246 



♦ KNO^A/'LEDGE 



[September 1, 1888. 



So seems this gorgeous beauty to mine eyes. 

 Fain would I woo her, but I dare not speak. 



She's beautiful, and therefore to be woo'd ; 

 She is a woman, therefore to be won. 



But no one can imagine that Shakespeare wrote the lines ; — 



SUF. I'll win this Lady Margaret ! For whom? 



Why, for my king ! Tush ! he's a wooden thing. 

 Makg. He talks of wood. It is some carpenter. 



Many parts of this scene, as indeed of others in the play, 

 read like actors' gag, showing rather what was thought 

 likely to jjlease the groundlings than what any of the 

 dramatists of the company could have deliberately written. 



MR. DONNELLY'S CIPHERING. 



3-5 thecalculation of chance.^ seemsto be bewilder- 

 ing to many, and specially imposing when it 

 runs into large numbers, I deem it desirable 

 to caution the non-mathematical community 

 against Mr. Donnelly's truly bewildering 

 and in a twofold sense imposing statements 

 in regard to the evidence of the " law of 

 chances " in favour of his cryptogram. He evidently under- 

 stands the doctrine of chances as little as he understands 

 the cipher Bacon really invented — or rather, as little as he 

 understood that cipher before the Pall Mall Gazette 

 explained to him its working in the capital article, " A 

 Mammoth Mare's Nest." I suppose he understands that 

 system now, though, strangely enough, in his " case for " his 

 " Cryptogram " he nowhere thinks it necessary to explain 

 how he came so thoroughly to miss the sense of Bacon's 

 clear explanation of the five-letter cipher. (In passing I 

 may note a point which the author of " A Mammoth Mare's 

 Nest " omitted to mention, viz., that the passages used by 

 Bacon in illustration of his cipher were originally, like the 

 body of the work, in Latin, so that Mr. Donnelly's ingenious 

 idea of " capitalising " ALL and IS in a passage which 

 chances to contain these words out of the sentence " All is 

 lost," is seen to be singularly ludicrous — the Latin being 

 Perditm res, and no such word as perditce appearing in the 

 passage quoted by Bacon from Cicero — Uijo omni officio ac 

 potius pietate errja te, &c. 



Mr. Donnelly olfers to reveal to the editor of the Pall 

 Mall Gazetlr, in confidence, his fundamental cipher-number, 

 if it be acknowledged that the thousands of words in his 

 story cannot have come out by accident. He illustrates 

 what he takes to be the nature of the chances as follows : — 

 If the number were 740, " there are 739 chances to 1 that the 

 cipher word needed will be the 7J:0th ; if, now, the first six 

 words of the Lord's Prayer are fovmd, each of them standing 

 as the 740th word, one after the other, in a composition, 

 there is but one chance against 232,065,922,400,000, or one 

 chance against 232 trilliojis " (our more sensible English 

 system of numeration would say billions) " that this could 

 happen by accident." And he goes on to speak of the prac- 

 tically infinite chances against the whole of the Lord's 

 Prayer being found in the same systematic manner. 



There is not the least semblance of correctness in any of 

 the statements made in regard to this illustrative case ; 

 though I am bound to admit that if there had been, if even 

 every word of the argument were sound, the case would not 

 be in the slightest degree illustrative of INIr. Donnelly's 

 work, so that his position will not be at all weakened (it 

 could not possibly be weaker than it is) by my sliowing that 

 his chance argument is all (in the Baconian cipher) 

 Chro/i onhot ontho loyos ! as the " Mammoth Mare's Nest " 



article justly says of the whole cryptogram — a mystic word 

 which, being interpreted, signifies Bosh ! 



The chance that any particular word will be the 740th 

 (counted from any assigned place) is no more to be regarded 

 as 1 in 740 than as 1 in 10, or 20, or 1,000. Counting any 

 number of words brings us to some word, whether we count 

 10, or 20, or 740, or 1,000; and the chance that that word 

 will be some particular word, named beforehand, is not 

 aflfected by the number of words we count : it is simply the 

 chance that a word taken at random will be that particular 

 word. This chance depends on the nature of the word 

 itself We are more likely to be led by our count to such 

 a word as a, the, ami, is, it, or to than to such a word as 

 cryptogram or impecuniosity, because in any composition 

 simple words occur oftener than complex ones. To put a 

 fixed and definite chance down for each of the words Our, 

 Father, xkIio, art, in, and Heaven indicates complete mis- 

 apprehension of the doctrine of probabilities — even of its 

 merest elements. 



One can see what Mr. Donnelly tried to do, fondly 

 imagining he was applying the law of chances. Having 

 six words, he sets the chance of these occui-ring at 1, or 

 certainty, for the first word (since some word miisl be 

 reached to start with), and at j\^ for each of the other 

 five. Thus the chance for the six is 1 in 740 raised to the 

 fifth power, or 740 x 740 x 740 x 740 x 740. He has gone 

 wrong in his ciphering — naturally — for the fifth power of 

 740 is 221,900,602,400,000, not 232,06.^,922,400,000; but 

 this is fair work for Mr. Donnelly, and much nairer than he 

 gets in working out his own cipher system. 



Mr. Donnelly shows later his utter misapprehension of 

 the law of chances by inviting us to apply that law to 

 determine how many quintillions there are against one 

 that the coherent words (!) " with his quick wit and his big 

 belly " would come out by accident from his free-and-easy 

 system of counting. The law of chances has no bearing on 

 such a question. One might as reasonably ask that the law 

 of chances should be applied to determine how many quin- 

 tillions to one there are against the adoption by Bacon of an 

 imbecile cipher-system to hide under a rubbish. heap what 

 we are told he was painfully anxious to disclose ; or to find 

 the odds against Bacon's writing in bad Victorian English 

 the feeble and scurrilous twaddle attribttted to him in " The 

 Great Cryptogram " ; or to determine the chances that 

 Bacon, or even Shakespeare himself, hampered in his 

 writing by the multitudinous conditions imagined by Mr. 

 Donnelly, could produce a noble play; or lastly, to indicate 

 the probability of that man detecting a recondite though 

 semi-idiotic cipher-system who had failed to understand the 

 simple and sensible sj'stem really invented (and clearly 

 explained) by Bacon himself. 



The real problem in chances involved in Mr. Donnelly's 

 work has been, throughout, simply the following : — 



When, at any stage of his progress, Mr. Donnelly has 

 needed a particular word, what has been the chance that, 

 with the varied ways in ichich he permits hims'lf to count, 

 he tcill reach that loord, making his count apparently corre- 

 spond ivith one of those ways (modi^fied by one or other of 

 his various methods) ? This chance cannot be determined 

 mathematically, but from such study as men of sense can 

 aflbrd to devote to Mr. Donnelly's work, it is obvious that 

 the chance is at least ten thousand to one. 



Per contra, here is another question in chances not mathe- 

 matically determinable : — 



Granted that, as more than one critic has pointed out, 

 " any one can construct any kind of narrative " out of any 

 volume whatsoever, after Mr. Donnelly's fashion, what is 

 the chance that any one else will do it 1 " It will be 

 observed," says Mr. Donnelly in italics, " that no one has 



