﻿358 Prof. Cayley on the Attraction of 



proceeded from some object at S' ; let l n be the angle B L S', 

 then (Main, i Prac. Astron.') 



sin 4 _ r fi 

 sin* r + h p n ' 



where z> the apparent zenith distance, is in this case 90°, and 

 fjb , fin the refractive indices of dry atmospheric air at the surface 

 of the earth and at the highest point of the atmosphere respec- 

 tively. The value of fi is 1*000294, and that of fj, n is, of course, 

 unity. 



But l n —<f> = z—v J 



therefore 



4=90 o +(£-v=90°-i(<9-3<£), 

 and therefore 



r o + A=/* o ?osec£(0 — 30); 



and if we take \{6 — 3</>) to be 7° 15' ±15', the resulting value 

 of h is 33 miles + 2 miles. 



This result found by refraction is therefore in accordance with 

 the value of h already found by means of the elastic properties of 

 air ; but, as we have already said, this method does not admit of 

 any accuracy. 



With regard to that medium whose existence is made apparent 

 by shooting-stars, and by displays of the aurora borealis at great 

 distances above the earth's surface, there is very little to be said 

 at present. If it is a ponderable fluid of definite extent, it must 

 be of a different nature to atmospheric air, and it will bear about 

 the same relation to the atmosphere that the atmosphere itself 

 does to the ocean surrounding the earth ; but whatever may be 

 its nature, it must be distinguished from the atmosphere proper, 

 the subject of the above article. 



XLVII. On the Attraction of a Terminated Straight Line. 

 By Professor Cayley, F.R.S.* 



RITE for shortness (a, b, c ; e) to denote the shell included 

 between the ellipsoids 



r 2 ifi z* r 2 ?y 2 2* 



J + l + ^la^+l+^a-M)* 



(where e is indefinitely small) ; then, if the ellipsoids 

 x* V 2 z 1 '\x? iP- z 2 



^tl + ^lw^ + js + ^-l 



are confocal, the attractions of the shells (a, b, c; e) and (a', b\ d; e) 



upon any exterior point P are proportional to their masses. 



* Communicated by the Author. 



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