210 



• KNOWLEDGE 



[April G, 1883. 



.t'S 



'W^^'^m 



" Let KnowleHire grow from more to more." — At.FREn Tennvson. 



3lrttn-6 to tl)e editor. 



Only a small proportion of Letters received can possihly he in- 

 Kerted. Correspondents must not be offended, therefore, should their 

 letters not appear. 



All Kditorial communications should be addressed to the Editor of 

 Knowledge ; all Business communications to the Publishers, at the 

 Office, 74, Great Queen-street, W.C. If this is not attended to, 



DELAYS arise FOR WHICH THE EDITOR IS NOT RESPONSIBLE. 



All Remittances, Cheques, and Post Office Orders should he made 

 payahle to Messrs. Wyman & Sons. 



The Editor is not responsible for the opinions of correspondents. 



No C0M.MUNICATI0NS ARK ANSWERED BY POST, EVEN THOCGH STAMPED 

 AND DIRECTED ENVELOPE BE ENCLOSED. 



ST.A.YS AND FAT. 



[774] — For their own sakes, and for that of the forthcoming 

 generation, it is to be hoped that Knowledge has many readers 

 among the fair sex, and that all of them have carefully followed 

 the discussions on stays. The demolition of every argument in 

 favour of those barbaric bandages has been so complete that 

 reasoning readers must be urged to make the effort necessary to 

 overcome the vicious habit of wearing them. The letter by a lady, 

 page 1G2, shows how it is to be done so cleverly and practically, as 

 to leave no excuse for continuous leaning on the delusive support. 



The letter of " Lennox Browne, F.R.C.S." supplies a further 

 argument beyond that wliich he has used. The tight-lacing variety 

 of the liuman species care little for health or comfort, and are not 

 much addicted to reasoning ; they are not to be warned by any de- 

 monstration of damaged lungs, weakened muscles and congested 

 brains, but there is one horror which none can bear to contemplate 

 — ^viz., fat. 



What is tat ? It is an accumulation of unburnt body-fuel. How 

 can we get rid of it when accumulated in excess ? Simply by burn- 

 ing it away — this burning being done by means of the oxygen 

 inhaled by the lungs. If, as llr. Browne has shown, a lady with 

 normal lung capacity of 125 cubic inches, reduces this to 78 inches 

 by means of her stays, and attains 118 inches all at once on leaving 

 them off, it is certain that her prospects of becoming fat and flabby, 

 as she advances towards middle age, are greatly increased by tight- 

 laeing and the consequent suppression of natural respiration. 



Formerly, when I lectured to ladies on Philosophy and the Laws 

 of Health, I displayed the well-known features of the Venus de 

 Medici, and the victim of tight-lacing, with her contracted waist 

 and crushed ribs. I fear that there were some among my pupils 

 who admired the latter, and (h-ew mental pictures of how a riding 

 habit might be fitted thereon. 



It would bo well to supplement these by a third picture, showing 

 the effect of suppressed respiration and want of muscular exercise 

 on the figure, when the victim had attained the age of forty, or 

 thereabouts. W. Mattieu Williams. 



SATURN'S RINGS. 



[775] — Whilst agreeing with Professor Adams that the figure of 

 Saturn and his rings sent to you by me finiu Vol. I. of " Philo- 

 sophical Transactions" might have been caused in the way he 

 suggests, I do not think that it was so. The very object of the 

 communication was to call attention to the " notches or hoUow- 

 ness," and to endeavour to find out whether others had observed 

 them. Letters are stated to have been written to "the worthy 

 author of tlie systeme of this planet, that he would now atten- 

 tively consider the present figure of hisnn.ics or riiir; to sec ivhether 

 the nppearaiice be to him as in this figure." If there had been no 

 " notclies or hollowness " there would have been nothing to write 

 about. Again, tlio writer of the notice states that " it was thought 

 fit to insert hoi-e tho newly-related account," "that other curious 

 men in other places might bo engaged to join their observations 

 witli him, to see whether they can find tho like appearance to that 

 represented here, especially such notches or hollowness as at A and 



B." All this follows naturally from Ball's expression, " A little 

 hollow above and below." In the number for July 2, ICGO, there is 

 another good sketch of Saturn, referring to an observation made by 

 Hook on June 29, 16G6. No reference is made to Ball's observa- 

 tion. The communication refers to " black lines crossing tho ring 

 and crossing tho body " as being plainly perceptible. Hook says, 

 " Wliether shadows or not I dispute not." Thos. Ward. 



ROTATION OF PLANETS. 



[77G] — We are told that the planets are retained in their orbits 

 by tho compound action of two mutually opposing forces : — first, 

 the centripetal force, or gravitation, by which a body is attracted to 

 t he centre of gravity, which, in the case of the planets, is the sun ; 

 and secondly, the centrifugal force [now generally called tendency, 

 rather than force, R.P.], by which a body in motion tends to pro- 

 ceed in a straight line. But what force causes our planet to revolve 

 on its own imaginary axis, .and that with such unvarying speed ? If 

 set going at first, like a top from the string, how is it that its speed 

 does not gradually relax, and at length come to an end ? 



G. M. (Southport). 



[The rotation could only be "slowed" by some resisting force. 

 Where is any exerted ?] 



THE MOON'S VERTEX. 



[777] — Perhaps the following considerations may tend to clear up 

 the diffieulty expressed by Mr. F. C. Green, at the conclusion of 

 letter 75!) (p. 168). Imprimis, the angles of stars from the 

 moon's vertex are given in the fortnightly " Face of the Sky " for 

 Greenwich. Of course, they would vary with change of latitude, 

 &e. In the next place, the great circle passing through the pole and 

 the Moon's centre would only give us the Moon's vertex when she 

 was on the meridian. It would intersect her upper limb at its 

 north point. The method of obtaining the vertex from this — in other 

 words, of finding the angle formed by the intersection of a vertical 

 circle and hour circle, for any latitude, declinatisn, and hour angle 

 of the Moon from the meridian — is a matter of spherical trigono- 

 metry, which will be best illustrated by a figure .and example. 



Here P N is the latitude, which we will^call (p. P M the Moon's 

 N. Polar distance, the complement of which is her declination S. 

 Z P M her hour angle, which we call P. Z M, her zenith distance. 

 Then, from Z draw Z Q perpendicular to P M, and call P Q,.r. Now, 

 cos P= tan ,c . tan ip : or, tan r = cos P . cot ^. 



Again, sin QM : sinPQ::tan P : tan M : or,tanM = ®lB^^i''"? 



sin Q M 



= sinji^tanP rpj^j^ j^^gjg g^ jj^ tj,e one we are seeking, is technically 



cos (x + S) 

 called the parallactic angle. Let us try to make this intelligible by 

 putting our example into figures. In latitude 54" 11' N, the moon 

 is 4h. 20m. from the meridian, and her North Declination is 16° 30'. 

 What is her parallactic angle? Here we have P = 4h. 20m.=65°, 

 = 54° 11', and ^ = 16° 30'. 



Then we say cos P 65° 9625948 sm r 16° 57' 40" 9-4(i4970 



cot 54° 11' 9858336 tan P 65° 0-331328 



j;= 16° 57' 40" tan 9-484284 sec (.i- + f) 33° 27' 40" 0-07S6!'9 



Parallactic angle = 36° 51' 57" tan 9-874097 



So that the moon's vertex would be 36° 51' 57" from her North 

 Point. It is, of course, needless to remind Mr. Green with refer- 

 ence to the last formula, that multiplying by the secant is the same 

 as dividing by the cosine. 



A Fellow of the Royal Astronomical Society. 



THE HAMILTONIAN SYSTEM. 



[778] — Having read your articles on the Hamiltonian system, 

 and having been anxious to acquire German, I determined to make 

 use of this method. I chose " Robinson der Junger," and this is 

 how I worked. I read over carefully two jiages, noting words 

 which wore new to me. Then I read those two pages carefully in 

 the original German. The next day I read two more pages, and so 



