Chapter II: Part 2

The reasoning habit of the educated community, in four cases out of five, permits universal propositions to be stated at one time, and denied, _pro re nata_,[70] at another. "Before we proceed to consider any question involving physical principles, we should set out with _clear ideas_ of the naturally possible and impossible." The eminent man who said this, when wanting it for his views of mental education (!) never meant it for more than what was in hand, never assumed it in the researches which will give him to posterity! I have heard half-a-dozen defences of his having said this, not one of which affirmed the truth of what was said. A worthy clergyman wrote that if A. B. had said a certain thing the point in question would have been established. It was shown to him that A. B. _had_ said it, to which the reply was a refusal to admit the point because A. B. said it in a second pamphlet and in answer to objections. And I might give fifty such instances with very little search. Always assume more than you want; because you cannot tell how much you may want: put what is over into the didn't-mean-that basket, or the extreme case what-not.

PROTESTANT AND PAPAL CHRISTENDOM.

Something near forty years of examination of the theologies on and off--more years very much on than quite off--have given me a good title--to myself, I ask no one else for leave--to make the following remarks: A conclusion has _premises_, facts or doctrines from proof or authority, and _mode of inference_. There may be invention or {34} falsehood of premise, with good logic; and there may be tenable premise, followed by bad logic; and there may be both false premise _and_ bad logic. The Roman system has such a powerful manufactory of premises, that bad logic is little wanted; there is comparatively little of it. The doctrine-forge of the Roman Church is one glorious compound of everything that could make Heraclitus[71] sob and Democritus[72] snigger. But not the only one. The Protestants, in tearing away from the Church of Rome, took with them a fair quantity of the results of the Roman forge, which they could not bring themselves to give up. They had more in them of Martin than of Jack. But they would have no premises, except from the New Testament; though some eked out with a few general Councils. The consequence is that they have been obliged to find such a logic as would bring the conclusions they require out of the canonical books. And a queer logic it is; nothing but the Roman forge can be compared with the Protestant loom. The picking, the patching, the piecing, which goes to the Protestant _termini ad quem_,[73] would be as remarkable to the general eye, as the Roman manufacture of _termini a quo_,[74] if it were not that the world at large seizes the character of an asserted fact better than that of a mode of inference. A grand step towards the deification of a lady, made by alleged revelation 1800 years after her death, is of glaring evidence: two or three additional shiffle-shuffles towards defence of saying the Athanasian curse in church and unsaying it out of church, are hardly noticed. Swift has bungled his satire where he makes Peter a party to finding out what he wants, _totidem syllabis_ and _totidem literis_, {35} when he cannot find it _totidem verbis_[75] This is Protestant method: the Roman plan is _viam faciam_; the Protestant plan is _viam inveniam_.[76] The public at large begins to be conversant with the ways of _wriggling out_, as shown in the interpretations of the damnatory parts of the Athanasian Creed, the phrases of the Burial Service, etc. The time will come when the same public will begin to see the ways of _wriggling in_. But one thing at a time: neither Papal Rome nor Protestant Rome was built--nor will be pulled down--in a day.

The distinction above drawn between the two great antitheses of Christendom may be illustrated as follows. Two sets of little general dealers lived opposite to one another: all sold milk. Each vaunted its own produce: one set said that the stuff on the other side the way was only chalk and water; the other said that the opposites sold all sorts of filth, of which calves' brain was the least nasty. Now the fact was that both sets sold milk, and from the same dairy: but adulterated with different sorts of dirty water: and both honestly believed that the mixture was what they were meant to sell and ought to sell. The great difference between them, about which the apprentices fought each other like Trojans, was that the calves' brain men poured milk into the water, and the chalk men poured water into the milk. The Greek and Roman sects on one side, the Protestant sects on the other, must all have _churches_: the Greek and Roman sects pour the New Testament into their churches; the Protestant sects pour their churches into the New Testament. The Greek and Roman insist upon the New Testament being no more than part and parcel of their churches: the Protestant insist upon their churches being as much part and parcel of the New Testament. All dwell vehemently upon the doctrine that there must be milk {36} somewhere; and each says--I have it. The doctrine is true: and can be verified by any one who can and will go to the dairy for himself. Him will the several traders declare to have no milk at all. They will bring their own wares, and challenge a trial: they want nothing but to name the judges. To vary the metaphor, those who have looked at Christianity in open day, know that all who see it through painted windows shut out much of the light of heaven and color the rest; it matters nothing that the stains are shaped into what are meant for saints and angels.

But there is another side to the question. To decompose any substance, it must be placed between the poles of the battery. Now theology is but one pole; philosophy is the other. No one can make out the combinations of our day unless he read the writings both of the priest and the philosopher: and if any one should hold the first word offensive, I tell him that I mean _both_ words to be _significant_. In reading these writings, he will need to bring both wires together to find out what it is all about. Time was when most priests were very explicit about the fate of philosophers, and most philosophers were very candid about their opinion of priests. But though some extremes of the old sorts still remain, there is now, in the middle, such a fusion of the two pursuits that a plain man is wofully puzzled. The theologian writes a philosophy which seems to tell us that the New Testament is a system of psychology; and the philosopher writes a Christianity which is utterly unintelligible as to the question whether the Resurrection be a fact or a transcendental allegory. What between the theologian who assents to the Athanasian denunciation in what seems the sense of no denunciation, and the philosopher who parades a Christianity which looks like no revelation, there is a maze which threatens to have the only possible clue in the theory that everything is something else, and nothing is anything at all. But this is a paradox far beyond my handling: it is a Budget of itself. {37}

RELIGION AND PHILOSOPHY.

Religion and Philosophy, the two best gifts of Heaven, set up in opposition to each other at the revival of letters; and never did competing tradesmen more grossly misbehave. Bad wishes and bad names flew about like swarms of wasps. The Athanasian curses were intended against philosophers; who, had they been a corporation, with state powers to protect them, would have formulized a _per contra_. But the tradesmen are beginning to combine: they are civil to each other; too civil by half. I speak especially of Great Britain. Old theology has run off to ritualism, much lamenting, with no comfort except the discovery that the cloak Paul left at Troas was a chasuble. Philosophy, which always had a little sense sewed up in its garments--to pay for its funeral?--has expended a trifle in accommodating itself to the new system. But the two are poles of a battery; and a question arises.

If Peter Piper picked a peck of pepper,
Where is the peck of pepper Peter Piper picked?

If Religion and Philosophy be the two poles of a battery, whose is the battery Religion and Philosophy have been made the poles of? Is the change in the relation of the wires any presumption of a removal of the managers? We know pretty well who handled the instrument: has he resigned or been[77] turned out? Has he been put under {38} restriction? A fool may ask more questions than twenty sages can answer: but there is hope; for twenty sages cannot ask more questions than one reviewer can answer. I should like to see the opposite sides employed upon the question, What are the _commoda_, and what the _pericula_,[78] of the current approximation of Religion and Philosophy?

All this is very profane and irreverent! It has always been so held by those whose position demands such holding. To describe the Church as it is passes for assailing the Church as it ought to be with all who cannot do without it. In Bedlam[79] a poor creature who fancied he was St. Paul, was told by another patient that he was an impostor; the first maniac lodged a complaint against the second for calling St. Paul an impostor, which, he argued, with much appearance of sanity, ought not to be permitted in a well regulated madhouse. Nothing could persuade him that he had missed the question, which was whether _he_ was St. Paul. The same thing takes place in the world _at large_. And especially must be noted the refusal to permit to the _profane_ the millionth part of the licence assumed by the _sacred_. I give a sound churchman the epitaph of St. John Long; the usual pronunciation of whose name must be noted--

"Behold! ye quacks, the vengeance strong
On deeds like yours impinging:
For here below lies St. John Long[80]
Who now must be _long singeing_."

How shameful to pronounce this of the poor man! What, Mr. Orthodox! may I not do in joke to one pretender what {39} you do in earnest--unless you quibble--to all the millions of the Greek Church, and a great many others. Enough of you and your reasoning! Go and square the circle!

The few years which end with 1867 have shown, not merely the intermediate fusion of Theology and Philosophy of which I have spoken, but much concentration of the two extremes, which looks like a gathering of forces for some very hard fought Armageddon. Extreme theology has been aiming at a high Church in England, which is to show a new front to all heresy: and extreme philosophy is contriving a physical organization which is to _think_, and to show that mind is a consequence of matter, or thought a recreation of brain. The physical speculators begin with a possible hypothesis, in which they aim at explanation: and so the bold aspirations of the author of the _Vestiges_ find standing-ground in the variation of species by "natural selection." Some relics--so supposed--of extremely ancient men are brought to help the general cause. Only distant hints are given that by possibility it may end in the formation of all living organisms from a very few, if not from one. The better heads above mentioned know that their theory, if true, does not bear upon morals. The formation of solar systems from a nebular hypothesis, followed by organizations gradually emerging from some curious play of particles, nay, the very evolution of mind and thought from such an apparatus, are all as consistent with a Personal creative power to whom homage and obedience are due, and who has declared himself, as with a blind Nature of Things. A pure materialist, as to all things visible, may be even a bigotted Christian: this is not frequent, but it is possible. There is a proverb which says, A pig may fly, but it isn't a likely bird. But when the psychological speculator comes in, he often undertakes to draw inferences from the physical conclusions, by joining on his tremendous apparatus of _a priori_ knowledge. He deduces that he can _do without_ a God: he can deduce all things {40} without any such necessity. With Occam[81] and Newton he will have no more causes than are necessary to explain phenomena _to him_: and if by pure head-work combined with results of physical observation he can construct his universe, he must be a very _unphilosophical_ man who would encumber himself with a useless Creator! There is something tangible about my method, says he; yours is vague. He requires it to be granted that his system is _positive_ and that yours is _impositive_. So reasoned the stage coachman when the railroads began to depose him--"If you're upset in a stage-coach, why, there you are! but if you're upset on the railroad, where are you?" The answer lies in another question, Which is most positive knowledge, God deduced from man and his history, or the postulates of the few who think they can reason _a priori_ on the tacit assumption of unlimited command of data?

We are not yet come to the existence of a school of philosophers who explicitly deny a Creator: but we are on the way, though common sense may interpose. There are always straws which show the direction of the wind. I have before me the printed letter of a medical man--to whose professional ability I have good testimony--who finds the vital principle in highly rarefied oxygen. With the usual logic of such thinkers, he dismisses the "eternal personal identity" because "If soul, spirit, mind, which are merely modes of sensation, be the attribute or function of nerve-tissue, it cannot possibly have any existence apart from its material organism!" How does he know this _impossibility_? If all the mind _we_ know be from nerve-tissue, how does it appear that mind in other planets may not be another thing? Nay, when we come to _possibilities_, does not his own system give a queer one? If highly rarefied oxygen be vital power, more highly rarefied oxygen {41} may be more vital and more powerful. Where is this to stop? Is it _impossible_ that a finite quantity, rarefied _ad infinitum_, may be an Omnipotent? Perhaps the true Genesis, when written, will open with "In the beginning was an imperial quart of oxygen at 60 deg. of Fahrenheit, and the pressure of the atmosphere; and this oxygen was infinitely rarefied; and this oxygen became God." For myself, my aspirations as to this system are Manichaean. The quart of oxygen is the Ormuzd, or good principle: another quart, of hydrogen, is the Ahriman, or evil principle! My author says that his system explains Freewill and Immortality so obviously that it is difficult to read previous speculations with becoming gravity. My deduction explains the conflict of good and evil with such clearness that no one can henceforward read the New Testament with becoming reverence. The surgeon whom I have described is an early bud which will probably be nipped by the frost and wither on the ground: but there is a good crop coming. Material pneuma is destined to high functions; and man is to read by gas-light.

THE SUN AN ELECTRIC SPACE.

The solar system truly solved; demonstrating by the perfect harmony of
the planets, founded on the four universal laws, the Sun to be an
electric space; and a source of every natural production displayed
throughout the solar system. By James Hopkins.[82] London, 1849, 8vo.

The author says:

"I am satisfied that I have given the true _laws_ constituting the _Sun_ to be _space_; and I call upon those disposed to maintain the contrary, to give true _laws_ showing him to be a body: until such can be satisfactorily established, I have an undoubted claim to the credit of my theory,--That the Sun is an _Electric Space_, fed and governed by the {42} planets, which have the property of attracting heat from it; and the means of supplying the necessary _pabulum_ by their degenerated air driven off towards the central space--the wonderful alembic in which it becomes transmuted to the revivifying necessities of continuous action; and the central space or Sun being perfectly electric, has the counter property of repulsing the bodies that attract it. How wonderful a conception! How beautiful, how magnificent an arrangement!

"O Centre! O Space! O Electric Space!"

JOSEPH ADY.

1849. _Joseph Ady_[83] is entitled to a place in this list of discoverers: his great fault, like that of some others, lay in pushing his method too far. He began by detecting unclaimed dividends, and disclosing them to their right owners, exacting his fee before he made his communication. He then generalized into trying to get fees from all of the _name_ belonging to a dividend; and he gave mysterious hints of danger impending. For instance, he would write to a clergyman that a legal penalty was hanging over him; and when the alarmed divine forwarded the sum required for disclosure, he was favored with an extract from some old statute or canon, never repealed, forbidding a clergyman to be a member of a corporation, and was reminded that he had insured his life in the ---- Office, which had a royal charter. He was facetious, was Joseph: he described himself in his circulars as "personally known to Sir Peter Laurie[84] and all other aldermen"; which was nearly true, {43} as he had been before most of them on charges of false pretence; but I believe he was nearly always within the law. Sir James Duke, when Lord Mayor, having particularly displeased him by a decision, his circulars of 1849 contain the following:

"Should you have cause to complain of any party, Sir J. Duke has contrived a new law of evidence, viz., write to him, he will consider your letter sufficient proof, and make the parties complained of pay without judge or jury, and will frank you from every expense."

I strongly suspect that Joseph Ady believed in himself.

He sometimes issued a second warning, of a Sibylline character:

"Should you find cause to complain of anybody, my voluntary referee, the Rt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see justice done you without any charge whatever: he and his toady, -- ---- ----. The accursed of Moses can hang any man: thus, by catching him alone and swearing Naboth spake evil against God and the King. Therefore (!) I admit no strangers to a personal conference without a prepayment of 20s. each. Had you attended to my former notice you would have received twice as much: neglect this and you will lose all."

ON MODERN ASTROLOGY.

Zadkiel's Almanac for 1849. Nineteenth number.

Raphael's Prophetic Almanac for 1849. Twenty-ninth number.

Reasons for belief in judicial astrology, and remarks on the dangerous
character of popish priestcraft. London, 1849, 12mo.

Astronomy in a nutshell: or the leading problems of the solar system
solved by simple proportion only, on the theory of magnetic attraction.
By Lieut. Morrison,[85] N. N. London (_s. a._) 12mo.

{44}

Lieut. Morrison is Zadkiel Tao Sze, and declares himself in real earnest an astrologer. There are a great many books on astrology, but I have not felt interest enough to preserve many of them which have come in my way. If anything ever had a fair trial, it was astrology. The idea itself is natural enough. A human being, set down on this earth, without any tradition, would probably suspect that the heavenly bodies had something to do with the guidance of affairs. I think that any one who tries will ascertain that the planets do not prophesy: but if he should find to the contrary, he will of course go on asking. A great many persons class together belief in astrology and belief in apparitions: the two things differ in precisely the way in which a science of observation differs from a science of experiment. Many make the mistake which M. le Marquis made when he came too late, and hoped M. Cassini[86] would do the eclipse over again for his ladies. The apparition chooses its own time, and comes as seldom or as often as it pleases, be it departed spirit, nervous derangement, or imposition. Consequently it can only be observed, and not experimented upon. But the heavens, if astrology be true, are prophesying away day and night all the year round, and about every body. Experiments can be made, then, except only on rare phenomena, such as eclipses: anybody may choose his time and his question. This is the great difference: and experiments were made, century after century. If astrology had been true, it must have lasted in an ever-improving state. If it be true, it is a truth, and a useful truth, which had experience and prejudice both in its favor, and yet lost ground as soon as astronomy, its working tool, began to improve.

1850. A letter in the handwriting of an educated man, dated from a street in which it must be taken that educated persons live, is addressed to the Secretary of the {45} Astronomical Society about a matter on which the writer says "his professional pursuit will enable him to give a satisfactory reply." In a question before a court of law it is sworn on one side that the moon was shining at a certain hour of a certain night on a certain spot in London; on the other side it is affirmed that she was clouded. The Secretary is requested to decide. This is curious, as the question is not astrological. Persons still send to Greenwich, now and then, to have their fortunes told. In one case, not very many years ago, a young gentleman begged to know who his wife was to be, and what fee he was to remit.

Sometimes the astronomer turns conjurer for fun, and his prophesies are fulfilled. It is related of Flamsteed[87] that an old woman came to know the whereabouts of a bundle of linen which had strayed. Flamsteed drew a circle, put a square into it, and gravely pointed out a ditch, near her cottage, in which he said it would be found. He meant to have given the woman a little good advice when she came back: but she came back in great delight, with the bundle in her hand, found in the very place. The late Baron Zach[88] received a letter from Pons,[89] a successful finder of comets, complaining that for a certain period he had found no comets, though he had searched diligently. Zach, a man of much sly humor, told him that no spots had been seen on the sun for about the same time--which was true,--and assured him that when the spots came back, the comets would come with them. Some time after he got a letter {46} from Pons, who informed him with great satisfaction that he was quite right, that very large spots had appeared on the sun, and that he had found a fine comet shortly after. I do not vouch for the first story, but I have the second in Zach's handwriting. It would mend the joke exceedingly if some day a real relation should be established between comets and solar spots: of late years good reason has been shown for advancing a connection between these spots and the earth's magnetism.[90] If the two things had been put to Zach, he would probably have chosen the comets. Here is a hint for a paradox: the solar spots are the dead comets, which have parted with their light and heat to feed the sun, as was once suggested. I should not wonder if I were too late, and the thing had been actually maintained. My list does not contain the twentieth part of the possible whole.

The mention of coincidences suggests an everlasting source of explanations, applicable to all that is extraordinary. The great paradox of coincidence is that of Leibnitz, known as the _pre-established harmony_, or _law of coincidences_, by which, separately and independently, the body receives impressions, and the mind proceeds as if it had perceived them from without. Every sensation, and the consequent state of the soul, are independent things coincident in time by the pre-established law. The philosopher could not otherwise _account for_ the connection of mind and matter; and he never goes by so vulgar a rule as _Whatever is, is_; to him that which is not clear as to how, is not at all. Philosophers in general, who tolerate each other's theories much better than Christians do each other's failings, seldom revive Leibnitz's fantasy: they seem to act upon the maxim quoted by Father Eustace[91] from the {47} Decretals, _Facinora ostendi dum puniuntur, flagitia autem abscondi debent_.[92]

The great _ghost-paradox_, and its theory of _coincidences_, will rise to the surface in the mind of every one. But the use of the word _coincidence_ is here at variance with its common meaning. When A is constantly happening, and also B, the occurrence of A and B at the same moment is the mere coincidence which may be casualty. But the case before us is that A is constantly happening, while B, when it does happen, almost always happens with A, and very rarely without it. That is to say, such is the phenomenon asserted: and all who rationally refer it to casualty, affirm that B is happening very often as well as A, but that it is not thought worthy of being recorded except when A is simultaneous. Of course A is here a death, and B the spectral appearance of the person who dies. In talking of this subject it is necessary to put out of the question all who play fast and loose with their secret convictions: these had better give us a reason, when they feel internal pressure for explanation, that there is no weathercock at Kilve; this would do for all cases. But persons of real inquiry will see that first, experience does not bear out the asserted frequency of the spectre, without the alleged coincidence of death: and secondly, that if the crowd of purely casual spectres were so great that it is no wonder that, now and then the person should have died at or near the moment, we ought to expect a much larger proportion of cases in which the spectre should come at the moment of the death of one or another of all the cluster who are closely connected with the original of the spectre. But this, we know, is almost without example. It remains then, for all, who speculate at all, to look upon the asserted phenomenon, think what they may of it, the thing which is to be explained, as a _connection_ in time of the death, and the {48} simultaneous appearance of the dead. Any person the least used to the theory of probabilities will see that purely casual coincidence, the _wrong spectre_ being comparatively so rare that it may be said never to occur, is not within the rational field of possibility.

The purely casual coincidence, from which there is no escape except the actual doctrine of special providences, carried down to a very low point of special intention, requires a junction of the things the like of each of which is always happening. I will give three instances which have occurred to myself within the last few years: I solemnly vouch for the literal truth of every part of all three:

In August 1861, M. Senarmont,[93] of the French Institute, wrote to me to the effect that Fresnel[94] had sent to England, in or shortly after 1824, a paper for translation and insertion in the _European Review_, which shortly afterwards expired. The question was what had become of that paper. I examined the _Review_ at the Museum, found no trace of the paper, and wrote back to that effect at the Museum, adding that everything now depended on ascertaining the name of the editor, and tracing his papers: of this I thought there was no chance. I posted this letter on my way home, at a Post Office in the Hampstead Road at the junction with Edward Street, on the opposite side of which is a bookstall. Lounging for a moment over the exposed books, _sicut meus est mos_,[95] I saw, within a few minutes of the posting of the letter, a little catch-penny book of anecdotes of Macaulay, which I bought, and ran over for a minute. My eye was soon caught by this sentence: "One of the young fellows immediately wrote to the editor (Mr. Walker) {49} of the _European Review_." I thus got the clue by which I ascertained that there was no chance of recovering Fresnel's paper. Of the mention of current reviews, not one in a thousand names the editor.

In the summer of 1865 I made my first acquaintance with the tales of Nathaniel Hawthorne, and the first I read was about the siege of Boston in the War of Independence. I could not make it out: everybody seemed to have got into somebody else's place. I was beginning the second tale, when a parcel arrived: it was a lot of old pamphlets and other rubbish, as he called it, sent by a friend who had lately sold his books, had not thought it worth while to send these things for sale, but thought I might like to look at them and possibly keep some. The first thing I looked at was a sheet which, being opened, displayed "A plan of Boston and its environs, shewing the true situation of his Majesty's army and also that of the rebels, drawn by an engineer, at Boston Oct. 1775." Such detailed plans of current sieges being then uncommon, it is explained that "The principal part of this plan was surveyed by Richard Williams, Lieutenant at Boston; and sent over by the son of a nobleman to his father in town, by whose permission it was published." I immediately saw that my confusion arose from my supposing that the king's troops were besieging the rebels, when it was just the other way.

April 1, 1853, while engaged in making some notes on a logical point, an idea occurred which was perfectly new to me, on the mode of conciliating the notions _omnipresence_ and _indivisibility into parts_. What it was is no matter here: suffice it that, since it was published elsewhere (in a paper on _Infinity_, _Camb. Phil. Trans._ vol. xi. p. 1) I have not had it produced to me. I had just finished a paragraph on the subject, when a parcel came in from a bookseller containing Heywood's[96] _Analysis of Kant's Critick_, 1844.

{50} On turning over the leaves I found (p. 109) the identical thought which up to this day, I only know as in my own paper, or in Kant. I feel sure I had not seen it before, for it is in Kant's first edition, which was never translated to my knowledge; and it does not appear in the later editions. Mr. Heywood gives some account of the first edition.

In the broadsheet which gave account of the dying scene of Charles II, it is said that the Roman Catholic priest was introduced by P. M. A. C. F. The chain was this: the Duchess of Portsmouth[97] applied to the Duke of York, who may have consulted his Cordelier confessor, Mansuete, about procuring a priest, and the priest was smuggled into the king's room by the Duchess and Chiffinch.[98] Now the letters are a verbal acrostic of _Pere Mansuete a Cordelier Friar_, and a syllabic acrostic of _PortsMouth and ChifFinch_. This is a singular coincidence. Macaulay adopted the first interpretation, preferring it to the second, which I brought before him as the conjecture of a near relative of my own. But Mansuete is not mentioned in his narrative: it may well be doubted whether the writer of a broadside for English readers would use _Pere_ instead of _Father_. And the person who really "reminded" the Duke of "the duty he owed to his brother," was the Duchess and not Mansuete. But my affair is only with the coincidence.

But there are coincidences which are really connected without the connection being known to those who find in them matter of astonishment. Presentiments furnish marked cases: sometimes there is no mystery to those who have the clue. In the _Gentleman's Magazine_ (vol. 80, part 2, p. 33) we read, the subject being presentiment of death, as follows: "In 1778, to come nearer the recollection of {51} survivors, at the taking of Pondicherry, Captain John Fletcher, Captain De Morgan, and Lieutenant Bosanquet, each distinctly foretold his own death on the morning of his fate." I have no doubt of all three; and I knew it of my grandfather long before I read the above passage. He saw that the battery he commanded was unduly exposed: I think by the sap running through the fort when produced. He represented this to the engineer officers, and to the commander-in-chief; the engineers denied the truth of the statement, the commander believed them, my grandfather quietly observed that he must make his will, and the French fulfilled his prediction. His will bore date the day of his death; and I always thought it more remarkable than the fulfilment of the prophecy that a soldier should not consider any danger short of one like the above, sufficient reason to make his will. I suppose the other officers were similarly posted. I am told that military men very often defer making their wills until just before an action: but to face the ordinary risks intestate, and to wait until speedy death must be the all but certain consequence of a stupid mistake, is carrying the principle very far. In the matter of coincidences there are, as in other cases, two wonderful extremes with every intermediate degree. At one end we have the confident people who can attribute anything to casual coincidence; who allow Zadok Imposture and Nathan Coincidence to anoint Solomon Selfconceit king. At the other end we have those who see something _very curious_ in any coincidence you please, and whose minds yearn for a deep reason. A speculator of this class happened to find that Matthew viii. 28-33 and Luke viii. 26-33 contain the same account, that of the demons entering into the swine. Very odd! chapters tallying, and verses so nearly: is the versification rightly managed? Examination is sure to show that there are monstrous inconsistencies in the mode of division, which being corrected, the verses tally as well as the chapters. And then how comes it? I cannot go on, {52} for I have no gift at torturing a coincidence, but I would lay twopence, if I could make a bet--which I never did in all my life--that some one or more of my readers will try it. Some people say that the study of chances tends to awaken a spirit of gambling: I suspect the contrary. At any rate, I myself, the writer of a mathematical book and a comparatively popular book, have never laid a bet nor played for a stake, however small: not one single time.

It is useful to record such instances as I have given, with precision and on the solemn word of the recorder. When such a story as that of Flamsteed is told, _a priori_ assures us that it could not have been: the story may have been a _ben trovato_,[99] but not the bundle. It is also useful to establish some of the good jokes which all take for inventions. My friend Mr. J. Bellingham Inglis,[100] before 1800, saw the tobacconist's carriage with a sample of tobacco in a shield, and the motto _Quid rides_[101] (_N._ & _Q._, 3d S. i. 245). His father was able to tell him all about it. The tobacconist was Jacob Brandon, well known to the elder Mr. Inglis, and the person who started the motto, the instant he was asked for such a thing, was Harry Calender of Lloyd's, a scholar and a wit. My friend Mr. H. Crabb Robinson[102] remembers the King's Counsel (Samuel Marryat) who took the motto _Causes produce effects_, when his success enabled him to start a carriage.

The coincidences of errata are sometimes very remarkable: it may be that the misprint has a sting. The death of Sir W. Hamilton[103] of Edinburgh was known in London on a Thursday, and the editor of the _Athenaeum_ wrote to {53} me in the afternoon for a short obituary notice to appear on Saturday. I dashed off the few lines which appeared without a moment to think: and those of my readers who might perhaps think me capable of contriving errata with meaning will, I am sure, allow the hurry, the occasion, and my own peculiar relation to the departed, as sufficient reasons for believing in my entire innocence. Of course I could not see a proof: and two errata occurred. The words "addition to Stewart"[104] require "_for_ addition to _read_ edition of." This represents what had been insisted on by the Edinburgh publisher, who, frightened by the edition of Reid,[105] had stipulated for a simple reprint without notes. Again "principles of logic and mathematics" required "_for_ mathematics _read_ metaphysics." No four words could be put together which would have so good a title to be Hamilton's motto.

April 1850, found in the letter-box, three loose leaves, well printed and over punctuated, being

Chapter VI. Brethren, lo I come, holding forth the word of life, for so
I am commanded.... Chapter VII. Hear my prayer, O generations! and walk
by the way, to drink the waters of the river.... Chapter VIII. Hearken
o earth, earth, earth, and the kings of the earth, and their armies....

A very large collection might be made of such apostolic writings. They go on well enough in a misty--meant for mystical--imitation of St. Paul or the prophets, until at last some prodigious want of keeping shows the education of the writer. For example, after half a page which might {54} pass for Irving's[106] preaching--though a person to whom it was presented as such would say that most likely the head and tail would make something more like head and tail of it--we are astounded by a declaration from the _Holy Spirit_, speaking of himself, that he is "not ashamed of the Gospel of Christ." It would be long before we should find in _educated_ rhapsody--of which there are specimens enough--such a thing as a person of the Trinity taking merit for moral courage enough to stand where St. Peter fell. The following declaration comes next--"I will judge between cattle and cattle, that use their tongues."

THE FIGURE OF THE EARTH.

The figure of the earth. By J. L. Murphy,[107] of Birmingham. (London
and Birmingham, 4 pages, 12mo.) (1850?)

Mr. Murphy invites attention and objection to some assertions, as that the earth is prolate, not oblate. "If the philosopher's conclusion be right, then the pole is the center of a valley (!) thirteen miles deep." Hence it would be very warm. It is answer enough to ask--Who knows that it is not?

*** A paragraph in the MS. appears to have been inserted in this place
by mistake. It will be found in the Appendix at the end of this
volume.--S. E. De M.

PERPETUAL MOTION.

1851. The following letter was written by one of a class of persons whom, after much experience of them, I {55} do _not_ pronounce insane. But in this case the second sentence gives a suspicion of actual delusion of the senses; the third looks like that eye for the main chance which passes for sanity on the Stock Exchange and elsewhere:

15th Sept. 1851.

"Gentlemen,--I pray you take steps to make known that yesterday I completed my invention which will give motion to every country on the Earth;--to move Machinery!--the long sought in vain 'Perpetual Motion'!!--I was supported at the time by the Queen and H.R.H. Prince Albert. If, Gentlemen, you can advise me how to proceed to claim the reward, if any is offered by the Government, or how to secure the PATENT for the machine, or in any way assist me by advice in this great work, I shall most graciously acknowledge your consideration.

These are my convictions that my SEVERAL discoveries will be realized: and this great one can be at once acted upon: although at this moment it only exists in my mind, from my knowledge of certain fixed principles in nature:--the Machine I have not made, as I only completed the discovery YESTERDAY, Sunday!

I have, etc. ---- ----"

To the Directors of the
London University, Gower Street.

ON SPIRITUALISM.

The Divine Drama of History and Civilisation. By the Rev. James Smith,
M.A.[108] London, 1854, 8vo.

I have several books on that great paradox of our day, _Spiritualism_, but I shall exclude all but three. The bibliography of this subject is now very large. The question is one both of evidence and speculation;--Are the facts {56} true? Are they caused by spirits? These I shall not enter upon: I shall merely recommend this work as that of a spiritualist who does not enter on the subject, which he takes for granted, but applies his derived views to the history of mankind with learning and thought. Mr. Smith was a man of a very peculiar turn of thinking. He was, when alive, the editor, or _an_ editor, of the _Family Herald_: I say when alive, to speak according to knowledge; for, if his own views be true, he may have a hand in it still. The answers to correspondents, in his time, were piquant and original above any I ever saw. I think a very readable book might be made out of them, resembling "Guesses at Truth:" the turn given to an inquiry about morals, religion, or socials, is often of the highest degree of _unexpectedness_; the poor querist would find himself right in a most unpalatable way.

Answers to correspondents, in newspapers, are very often the fag ends of literature. I shall never forget the following. A person was invited to name a rule without exception, if he could: he answered "A man _must_ be present when he is shaved." A lady--what right have ladies to decide questions about shaving?--said this was not properly a rule; and the oracle was consulted. The editor agreed with the lady; he said that "a man _must_ be present when he is shaved" is not a _rule_, but a _fact_.

[Among my anonymous communicants is one who states that I have done injustice to the Rev. James Smith in "referring to him as a spiritualist," and placing his "Divine Drama" among paradoxes: "it is no paradox, nor do _spiritualistic_ views mar or weaken the execution of the design." Quite true: for the design is to produce and enforce "spiritualistic views"; and leather does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well, and have often talked to him on the subject: but more testimony from me is unnecessary; his book will speak for itself. {57} His peculiar style will justify a little more quotation than is just necessary to prove the point. Looking at the "battle of opinion" now in progress, we see that Mr. Smith was a prescient:

(P. 588.) "From the general review of parties in England, it is evident that no country in the world is better prepared for the great Battle of Opinion. Where else can the battle be fought but where the armies are arrayed? And here they all are, Greek, Roman, Anglican, Scotch, Lutheran, Calvinist, Established and Territorial, with Baronial Bishops, and Nonestablished of every grade--churches with living prophets and apostles, and churches with dead prophets and apostles, and apostolical churches without apostles, and philosophies without either prophets or apostles, and only wanting one more, 'the Christian Church,' like Aaron's rod, to swallow up and digest them all, and then bud and flourish. As if to prepare our minds for this desirable and inevitable consummation, different parties have been favored with a revival of that very spirit of revelation by which the Church itself was originally founded. There is a complete series of spiritual revelations in England and the United States, besides mesmeric phenomena that bear a resemblance to revelation, and thus gradually open the mind of the philosophical and infidel classes, as well as the professed believers of that old revelation which they never witnessed in living action, to a better understanding of that Law of Nature (for it is a Law of Nature) in which all revelation originates and by which its spiritual communications are regulated."

Mr. Smith proceeds to say that there are _only_ thirty-five incorporated churches in England, all formed from the New Testament except five, to each of which five he concedes a revelation of its own. The five are the Quakers, the Swedenborgians, the Southcottians, the Irvingites, and the Mormonites. Of Joanna Southcott he speaks as follows: {58}

(P. 592.) "Joanna Southcott[109] is not very gallantly treated by the gentlemen of the Press, who, we believe, without knowing anything about her, merely pick up their idea of her character from the rabble. We once entertained the same rabble idea of her; but having read her works--for we really have read them--we now regard her with great respect. However, there is a great abundance of chaff and straw to her grain; but the grain is good, and as we do not eat either the chaff or straw if we can avoid it, nor even the raw grain, but thrash it and winnow it, and grind it and bake it, we find it, after undergoing this process, not only very palatable, but a special dainty of its kind. But the husk is an insurmountable obstacle to those learned and educated gentlemen who judge of books entirely by the style and the grammar, or those who eat grain as it grows, like the cattle. Such men would reject all prological revelation; for there never was and probably never will be a revelation by voice and vision communicated in classical manner. It would be an invasion of the rights and prerogatives of Humanity, and as contrary to the Divine and Established order of mundane government, as a field of quartern loaves or hot French rolls."

Mr. Smith's book is spiritualism from beginning to end; and my anonymous gainsayer, honest of course, is either ignorant of the work he thinks he has read, or has a most remarkable development of the organ of imperception.]

A CONDENSED HISTORY OF MATHEMATICS.

I cut the following from a Sunday paper in 1849:

"X. Y.--The Chaldeans began the mathematics, in which the Egyptians excelled. Then crossing the sea, by means {59} of Thales,[110] the Milesian, they came into Greece, where they were improved very much by Pythagoras,[111] Anaxagoras,[112] and Anopides[113] of Chios. These were followed by Briso,[114] Antipho, [two circle-squarers; where is Euclid?] and Hippocrates,[115] but the excellence of the algebraic art was begun by Geber,[116] an Arabian astronomer, and was carried on by Cardanus,[117] Tartaglia,[118] Clavius,[119], Stevinus,[120] Ghetaldus,[121] Herig_e_nius,[122] Fran. Van Schooten [meaning Francis Van Schooten[123]], Florida de Beau_m_e,[124] etc."

Bryso was a mistaken man. Antipho had the disadvantage of being in advance of his age. He had the notion of which the modern geometry has made so much, that of {60} a circle being the polygon of an infinitely great number of sides. He could make no use of it, but the notion itself made him a sophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab astronomer, and a reputed conjurer in Europe, seems to have given his name to unintelligible language in the word _gibberish_. At one time _algebra_ was traced to him; but very absurdly, though I have heard it suggested that _algebra_ and _gibberish_ must have had one inventor.

Any person who meddles with the circle may find himself the crane who was netted among the geese: as Antipho for one, and Olivier de Serres[126] for another. This last gentleman ascertained, by weighing, that the area of the circle is very nearly that of the square on the side of the inscribed equilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did not pretend to more than approximation; but Montucla and others misunderstood him, and, still worse, misunderstood their own misunderstanding, and made him say the circle was exactly double of the equilateral triangle. He was let out of limbo by Lacroix, in a note to his edition of Montucla's _History of Quadrature_.

ST. VITUS, PATRON OF CYCLOMETERS.

Quadratura del cerchio, trisezione dell' angulo, et duplicazione del
cubo, problemi geometricamente risolute e dimostrate dal Reverendo
Arciprete di San Vito D. Domenico Anghera,[127] Malta, 1854, 8vo.

{61}

Equazioni geometriche, estratte dalla lettera del Rev. Arciprete ... al
Professore Pullicino[128] sulla quadratura del cerchio. Milan, 1855 or
1856, 8vo.

Il Mediterraneo gazetta di Malta, 26 Decembre 1855, No. 909: also 911,
912, 913, 914, 936, 939.

The Malta Times, Tuesday, 9th June 1857.

Misura esatta del cerchio, dal Rev. D. Anghera. Malta, 1857, 12mo.

Quadrature of the circle ... by the Rev. D. Anghera, Archpriest of St.
Vito. Malta, 1858, 12mo.

I have looked for St. Vitus in catalogues of saints, but never found his legend, though he figures as a day-mark in the oldest almanacs. He must be properly accredited, since he was an archpriest. And I pronounce and ordain, by right accruing from the trouble I have taken in this subject, that he, St. Vitus, who leads his votaries a never-ending and unmeaning dance, shall henceforth be held and taken to be the patron saint of the circle-squarer. His day is the 15th of June, which is also that of St. Modestus,[129] with whom the said circle-squarer often has nothing to do. And he must not put himself under the first saint with a slantendicular reference to the other, as is much to be feared was done by the Cardinal who came to govern England with a title containing St. Pudentiana,[130] who shares a day with _St. Dunstan_. The Archpriest of St. Vitus will have it that the square inscribed in a semicircle is half of the semicircle, or the circumference 3-1/5 diameters. He is active and able, with {62} nothing wrong about him except his paradoxes. In the second tract named he has given the testimonials of crowned heads and ministers, etc. as follows. Louis-Napoleon gives thanks. The minister at Turin refers it to the Academy of Sciences, and hopes so much labor will be judged _degna di pregio_.[131] The Vice-Chancellor of Oxford--a blunt Englishman--begs to say that the University has never proposed the problem, as some affirm. The Prince Regent of Baden has received the work with lively interest. The Academy of Vienna is not in a position to enter into the question. The Academy of Turin offers the most _distinct_ thanks. The Academy della Crusca attends only to literature, but gives thanks. The Queen of Spain has received the work with the highest appreciation. The University of Salamanca gives infinite thanks, and feels true satisfaction in having the book. Lord Palmerston gives thanks, by the hand of "William San." The Viceroy of Egypt, not being yet up in Italian, will spend his first moments of leisure in studying the book, when it shall have been translated into French: in the mean time he congratulates the author upon his victory over a problem so long held insoluble. All this is seriously published as a rate in aid of demonstration. If these royal compliments cannot make the circumference of a circle about 2 per cent. larger than geometry will have it --which is all that is wanted--no wonder that thrones are shaky.

I am informed that the legend of St. Vitus is given by Ribadeneira[132] in his lives of Saints, and that Baronius,[133] in {63} his _Martyrologium Romanum_, refers to several authors who have written concerning him. There is an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_ (ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of _all_ dances; so that I was not so far wrong in making him the protector of the cyclometers. Why he is represented with a cock is a disputed point, which is now made clear: next after _gallus gallinaceus_[135] himself, there is no crower like the circle-squarer.

CELEBRATED APPROXIMATIONS OF [pi].

The following is an extract from the _English Cyclopaedia_, Art. TABLES: