602 
MR. LUBBOCK’S RESEARCHES 
+ { R 3 + e- R 3 -f ef R s + &c} ecos (int — in t t — n t + w) 
-f“ &c. 
[ 3 ] 
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 
it + 3x 
43 
i t + 3 x + z 
2 
X 
23 
2 X + 2 
44 
3 x — z 
3 
it — x 
24 
it — 2x — z 
45 
i t — 3 x + 2 
4 
i t 4" ^ 
25 
i t -f- 2 x z 
46 
i t 4- 3 x — 2 
5 
z 
26 
2 X — 2 
47 
2x + 2z 
6 
it — z 
27 
it — 2 x + z 
48 
it — 2x — 2z 
7 
it -f- z 
28 
i t + 2 x — 2 
49 
it-f-2x + 2z 
8 
2 x 
29 
x -f 2 z 
50 
2x — 2 z 
9 
it — 2 x 
30 
it — x — 2 2 
51 
it — 2 x + 2z 
10 
it + 2x 
31 
i t + x + 2 z 
52 
i t + 2 x — 2 z 
11 
x + z 
32 
X — 2 2 
53 
X + 3 2 
12 
it — X — 2 
33 
it — x + 2 z 
54 
it — x — 3 z 
13 
i t -f- & “1“ ^ 
34 
i t + x — 2 z 
55 
i t + x + 3 2 
14 
X — z 
35 
3 2 
56 
x — 3 z 
15 
it — x — z 
36 
it — 3 z 
57 
it — x + 3 z 
16 
it + x — z 
37 
i t + 3 z 
58 
i t + x — 3 2 
17 
2 z 
38 
4 x 
59 
4 2 
18 
it — 2z 
39 
i £ — 4x 
60 
it — 4 z 
19 
it + 2z 
40 
it + 4 x 
61 
it + 4z 
20 
3 x 
41 
3 x + z 
, , e 2 /, 3 e 2 \ e 2 /, 2 e"\ „ , 9 , 0 , 4 4 
r = 1 + — — ell — — ) cos x — ( 1 — ) cos 2 x + — e 3 cos 3 x + — e 4 cos 4 x 
2 \ o / 2 \ 3 / 8 3 
ill = e «— f 1 cos a? — e 1 — cos 2 x + ~ e 2 cos 3 x + ^ e 3 cos 4 a; 
de \ 8 / \ 3 / o 3 
^=l(‘ + t)-(‘ -1 < ’ , ) C0SX_ ^ c (‘ " 
[0] [2] [8] 
17 71 
e- cos 3 .r e 3 cos 4 £ 
ft 94 
[20] [35] 
= 2 ^ 1 — sin x + A-e ^ 1 — e 2 ^ sin 2 x -f ^ e 2 sin 3 x + AA e 2 sin 4 x 
[2] [8] [20] [35] 
d it _ d 71 d r ^ d it d[X 
de dr de dxde 
rd K dr d J? d_A 
dr r d c d /. d e 
