May 12, 1882.] 



KNOWLEDGE • 



59^ 



9n^ins! to Conreponlifnt^. 



•,'An eomaHnir,!Hc^n f«r Ih, T.dUor rtqiiWinj tarly al/rHlioy) ihinl,! reach Ihl 

 Ofice OH or before the Sttturdai/ prfeeJing Ike current istue oj' KxoiTLBDel, the 

 iMcremeing dreulation qf lekick compels ut to go to preea early in the veek. 



Hcrrs to Cokebspo^drxth. — 1. yo qnettion* ael-inff for ecientijie infornntion 

 Mm 6* annc-reil throvgh the poet. 2. Lettert tent to the Editor for corrrepondente 

 tmMMOt be forvarded ; nor can the itamee or addreeeee <if eorretpondente be gii^n ih 

 OMVn- (o /Ticrle in^niViVf. 3. Corrnpomlenlt thiuld xrile on one ti-le oii/» of 

 Ou paper, and put dr^irinije on u teparale lent. 4. JJ.Jr* Utter ihontd hare a title, 

 and in repltiKng to a tetter, r^eretwe ihouU be m tde to itt number, the page on 

 mkich it appenri, and it* title. 



X. K. Yon will see (hat tlio oppononts of Dr. Kocli's ronclusions 

 use argamcntg which, if accepted, woald render fresh expcrimonts 

 necess.irv. Hcwover, there can be no question you are rifjht in 

 asserting the general principle, that to repeat experiments by which 

 a truth has already been established is simply cruelly. Only doubt 

 can justify the renewal of eri)eriments of the kind. — W. String- 

 field. We have posted your letter to " George," and have sent your 

 communication to the publishers. Thanks. — Boyd Moss. We thank 

 you; but the discussion of the general question of vivisection is not 

 suited to our columns. In company with Professor Tyndall's in- 

 teresting communication about consumption, wo printed his inci- 

 dental allusion to the necessity of certain oxjieriments ; but that 

 does not open up a discussion on a subject already overworn. I am 

 anro neither Professor Tvudall nor any true student of science 

 would advocate other than such carefully-arranged experiments as 

 you describe. — Alex. Scott. The paragraph you referred to was 

 borrowed through another source; wo named the original source, 

 the "Journal of the Society of Chemical Industry," but wo do not 

 know the publishers. The address, " Publishers of the Journal," 

 Ac, would, wo imagine, be sufficient. — Constant Eeahek and 1!e- 

 COMMENDER. Thanks. The quotation was made by a correspondent, 

 and seemed so suitable that we added it to our set. If incorrect we 

 must remove it, for as corrected it does not seem so suitable: the 

 motto, " Orthodoxy is God's Truth," is open to misconception. — 

 P. W. Clayden. The eclipse to which you refer was that of Sept. 7, 

 1820, well seen, as a partial eclipse, throughout the British Isles. — 

 W. Dale. Letter received, and shall appear. — C. J. Watson. The 

 theory is i|nite untenable ; everything known about the action of 

 solar heat, as of solar light, indicates radiation, and everything 

 known about the sun indicates that its globe is intensely heateil. — 

 Canadensis. It is a mere accident that some articles of mine are 

 inserted as " By the Editor," others by " R. K. Proctor." The 

 " Answers to Correspondents " are not all by the same hand. I 

 write most of them, because no one else would be willing to '\Tado 

 tlirough so much of the correspondence which reaches the office 

 of Knowledge. "Conducted by K. A. Proctor" means "edited," 

 or rather includes it and something more. — Desmond. Enlarg- 

 ing Knowledge, and making the price Cd., might have the f fleet of 

 increasing the " circulation among tho higher and superior educated 

 tranches of society," but it would pu^ it beyond the reach of many 

 to whom 1 wish to be of use. Those who will not take a i)apor 

 \ieeause it only costs twopence would hardly help us much. No ; 

 onr plan was to make Knowledge as low-priced as possible, and to 

 give as much as we possibly could for the money. To that plan we 

 must adhere. To create a circulation, and after bringing our paper 

 into request, to increase tho price of it, would not be fair. — W. 

 Gadd. I fear it will bo impossible to find space. — C. Carter Braine. 

 Will ask engraver if he can manage it. "Brake" is correct, but 

 some prefer " break." — Jos. OFtORD. Many thanks. Will use as 

 soon as po.ssiUe. — Another Hater ok Superstition. No fear 

 of a theological controversy; but why should ynu object more 

 to tho term Almighty than to the term Infinite ? What 

 ore natural causes and events, but those operations which, 

 being finite, we can understand, or hope to understand ? 

 Outside of them lies tho infinite. To speak of infinite time 

 may bo idle, seeing that wo cannot conceive either ; but any 

 one may do so without offence ; ho may equally speak ■without 

 offence of Infinite Power. There is nothing necessarily theo- 

 logical in tho conception. — Erin go Bragh. Fear Otto of 

 Hoses somewhat outside our line. — E. H. B. Stephen-son. It 

 Has been by noting changes among tho stars that the sun's 

 motion in spaco has been recognised ; but the changes are too 

 alight for ordinary observation. Some of them have only been 

 detected after centuries of observation. Tyndall's book on " Dust 

 and Disease" (Longmans) would suit you, 1 think; but the subject 

 in very wide. Thanks for lines, but fear some would object to them 

 as having rather a goody-goody tone. — A. C. H. If that were so, 

 how could a ship sail close to the wind ? Estimating as you do 

 the driving force of tho wind, tho action of a wind d^ad abeam 

 would produce no way at all, except leeway, and a wind six points 

 (67t degrees) from a ship's course would drive her astern. You 



can only resolvo tho wind's action as I havo done, viz., parallel 

 to the sail and square to it, then this last part must be resolved 

 in direction of ship's course and square to it. 'I'ho wind 

 thus dealt with must bo the relative wind, viz., that which seems 

 to blow when tho ship is travelling on her course at whatever 

 rate she may havo at the moment.— T. P. GARRf:Tr. Thanks, but 

 it reaches two members of staff.— Si'iisCRiBER TO Knowledge. Wo 

 can give no information as to either advertisement. No telescopes 

 pnicurable at tho ofBoo of Knowledge, or sold directiy or indirectly 

 through tho agency of publishers or proprietors of the jiaper. 

 Regret that no correspondent has boon able to reply to qn^ition 

 about sulphur cast (query 2G6, Fob. 21).— A Churchman. 1 should 

 imagine the Rev. Dr. Luldon would bo a better judge than you 

 can be on that subject. But then, your letter being anonymous, 

 you maj- answer that as I do not know who you ai-e, I cannot tell 

 "whether you aro a judge or not. After all, what can it matter to 

 vou, being so sure as you are of your opinion, whether others think 

 differently or not ? — S. C. Gaukekt. Tho gonerali.sation is bold ; 

 cortainlvso much has not yet been proved. — Cycloid. Certainly, tho 

 lowest point is for the moment at rest, tho uppermost moving twice as 

 fast as the circle's centre. You ask, why ? Tho answer is, because at 

 tho lowest point the advancitig motion of tho circle as a whole ia 

 exactly counterbalanced by the (there) receding motion of tho cir- 

 cumference due to rotation. At tho uppermost point both thoso 

 motions are in tho same direction. If v bo the rate at which the 

 centre advances, and also that at which, wero tho centre at rest, a 

 ])oint on tho circumference would be moving on account of rota- 

 tion, then the velocity of the lowest point is v-v, or 0, while that 

 of the uppermost point is I'-H', or 2r.— Solarium. Tho correct 

 angle for tho gnomon of a sundial to bo erected on ' Stroatham 

 Common would bo 51|°. There may bo a minute or two of 

 difference between 51° 31', the latitude of London, and that of 

 Streutham, but it would bo impossible to make a gnomon so pre- 

 cisely as to take this into account. The best way to place the stylo 

 is by the sun, not by the pole star. At true solar noon (which you 

 can' get from " Whi'taker's Almanack," if you have true clock time, 

 by adding or subtracting tho equation of time according to tho 

 date), the style must have its shadow in its own plane. Thus, 

 on May 12, see " Whitaker's Alm.anack," p. 31, tho sua is 3m. 52s. 

 before" the clock, so that the sun is due south at 3m. 523. to twelve 

 clock time. Tho stylo can then bo set with its piano vortical, and 

 due north and south, the slant edge, of course, pointing towards 

 the pole of the heavens, or due north, 52i'' above the horizon. — A 

 Con.stant Reader. We must not trespass on the province of 

 medical men. A surgeon who has seen the formation would 

 know better than correspondents who had not ; and we should 

 be afraid of advice being given which might lead to mischief. 



[About two pages of " Answers " have been unavoidably held over.] 



©MX iHatlKiiiatiral Column. 



THE LAWS OF PROBABILITY. 

 By the Editor. 



TUB law enunciated at the close of the last paper enables us to 

 determine the probability that a certain series of results will 

 follow, in a certain definite order, when any definite trial, as a 

 tossing, drawing, or the like, is repeated such and such a number 

 of times; but it does not tell us what the jirobability is that so 

 many results out of the total number will be of one kind, without 

 regard to order. For example, suppose there are tliree white balls 

 and seven black balls in a bag, and that wo draw a ball five times, 

 always at raidom, and always returning the drawn ball. Then, tho 

 chance that tho drawings give, first a white ball, then three black 

 balls, then a white ball, is as follows : — 



l.lxlxl.ljor^O?^^ 

 10 10 10 10 10 lOUOOO 



— the odds in fact aro more than 30 to 1 against such a result. But 

 the probability that two drawings out of the five will give a white 

 ball and that threo drawings will give a black ball is very different. 

 The odds are against such a result ; but they aro Jiot nearly so heavy 

 as against tho former. This is easily seen ; because the particular 

 succession above considered is only one out of several results which 

 would give two white drawings and threo black ones. If we con- 

 sider in how many ways this i)roportion of white and black drawings 

 may bo brought about, wo shall bo led to recognise the true method 

 of determining the probability of this result. 



Call a white drawing w, and a black drawing 6. Then the above 

 particular result is represented by the arrangement, to 6 5 6 «). Bnt 



