 'Sir Isaac has certainly obtained the credit of completing the system, but really he has only half done his work.'  'How is that,' inquired my friend the Doctor.  My reply was 'You will observe his system shows the earth traverses round the sun on an inclined plane; the consequence is, there are four powers required to make his system complete:
        1st. The power of attraction.
        2ndly.  The power of repulsion.
        3rdly.  The power of ascending the inclined plane.
        4thly.  The power of descending the inclined plane.
You will thus easily see the four powers required, and Newton has only accounted for two; the work is therefore only half done.' Upon due reflection the Doctor said, 'It certainly was necessary to have these four points cleared up before the system could be said to be complete.'"
    I have no doubt that Mr. Frost, and many others on my list, have really encountered doctors who could be puzzled by such stuff as this, or nearly as bad, among the votaries of existing systems, and have been encouraged thereby to print their objections.  But justice requires me to say that from the words "power of repulsion by virtue of the centrifugal motion of the earth," Mr. Frost may be suspected of having something more like a notion of the much-mistaken term "centrifugal force" than many paradoxers of greater fame.
    The system laid down by Mr. Frost, though intended to be substantially that of Lodowick Muggleton, is not so vagarious.  It is worthy of note how very different have been the fates of two contemporary paradoxers, Muggleton and George Fox.  They were friends and associates, and commenced their careers about the same time, 1647-1650.  The followers of Fox have made their sect an institution, and deserve to be called the pioneers of philanthropy.  But though there must still be Muggletonians, since expensive books are published by men who take the name, no sect of that name is known to the world.  Nevertheless, Fox and Muggleton are men of one type, developed by the same circumstances; it is for those who investigate such men to point out why their teachings have had fates so different.  Macaulay says it was because Fox found followers of more sense than himself.  True enough; but why did Fox find such followers and not Muggleton? The two were equally crazy, to all appearance; and the difference required must be sought in the doctrines themselves.
    Fox was not a rational man, but the success of his sect and doctrines entitles him to a letter of alteration of the phrase which I am surprised has not become current.  When Conduitt, the husband of Newton's half-niece, wrote a circular to Newton's friends, just after his death, inviting them to bear their parts in a proper biography, he said, "As Sir I. Newton was a national man, I think every one ought to contribute to a work intended to do him justice."  Here is the very phrase which is often wanted to signify that celebrity which puts its mark, good or bad, on the national history, in a manner which cannot be asserted of many notorious or famous historical characters.  George Fox and Newton are both national men.
    Dr. Roget's Thesaurus gives more than fifty synonyms — colleagues would be the better word — of "celebrated," any one of which might be applied, either in prose or poetry, to Newton or to his works, no one of which comes near to the meaning which Conduitt's adjective immediately suggests.  The truth is, we are too monarchical to be national.  We have the Queen's army, the Queen's navy, the Queen's highway, the Queen's English, etc.; nothing is national except the debt.  That this remark is not new is an addition to its force; it has hardly been repeated since it was first made.  It is some excuse that nation is not vernacular English; the country is our word, and countryman is appropriated.

The conspiracy of the Bullionists as it affects the present system of the money laws.  By Caleb Quotem.  Birmingham, 1847.
    This pamphlet is one of a class of which I know very little, in which the effects of the laws relating to this or that political bone of contention are imputed to deliberate conspiracy of one class to rob another of what the one knew ought to belong to the other.  The success of such writers in believing what they have a bias to believe, would, if they knew themselves, make them think it equally likely that the inculpated classes might really believe what it is their interest to believe.  The idea of a guilty understanding existing among fundholders, or landholders, or any holders, all the country over, and never detected except by bouncing pamphleteers, is a theory which should have been left for Cobbett to propose, and for Apella to believe.

THEISM INDEPENDENT OF REVELATION.
The Reasoner.  No. 45.  Edited by G. J. Holyoake.  Price 2d.  Is there sufficient proof of the existence of God?  1847.
    This acorn of the holy oak was forwarded to me with a manuscript note signed by the editor, on the part of the "London Society of Theological Utilitarians," who say, "they trust you may be induced to give this momentous subject your consideration."
    The supposition that a middle-aged person, known as a student of thought on more subjects than one, had that particular subject yet to begin, is a specimen of what I will call the assumption-trick of controversy, a habit which pervades all sides of all subjects.
    The tract is a proof of the good policy of letting opinions find their level, without any assistance from the Court of Queen's Bench.  Twenty years earlier the thesis would have been positive, "There is sufficient proof of the non-existence of God," and bitter in its tone.  As it stands, we have a moderate and respectful treatment — wrong only in making the opponent argue absurdly, as usually happens when one side invents the other — of a question in which a great many Christians have agreed with the atheist: can the existence of God be proved independently of revelation?
    Many very religious persons answer this question in the negative, as well as Mr. Holyoake.  And, this point being settled, all who agree in the negative separate into those who can endure skepticism, and those who cannot; the second class find their way to Christianity.
    This very number of The Reasoner announces the secession of one of its correspondents, and his adoption of the Christian faith.  This would not have happened twenty years before: nor, had it happened, would it have been respectfully announced.
    There are people who are very unfortunate in the expression of their meaning.  Mr. Holyoake, in the name of the "London Society" etc., forwarded a pamphlet on the existence of God, and said that the Society trusted I "may be induced to give" the subject my "consideration."  How could I know the Society was one person, who supposed I had arrived at a conclusion and wanted a "guiding word?"
    But so it seems it was; Mr. Holyoake, in the English Leader of October 15, 1864, and in a private letter to me, writes as follows: "The gentleman who was the author of the argument, and who asked me to send it to Mr. De Morgan, never assumed that that gentleman had 'that particular subject to begin' — on the contrary, he supposed that one whom we all knew to be eminent as a thinker had come to a conclusion upon it, and would perhaps vouchsafe a guiding word to one who was, as yet, seeking the solution of the Great Problem of Theology.  I told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he must be content to wait.  On some day of courtesy and leisure he might have the kindness to write.'  Nor was I wrong — the answer appears in your pages at the lapse of seventeen years."
    I suppose Mr. Holyoake's way of putting his request was the stylus curiæ of the Society.  A worthy Quaker who was sued for debt in the King's Bench was horrified to find himself charged in the declaration with detaining his creditor's money by force and arms, contrary to the peace of our Lord the King, etc.  It's only the stylus curiæ, said a friend: I don't know curiæ, said the Quaker, but he shouldn't style us peace-breakers.
    The notion that the non-existence of God can be proved, has died out under the light of discussion; had the only lights shone from the pulpit and the prison, so great a step would never have been made.
    The dictum that Christianity is "part and parcel of the law of the land" is also abrogated; at the same time, and the coincidence is not an accident, it is becoming somewhat nearer the truth that the law of the land is part and parcel of Christianity.
    It must also be noticed that Christianity was part and parcel of the articles of war; and so was duelling.  Any officer speaking against religion was to be cashiered; and any officer receiving an affront without, in the last resort, attempting to kill his opponent, was also to be cashiered.