IN PHYSICAL ASTRONOMY. 
45 
Let R n denote the coefficient of the cosine in the development of R which 
corresponds to the number n multiplied by e or e ; , &c. Thus 
r,= /-i^+ ^JLb 30 -- ; ?—b 3 , See p. 3 1 
1 a;- 2 a;- ’ 2 a; 3,1 4 a ( 2 3,4 / H 
Since being the differential of R with respect to s, consider- 
ing z — m and z — v constant 
\ =n j 1 + 2 r 0 j * + £ 
sin (nt — n.t+ s — e,) 
(»-»/) 
+ 
9 / r ( i e2 \ _i_ e2 /v I *. \1 TO, / /, , e 2 \ afijj* 2 e 8 afi,ti 2 e^aR^n 1 1 
2 1 H 1 ~ 2 ) + 2 (r “ + f|8> / ~ 7 1 V + + ( 3 « - 2 », ) + grriij ) } 
sin (2 n t — 2 n t t + 2 e — 2 £,) 
(2 m — 2 n ( ) 
+ j 2 ( r 3 ( 1 — -lA + 11 (,- 10 + r 13 ) 1 — 3 / ( ] + il\ _. a R * n + 3e?g j?'»” + 3e 2 a Y 1 
1 1\ 2/ 2 / p \\ 2j(n—n l ) (4n — 3n t ) (2n—3n i )J] 
sin (3 n t — 3 n t t + 3 s — 3 e y ) 
(3 w — 3 rc,) 
+ {2 \rjl- e l) + $(r n + r l ,)\~!!h!(i + ll\_ a 3jL + + 4 JL?JLm1 1 I 1 
l 1 V 2 / 2 J ft 2 ) (n — n t ) (5n — 4n t ) (3n — 4n l )}j 
sin (4 n t — 4 n / 1 + 4 e — 4 e ; ) 
( 4 rc — 4 «,) 
1 [ n / , r i\ to J aU 6 n I 1 e , , 
+ iH r * + 2j~7i ~— + or^)lh, smi "‘‘ + l '-’ !J > 
+ {2ir s +^^ — — q a ” 1 I sin (2n* — n ( i + 2 e — e, — w) 
l V 2 / [t L (2 n - «,) («-h,)J J(n-n) ' 1 
2 ( ry+ ^) “ -{ n 2a v ) i ; T ”V sin (3 » < — 2 w £ -f 3 e — 2 £, — ct) 
\ 2/ ft 1(3 n — 2 n,) (n — n t ) J J (3n — 2 » ( ) 
. J 2 I r 3 \ ”»< / 3 a R 10 w we 
l V 10 2/ ft 1 (4 n — 3 n t ) (n — n t )\ \(4n — 3n l ) 
sin (4 n t — 3 n i t + 4 e — 3 £, — za) 
