IN PHYSICAL ASTRONOMY. 
337 
h 2 e d 7S -f {2 + cos X} sin X r 2 d X — h 2 r 2 cos X (~j~) d X = 0 
, . a cos (X — v) /d R\ . 
dl + ^-V“ (dl)dx = 0 
d, + r 2 _I_^—)dX = 0 
by equation, p. 336, line 12, [h a (1 — e 2 ) = h 2 , and by equation, line 17, e — e'. 
de = -^^2e—- 2 cos (u — a) — e sin (u — a) 2 j> d R — ~~ sin ( u — a) ("j—) d v 
edo!=y|e cos (u — a) — 2 sin (u — a) d R + —■ cos (u — • a) (^r) d v 
J'n d £ + £ — 73 = t» — cs — e sin (u — a) 
ds — d 73 — — {1 — e cos (u — a) } d a — sin (u — a) d e 
i 
d t - d » = - a , - v \ d. - { a(1 r _^ + 1 } sin ( U — «)de 
Z 4 
= a { 1 — ■ e cos (u — a) } 
1 4- e cos (x — ot) 
d « = ~ cos (X - w) + e + e cos (X - n)zj (i|) 
a? ndt V l — e* • \ /d -R\ 
. r sin (X - 
e d t < r = 
f 4 
f=i { 2 + e cos ( x - ®) } sin (* - w ) (ttx) 
. a 2 n d £ V 1 — e 2 /. \ { d R \ 
+ COS (X - nr) 
d £ - dnr = - ynr^dnr + ff n{ 1 (^) 
v p { 1 + e cos (X — ra-) } V d r / 
If the longitudes be reckoned from the perihelion of the planet P, 
d« a n (cos X + g) / dR\ _ 7 n,a^n V 1 — e 1 j" rj sin A/ r sin 
dt f 4 -v/ 1 - e 2 V"dX/ ~ p | r ; 3 ~*~{ r s_2rr/ 
sin X — r, sm X, 
cos (X — X/) + r / ' 2 }^' 
2 x 2 
