254 



♦ KNOWLEDGE 



[Fbb. 21, 1882. 



tlin (JifTorRnt rosulto, and tho oddH rospectiug tliem, aro as 

 follows : — 



ObuM. Oddl. 



All hfi»cl« or nil UiilH M2Htli ... 127 t<i 1 agiiiiiMl. 



All l)iil 1. Ik-ikU, or tails ... I- ICtli ... 15 to 1 aKniiiHl. 



.Ml but 'J, lii'iidn, or tnilB ... 7- 32nda ... 26 to 7 aKniniil. 



.Ml but :i. IkikIh, or tnilM ... 7- lUthH ... tu 7 UKuiuHt. 



Four lu-ii(l8 anil f.iiir tniU ....'I5-I28llui ... 03 to 35 againxt. 



Tho iiicst prol>abl» of all events in this cose, as in tho last, 

 is that thorc will lie 2 more heads than tails, or vicn vktsA ; 

 mid wluTi-as in tliu former case it was an even chance that 

 there would lie just this discrepancy, tho odds in the 

 present ca.se are 9 to 7 against it. But tho chanci; that 

 thei-e will he this discrepancy at leaol, is greater with thi- 

 greater iiuiiilier of trials. For in the former ca.so tho odds 

 were hut •"> to .'J, or 17."> to lO.'), against ahsolutt; ciiuality, in 

 the present case they are 9.'{ to .'55, or 27'J to lO."} against 

 it. And it can lie shown that it becomes less and less 

 likely the greater the (even) number of tossings, that there 

 will 1)6 absolute equality. Yet, on the other hand, in the 

 oases considered, the chance that heads will exceed tails, or 

 tails heads, not liy a given amount, Ijut in a given degree, 

 diminishes as the number of tossings is increased. Thus 

 with 4 tossings, the chance that heads mil be to tails as 

 •'5 to 1 (or vice versA) is, as we have seen, one half ; with 8 

 tossings the chance of this relation holding (G of one kind, 

 two of the other) is only 7-32nds. Again, the chance that 

 heads will be to tails, or vice versd, in a ratio of not less 

 than 3 to 1 is S-Sths in the former case ; in the latter 

 (adding together l-128th, l-16th, and 7-32nds), we find it 

 to be only 37-128tlis ; in one case the odds are 5 to 3 in 

 favour of that amount of discrepancy at least, in the other 

 they are 91 to 37 against there being a discrepancy so 

 great. 



But some correspondents ask whether, even in matters 

 of pure chance, there may not be something more than 

 mere accident, — whether some men may not have a certain 

 degree of good fortune given to them, — whether, in line, 

 what is called luck may not in some degree depend on 

 Providence This takes us a little outside the domain of 

 science ; but as it does not bi-ing us upon any of the vexed 

 (juestions of dogmatic religion, I will venture to make a 

 remark or two on this (in reality) unscientific aspect of the 

 question. To the student of science it appears as absurd 

 to imagine that the laws of nature would be set on one side 

 in matters of pure chance (for even in coin tossing nothing 

 short of a miracle can cause the law of averages to be 

 departed from — in the long run — either in favour of any- 

 one or against him) as it would be to conceive that an 

 experimenter favoiu-ed l)y Providence might get a mi.xture 

 of carbonic acid gas* and nitrogen to behave like a mixture 

 of oxygen and hydrog(!n, or as it would be to suppose that 

 during Darwin's researches into the work of earth-worms, 

 these creatures, siiadente diaholo, acted in a way not 

 natural to their kind. If in the case of so-called lucky 

 gamblers, a supernatural power, good, bad, or indillcrent, 

 has been at work, science has no power of dealing with 

 the phenomena. All science can say is, that the observed 

 and recorded phenomena agree precisely with those which 

 can be shown to be necessary con.sequences of the laws of 

 probabilities : all she can do is to go on dealing with the 

 matter precisely as a Pasteur would go on dealing with the 

 observed phenomena of disease germs, uninfluenced by any 

 suggestions that diseases wore produced by supernatural 

 agencies. 



• I nm perfectly awaro that what waa called carbonic acid gaa 

 twenty years ago now goes by another name; and I am equally 

 •iw.'iro that a (echnical moaninp is given to the word " mixture " 

 other than its ordinary significaiico. But I am not addressing 

 chemists just now. 



So far, i have simply considered what science necessarily 

 does in such cases, 'i'he student of science can do no 

 otherwise. But I may iiot<', in passing, that just as there 

 K«!ems to be something irrtrverent in the suggestion of 

 I'rovidence arranging for the " breaking of the bank " by a 

 (larcia or any other unprincipled gambler, so the general 

 suggestion that Provid(;iice, and not the laws which have; 

 been assigned to the universe (how or why wo know not), 

 is to be cr(-dit<'d or discredited with all the chances or 

 coincidences which seem surprising to us, appears to me 

 singularly dangerous to the faith of tho weaker minded. 

 Because, while many of these coincidences have Ijeen satis- 

 factory enough in their results, at least as many have been 

 very much the reverse, and not a few utterly deplorable. 



Take for instance the following ca.se : — 



In the winter and early spring of 1881, in America, 

 railway accidents were very common (231 happened in the 

 first two months of that year), and any one who had (as I 

 had) much railway travelling to do at that time had a very 

 fair chance of coming in for wounds and contusions, if not 

 worse.* Now it so chances that at the end of February, a 

 train was wrecked in Missouri, in which two persons were 

 killed and many injured. Another train was sent, carr3riiig 

 several medical men, and a number of appliances for the 

 relief of tlie wounded. By a most unfortunate chance, this 

 train, thus forwarded to help many suffering persons, was 

 itself wrecked ; seven persons were killed, including several 

 of the doctors. If we are not to consider this strange and 

 sad coincidence as belonging to the chapter of accidents, as 

 due to the chances which always affect events depending 

 on natural causes (as the weakening of embankments by 

 frost and thaw, the action of winds, rain, snow-drifts, ic), 

 must we regard it as due to special intervention of Provi- 

 dence t Science tells us, and experience confinus her 

 teaching, that in the game man plays (or his contest, if you 

 will) with nature, the laws of nature are as laws of the 

 Medes and Persians, that he must not expect to have his 

 moves back, or any help outside the laws assigned (inex- 

 plicably so far as we are concerned) to nature : if he does 

 expect this, he will most assuredly be disappointed. 



THE CRYSTAL PALACE ELECTRICAL 

 EXHIBITION. 



Third Notice. 



THE most casual observer can discern some improve- 

 ment during the past week, although there still 

 remains a great deal to be done before anything like com- 

 pleteness can be said to be attained. Some of the exhibits 

 exist only in the catalogue, and it seems apparent that no 

 attempt will be made to proceed any further than a dis- 

 play of advertisements. It has occurred to us that some 



* For my own part, I thought it exceedingly likely that befora 

 tlie leeture season came to an end, my lecturing miglit be inter- 

 rupted. As week passed after week without an accident, I neither 

 judged that the next journey was more likely or that it was less 

 likely to be disastrous. At last, towards the end of February, my 

 turn came. The train I was in was pitched over an embankment, 

 not far from Kichmoud, Missouri, falling some twenty or thirty 

 feet, and a stove drove its way tliroiigh a stout plank within two 

 inches of the place where my head lay. Was I lucky or unlucky ? 

 unlucky in going by that particular train; or, being in it, lucky in 

 escaping with no injuries worse than a nearly fractured skull and a 

 nearly broken leg. As I and the other passengers looked at tho 

 shattered interior of the car, wo thought ourselves lucky to be alive j 

 as we considered the various damages which our persons and 

 property had sustained, we took a different view. (The accident 

 turned out afterwards to have been singularly fortunate for me, but 

 that is a detail.) 



