May 19, 1882. j 



♦ KNOWLEDGE ♦ 



613 



i'uint of oater wheel is — !-'. Thus the limiting velocity is 

 deduced from tl e equation — 



2 ~ R 



gdi: 



or I- = i 



2h 



Tliia is, of course, only a rough treatment of tlio problem, obtained 

 liv regarding the carriage as if its wholu- uiuss were at the centre 

 ^jf gravity. It shows that for a given velocity the stability 

 iiicreases with the distance between the wheels and the large- 

 ness of the turning circle, and diminishes with the height of the 

 •<-ciitro of gravity above the ground. (In the above, j = 32'2.) — 

 K. D. G. Thanks ; your method, and any common-sense method, 

 i« better than the ordinary rales for dividing decimals. — K. H. 

 Xi.-BETT. (1.) The moon does occult stars continually; but the 

 Nautical Almanac only gives the occcltations of certain catalogued 

 sfars. (2.) The ttars in the field of view of a telescope are not so 

 rj-i«wiled that the new moon would seem like a dtirk circle on the 

 Htai'lit background, even if the new moon were black, which, 

 however, is not the case. — E. I). Abi iiiiiai.ii. Many thanks for 

 your letter and paper. There can be no doubt on the subject. 

 I should be glad to hear from you at your convenience. — II. Clijt. 

 .Many thanks; bat we have not space. — S. UOPKIXSON. I hope 

 %-»>ur bet was onlj- imaginary, though, if made, it was certainly won. 

 Tlio question is. If the odds are the same on two independent events, 

 .•i.v'l the betting is even that both happen, what are the odds on each 

 stl>arately ? Let the chance of each bo .r, then the chance that 

 li.th will happen is r'; but this, on the supposition that it is even 



letting, is one-half, ori' = }, and r = — -jt: =-707 approximately. 



'i'iie chance of each event being 707-1, OOOths, the odds on each 

 <•% .-nt separately, are 707 to 293, or roughly 7 to 3. — W. Watson. 

 Viu object to severity, and probably to unfairness : and to illustrate 

 ^'lnr fairness and gentleness you characterise my answers to corre- 

 >l ondonts as a weekly dose of sulphuric acid, and contrast them 

 irifavourably with those given in a contemporary paper. Now, I have 

 i:ik?n the answers given under this heading in the last five numbers 

 ff Knowledge, and I find that ronghly only about one answer in 

 iT.enty is severe at all, ten or twelve neutral, and the rest 

 useful replies to sensible queries. I have not here ooanted forty or 

 tiiry replies which, in my anxiety to meet the requirements of 

 readers, have been obtained from experts, and paid for at the same 

 r:ite as original articles. About one answer in forty since Kxow- 

 I VDGE first appeared has been really severe ; that is. not meant for 

 I'anter, such as any sensible person would either take good- 

 Immonredly, or answer in kind. I venture to say that every really 

 j-evere reply has been more than meritetl. 1 have no fault to find 

 with the answers in the journal yon name ; but I happen to know 

 tl-at the paradoxical and the idiotic, the sour-tempered and the 

 ni-.ilicious among the correspondents of that journal were long since 

 ■weeded out by treatment far severer than any applied in Know- 

 i.f.riGE, greatly to the gain of that journal and its readers. When 

 the saiue work has been done (more easily. I trust) here, our 

 jinswcrs to correspondents will no longer need even that occasional 

 drop of diluted sulphuric acid which your imagination has modified 

 into pure and pervading vitriol. — ScnooL-Bov. Thanks (you write 

 a very bold band for a school-boy). You are quite right; in our 

 haste^for be it known that answers have to be very hurriedly 

 •written or not at all — in the " fourthly " example at foot of 

 »ecor.d column of p. 576, we did, as yon say, shift the decimal 

 jioint different ways, instead of the same way. Th3 quotient, 

 as you say, has only two integral digits. Good boyi — 

 tiR-VP.ATiii. Von are right: Professor Huxley's remark that mercury 

 expands more than the glas.' holding it, and that therefore the baro- 

 meter is higher on a hoc day, is nnsound. The size of the tube in 

 110 way affects the height of the mercurial column. The diminution 

 tit the specific gravity of the mercury is, of course, the true cause 

 of the greater height, eaieri.t paribus, on a hot day. His remark at 

 p. 355, that the earth moving more rapidly as it approaches the sun, 

 neutralises any augmentation of heat which may be due to increased 

 nearness to the sun, is even more obviously incorrect. — Cogito. Yes : 

 the word centrifugal (p. 565. col. 2, line 12 from the bottom) should 

 obviously have beea centripetal; as the "copy" was printed 



itter, the mistake should not have occurred. — H. E. Kilbv. 

 i pparchus first suggested that method of determining the 



IS distance. Theoretically sound, it fails utterly in prac- 



', as exolained in the fir.'st chapter of my treatise on 

 sun. — M. E. Bexham. We must content ourselves with 



tices of men and women who have in some way ailvanced 

 ■. ■•■ntific researches. — C. Moon. Kindly send the trigonometrical 



method : if you will also rend the " fly," I will try to get the 

 information you require.— W. S. S. S. Place of Uranuj can bo 

 determined from tlie zodiacal map in Part IV. — W. S. D. (Chro- 

 nological.) Your Association cannot teach astronomers anything 

 about eclipses, past or future; it is evident, on the contrary, that 

 you have much to learn. Your views about eclipses, transits, &c., 

 are such as heg'^'H-rs very naturally form.- Intbo-Geogbamiicis. 

 No, they do not correspond ; if the celestial sphere were a plane, 

 they might. The outlines of constellations have no fixed pocitions 

 like those of continents and seas ; but are carried along so as to 

 include the stars shown in their proper constellations. — M. J. B. 

 "Norma" must be the constellation you refer to ; it was invented 

 by Lacaille.— C. .T. Caswei.i.. Thanks for kindly words. We note your 

 question about Venus in daytime. — J. 15. Question recently an- 

 swered (in Answers to Correspondents). — E. W. White. The subject 

 is one of great interest ; the influence certain ; but that there is any 

 magnetism in the matter more than doubtful. — J. McGkicok Allan. 

 Thanks, but it has bu^cn already done in our columns. — E. SESiaENT. 

 We know of no treatit^e on the Flora of Singapore. — J. O. Do not 

 know who is the publisher of J.I!. Young's "Solutions of Cubic 

 and Biquadratic Equations."— J. Hameb. The polar axis of a 

 heavenly body is that axis en which it rotates, and the equator is 

 that great circle of the body which is at right angles to the axis of 

 rotation. Was not my note of admiration, then, justified by your 

 remark that the moon, instead of rotating on its polar axi.^, rotates 

 on an (q latorial one ? It is a contradiction in terms. If you had 

 said, as I think you mean, that the moon rotates on an axis directeil 

 earthward, I should have understood you. You might then siinply 

 have said the moon's jiolar axis is directed towards the earth. The idea 

 is erroneous, but not self-contradictory, like the other. The moon's axis 

 is very nearly at right angles to the plane of her orbit round the 

 earth, and she rotates in it once in each revolution round the 

 earth.— Bbl-ck Cook (1). The angle ARB exceeds APB by the sum 

 of the angles PAR, PBR (this follows obviously by joining PR. 

 producing and applying Eoclid I., 16). Pimilariy the angle ARB 

 falls short of the angle AQB by the sum of the angles QAR, QBR. 

 Hence, since angle PAR = QAR, and PBQ = QBR,'we get, by adding, 

 twice the angle ARB = angle APB -h angle AQB or is constant. — 

 Q. E. D. (2). For action of syphon we must refer you to elementary 

 treatises. (3). If n is even, its square root will contain - digits. 



+ 1 



If n is odd, its square root will contain 



Both eases are included in the formula. 

 1 ( 



or 1 I 2n -H - ( - 1)- 



(-1)" 



digits. 



i 

 ) 



BIOLOGICAL. 

 Yang fottin (Aspull, near Wigan. Why don't correspondents at 

 least write their pseudonyms plainly?). 1. There are no per- 

 ceptible morphological differences between man's red blood-globules 

 and those of the liigher apes — indeed, no physiologist can venture 

 to swear in a court of law which is the blood of a pig and which 

 that of a man— so close are the resemblances. Differences there 

 may and must be, but they are those dependent on minute structure, 

 and not on any broad lines of bodily conformation. To all intents 

 and purposes the blood globules of man and higher apes are similar 

 in size and structure. With the exception of the Camelidoe, all 

 <iuadrupeds have round, uneleaved blood globules. 2. So far 

 as we know, the higher apes coincide nearly with man in their 

 gestation. 3. Regarding the occurrence of puberty in the higher 

 apes, we still re<|uire exact information. 4. The tail in the highest 

 apes is relatively as nidimentary as in man. On a priori grounds, 

 we should presume that in the embryo of a tailless ape the tail 

 might persist longer than in the human embryo, but no exact 

 observations have been yet made on the gestation of apes. 

 5. JIan's teeth have no break or interval (a peculiarity shared in 

 by the little lemur, Tarfius). whereas in the gorilla, for example, 

 there is a break. The n Kinder is the same, and the arrangement 

 similar in man and the gorilla ; and even in a baboon, the same 

 number and arr,angement exist ; but in both gorilla and baboon 

 there are to be seen ilidorenccs in the pattern and shape from those 

 of human teeth. The dental formula of all the old world apes is, 

 in fact, the same as that of man : 4 incisors, 2 canines, 2 premolars, 

 and 3 molars in each jaw. 



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 Pond's Extract is a certain cure for ITiplnorrhoids. 

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 Pond's Extract will heal Bums and Wounds. 

 Pond's Extract will cure Sprains and Bruises. 



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