THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 171 
With 0 =5° 44 46, == PAB Oil 1” (5), = 7B Al MO tes 
we compute the auxiliary constants for the equator from the formule 
. tg 
cote A = — tg 2 cos 7 iG dy = = 
g g » WY ED = Coe 
— ose cos (£, + «) 
cote B= — ae (Zo ; 
tg 2 cos E, cos ¢ 
cot (6) ee au : sin (Fo a ©) 
tg 83 cos E, sin ¢ 
: ‘5 si OSé« 0 sin 2 sin « 
sm @ = oes 2 sin 6 = SE ECORI sin G! — $3 § = 
sin A sin B sin C 
The values of sin a, sin 0, sin ¢ are always positive, and the angle E, is always 
less than 180°. 
As a check we have 
sin } sin ¢ sin (C — B) 
YU a ane cost 
We find 
A = 293° 45’ 29’’.3, B= 2022 59746795 C’ = 210° 45’ 55’.0 
log sin a = 9.999645, log sin 6 = 9.977735, log sin ec = 9.498012 
Applying néz = + 4’ 45’.2 to the value of g, we have 
nz = 339° 24’ 215 
By means of g or nz = E — e sin E we find 
E = 337° 39’ 23.4 
Then from 
Jr, sin $v = J/a(1 +e) sin 3 E 
Jr, cos} v = /a(l1—e)cos3 E 
