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 ; 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 circ.u.mference 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 ; .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. .h.i.t it exactly.

A literary journal could hardly admit as much as the preceding, if it stood alone. But in my present undertaking it pa.s.ses 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 a.s.sertion 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 circ.u.mference to a unit of diameter. This most impudent and successful impostor holds false t.i.tle-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 circ.u.mference 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 circ.u.mference by the straight line and circle, used as in Euclid. The general run of circle-squarers, hearing that the quadrature is not p.r.o.nounced 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 a.s.sault; 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 a.s.sumption 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. x.x.xii. 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 ma.s.s 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 subst.i.tute 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 G.o.dliness, Or tender-hearted conscience, And zeal for gospel truths profess,-- Does sacred instantly commence, And all that dare but question it are straight p.r.o.nounced th' uncirc.u.mcised 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 a.s.sure 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 G.o.d 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 cla.s.ses: the _acknowledged_ ([Greek: h.o.m.ologoumena]), 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 cla.s.s, 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 ent.i.tled 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 f.a.ggots 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 nonent.i.ty 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 pa.s.s_.... 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 pa.s.s, 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 pa.s.s" 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 pa.s.s when it happens, and _came_ to pa.s.s afterwards. But as the original is Greek, we must look at the Greek: it is [Greek: dei genesthai]

for "must come to pa.s.s," and we know that [Greek: egeneto] is what is usually translated "came to pa.s.s." 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 surpa.s.s 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 a.s.signed 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 h.e.l.lebore, 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 plat.i.tude 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 a.s.sociations,--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 p.u.s.s.y." But in the case before me there is a rule of three sums to do; as baby : p.u.s.s.y 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.