IN PHYSICAL ASTRONOMY. 
23 
mg a solution of the problem by making the constants n, c , y, co, \p 0 and 
<Po vary, 
d n = 0 
sin — (n< + y)dc + c cos (« * + y) d y 4- n e cos (nt + y)dt 
J - C 
2^ 
d t | (k + k') sin ($ + i t + e) + (k — k') sin (<p — it — s) | 
C- A 
cos- 
C — A . C-A 
A - C .C-A 
A {nt + y)dc — c—j— sin — — («t4-y)dy — — — «csin A (»*4-y)d* 
A-C 
2 A 
- d t + k') cos (<p + i t + s) + (k — k') cos (<p — i t — s) | 
since <p = <p 0 + n t nearly 
dc — ~2A~ df { — (* + h ') cos (‘Po + nt 4 - — A — ( nt +Y) + ** + «) 
— (k — k') cos (Vo + n t 4- C (n t + y) — i t — e'j | 
C-A , A-C 
dy 4- 
ncdt — 
A-C 
2 A 
d t | (k + k') sin ( '<p 0 + n t 4- ~J~( n * + y) + i* + £^ 
+ (k — k') sin (p 0 + « < + ~~J~ ( w 1 + Y) — i 1 — e ) } 
, . dc A . / C . . C — A \ . c C — A ( C C-A \ , n 
d " + ^ c s,n U"‘ + — d + » — cos U’ ,<+ — y) i r=° 
d'J'o 
d c A 
nsin w C 
cos 
rasinw A 
( C . . C — A \ . c cos w A ( C . C— A \ . 
( — r n t+ — y J 4 : - — cos I — nt 4 — y ) d i 
\A A ' ) nsin w 9 C \A A ' / 
, c C-A . ( C , . C-A 
4 : ; — sin 
. . dc A / C . . C — A 
a<p 0 - — ; — — cos ( — n t 4- — — 
nsinw C V A A 
(C .. C-A \ , c A n ( 
I — nt 4- — — — y 1 4- — - — - — cos ( 
A r ) nsinw 2 C \ 
c A n ( C , . C- A 
n sin w l C \A A 
y^ d w 
. c C — A . / C C — 
4* — ; — sin I — n t 4- 
nsinw A 
(-2” ,+ ^d dy=0 
From the preceding expressions it may be inferred that 
n = constant. 
= series of cosines without any constant quantity, unless the mean mo- 
