THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 10 
In a similar way we have 
(0) = BP Sa ey 
il = ts @ T258 > 7 
Col 
a 
(35) 
In case of the third coordinate we also compute the coefficients of the arguments 
having no angle y from those having + y. For this purpose, putting x = 0 in the 
expression for a’ we have 
d PO) ad RO a -+- a) 
OF SS eS Oe) (—1) 
Cy = We apart CLE 1g = 4 (4 + o ); 
where 
dk 
9 de 
n — 
B d R® 
de 
For 7) we then have 
(0) 
72 =—(Be+ Ye + etc.). (36) 
Perturbation of the Third Codrdinate. 
Let 6 the angle between the radius-vector and the fundamental plane, 
@ the inclination of the plane of the orbit to the fundamental plane, 
v —o the angular distance from the ascending node to the radius-vector. 
We have then 
sin 6 = sin 7 sin (v—o). 
If we use for 7 and o their values for the epoch and call them 2 and Qo, & being 
the longitude of the ascending node, we have 
sin b = sin % sin(v— Q)) + 8; 
s is the perturbation. 
Thus we find 
s = sin 7sin (v—o) —sin 4%, sin (v— Qj). 
A. P. S.— VOL. N. XIX. 
