222 
MR. IVORY ON THE THEORY 
wherefore, by substituting and dividing all the terms by e sin (v — m), 
edm = ~ . p e .hdh- cos (*? — .r 2 dv. 
But hdh= d 1 dv, and, 
, \ 1 (dr . dr dv\ 
- cos (v - ro ) = - { re + Tv . Te ): 
wherefore, 
e 
, f dv (d R\ (dr dr dv\ (d R\ r 2 dv 
\_de\dv) ' \de' dv' de) \dr) ) a * 
and, because r 2 dv = a 2 ^/1 — e 2 . d £, 
d e 
(16) 
The variation of s, the longitude of the epoch, must be deduced from the 
equation (9), viz. 
a 9 V” 1 — c 2 / i 7 \ 7 
-^- (ds — dm) = — j-de — dvs. 
From tliis d e may be eliminated by means of the equation (7), viz. 
2 
— hdh = cos (v — m) de + e sin (v — m) dm; 
and the result will be 
a 3 1 — e 2 . cos (p — m) 
r 2 
(de — dm) = 
— T • de^dh - -j cos {v - m) — e sin (v — m) ^ 1 t/s?. 
Now the coefficient of r/ m is equal to 
/i 9\ a 2 / x 2ae 
(1 — e 2 ) ^5 COS (v-m) - — ; 
wherefore, by multiplying by r 2 , we get 
a 2 1 — e 2 . cos (v — m) [dz — dm) = — 2 r . ^ . h d h 
— a { a (1 — e 2 ) cos (y — w) — 2 r e} (for ; 
