170 A NEW METHOD OF DETERMINING 
Reducing the above date to Berlin Mean Time, and applying the aberration 
time, we have, for the observed date, 1894, Sept. 19, 72800, 
OG = sas? UB) sel, g = 60° 24’.1. 
Forming the arguments of the perturbations with these, we find 
noz = + 4 437.2, ps LBB, ee OH (Sy 
To convert » into radius as unity and in parts of the logarithm of the radius 
vector we multiply by the modulus whose logarithm is 9.63778, and divide by 206264’.8. 
Thus we have from » = + 3”.6, the correction, + .000008, to be applied to the loga- 
rithm of the radius vector. ; 
U 4 
In case of —— = — 2’.8, we have 
cost 
(2a — 28 S<alcos = 1 a) 
Converting into radius as unity, we have éz’ = — .000055. 'The codrdinate 2’ is per- 
pendicular to the plane of the orbit. As we will use coordinates referred to the 
equator we have, to find the changes in a, y, z, due to a variation of 2’, which we have 
designated by éz’, the following expressions : 
da = (sin 7 sin 2) dz’ 
doy = (— sin 7 cos Q cos ¢ — cos? sin «) éz’ 
dz = (— sin 7 cos Q sin e + cos 7 cos «) 42 
where ¢ is the obliquity of the ecliptic. 
For 1894 we find 
da = (— .0404) dz’, dy = (— .3123) de’, oz = (4.9491) dz’ 
And for the date we have 
da = + .)00001 dy = + .000011 dz = — .000033 
