182 



NOTES AND QUEEIES. 



[Sept. 8. 1855. 



siderable resemblance to another ; still more one 

 set of ten thousand to another set ; and so on. 



The manner in which I imagine that the truth 

 of asserted authorship might probably be tested, 

 and which I am confident will one day be carried 

 into practice, will bear, and perhaps require, a 

 few preliminary illustrations for those who are not 

 accustomed to "that elaborate delusion" — the 

 theory of probabilities. 



According to the predictions of this delusion, 

 if a halfpenny be tossed until head arrives, which 

 may happen at the first toss, or may be deferred 

 until the hundredth — and if a large number of 

 trials be made, each trial consisting of tosses re- 

 peated until head arrives — the result will be as 

 follows. About one half of the trials will end at 

 the first toss ; about one- fourth at the second ; 

 about one-eighth at the third ; and so on. 



Buffon made 2048 trials, and registered the 

 results. A pupil of mine repeated the experi- 

 ment ; and I put the two side by side in my 

 Formal Logic. Since that publication, two gen- 

 tlemen have tried it again, and have communi- 

 cated with me. I now publish the four results 

 in the columns B, H, P, A ; the first column being 

 the prediction made by the delusion : 



Any one of the lines, say 9, may be explained 

 as follows : — Out of 2048 trials, the most probable 

 prediction is that, in four of them, head shall not 

 appear till the ninth toss. BufFon found six, H. 

 found Jive, P. and A. both found three. Of the 

 44 cases in the first eleven lines, 5 are according 

 to prediction, 17 below, and 22 above. 



The tendency towards agreement which is so 

 perceptible in the preceding lines, is distinctly seen 

 in the phenomena of the physical and even of the 

 moral order of things. Even in such a case as the 

 tendency to commit murder, a nation shows that 

 its circumstances produce a tolerably steady aver- 

 age from year to year. The numbers of murders 

 brought to justice in France in the six vears 



No. 306.] 



1826-31 were 241, 234, 227, 231, 207, 266; the 

 year following an armed revolution showing a 

 perceptible increase. Of these the largest sepa- 

 rate lots were perpetrated with knives and with 

 fire-arms. For each 10 murders committed with 

 knives there were, roughly, committed with fire- 

 arms, 14, 16, 18, 13, 13, 26, in the six years ; the 

 effect of the revolution being again very distinctly 

 marked. 



When the habits of a single individual are in 

 question, and in a matter which can be submitted 

 to tens of thousands of trials, it will certainly be 

 found that very slight differences of average are 

 sufl5cient to mark the difference between different 

 individuals. And of all easy tests, perhaps the 

 easiest is the average number of letters in his word. 

 There is no doubt that some writers have a natural 

 preference for longer words than others. If the 

 law which has never failed elsewhere should hold 

 true here, we are to expect that if, upon one ten 

 thousand of consecutive words taken from each 

 author, Johnson should show, one word with 

 another, a quarter of a letter per word more than 

 Addison, the same result, or one very near it, 

 would occur in another ten thousand taken from 

 each writer. A writing attributed, but falsely, 

 to an author, might possibly be detected by its 

 average word exhibiting such a difference from 

 that of the indubitable writings, as never appears 

 between those undoubted writings themselves. 



I should expect that experiment would establish 

 the following results : — 1. That the difference be- 

 tween the average word of any one writer and 

 any other, in the same language, is but a fraction, 

 perhaps rather a small fraction, of a letter. 2. That 

 this small fraction of difference would be well esta- 

 blished, between any two given writers, by re- 

 peated comparisons of large masses of their words. 

 3. That the difference established by comparing 

 the same writer at different ages, or on two differ- 

 ent subjects, would be trifling compared with that 

 existing between different writers : provided al- 

 ways that the two subjects did not differ by one 

 of them requiring very large importations of tech- 

 nical or foreign words, as compared with the other. 

 It must be observed, that no amount of agree- 

 ment would absolutely establish sameness of au- 

 thorship, though it might lend an additional pre- 

 sumption in disputed cases. For different writers 

 may be of very nearly the same average. But, if 

 my conjectures be correct, a sufficient want of 

 agreement might wholly upset the supposition of 

 common authorship, by showing a difierence such 

 as is never found between two undisputed writings 

 of the same author. 



An experiment on a sufficient scale would in- 

 volve some trouble and expense : but that, as 

 faith in the law of averages increases, such an ex- 

 periment will be made, I feel very certain. 



A. De Morgan. 



