276 



♦ KNOWLEDGE 



[October 1, 1887. 



Go. Making a go of anything, is succeeding in it. 

 Probably the usage is derived from the old-fashioned way of 

 starting a race with the word " go," pronounced so soon as 

 the starter sees that the contestants are on equal terms. A 

 false start is no yo. In England, oddly enough, we have 

 the negative form of this usage, while we seldom hear the 

 positive form, except provincially. An Englishman will 

 say, " It's no go," who would scarcely think of saying 

 " It's a go." 



"Go GOOD," for taste good may be regarded as not less 

 English than American. 



" Go A CKUISE," used for " take a walk or ride," is 

 nautical English, and probably as much used in English 

 maritime counties as in New England, where, indeed, it 

 is almost limited to .seaside places. 



Go AHEAD. Although in its verbal sense this is a good 

 old English expression, it is claimed as specially charac- 

 teristic of Americans to go ahead, and used adjectively go 

 ahead may be regarded as distinctively American. It is 

 perhaps characteristic of the three great divisions of EnglLsh- 

 speaking races that our favourite expression in the old 

 country is " All right," while the favourite American ex- 

 pression is " Go ahead," and in Australasia men say " No 

 fear." This triple set of sayings is better than the French 

 aspiration (rather more than satisfied now perhaps) for la 

 gloire, or the a;eneral submLssion of Continental nations to 

 military discipline. We English-.speaking races find fault 

 with each other, forgetting our kinship ; we laud this, 

 that, and the other distinction, often mere tinselling, of 

 other races ; but where now, or in the past of the world, 

 has any race, regarded collectively, made a deeper mark in 

 the history of the world ? What other race, or set of races, 

 has ever so definitely acted on the triple principle, or has so 

 thoroughly justified it — See that all is right, then go 

 ahead, and fear not. Despite the savagery shown too often 

 by British Buncombe, by American spread-eagleism, and by 

 Australian assertion of " Australia for the Australians," 

 the English-speaking races have alwaj'S shown (on the whole) 

 the sense of duty expressed in our British " All right," the 

 aspiration for progress exjjressed in the American " Go 

 ahead," and the confident but unboasting courage expressed 

 by the Australasian " No fear." 



To Go BACK ON. This peculiar expression for turning 

 against, or forsaking any one, must surely be an A mericanism. 

 I have never heard it in any part of Great Britain, nor have 

 I ever met with any one who had. Even in America the 

 expression is not general. It is Western, or ratlier, had its 

 origin in the West. Every English reader remembers the 

 humorously pictured pei-plexity of the clergyman from the 

 East, when told that the defunct miner " Never went back 

 on his mother." I imagine, but without a particle of 

 authority for the supposition, that the expression was first 

 used by teamsters, and was suggested by the going back of 

 a waggon on a steep slope unless blocked. Such experiences 

 must have been common in the old waggoning times out 

 West, in the mining region of the Rocky Mountains. 

 Virgil evidently had some such idea in his well-known 

 description of the oarsman pulling against stream. He says 

 he has seen things go back on the labourer — 

 . . . retro stcblapsa referri ; 

 Non aliter quam qui adverse vix flumine lembum 

 Remigiis subigit, si brachia forte remisit, 

 Atque ilium in praeceps prono rapit alveus amni. 



Photographs of the sun were taken at Greenwich Observatory 

 on 199 days during 1886, while photographs from India filled in the 

 gaps for 161 days, so that the record of observations is complete for 

 all but two days. The area of sun-spots and faculje has continued to 

 decline during 1886 and 1887. There were si.xty-ono days in 1886, 

 and from October to April 17 last, seventy-three days on which no 

 spots appeared. 



STRANGE CHANCES. 



^HE question of the occurrence of unusual 

 events, such as that considered in the 

 article, " A Perfect Innings at Cricket," 

 last month, when only a sufficient number 

 of trials is allowed, leads to some of the 

 commonest difficulties in regard to matters 

 of chance. Indeed, one may say that the 

 very elect are apt to be deceived in such matters — meaning 

 here by the very elect, mathematicians themselves. 



It is noteworthy, indeed, that problems in chance are very 

 apt to deceive mathematicians whose researches have lain in 

 other directions. A well-known example of this is the case 

 of d'Alembert, when the very simple problem was pro- 

 pounded to him. What is the chance of tossing heads once 

 at least in two trials? He replied, and not hastily, but 

 after careful study of the matter, " Two in three, or the odds 

 are two to one in favour of success." In reality, the chance 

 is three in four, or the odds are three to one in favour 

 of tossing one head at least. Yet d'Alembert's reasonmg 

 seems at first sound, and was long held by him to be un- 

 answerable : — There are three possible events, viz., both 

 tossings may give head, or both may give tail, or one may 

 be of one sort, the other of the other ; of these three events 

 only one is unfavourable ; since, then, two out of three 

 events are favourable and one not, the chances of success 

 are two out of three, and the odds in favour of success are two 

 to one. The error lies in omitting to notice that one of the 

 thi-ee events is twice as likely as either of the other two ; 

 for while we can only get two heads in one way, and two 

 tails in one way, we can get a head and a tail in two ways ; 

 viz., first tossing head, second tail, or first tossing tail, 

 second head. There are, in fact, four possible events, viz., 

 head, head ; head, tail ; tail, head ; and taU, tail : and 

 these four are equally likely. Wherefore, since only one is 

 unfavourable, the chances are three in four for success, or 

 the odds against failure are three to one. 



The words italicised are those which in every such dis- 

 cussion of a chance problem must always be represented ; 

 that is, the question of the probability of the different kinds 

 of result must always be considered as well as their mere 

 number. 



But this problem of d'Alembert's might be treated like 

 our cricket problem ; and for my own part I prefer always 

 that more general way of treating such problems. Thus the 

 real question is. What is the chance that " tail " will be 

 tossed at both trials 1 Now the chance at each trial is 

 clearly one-half, hence the chance that both trials will give 

 a " tail " is a half multiplied by a half, or one quarter ; that 

 is, one in four, or the odds are three to one against this 

 happening. 



If we dealt in this way with the probability of tossing 

 head once at least in twenty trials, we should find it to be 

 1,048,575 out of 1,048,576, or the odds against tossing 

 always tails (or always heads) in twenty trials are 

 1,048,575 to 1. 



But it is in watching, or thinking about, a great number 

 of trials, that errors are most commonly made. The laws of 

 probability a.ssure us that if a thousand millions of trials 

 were made, there would be nearly a thousand cases in which 

 " heads " would be tossed twenty times in succession — each 

 trial being independent, so that as soon as a " tail " appeared 

 the trial would be concluded, and a fresh one have to be 

 begun. And further, the laws of probabilitj' assure us 

 that, although on the average there would be only one such 

 marvellous run of heads in 1,048,576 trials, yet the chance 

 of tossing twenty heads in 1,048,576 trials would be more 

 than one-half, or the odds would be in favour of such an 



