METEORS OF AUGUST AND NOVEMBER. ^33 



meteor's radius vector and heliocentric longitude being sensibly the same as 

 the observer's, and within quantities of the order of the earth's mean distance 

 divided by its semi-diameter, the same as those of the earth's centre, those of 

 the latter may be employed in the computation with sufficient precision, and 

 we shall have, denoting by n the heliocentric longitude of the point [I J] and 

 making u = the angle of inclination of the meteor's tangential direction to its 

 radius vector, reckoned in the plane of its orbit in the order of the actual 

 motion, 



n = ® + U 



SI = ®, for northern = for southern convergent point 



n — S2 = n — © " = n — © " " 



cot i = cot b sin {I — gi) 

 cos u = cos b cos {I — ®) 

 g r sinu ^ \/p — \/a cos ^ 

 p = semiparameter 



1 



a = 



r — g" 



sin ^ = e = sine of angle of eccentricity. 

 V = true anomaly 

 (16) E = eccentric do, 



, M = mean do. ■ 



e r cos V = p — r = a cos^ <^ -— r 

 r sin V = a cos ^ sin E 

 M= E — e sin jE 

 7t = © — V = a — U — V 

 k = Gaussian constant = 0.0172021 

 6) = 206264.67 = radius in seconds 

 n = k \/ {i + (i) a~ t = a~ ' , for Jc = 1, and [i = 0. 

 T ~ a^ = periodic time in siderial years. 

 ti = interval since preceding new year 

 H = 7t + M — n t, = epoch for preceding new year. 



The values of Table VI. were computed by formulae (W), (is), and (i^). The 

 numerical values of the fundamental equations are here subjoined, as they may 

 save the labour of fresh computation by others who may engage in similar 

 VIII. — 2 I 



