]VIay 15, 1885.] 



♦ KNOWLEDGE ♦ 



405 



t^" 



_^ V ' -LUSTRATED 



MAGAZINE OF SCIENCE 



PlainlyWorded-ExactlyDescribed 



c 



LOSDOX- FRIDAY, MAY 15, 1885. 



Contents of No. 185. 



PAGl 



Mi'teors and Falling Stars. By 

 R. A. Proator *.'5 



The YooD^ Electrician. (i7iif«.) 

 BtW. SUngo 406 



The'PhilosophT of Clothing. VIII. 

 By W. Mattieu Williams -107 



Pleasant Hours with the Micro- 

 scope. ilHut.) Bt H. J. Slack 403 



Other Worlds than Ours 410 



iM.'Vclesin 1835. {lUus.) 411 



Chapters on Modern Domestic 

 Economy. {Illu$.) 413 



Evolution of the Sense of Beauty. 

 By C. C.W.Naden 414 



PAOB 



Firearms and Military AVoaponB at 



the Inventions Exhibition 415 



First Star LesBone. {With Map.) 



Br K. A. Proctor 41G 



George Eliot's Dog, By Kobert 



Buchanan 41*> 



Flij^ht of the Buzzard 418 



Editorial Gossip 419 



Reviews 419 



Correspondence 420 



Our Mathematical Column 423 



Our Inventors' Column 4^i 



Our Whist Column; 42-5 



Our Chess Column 425 



METEORS AXD FALLING STARS. 



By Richard A. Proctor. 



{Continued from page 386.) 



LET it be remembered that the conditions of the pro- 

 blem are purely dynamical. We know that a 

 comet's head obeys the laws of gravity, and whatever 

 peculiarities may affect the motions of the matter of 

 comets' tails are not by any means such as would help to 

 render easier the captures conceived by SchiaparellL Con- 

 lining ourselves, then, to gravity, we can determine readily 

 in what way a comet might be captured. Take the case of 

 a particle travelling towards our solar system from out of 

 the interstellar depths under the influence of the sun's at- 

 traction. Such a particle may be regarded as practically ap- 

 proaching the sun from an infinite distance,* and we know its 



• The point considered is the velocity of the particle at given 

 distances from the sun ; and the estimated velocity is appreciably 

 the same whether the particle be supposed to come from the dis- 

 tance of the nearest star or from an infinite distance. This is 

 easily seen from the formula 



^t-^) 



where r represents the radius of a circular orbit described with 

 velocity i', and V is the velocity at distance r, of a body travelling 

 in an orbit having mean distance a. For, regarding the earth's 

 orbit as unity, put 



r = earth's distance = unity, 



f = earth'3 velocity = 183. 



taking a mile as the unit of length, and a second as the tinit of 

 time ; (though we have put r = unity, this does not force ns to take 

 T as our unit of length, because we only require to consider the 

 ratio in what follows). Then we have — 



V = 18-3v/2 



'V 2 a 



23-9 ' 1--:^- 



4 a 



1_ 

 32 n^ 



-Ac. 



= 25-9, 



if a is made infinite. But if a be taken equal to half the distance 

 of Alpha Centauri, say = 100,000, we have 



V=25-9-O-00O06475-O-OOOOOO00O8O9373 -smaller terms, 



all the terms after the first being together manifestly less than 

 0-00007, or about 4i inches. In other words, whereas a body 

 approaching the sun from infinity would have a velocity of about 

 25'9 miles per second, a body approaching the sun from the distance 

 of Alpha Centauri, so that its mean distance may be regarded as 



velocity at given distances fiom the sun. Thus, when at the 

 distance of Neptune its velocity would be I 7 miles per second; 

 at the distance of Uriinus, 59 miles per second ; of Saturn, 

 S-3 miles; of Jupiter, ll-l miles; of the asteroids, from 

 l."i to IG niile.s per second ; and the velocity in crossing the 

 distances of Mars, the Earth, Venus, and Mercury, would 

 be 20 S miles, 25 9, 30-3, and 41 ■4 miles per second re- 

 spectively. Now we know that the greatest velocity which 

 any given planet can communicate to a body approaching 

 it under its .sole influence from interstellar space, is very 

 much less than the velocity which such ()lanet can commu- 

 nicate to a body approaching it under the sun's influence in 

 addition to its own. For the comnuinication of velocity to 

 amoving body is a proce.«s requiring time, and in the latter 

 of the two cases just considered tho body is for a much 

 smaller time under the influence of the planet.* And the 

 velocity which a planet can communicate under any cir- 

 cumstances represents the velocity which, under similar 

 circumstances, the planet can withdraw from a moving body. 

 So that Jupiter, Saturn, Uranus, and Neptime are severally 

 unable to tleprivo a particle which, drawn in by the sun's 

 attraction, passes near to them, of more than a portion of 

 the velocity which these planets are respectively able to 

 communicate to a body approaching them from infinite 

 space. Taking, for example, the case of Jupiter, we may 

 regard 38 miles per second as a sort of negative fund from 

 which Jupiter would have the power of drawing, to reduce 

 the velocity of bodies moving from him, if Jupiter were 

 the .sole attracting influence under which such bodies had 

 acquired their velocity ; hut in the case of bodies which 

 have been drawn inwards by the sun's attraction, the fund 

 is reduced to about 28 miles per second. Now this might 

 seem ample when we remember that the velocity of a body 

 crossing the path of Jupiter under the sun's influence alone 

 would be but ll'l miles per second. But it is to be 

 observed that the estimate only applies to bodies moving 

 all but directly from Jupiter, and coming all but into 

 contact with his surface. The power of Jupiter in this 

 respect diminishes rapidly with distance from the surface. 

 At a distance from Jupiter's centre equ.al to four times his 

 radius, his power is already diminished one-half, and this 

 distance is far within that of even his nearest satellite. 

 Moreover, it is to be noticed that a body which moves in 

 such sort that Jupiter exerts his most powerful retardative 

 influence, must have moved for some time previously in 

 such a way that Jupiter exerted nearly his most powerful 

 accelerative influence.! It may be readily shown to be 

 impossible for Jupiter to withdraw much more velocity 

 than he had already communicated ; and similar remarks 

 apply, of course, to Saturn, Uranus, and Neptune. 



{To he continued.) 



half the distance of that star, would have a velocity less by 

 i\ inches per second, a difference so small that it may be regarded 

 as evanescent. It is a curious consideration, however, that minute 

 though such differences are when we are merely comparing velo- 

 cities, yet distances due to such differences in the enormous time- 

 intervals which tho study of comets introduces to our consideration, 

 are to be measured by thousands of miles. 



* See the accompanying papers on the " Mathematics of Meteoric 

 Motion." 



t It is manifest that a particle in approaching from without 

 must be, in tho first instance, accelerated by any planet to which 

 it draws near, no matter what the direction may be in which the 

 particle arrives. It may begin to be retarded, however, before it 

 has reached the distance from the sun at which the disturbing 

 planet is travelling. In any discussion of the change of path as to 

 position, we should need to inquire very carefully into the manner 

 of approach ; but in the above discussion we are only inquiring 

 into the charge of velocity. 



