IN PHYSICAL ASTRONOMY. 
293 
+ 
3 a 
32 “a^ 
/ 3 a 7 
a 2 A 
2 a/ 5,4 
4a/ 5 ’ 5 J 
a 2 
f 3 a 
l 4 a/ 
,*5,4- 
a 2 , 
'2 a/ 5,5 ’ 
a 
4" ^ 
9a 
32 a ; 
f 3 d 7 
{47 
a ~ h 
2 a/ 3 ’ 6 
•iW 
a 2 
r 75 
[64 
a t, 
a/ 5 ’ 4 
27 
32 
a 2 , 
-A j - 
3 a 
64 a/ 
3a J 
' 57 a b- , 
19 a2 5 - 
a f 
1 
2 a t [ 
. 64 a/ 2 3 ’ 3 
32 a/ 0,4 
64 a/ °’ 3 
J 
and adding the terms which depend upon b 3 , 
a , a 2 , , a , .45 a- , 63 a 3 7 (21 a/ + 96 a 2 ) „ 7 
~9 6 a/ 3,4 16 a/ 3 ’ 5 + 12 a/ 3,6 + 32 a/ 5,3 32 a/ 3,4 + 128a/ a bb ’ 5 
9 a 3 7 9 a/ / 
~ 64 a? 5)6 “ 1 98 a 3 
128 a. 
which may be still further reduced. R m , J? 213 , /? 2;3 , and J? 312 may be obtained 
in a similar manner. 
The following Table shows the arguments which, by their combination with 
the arguments 1, 2, 3, 12, 13, 31, 32, 64, 65, 73, 74, 112, and 113, 
by addition and subtraction produce the arguments 155, 174, 213, 
273, and 312. 
1 1 
2 
3 
12 
13 
31 
32 
64 
65 
73 
74 
112 
113 
155 j 
154 
156 
153 
157 
152 
158 
53 
52 
11 
- 10 
192 
191 
[-155 
m{ 
173 
172 
171 
72 
71 
53 
52 

11 
192 
191 
,174 
175 
176 
177 
- 30 
- d 
- 10 
co 
01 
212 
211 
-210. 
111 
72 
71 
11 
>213 
214 
215 
216 
-110 
-231 
-232 
- 30 
- 41 
- 10 
273 { 
272 
271 
-270. 
131 
330 

-273 
274 
275 
276 
-130 
-291 
-292 
-331 
312{ 
311 
-310. 
-321. 
131 
330 
] 
-312 
313 
314 
315 
-130 
-291 
-292 
-331 J 
If 
r S, — = r\ cos ( nt — n t t) + r' 2 cos(2w£ — 2 n t t) + r' : ,cos (3 n t — 3 n t t) + er\„cos(n t — 2n t t + w) 
+ er'u cos (2 nt — 3 n ; t + •or) -f &c. 
r, $ . — =r/,cos(re^— re/) + r/ 2 cos (2nt — 2n l t) + r/ 3 cos (3re t— 3ra/) + er/, 2 cos (re t — 2 re/ + w) 
r i 
+ er/ 13 cos (2re £ — 3w/ + ot) + &c. 
J X = X, sin (re t — re/) + X 2 sin (2 nt — 2 re/) + X 3 sin (3 re t — 3 »/) + e > 12 sin (re t — 2 re/ + ot) 
+ e X 13 sin (2 re t — 3 re/ rer) + &c. 
