128 METEORS OF AUGUST AND NOVEMBER. 



§ VIII. — Investigation of the FoRMULiE for computing the elliptic Ele- 

 ments OF an Asteroid from its observed relative Velocity and Di- 

 rection. 



Having stated the general principles bj which this modification of the cos- 

 mical theory is deduced from known facts, I shall proceed to point out the me- 

 thod of computation by which the data in Table VI. are obtained. 



For this purpose let the true motion of the meteors and observer in space, as 

 well as their difference, or the relative motion of the meteors, be referred to the 

 rectangular co-ordinates X, Y, & Z, having their positive values respectively 

 directed towards the vernal equinox, the summer solstice, and north pole of 

 the ecliptic, and let these motions be referred respectively to the sun's mass, 

 earth's mean solar second, mean distance, and mean linear velocity,^* as the 

 units of mass, time, space, and velocity. Let Go, Lo, and Bo denote respec- 

 tively the earth's centre's true velocity, and the longitude and (latitude = 0) 

 of the point Lo of the ecliptic towards which the earth's centre is moving in a 

 tangential direction. Then, by the usual formulae for the transfer from rec- 

 tangular to polar co-ordinates, we have 



Xo = Go cos Lo cos jBo 



(4) Yo= Go sin Lo cos Bo 



Zo = Go sin Bo — 0. 



In the same manner we have for the true tangential motion of the meteors in 

 their orbit towards the point [/ J] wnth the velocity g, 



z =■ g cos / cos h 



(5) y — 9 sin I cos b 



z ■=■ g sin h 



and for their relative motion towards the point [/I /i3] with the velocity y 



^ = y cos ?. cos /? 



(6) yj = y sin /I cos /? 



<^ = y sin /5. 



Also (^) denoting the geographical latitude, (the eccentricity of the earth's me- 

 ridian being neglected,) and making (G) = 365.2564 x sin (8". 5776), G, = 

 ( G) cos (<?)), fi the siderial time, o the obliquity of the ecliptic, we have for the 

 velocity of the observer's actual rotary motion referred to the same axes, 



k 



** This unit is , where k is the Gaussian constant given above. 



86400 - 



