March 10, 1882.] 



KNOWLEDGE 



413 



;iik1 have to work my very hardest, I always go withont stimntants 

 (f any sort. In ordinary working time I am a very moderate 

 .Iriiikcr; in holiday time, like Mr. Foker, I " take my whack " with 

 •'M'rest; but then I do not believe in holiday-making ; it means, 

 [li me, "getting out of working order." — F. A. B. Your first 

 • rv a statement — namely, that coronal ring was perfect round 

 ,,,.»>n at first quarter. Other query inserted; letter (abstract) also. 

 1 hanks. — StR U. Thompson-. I take some blame to myself, for I 

 l;:ul read your book, and remembered well that there was therein no 

 jlvocacy of vegetarianism. — M. S. Thanks. — E. G. D. Your 

 ! ioro than thirty notes, criticisms, and suggestions" came 

 ■n us all "loo too" much at once, and many related to 

 tiers already, as wo hoped, disposed of. Others have had 

 ro to complain of than yourself; but if what you wished done 

 you were done for all, we should want si.xty pages weekly, and 

 paper alone would cost much more than oiu' weekly price. What 

 uld we do.' Advise proprietors to raise price? Thanks; we 

 iL-r not, if by any possibility we can avoid it. But, as you will 

 . it so, we reply, " Farewell." Try to be a little more reason- 

 ' with the next periodical you take. — E. V. II. Fear you cannot 

 a really good account of the comet of 1813 ; the best that was 

 : itten about it lies buried h\ proceedings of astronomical societies. 

 '' "meteoric theory of comets" (scarcely a theory now) has 

 ■n dealt with fully by several writers, myself among others. It 

 t. be considered shortly in these pages. — E. BfRKE. The version 

 _-iv(n in the work you mention long since disposed of by Leverrier. 

 — ,T. H. CoBBETT. I think both Parallax and Mr. Xewton Cros- 

 !;uicl would feel insulted at the suggestion that they are one and the 

 ■nt'. If eitlier could destroy accepted astronomy, the other would 

 ! upon him. In the theory of Pai-allax (who is by no means the same 

 ' ur too livelj- Hampden) the earth is not compared to a Stilton 

 ese more than to a Dutch cheese. The earth has only one side — 

 lop ; the north pole is the centre ; there is no south pole, but in 

 - !iiead we have the circumference. Dimensions I do not know. 

 Hampden" tells me one thing; "Parallax" used to .assert another. 

 If you quote cither, the advocate of the other — whether " Hamp- 

 '!i ii" or "Paralla.'c" — tells you you know nothing of the Zetetic 

 If that advocate chances to be " Hampden," he calls 

 l; coward, or a lily-livered, perjured villain, or something 

 rt. It is a way he has. "Parallax" is very different. 

 li'- is not only gentlemanly, but he is "like Cerberus, three gentle- 

 iiK-u at once." At least, to my certain knowledge, "Parallax" 

 v,:s Mr. Rowbotham in 1864; De Morgan savs of him (" Para- 

 :ms," p. 30t>,) that at Trowbridge, in 1849, he was S. Gonlden ; 

 1 now he is Dr. Burley. — J. Mukrat. Y'es ; other notes and 

 Ljrams (gracious goodness!) received. Sorry "the Ptolemaic 

 lesceado system will not allow any spots on the sun," only 

 wing them to pass in the same way asA'enus. Astronomers are 

 kinder. — J. A. M. Solutions 1,2, 3 received; hope with you, the 

 :k is tlioroughly cooked now. — E. P. T. Gregory's Electrical 

 ■ory plausible as you say, but, as you also say, quite irreconcil- 

 ■ with Dr. Ball's views; equally irreconcilable with laws of 

 namics. — Carus. The more hydrogen in a balloon — the hydrogen 

 ii;^' enclosed in elastic case, so that it is nearly at same pressure 

 ~urrounding atmosjphere — the greater the lifting power; other- 

 ■, the reverse. If an air-tight case is so made as to be of cou- 

 nt dimensions, the more hydrogen you force into it the less will 

 ! he raising power. As to the other query, please specify the 

 1 of work you require on palaeontology — technical, popular, or 

 it? — Eli Wailis. If you want to see what stars lie towards, 

 the south west, hold the map so that the words south-western 

 i i/.on are vertically below the map's centre, then between the 

 li-westem boundary and that centre, which represents the point 

 (head, yon will see in the map the stars you want. — Fakmku. Letter 

 rked for insertion. — J. A. Ollarf. Xot a tenth of the space you 

 ■ It is available. — 3ehald Massey. Thanks; but question of 

 -'s descent is rather a biological than a pliilological one. 



?Ltttn-£i lAfrribrlj. 



H. Muirhead, W. H. Morgan, Aspiring Artist, J. Hartington, 

 L. M. N., K. Mongar (?), M. Emerson, P. T. L., Aud.ix, Peter 

 Parley, Sucking Uerschel (must not suck brains), E. F., Mater- 

 familias, Petcrkin, Excelsior, J. North, M. Weatherwit, St. Pancras, 

 Q. E. D., F. v., Formosa, Empty Noddle (tr\- to fill), James 

 LogersoU, Amorj', N. C, Philip St. John, Northern Lad, Calais- 

 Donvres, Amplitude, N. Tressingham, . Ccelebs, Shingly Beach, M. 

 Peterson, J. Short, &c., &c. 



PoxD's Extract is a certain core for Bhemnatism and Gout. 

 Pond'a Extract is a corlain cure for Hemorrhoids. 

 Pond's Extract is a certain cure for Neural^c paina. 

 Pond's Extract will heal Bums and Wounds, 

 bond's Extract will cure Sprains and Bruises. 



Sold by all Chemists. Get the gennine. [Adtt. 



©Ill- iBatftrmntiral Column, 



THE LAWS OF PROBABILITY. 

 By inB Editor. 



THE mathematical discussion of the laws of chance is regarded 

 by many mth suspicion, because they observe that while 

 the matters discussed are admitted by the very inquirer to be doubt- 

 ful, the conclusions arrived at are presented as matters of mathema- 

 tical certainty. But in reality this arises from a misapprehension 

 of the nature of the inquiry made by mathematicians into questions 

 relating to chance. A mathematician assigns a definite value, as if 

 it were certain, to the chance of winning a prize in a lottery (where 

 one prize only, let us say, can bo won) under given conditions ; but 

 ho does not assert that the event will confirm his opinions ; on the 

 contrary, he knows that whatever hajipens, the sum he names will 

 not be gained. He sav.s" tJtat, certainly, is the value of the chance, 

 but lie knows that either the prize will bo won, in which case more 

 than the sum he named will bo won, or lost, in which case the 

 drawer of the blank will win nothing. Ho cannot even say that in 

 any given number of trials the average amount won will be what 

 ho has named; he can only say that the greater the number 

 of trials, the nearer will the average amount won be to the amount 

 ho has named. On this point only he is certain, and not only can 

 his view be shown by logical reasoning to be sound, but multiplied 

 experience confirms it. The reasoning may not admit of being 

 grasped veiy easily, or, at any rate, very quickly. In particular 

 cases the mathematical determination of the value of a chance 

 may be so difficult that only advanced mathematicians can 

 master the demonstration. But even in such cases, experi- 

 ments can often be made quite easily, by which, with a, 

 little patience, the mathematical solution may be shown to 

 be correct. Take, for instance, one of the "chance methods" 

 of squaring the cii'cle. A straight rod of given length, and of 

 given square section, is tossed at random on to a grating of equi- 

 distant bars, and after gyrating in the air a number of times, falls 

 either athwart the bars or between them, according, one would say, 

 to pure chance (or bare chance, or mere chance, as you may choose 

 to call it). A mathematician says that the chance of the rod 

 falling through — the spaces between the bars being, of course, 

 wider than the rod — depends (in what seems an occult fashion) on 

 the relation between the circumference and the diameter of a 

 circle. The proof is not simple, and perhaps you fail to under- 

 stand it. But set some one to toss the rod (from a place where he 

 cannot see the cross-bars, and without any knowledge of their 

 position) a few thousands, or tens of thousands of times, and note 

 how often it falls tlirough, and how often it fails to fall through ; 

 you then find that the ratio of the two numbers approaches very 

 nearly, the more nearly the oftener the rod is thrown, to the ratio 

 assigned by the mathematician. The experiment maybe tried any 

 number of times, and always the result is the same. 



The science of probabilities is shown by such inst.ances as these 

 to be a science which can predict, even in matters of pure chance. 

 It is not a science which authoritatively lays down certain dicta, but 

 one which itself indicates ways in which it may be put to the test. 



But then, say objectors, ' probability is dealt with by mathe- 

 maticians in so artificial a manner, that these methods cannot 

 possibly have any ap)]licatiou to real events. At the very outset 

 there are conventional rules, which, so far as we can judge, might 

 just as well have been entirely different. 



In reality, however, the rules by which mathematicians deal with 

 probabilites are only conventional in the same sense that it is con- 

 ventional to measure lines by inches or by feet, to measure angles 

 by circular arcs, or to measure surfaces, solids, time intervals (what 

 you please, in fine, that mathematics can deal with) as mathema- 

 ticians do measure these quantities. 



Let us see what these conventions are : — 



In the first place, it is agreed that absolute certainty shall be 

 represented by unitv, absolute impossibility by 0, and therefore 

 (necessarily) different degrees of probability by different proper 

 fractions. "We can thus never have a chance greater than 1, for 

 nothing can be surer than the sure ; nor can we have a chance less 

 than 0, that is negative, for nothing can be more impossible than 

 the impossible. These are pure conventions. Wo might have 

 called certainty 10 or 100, or 59Jj. or anything we pleased; we 

 might equally have represented imiiossibility by any quantity, 

 positive or negative, or either certainty or improbability by a letter. 

 It is found convenient, however, to adoi>t the particular convention 

 mentioned, and so long as, having once adopted it, we uniformly 

 follow it, we shall no moro be likely to go astray tli.au when we 

 represent the number " three " by the figure three throughout an 

 arithmetical sum. 



