186 



♦ KNOWLEDGE ♦ 



[June 1, 1888. 



The method of calculation is simple. If the first of the 

 above questions is raised, and A be the player whose chance 

 is to be considered, then the chance that he wins the first 

 game is -i, and the chance that he wins the second con- 

 sidered afone is a'so ^ ; but as ho only has ^ a chance of 

 entering on this second game as a winner of the first, Lis 

 chance of winning both games is only ^ of i, or ^. So his 

 chance of winning the third game is ^ ; but his clianoe of 

 winning it as already a winner of the first two is only 5 of 

 i), or \. Proceeding in this way, we find A's chance of 

 winning the first fours game J of ^, or j'^y ; of winning the 

 first five, -jV of h, or ^V; of winning the first six, ~|'j of ^, 

 or ^'4- ; first seven, ywj ; first eight, -^^ij^; and, finally, A's 

 chance of winning the first nine games is t|^, or the odds 

 are 511 to 1 against that event. 



* * * 



The second question only differs in asking the odds 

 against A or B (one of whom must win the first game) 

 winning the remaining eight. The chance, as already shown, 

 is j! ij ; the odds, therefore, are 255 to 1. 



Tf a number of games are played, it is easy to see that 

 the chances against the event in question are not so heavy. 

 Suppose, for instance, fifty games are played. Then the 

 run of nine games has a chance of occurring with the first 

 nine, i.e. beginning with the first game, or with the second, 

 or third, and so on up to the forty-second game. 



The particular case mentioned by my correspondent — the 

 occurrence, namely, of nine events of the same kind in 

 succession, where the chances are even at each trial — might 

 be suppo.sed to have occurred when O.-cford beat Cambridge 

 in the 'Varsity boat race from 18G1 to 18G9 inclusive. But 

 the probability is that there was a definite superiority in the 

 Oxford style in those days. And it is to be noticed that 

 when the chance is sm.all for an observed event, assuming 

 the conditions equal, the occurrence of the event leads to a 

 presumption that the conditions are not strictly equal, this 

 presumption increasing in weight as the preponderance of 

 events of one particular kind over events supposed originally 

 to be of equal likelihood grows greater. 



* * * 



The Sidereal Messemjer is not content with the progress 

 of events described in Knowledge for April last under 

 " Gossip," pp. 1.38, 139. I considered the editor of that use- 

 fully compiled little magazine had no right to drag from the 

 columns of the San Francisco Kxaminer (a paper well 

 known for a certain C'alifornian vulgarity) a controversy 

 which began with the unprovoked publication of rude, men- 

 dacious things said of me by Mr. Holden in an " interview." 

 If he did drag these improprieties into a magazine otherwise 

 respectable, though dull, he might at least have put in my 

 own reply to the stream of falsehoods which had trickled 

 from Mr. Ilolden's pen. instead of introducing that stream 

 undiluted by truth. He thus left me no choice but to write 

 a new reply. (I could not at the moment find the only 

 copy I had of the Examiner correspondence, and if I had I 

 should not — for reasons — have been very willing to trust 

 it out of my hands exce))t where I knew very certainly that 

 I should see it again.) !My brief reply to the Sidereal Mes- 

 senger did not explain, as my full reply to the Examiner 

 had done, that the w.ay in which I had saved Holden's 

 name from rejection had been simply by silence. The fact 

 is, as I said last April, it did not seem ahsoluteli/ necessary 

 to explain in one and the same letter that I i-egarded a per- 

 son as utterly unworthy of a certain distinction, and that I 

 had not actively supported his name for that distinction. 



It did not seem to me possible that any man having a 

 modicum of sense combined with some idea of the ways of 

 men of honour would misunderstand so pre);osterously my 

 remark, that the name of one whom I had described as 

 unworthy would have been rejected with contempt had I 

 not spared him. 



* * * 



The fact is, I had been so careful in avoiding any men- 

 tion of the fellow's wrong-doing, from the day when I found 

 out that it was no mere penny-a-liner who had behaved so 

 badly, but one who mixed with such men as Newcomb, 

 Harkness, Hall, Eastman, and others whom I esteem, that 

 I hold myself entitled to some consideration on account of 

 this silence alone. Among those who read these lines 

 there will probably be some of my friends who were on the 

 Council of the Astronomical Society when the election in 

 question took place. They knew that I uttered no word, 

 ottered no suggestion, simply did nothing in regard to the 

 person in question. They knew me well enough to bo 

 assured that I am neither foolish enough nor false enough to 

 speak of active support, or to imply the support of actual 

 voting on the Council, when ninety-nine out of every bun. 

 dred who would hear of such statements would know that 

 at the time I had long .since withdrawn from all active 

 participation in the Royal Astronomical Society's business, 

 while most of the ninety-nine would consider little short of 

 shameful any active support of one of whom I think as I do 

 of this person. 



Yet this Western editor of a miniature magazine of 

 science in remote Minnesota confidently pretends to suppose 

 that I would select his scarca known piges to add a ridicu- 

 lous and inefleetive untruth to the true and just thong- 

 strokes which I have felt it my duty to inflict on a wrong- 

 doer (after finding ten years of silence misunderstood and 

 unappreciated). He asks me to apologise for what I have 

 not said, and for what, had I said it, would have been no 

 injury at all, whether true or not; while he declines (or 

 pi'obably is unable) to see that what I have said implies an 

 estimate of his protiye's character which would render 

 injury impossible. 



* * * 



I iMACixE the editor of the Sidereal Messenger is unable 

 to forgive the circumstance that in an early volume of 

 Knowledge I had to comment on the poverty of original 

 matter in his little magazine (priced at tenpence !). But he 

 has done better with the magazine since ; though it is still 

 rather too much of a compilation, and much too small for its 

 price. He ought rather to be grateful than angry for sug- 

 gestions which doubtless had their share in cau.sing so notice- 

 able an improvement. 



Mr. J. Fraser, author of a new and entirely inadmissible 

 theory about gravity, has remained dissatisfied with the 

 treatment he has I'eceived in these columns. It will bo 

 remembered that his pamphlet was noticed in Knowledge 

 for August last, p. 23G,and that in Knowledge for October, 

 p. 282, 1 had to explain in " Oossip," in response to his 

 appeal to myself personally, that the author of the notice 

 had certainly not, as he supposed, acted with wilful unfair- 

 ness, while I expressed my all but certainty that there was 

 not even any uncon-scious unfiiirness. On carefully reading 

 through the pamphlet, I found that, as I supposed, the 

 notice was perfectly just, Mr. Fraser's theory being abso- 

 lutely untenable. As I had promised to state in these 

 columns the result of my reading of the pamphlet, (/'I found 

 that Mr. Fraser had really made good his case, I supposed 

 that he would take my silence as signifying that I had failed 



