Chapter VIII: Part 8

The feeling which tempts persons to this problem is that which, in romance, made it impossible for a knight to pass a castle which belonged to a giant or an enchanter. I once gave a lecture on the subject: a gentleman who was introduced to it by what I said remarked, loud enough to be heard by all around, "Only prove to me that it is impossible, and I will set about it this very evening."

This rinderpest of geometry cannot be cured, when once it has seated itself in the system: all that can be done is to apply what the learned call prophylactics to those who are yet sound. When once the virus gets into the brain, the victim goes round the flame like a moth; first one way and then the other, beginning where he ended, and ending where he begun: thus verifying the old line

"In girum imus nocte, ecce! et consumimur igni."[353]

Every mathematician knows that scores of methods, differing altogether from each other in process, all end in this mysterious 3.14159..., which insists on calling itself the circumference to a unit of diameter. A reader who is competent to follow processes of arithmetic may be easily satisfied that such methods do actually exist. I will give a sketch, carried out to a few figures, of three: the first two I never met with in my reading; the third is the old method of Vieta.[354] [I find that both the first and second methods are contained in a theorem of Euler.]

What Mr. James Smith says of these methods is worth noting. He says I have given three "_fancy_ proofs" of the value of [pi]: he evidently takes me to be offering demonstration. He proceeds thus:--

"His first proof is traceable to the diameter of a circle {211} of radius 1. His second, to the side of any inscribed equilateral triangle to a circle of radius 1. His third, to a radius of a circle of diameter 1. Now, it may be frankly admitted that we can arrive at the same result by many other modes of arithmetical calculation, all of which may be shown to have some sort of relation to a circle; but, after all, these results are mere exhibitions of the properties of numbers, and have no more to do with the ratio of diameter to circumference in a circle than the price of sugar with the mean height of spring tides. (_Corr._ Oct. 21, 1865)."

I quote this because it is one of the few cases--other than absolute assumption of the conclusion--in which Mr. Smith's conclusions would be true if his premise were true. Had I given what follows as _proof_, it would have been properly remarked, that I had only exhibited properties of numbers. But I took care to tell my reader that I was only going to show him _methods_ which end in 3.14159.... The proofs that these methods establish the value of [pi] are for those who will read and can understand.

200000000 31415 3799
66666667 2817
26666667 1363
11428571 661
5079365 321
2308802 156
1065601 76
497281 37
234014 18
110849 9
52785 5
25245 2
12118 1
5834
-------- -------- -------
314153799 31415 9265

{212}

1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on. The sum of all is the circumference of that diameter. The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure. Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

2. To the square root of 3 add its half. Take _half_ the third part of this; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum is the circumference to a unit of diameter.

Square root of 3.... 1.73205081
.86602540
------------
2.59807621
.43301270
.08660254
1855768
412393
93726
21629
5047
1188
281
67
16
4
1
------------
3.14159265

3. Take the square root of 1/2; the square root of half of one more than this; the square root of half of one more {213} than the last; and so on, until we come as near to unity as the number of figures chosen will permit. Multiply all the results together, and divide 2 by the product: the quotient is an approximation to the circumference when the diameter is unity. Taking aim at four figures, that is, working to five figures to secure accuracy in the fourth, we have .70712 for the square root of 1/2; .92390 for the square root of half one more than .70712; and so on, through .98080, .99520, .99880, .99970, .99992, .99998. The product of the eight results is .63667; divide 2 by this, and the quotient is 3.1413..., of which four figures are correct. Had the product been .636363... instead of .63667..., the famous result of Archimedes, 22-7ths, would have been accurately true. It is singular that no cyclometer maintains that Archimedes hit it exactly.

A literary journal could hardly admit as much as the preceding, if it stood alone. But in my present undertaking it passes as the halfpennyworth of bread to many gallons of sack. Many more methods might be given, all ending in the same result, let that result mean what it may.

Now since dozens of methods, to which dozens more might be added at pleasure, concur in giving one and the same result; and since these methods are declared by all who have shown knowledge of mathematics to be _demonstrated_: it is not asking too much of a person who has just a little knowledge of the first elements that he should learn more, and put his hand upon the error, before he intrudes his assertion of the existence of error upon those who have given more time and attention to it than himself, and who are in possession, over and above many demonstrations, of many consequences verifying each other, of which he can know nothing. This is all that is required. Let any one square the circle, and persuade his friends, if he and they please: let him print, and let all read who choose. But let him abstain from intruding himself upon those who have been satisfied by existing demonstration, until he is prepared {214} to lay his finger on the point in which existing demonstration is wrong. Let him also say what this mysterious 3.14159... really is, which comes in at every door and window, and down every chimney, calling itself the circumference to a unit of diameter. This most impudent and successful impostor holds false title-deeds in his hands, and invites examination: surely those who can find out the rightful owner are equally able to detect the forgery. All the quadrators are agreed that, be the right what it may, 3.14159... is wrong. It would be well if they would put their heads together, and say what this wrong result really means. The mathematicians of all ages have tried all manner of processes, with one object in view, and by methods which are admitted to yield demonstration in countless cases. They have all arrived at one result. A large number of opponents unite in declaring this result wrong, and all agree in two points: first, in differing among themselves; secondly, in declining to point out what that curious result really is which the mathematical methods all agree in giving.

Most of the quadrators are not aware that it has been fully demonstrated that no two numbers whatsoever can represent the ratio of the diameter to the circumference with perfect accuracy. When therefore we are told that either 8 to 25 or 64 to 201 is the true ratio, we know that it is no such thing, without the necessity of examination. The point that is left open, as not fully demonstrated to be impossible, is the _geometrical_ quadrature, the determination of the circumference by the straight line and circle, used as in Euclid. The general run of circle-squarers, hearing that the quadrature is not pronounced to be _demonstratively_ impossible, imagine that the _arithmetical_ quadrature is open to their ingenuity. Before attempting the arithmetical problem, they ought to acquire knowledge enough to read Lambert's[355] demonstration (last given in Brewster's[356] translation {215} of Legendre's[357] Geometry) and, if they can, to refute it. [It will be given in an Appendix.] Probably some have begun this way, and have caught a Tartar who has refused to let them go: I have never heard of any one who, in producing his own demonstration, has laid his finger on the faulty part of Lambert's investigation. This is the answer to those who think that the mathematicians treat the arithmetical squarers too lightly, and that as some person may succeed at last, all attempts should be examined. Those who have so thought, not knowing that there is demonstration on the point, will probably admit that a person who contradicts a theorem of which the demonstration has been acknowledged for a century by all who have alluded to it as read by themselves, may reasonably be required to point out the error before he demands attention to his own result.

_Apopempsis of the Tutelaries._--Again and again I am told that I spend too much time and trouble upon my two tutelaries: but when I come to my summing-up I shall make it appear that I have a purpose. Some say I am too hard upon them: but this is quite a mistake. Both of them beat little Oliver himself in the art and science of asking for more; but without Oliver's excuse, for I had given good allowance. Both began with me, not I with them: and both knew what they had to expect when they applied for a second helping.

On July 31, the Monday after the publication of my remarks on my 666 correspondent, I found _three_ notes in separate envelopes, addressed to me at "7A, University College." When I saw the three new digits I was taken rhythmopoetic, as follows--

Here's the Doctor again with his figs, and by Heavens!
He was always at sixes, and now he's at sevens.

To understand this fully the reader must know that the greater part of Apocalyptic interpretation has long been condensed, in my mind, into the Turkish street-cry--In the {216} name of the Prophet! figs! I make a few extracts. The reader will observe that Dr. Thorn grumbles at his _private_ letters being _publicly_ ridiculed. A man was summoned for a glutolactic assault; he complained of the publication of his proceeding: I kicked etc. _in confidence_, he said.

"After reading your last, which tries in every way to hold me up to public ridicule for daring to write you privately ['that you would be d----d,' omitted by accident] one would say, Why have anything to do with such a testy person? [Wrong word; no testy person can manage cool and consecutive ridicule. Quaere, what is this word? Is it anything but a corruption of the obsolete word _tetchy_ of the same meaning? Some think _touchy_ is our modern form of _tetchy_, which I greatly doubt]. My answer is, the poor man is lamentably ignorant; he is not only so, but 'out of the way' [quite true; my readers know me by this time for an out-of-the-way person. What other could tackle my squad of paradoxers? What other would undertake the job?] Can he be brought back and form one of those who in Ezekiel 37 ch. have the Spirit breathed into them and live.... Have I any other feeling towards you except that of peace and goodwill? [Not to your distinct knowledge; but in all those who send people to 'the other place' for contempt of their interpretations, there is a lurking wish which is father to the thought; 'you _will_ be d----d' and 'you _be_ d--d' are Siamese twins]. Of course your sneer at 666 brought plain words; but when men meddle with what they do not understand (not having the double _Vahu_) they must be dealt with faithfully by those who do.... [They must; which justifies the Budget of Paradoxes: but no occasion to send them anywhere; no preachee and floggee too, as the negro said]. Many will find the text Prov. i. 26 fully realized. [All this contains distinct assumption of a right 'of course' to declare accursed those who do not respect the writer's vagary].... If I could but get the [Hebrew: A], the Ox-head, which in Old Hebrew was just the Latin Digamma, F, out {217} of your name, and could then Thau you with the Thau of Ezekiel ix, 4, the [chi], then you would bear the number of a man! But this is too hard for me, although not so for the Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in so solemn a matter as the discussion of Holy Writ? [Is food for ridicule the right thing? Did I discuss Holy Writ? I did not: I concussed profane scribble. Even the Doctor did not _discuss_; he only enunciated and denunciated out of the mass of inferences which a mystical head has found premises for in the Bible]."

M 40
O 70
R 100
G 6
N 50
----
266
[Hebrew: t]=[chi] 400

[That ill opinions are near relations of ill wishes, will be detected by those who are on the look out. The following was taken down in a Scotch Church by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope into trouble; and we pray that thou wouldst be mercifully pleased to increase the same."]

Here is a martyr who quarrels with his crown; a missionary who reviles his persecutor: send him to New Zealand, and he would disagree with the Maoris who ate him. Man of unilateral reciprocity! have you, who write to a stranger with hints that that stranger and his wife are children of perdition, the bad taste to complain of a facer in return? As James Smith[359]--the Attorney-wit, not the Dock-cyclometer--said, or nearly said,

"A pretty thing, forsooth!
Is he to burn, all scalding hot,
Me and my wife, and am I not
To job him out a tooth?"

{218}

Those who think parody vulgar will be pleased to substitute for the above a quotation from Butler[360]:--

"There's nothing so absurd or vain
Or barbarous or inhumane,
But if it lay the least pretence
To piety and godliness,
Or tender-hearted conscience,
And zeal for gospel truths profess,--
Does sacred instantly commence,
And all that dare but question it are straight
Pronounced th' uncircumcised and reprobate,
As malefactors that escape and fly
Into a sanctuary for defence,
Must not be brought to justice thence,
Although their crimes be ne'er so great and high.
And he that dares presume to do't
Is sentenced and delivered up
To Satan that engaged him to't."

THE NUMBER OF THE BEAST.

Of all the drolleries of controversy none is more amusing than the manner in which those who provoke a combat expect to lay down the laws of retaliation. You must not strike this way! you must not parry that way! If you don't take care, we shall never meddle with you again! We were not _prepared_ for such as this! Why did we have anything to do with such a testy person? M. Jourdain must needs show Nicole, his servant-maid, how good a thing it was to be sure of fighting without being killed, by care and tierce.[361] "Et cela n'est il pas beau d'etre assure de son fait quand on se bat contre quelqu'un? La, pousse moi un peu, pour voir. NICOLE. Eh bien! quoi? M. JOURDAIN. Tout beau. Hola! {219} Ho! doucement. Diantre soit la coquine! NICOLE. Vous me dites de pousser. M. JOURDAIN. Oui; mais tu me pousses en tierce, avant que de pousser en quarte, et tu n'as pas la patience que je pare."

His colleague, my secular tutelary, who also made an anachronistic onset, with his repartees and his retorts, before there was anything to fire at, takes what I give by way of subsequent provocation with a good humor which would make a convert of me if he could afford .01659265 ... of a grain of logic. He instantly sent me his photograph for the asking, and another letter in proof. The Thor-hammerer does nothing but grumble, except when he tells a good story, which he says he had from Dr. Abernethy.[362] A Mr. James Dunlop was popping at the Papists with a 666-rifled gun, when Dr. Chalmers[363] quietly said, "Why, Dunlop, you bear it yourself," and handed him a paper on which the numerals in

I A C O B V S D V N L O P V S
1 100 5 500 5 50 5

were added up. This is almost as good as the _Filii Dei Vicarius_, the numerical letters of which also make 666. No more of these crazy--I first wrote _puerile_, but why should young cricketers be libelled?--attempts to extract religious use from numerical vagaries, and to make God over all a proposer of _salvation conundrums_: and no more of the trumpery hints about future destiny which is too great a compliment to call blasphemous. If the Doctor will cipher upon the letter in [Greek: en hoi metroi metreite metrethesetai humin][364] with _double Vahu_ cubic measure, he will perhaps learn to leave off trying to frighten me into gathering grapes from thorns.

Mystical hermeneutics may be put to good use by out-of-the-way people. They may be made to call the attention {220} of the many to a distinction well known among the learned. The books of the New Testament have been for 1,500 years divided into two classes: the _acknowledged_ ([Greek: homologoumena]), which it has always been paradox not to receive; and the _controverted_ ([Greek: antilegomena]), about which there has always been that difference of opinion which no scholar overlooks, however he may decide for himself after balance of evidence. Eusebius,[365] who first (l. 3, c. 25) recorded the distinction--which was much insisted on by the early Protestants--states the books which are questioned as doubtful, but which yet are approved and acknowledged by _many_--or _the many_, it is not easy to say which he means--to be the Epistles of James and Jude, the second of Peter and the second and third of John. In other places he speaks doubtingly of the Epistle to the Hebrews. The Apocalypse he does not even admit into this class, for he proceeds as follows--I use the second edition of the English folio translation (1709), to avert suspicion of bias from myself:--

"Among the _spurious_ [[Greek: nothoi]] let there be ranked both the work entitled the _Acts of Paul_, and the book called _Pastor_, and the _Revelation of Peter_: and moreover, that which is called the _Epistle of Barnabas_, and that named the _Doctrines of the Apostles_: and moreover, as I said, the _Revelation of John_ (if you think good), which some, as I have said, do reject, but others allow of, and admit among those books which are received as unquestionable and undoubted."

Eusebius, though he will not admit the Apocalypse even into the _controverted_ list, but gives permission to call it _spurious_, yet qualifies his permission in a manner which almost annihilates the distinctive force of [Greek: nothos], and gives the book a claim to rank (if you think good, again) in the controverted list. And this is the impression received by {221} the mind of Lardner, who gives Eusebius fully and fairly, but when he sums up, considers his author as admitting the Apocalypse into the second list. A stick may easily be found to beat the father of ecclesiastical history. There are whole faggots in writers as opposite as Baronius and Gibbon, who are perhaps his two most celebrated sons. But we can hardly imagine him totally misrepresenting the state of opinion of those for whom and among whom he wrote. The usual plan, that of making an author take the views of his readers, is more easy in his case than in that of any other writer: for, as the riddle says, he is You-see-by-us; and to this reading of his name he has often been subjected. Dr. Nathaniel Lardner,[366] who, though heterodox in doctrine, tries hard to be orthodox as to the Canon, is "sometimes apt to think" that the list should be collected and divided as in Eusebius. He would have no one of the controverted books to be allowed, by itself, to establish any doctrine. Even without going so far, a due use of early opinion and long continued discussion would perhaps prevent rational people from being induced by those who have the _double Vahu_ to place the Apocalypse _above_ the Gospels, which all the Bivahuites do in effect, and some are said to have done in express words. But my especial purpose is to point out that an easy way of getting rid of 665 out of 666 of the mystics is to require them to establish the Apocalypse before they begin. See if they even know so much as that there is a crowd of testimonies for and against, running through the first four centuries, which makes this book the most difficult of the whole Canon. Try this method, and you will escape beautiful, as the French say. Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an elaborate handling of this question. He concludes by saying that he cannot {222} venture to refuse his consent to the tradition that the Apostle is the author. This modified adherence, or non-nonadherence, pretty well represents the feeling of orthodox Protestants, when learning and common sense come together.

I have often, in former days, had the attempt made to place the Apocalypse on my neck as containing prophecies yet unfulfilled. The preceding method prevents success; and so does the following. It may almost be taken for granted that theological system-fighters do not read the New Testament: they hunt it for detached texts; they listen to it in church in that state of quiescent nonentity which is called reverent attention: but they never read it. When it is brought forward, you must pretend to find it necessary to turn to the book itself: you must read "The revelation ... to show unto his servants _things which must shortly come to pass_.... Blessed is he that readeth ... _for the time is at hand_." You must then ask your mystic whether things deferred for 1800 years were shortly to come to pass, etc.? You must tell him that the Greek [Greek: en tachei], rendered "shortly," is as strong a phrase as the language has to signify _soon_. The interpreter will probably look as if he had never read this opening: the chances are that he takes up the book to see whether you have been committing a fraud. He will then give you some exquisite evasion: I have heard it pleaded that the above was a _mere preamble_. This word _mere_ is all-sufficient: it turns anything into nothing. Perhaps he will say that the argument is that of the Papists: if so, tell him that there is no Christian sect but bears true witness against some one or more absurdities in other sects.

An anonyme suggests that [Greek: en tachei] may not be "soon," it may be "quickly, without reference to time when:" he continues thus, "May not time be 'at hand' when it is ready to come, no matter how long delayed?" I now understand what *** and *** meant when they borrowed my books and promised to return them quickly, it was "without {223} reference to time when." As to time at _hand_--provided you make a long _arm_--I admire the quirk, but cannot receive it: the word is [Greek: engus], which is a word of _closeness_ in time, in place, in reckoning, in kindred, etc.

Another gentleman is not surprised that Apocalyptic reading leads to a doubt of the "canonicity" of the book: it ought not to rest on church testimony, but on visible miracle. He offers me, or any reader of the _Athenaeum_, the "sight of a miracle to that effect, and within forty-eight hours' journey (fare paid)." I seldom travel, and my first thought was whether my carpet-bag would be found without a regular hunt: but, on reading further, I found that it was only a concordance that would be wanted. Forty hours' collection and numerical calculation of Greek nouns would make it--should I happen to agree with the writer--many hundred millions to one that Revelation xiii is superhuman. There is but one verse (the fifth) which the writer does not see verified. I looked at this verse, and was much startled. The Budget began in October 1863: should it last until March 1867--it is now August 1866--it is clear that I am the first Beast, and my paradoxers are the saints whom I persecute.

[The Budget _did_ terminate in March 1867: I hope the gentleman will be satisfied with the resulting interpretation.]

The same opponent is surprised that I should suppose a thing which "comes to pass" must be completed, and cannot contain what is to happen 1800 years after. All who have any knowledge of English idiom know that a thing _comes_ to pass when it happens, and _came_ to pass afterwards. But as the original is Greek, we must look at the Greek: it is [Greek: dei genesthai] for "must come to pass," and we know that [Greek: egeneto] is what is usually translated "came to pass." No word of more finished completion exists in Greek.

And now for a last round of biter-bit with the Thor-hammerer, of whom, as in the other case, I shall take no {224} more notice until he can contrive to surpass himself, which I doubt his being able to do. He informs me that by changing A into [Hebrew: t] in my name he can make a 666 of _me_; adding, "This is too hard for me, although not so for the Lord!" Sheer nonsense! He could just as easily have directed to "Prof. De Morg[Hebrew: t]n" as have assigned me apartment 7A in University College. It would have been seen for whom it was intended: and if not, it would still have reached me, for my colleagues have for many a year handed all out-of-the-way things over to me. There is no 7A: but 7 is the Museum of Materia Medica. I took the only hint which the address gave: I inquired for hellebore, but they told me it was not now recognized, that the old notion of its value was quite obsolete, and that they had nothing which was considered a specific in senary or septenary cases. The great platitude is the reference of such a difficulty as writing [Hebrew: t] for A to the Almighty! Not childish, but fatuous: real childishness is delightful. I knew an infant to whom, before he could speak plain, his parents had attempted to give notions of the Divine attributes: a wise plan, many think. His father had dandled him up-side-down, ending with, There now! Papa could not dance on his head! The mannikin made a solemn face, and said, _But Dod tood_! I think the Doctor has rather mistaken the way of becoming as a little child, intended in Matt. xviii. 3: let us hope the will may be taken for the deed.

Two poets have given images of transition from infancy to manhood: Dryden,--for the Hind is Dryden himself on all fours! and Wordsworth, in his own character of broad-nailed, featherless biped:

"The priest continues what the nurse began,
And thus the child imposes on the man."
"The child's the father of the man,
And I could wish my days to be
Bound each to each by natural piety."

{225}

In Wordsworth's aspiration it is meant that sense and piety should grow together: in Dryden's description a combination of Mysticism And Bigotry (can this be the _double Vahu_?), personified as "the priest,"--who always catches it on this score, though the same spirit is found in all associations,--succeeds the boguey-teaching of the nurse. Never was the contrast of smile and scowl, of light and darkness, better seen than in the two pictures. But an acrostic distinction may be drawn. When mysticism predominates over bigotry, we have the grotesque picturesque, and the natural order of words gives us _Mab_, an appropriate suggestion. But when bigotry has the upper hand, we see _Bam_, which is just as appropriate; for bigotry nearly always deals with facts and logic so as to require the application of at least one of the minor words by which dishonesty is signified. I think that M is the Doctor's initial, and that Queen Mab tickles him in his sleep with the sharp end of a 6.

(_Monday, August 21._) Three weeks having elapsed without notice from me of the Doctor, I receive a reminder of his existence, in which I find that as I am the Daniel who judges the Magi of Babylon, it is to be pointed out that Daniel "bore a certain number, that of a man (beloved), Daniel, ch. 10. v. 11, and which you certainly do not." Then, "by Greek power," Belteshazzar is made = 666. Here is another awkward imitation of the way of a baby child. When you have sported with the tiny creature until it runs away offended, by the time you have got into conversation again you will find the game is to be renewed: a little head peeps out from a hiding-place with "I don't love you." The proper rejoinder is, "Very well! then I'll have pussy." But in the case before me there is a rule of three sums to do; as baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I can.

The squaring of the circle and the discovery of the Beast are the two goals--and goals also--of many unbalanced intellects, and of a few instances of the better kind. {226} I might have said more of 666, but I am not deep in its bibliography. A work has come into my hands which contains a large number of noted cases: to some of my readers it will be a treat to see the collection; and the sight will perhaps be of some use to those who have read controversy on the few celebrated cases which are of general notoriety. It is written by a learned decipherer, a man who really knew the history of the subject, the Rev. David Thom,[368] of Bold Street Chapel, Liverpool, who died, I am told, a few years ago.

Anybody who reads his book will be inclined to parody a criticism which was once made on Paley's[369] Evidences--"Well! if there be anything in Christianity, this man is no fool." And, if he should chance to remember it, he will be strongly reminded of a sentence in my opening chapter,--"The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, _especially as to the mode of doing it_, a preliminary to inventing knowledge for himself." And this is reinforced by the fact that Mr. Thom, though a scholar, was not conspicuous for learning, except in this his great pursuit. He was a paradoxer on other points. He reconciled Calvinism and eternal reprobation with Universalism and final salvation; showing these two doctrines to be all one.

This gentleman must not be confounded with the Rev. John Hamilton Thom[370] (no relation), at or near the same {227} time and until recently, of Renshaw Street Chapel, Liverpool who was one of the minority in the Liverpool controversy when, nearly thirty years ago, _three_ heretical Unitarian schooners exchanged shotted sermons with _thirteen_ Orthodox ships of the line, and put up their challengers' dander--an American corruption of _d--d anger_--to such an extent, by quiet and respectful argument, that those opponents actually addressed a printed intercession to the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and Heretics." So much for the distinction, which both gentlemen would thank me for making very clear: I take it quite for granted that a guesser at 666 would feel horrified at being taken for a Unitarian, and that a Unitarian would feel queerified at being taken for a guesser at 666. Mr. David Thom's book is _The Number and Names of the Apocalyptic Beasts_, Part I, 1848, 8vo.: I think the second part was never published. I give the Greek and Latin solutions, omitting the Hebrew: as usual, all the Greek letters are numeral, but only M D C L X V I of the Latin. I do not give either the decipherers or their reasons: I have not room for this; nor would I, if I could, bias my reader for one rather than another.

D. F. Julianus Caesar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus; Silvester Secundus; Linus Secundus; {228} Vicarius Filii Dei; Doctor et Rex Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse Catholicae Ecclesiae Visibile Caput; Dux Cleri; Una, Vera, Catholica, Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina will also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres; Dic Lux ; Ludvvic; Will. Laud; [Greek: Lateinos];[372] [Greek: he latine basileia]; [Greek: ekklesia italika]; [Greek: euanthas]; [Greek: teitan]; [Greek: arnoume]; [Greek: lampetis]; [Greek: ho niketes]; [Greek: kakos hodegos]; [Greek: alethes blaberos]; [Greek: palai baskanos]; [Greek: amnos adikos]; [Greek: antemos]; [Greek: genserikos]; [Greek: euinas]; [Greek: Benediktos]; [Greek: Bonibazios g. papa x. e. e. e. a.], meaning Boniface III. Pope 68th, bishop of bishops the first! [Greek: oulpios]; [Greek: dios eimi he heras]; [Greek: he missa he papike]; [Greek: loutherana]; [Greek: saxoneios]; [Greek: Bezza antitheos] (Beza); [Greek: he alazoneia biou]; [Greek: Maometis]; [Greek: Maometes b.]; [Greek: theos eimi epi gaies]; [Greek: iapetos]; [Greek: papeiskos]; [Greek: dioklasianos]; [Greek: cheina]; [Greek: braski]; [Greek: Ion Paune]; [Greek: koupoks]; (cowpox, [Greek: s] being the _vau_; certainly the {229} vaccinated have the mark of the Beast); [Greek: Bonneparte]; [Greek: N. Boneparte]; [Greek: euporia]; [Greek: paradosis]; [Greek: to megatherion].

All sects fasten this number on their opponents. It is found in _Martin Lauter_, affirmed to be the true way of writing the name, by carrying numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn, found it in [Hebrew: JSHW NTSRJ] _Jesus of Nazareth_. I find on inquiry that this satire was actually put forth by some medieval rabbis, but that it is not idiomatic: it represents quite fairly "Jesus Nazarene," but the Hebrew wants an article quite as much as the English wants "the."

Mr. David Thom's own solution hits hard at all sides: he finds a 666 for both beasts; [Greek: he phren] (the mind) for the first, and [Greek: ekklesiai sarkikai] (fleshly churches) for the second. A solution which embodies all mental philosophy in one beast and all dogmatic theology in the other, is very tempting: for in these are the two great supports of Antichrist. It will not, however, mislead me, who have known the true explanation a long time. The three sixes indicate that any two of the three subdivisions, Roman, Greek, and Protestant, are, in corruption of Christianity, six of one and half a dozen of the other: the distinctions of units, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and Concordance at _ten_, _hundred_, _thousand_) of symbolizing differences of number in the subdivisions.

It may be good to know that, even in speculations on 666, there are different degrees of unreason. All the diviners, when they get a colleague or an opponent, at once proceed to reckon him up: but some do it in play and some in earnest. Mr. David Thom found a young gentleman of the name St. Claire busy at the Beast number: he forthwith added the letters in [Greek: st klaire] and found 666: this was good fun. But my spiritual tutelary, when he found that he could not make a beast of me, except by changing [Hebrew: A] into [Hebrew: T], solemnly referred the difficulty to the Almighty: this was poor earnest. {230}

I am glad I did not notice, in time to insert it in the _Athenaeum_, a very remarkable paradoxer brought forward by Mr. Thom, his friend Mr. Wapshare[373]: it is a little too strong for the general public. In the _Athenaeum_ they would have seen and read it: but this book will be avoided by the weaker brethren. It is as follows:

"God, the Elohim, was six days in creating all things, and having made MAN he entered into his rest. He is no more seen as a Creator, as Elohim, but as Jehovah, the _Lord_ of the Sabbath, and the Spirit of life in MAN, which Spirit worketh _sin in the flesh_; for the Spirit of Love, in all flesh, is Lust, or the spirit of a beast, So Rom. vii. And which Spirit is _crucified_ in the flesh. He then, as Jehovah--as the power of the Law, _in_ and _over_ all flesh, John viii. 44--increases that which he has made as the Elohim, and his power shall last for 6 days, or 6 periods of time, computed at a millennium of years; and at the end of which six days, he who is the Spirit of all flesh shall manifest himself as the Holy Spirit of Almighty Love, and of all truth; and so shall the Church have her Sabbath of Rest--all contention being at an end. This is, as well as I may now express it, my solution of the mystery in Hebrew, and in Greek, and also in Latin, IHS. For he that was lifted up _is_ King of the Jews, and is the Lord of all Life, working in us, both to will and to do; as is manifest in the Jews--they slaying him that his blood might be _good_ for the healing of the nations, of all people and tongues. As the Father of all _natural_ flesh, he is the Spirit of Lust, as in all _beasts_; as the Father, or King of the Jews, he is the Devil, as he himself witnesseth in John viii., already referred to. As lifted up, he is transformed into the Spirit of Love, a light to the Gentiles, and the glory of his people Israel.... For there is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was Satan, the Spirit of life in that body, is, in {231} Christ crucified, seen in the Spirit that is in all, and through all and over all, God blessed for ever."

All this seems well meant, and Mr. Thom prints it as convinced of its piety, and "pronounces no opinion." Mystics of all sorts! see what you may come to, or what may come to you! I have inserted the above for your good.

There is nothing in this world so steady as some of the paradoxers. They are like the spiders who go on spinning after they have web enough to catch all the flies in the neighborhood, if the flies would but come. They are like the wild bees who go on making honey which they never can eat, proving _sic vos non vobis_ to be a physical necessity of their own contriving. But nobody robs their hives: no, unlike the bees, they go about offering their ware to any who will take it as a gift. I had just written the last sentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received this morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out of the above account of the Rev. D. Thom, published Oct. 27: three notes had arrived before.

For curiosity I give one day's allowance, supposing these to be all: more may arrive before night.

29th Oct. 1866.

"Dear Sir,--

In re [swastika].[374]

"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern Tau' [Greek: Phaneroo]--To make manifest, shew, or explain; and this may satisfy the House of Joseph in Amos 5^c. While Belteshazzar = 666 may be also satisfactory to the House of David, and so we may have Zech. 10^c. 6^v. in operation when Ezekiel 37^c. 16^v. has been realised;--but there, what is the use of writing, it is all Coptic {232} to a man who has not [swastika], The Thau of the North, the double Vahu [Hebrew: W\qamats\W]. Look at Jeremiah 3^c. 8^v. and then to Psalm 83 for 'hidden ones' [Hebrew: TS\sheva\PW\dagesh\N\segol\Y Y\sheva\HW\qamats\H]--The Zephoni Jehovah, and say whether they have any connection with the Zephon _Thau_. The Hammer of Thor of Jeremiah 23^c. 29^v. as I gave you in No. 3 of my present edition.

Yours truly

LE CHEVALIER AU CIN."

_By Greek Power._

C = 20
H = 8
E = 5
V = 6
A = 1
L = 30
I = 10
E = 5
R = 100

A = 1
U = 400

C = 20
I = 10
N = 50
----
666

There will be thousands of Morgans who will be among the wise and prudent of Hosea 14^c. 9^v. when the Seventh Angel sounds, let me number _that One_ by Greek, Rev. 17^c. 1^v: {233}

S = 200
E = 5
x V = 6
E = 5
N = 50
T = 300
H = 8

A = 1
N = 50
x G = 6
E = 5
L = 30
----
666

V and G = 12 ought to be equal to one Gammadion or ^3[swastika]3 x 4 =
12, what say you?

London, October 29, 1866.

"Dear Sir,--

In re [swastika] versus [maltese cross].

However pretentious the X or [maltese cross] may be, and it is peculiarly so just now in this land; after all it is only made of two Roman V's--and so is only = [ one inverted](10)--and therefore is not the perfect number 12 of Revel^n, but is the mark of the goddess _Decima_!

Yours truly

WM. THORN."

Had the _one_ who sent forth a pastoral (Romish) the other day, remained amongst the faithful expectants, see how he would have numbered, whereas he sold himself for the privilege of signing

[maltese cross] HENRY E. MANNING.[375]

{234}

_By English Key._

H = 8
E = 5
N = 40
R = 80
Y = 140

E = 5
D = 4
W = 120
A = 1
R = 80
D = 4

M = 30
A = 1
N = 40
N = 40
I = 9
N = 40
G = 7
[swastika] = 12
----
666

Can you now understand the difference between [swastika] and [maltese
cross] or X? Look to my challenge.

Cutting from newspaper:--

ITALY.

Rome (_via_ Marseilles), October

Mr. Gladstone has paid a visit to the Pope.

_By Greek Power._

G = 6
L = 30
A = 1
D = 4
S = 200
T = 300
O = 70
N = 50
E = 5
----
666

And what then [swastika]?

{235}

In other letters _John Stuart Mill_ is 666 if the _a_ be left out; _Chasuble_ is perfect. _John Brighte_[376] is a _fait accompli_; and I am asked whether intellect can account for the final e. Very easily: this Beast is not the M. P., but another person who spells his name differently. But if John Sturt Mill and John Brighte choose so to write themselves, they may.

A curious collection; a mystical phantasmagoria! There are those who will try to find meaning: there are those who will try to find purpose.

"And some they said--What are you at?
And some--What are you arter?"

My account of Mr. Thom and his 666 appeared on October 27: and on the 29th I received from the editor a copy of Mr. Thom's sermons published in 1863 (he died Feb. 27, 1862) with best wishes for my health and happiness. The editor does not name himself in the book; but he signed his name in my copy: and may my circumference never be more than 3-1/8 of my diameter if the signature, name and writing both, were not that of my [circle square] ing friend Mr. James Smith! And so I have come in contact with him on 666 as well as on [pi]! I should have nothing left to live for, had I not happened to hear that he has a perpetual motion on hand. I returned thanks and kind regards: and Miss Miggs's words--"Here's forgivenesses of injuries! here's amicablenesses!"--rang in my ears. But I was made slightly uncomfortable: how could the war go on after this armistice? Could I ever make it understood that the truce only extended to the double Vahu and things thereunto relating? It was once held by seafaring men that there was no peace with Spaniards beyond the line: I was determined that there must be no concord with J. S. inside the circle; that this must be a special exception, like Father Huddleston {236} and old Grouse in the gun-room. I was not long in anxiety; twenty-four hours after the book of sermons there came a copy of the threatened exposure--_The British Association in Jeopardy, and Professor De Morgan in the Pillory without hope of escape_. By James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This exposure consists of reprints from the _Athenaeum_ and _Correspondent_: of things new there is but one. In a short preface Mr. J. S. particularly recommends to "_read to the end_." At the end is an appendix of two pages, in type as large as the work; a very prominent peroration. It is an article from the _Athenaeum_, left out of its place. In the last sentence Mr. J. Smith, who had asked whether his character as an honest Geometer and Mathematician was not at stake, is warned against the _fallacia plurium interrogationum_.[377] He is told that there is not a more honest what's-his-name in the world: but that as to the counter which he calls his character as a mathematician, he is assured that it has been staked years ago, and lost. And thus truth has the last word. There is no occasion to say much about reprints. One of them is a letter [that given above] of August 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of his quadratures; and the joke is that I am made to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to write in the _Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted! double commas, first person--I felt as I suppose did Wm. Wilberforce[378] when he set eyes on the affectionate benediction of the potato which waggish comrades had imposed on a raw Irish reporter as part of his speech. I felt as Martin[379] of {237} Galway--kind friend of the poor dumb creatures!--when he was told that the newspapers had put him in Italics. "I appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics? Do I ever speak in Italics?" I appeal to editor and readers, whether I ever squared the circle until a week or two ago, when I gave my charitable mode of reconciling the discrepant cyclometers.

The absurdity of the imitation of symbolic reasoning is so lusciously rich, that I shall insert it when I make up my final book. Somebody mastered Spanish merely to read Don Quixote: it would be worth while to learn a little algebra merely to enjoy this a b-istical attack on the windmills. The principle is, Prove something in as roundabout a way as possible, mention the circle once or twice irrelevantly in the course of your proof, and then make an act of Q. E. D. in words at length. The following is hardly caricature:--

To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of the House: let d = 666, the number of the Beast. Then of necessity d = a + b + c + 1; so that 1 is a harmonious and logical quantification of the number of which we are to take care. Now, b, the middle of our digital system, is, by mathematical and geometrical combination, a mean between 5 + 1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real mathematician can refuse without serious injury to his mathematical and geometrical reputation. It follows of necessity that 2 + 2 = 5, _quod erat demonstrumhorrendum_. If Simpkin & Marshall have not, after my notice, to account for a gross of copies more than would have gone off without me, the world is not worthy of its James Smith!

The only fault of the above is, that there is more {238} connection than in the process of Faber Cyclometricus: so much, in fact, that the blunders are visible. The utter irrelevance of premises to conclusion cannot be exhibited with the requisite obscurity by any one who is able to follow reasoning: it is high art displayed in a certain toning down of the _aegri somnia_, which brings them to a certain look of reproach to reasoning which I can only burlesque. Mr. J. S. produces something which resembles argument much as a chimpanzee in dolor, because balked of his dinner, resembles a thinking man at his studies. My humble attempt at imitation of him is more like a monkey hanging by his tail from a tree and trying to crack a cocoa-nut by his chatter.

I could forgive Mr. J. S. anything, properly headed. I would allow him to prove--_for himself_--that the Quadrature of the Circle is the child of a private marriage between the Bull Unigenitus and the Pragmatic Sanction, claiming tithe of onions for repeal of the Mortmain Act, before the Bishops in Committee under the kitchen table: his mode of imitating reason would do this with ease. But when he puts his imitation into my mouth, to make me what _he_ calls a "real mathematician," my soul rises in epigram against him. I say with the doll's dressmaker--such a job makes me feel like a puppet's tailor myself--"He ought to have a little pepper? just a few grains? I think the young man's tricks and manners make a claim upon his friends for a little pepper?" De Faure[380] and Joseph Scaliger[381] come into my head: my reader may look back for them.

"Three circlesquarers to the manner born,
Switzerland, France, and England did adorn,
De Faure in equations did surpass,
Joseph at contradictions was an ass.
Groaned Folly, I'm used up! What shall I do
To make James Smith? Grinned Momus, _Join the two_!"

{239}

As to my _locus poenitentiae_,[382] the reader who is fit to enjoy the letter I have already alluded to will see that I have a soft and easy position; that the thing is really a _pillowry_; and that I am, like Perrette's pot of milk,

"Bien pose sur un coussinet."[383]

Joanna Southcott[384] never had a follower who believed in her with more humble piety than Mr. James Smith believes in himself. After all that has happened to him, he asks me with high confidence to "favor the writer with a proof" that I still continue of opinion that "the best of the argument is in my jokes, and the best of the joke is in his arguments." I will not so favor him. At the very outset I told him in plain English that he has the whiphand of all the reasoners in the world, and in plain French that _il a perdu le droit d'etre frappe de l'evidence_[385]; I might have said _pendu_.[386] To which I now add, in plain Latin, _Sapienti pauca, indocto nihil_.[387] The law of Chancery says that he who will have equity must do equity: the law of reasoning says that he who will have proof must see proof.

The introduction of things quite irrelevant, by way of reproach, is an argument in universal request: and it often happens that the argument so produced really tells against the producer. So common is it that we forget how boyish it is; but we are strikingly reminded when it actually comes from a boy. In a certain police court, certain small boys were arraigned for conspiring to hoot an obnoxious individual on his way from one of their school exhibitions. This proceeding was necessary, because there seemed to be a permanent conspiracy to annoy the gentleman; and the {240} masters did not feel able to interfere in what took place outside the school. So the boys were arraigned; and their friends, as silly in their way as themselves, allowed one of them to make the defence, instead of employing counsel; and did not even give them any useful hints. The defence was as follows; and any one who does not see how richly it sets off the defences of bigger boys in bigger matters has much to learn. The innocent conviction that there was answer in the latter part is delightful. Of course fine and recognizance followed.