IN PHYSICAL ASTRONOMY. 
+ {+ ~^{ r3, “ A3 } “ ^r 2s i47} ee / sin (4^-^-2) 
29 
[138] 
+ { + i = { r ‘' _ x ‘} + ~ x| y 2 5 147 }e e, sin (4 t + x + z) 
[139] 
+ j- ^{ r ‘ ,_Xl } + ^{ rs, “ Aj } + ^y 2s w} ee / sin (4*-*-*) 
[140] 
+ {- (4 t + x — z) 
[141] 
+ { — ^ { r i'- A,} + ^ y 3 «i47 1 e,° sin (4 f — 2 z) 
[142] 
In order to verify the developments which have been given, suppose 
1 1 = m ‘ a . e cos (2 t — x) 
17 a t 3 
r 8 — = e. rJ cos z $ A = e. \ b sin z 
r 
neglecting l s, 
t being used in the sense nt — n t t. 
$ R = — '—j y —j a ee i{ cos (2 t — x) r-J cos z + sin (2 t — x) A 5 sin z } 
_ m, a _ / _ 38 f , cog (ot — x + z) — ^ r-' cos (2 t — x — z) 
a 3 '[ 17 , \7 K , 
+ ^ \ 5 cos (2 < — x + z) — X 5 cos (2 £ — a: — z) j> 
= ^|! j — ?||r 5 ' — As | ee,C0S (2 * — * + z) — ^ jr 5 ' + X 5 j ee, cos (2 * — z - z) j 
[15] [12] 
which terms are in fact given in the development of IR, p. 11 and p. 10. 
Development 
