602 
MR. LUBBOCK’S RESEARCHES 
+ {R 3 + e- R 3 + e^R s + &c} ecos (int — inj — n t + vr) 
[3] 
+ &c. 
where the indices are as follows, and the same as in my Lunar Theory, merely 
writing the indeterminate i instead of the number 2. 
0 
0 
21 
it — 3 x 
42 
it — 3 x — z 
1 
i t 
22 
i t + 3 x 
43 
i t + 3 x + z 
2 
X 
23 
2 x + z 
44 
3 x — z 
3 
it — x 
24 
it — 2x — z 
45 
i t — 3 x + z 
4 
it x 
25 
it + 2x + z 
46 
i t 4- 3 x — z 
5 
z 
26 
2 x — z 
47 
2x + 2z 
6 
it — z 
27 
it — 2 x + z 
48 
it — 2x — 2z 
7 
it z 
28 
i t + 2 x — z 
49 
it + 2x-j-2z 
8 
2x 
29 
x + 2 z 
50 
2x — 2 z 
9 
it — 2 x 
30 
it — x — 2 z 
51 
it — 2 x + 2z 
10 
it + 2x 
31 
it + x + 2 z 
52 
it + 2x — 2z 
11 
x + z 
32 
x — 2 z 
53 
x + 3 z 
12 
it — x — z 
33 
it — x + 2 z 
54 
it — x — 3 z 
13 
it + x + z 
34 
i t + x — 2 z 
55 
i t + x + 3 z 
14 
x — z 
35 
3 z 
56 
x — 3 z 
15 
it — x — z 
36 
it — 3 z 
57 
i t — x + 3 z 
16 
it + x— z 
37 
i t + 3 z 
58 
i t + x — 3 z 
17 
2 z 
38 
4 x 
59 
4 2 
18 
it — 2z 
39 
it — 4x 
60 
i t — 4 z 
19 
it + 2z 
40 
it + 4 x 
61 
it + 4z 
20 
3 x 
41 
3 x + z 
J'=l + 
e 2 /, 3 e 2 \ 
"2 -e ( sV C0SI 
-10 
2e 2 > 
3 ) 
9 4< 
l cos 2 x + — e 3 cos 3 x + — e 4 cos 4 x 
' 8 3 
dr_ 
de ~~ 6 
^1-jj- e 2 ^ cos# — e ^ 
'-¥) 
27 16 
| cos 2 x + — e 2 cos 3 x -\ -e 3 cos 4 x 
8 3 
|<M 
II 
^ cos X — 
M- 
l — — e 2 ^ cos2;c 
9 ) 
[0] 
[2] 
[8] 
17 71 
— — e 2 cos 3 x -e 3 cos 4 x 
8 24 
[20] [35] 
= 2 ^ 1 — sin x + — e ^ 1 — e 2 ^ sin 2 x + ~ e- sin 3 x + e 2 sin 4 x 
[2] [8} [20] [35] 
d R_ dRdr_j_dRdA 
de dr de dA de 
_ r d R dr d R d*. 
dr rde dA de 
