368 
MR. LUBBOCK’S RESEARCHES 
+ {- 2-8843819 r 12 + 37558426 R 12 + 2-3762929 RJ} sin (2 t-x- z) 
+ {2-1652119 v 13 - 1-8430088 R l3 — 9-9454546 R l3 '} sin (2 t + * + z) 
+ { — 3-3350850 r I4 + 4-0300110 R u + 2-6232753 R 14 '} sin (x - 2 ) 
+ { - 3-4377718r 15 + 4-1169189 R 15 + 2-7021571 R 15 'j sin (2 t-x + z) 
+ {2-1945476 r l6 - U9298049 R iS - 0-0433913 i? I6 '} sin (2 1 + x - z) 
+ {- 1-2465621 r 17 + 3-1977141 J? 17 + 3-1977141 R 17 '} sin 2 2 
+ {2-0153626 r I8 - 2-1927325 R I8 - 0-4983470 fl 18 '} sin (2 t - 2 2 ) 
+ {1 -8857018 r ly - 1-8857018 R ig ~ 0-1575509 Rj} sin (2 * + 2 2 ) 
+ {- 6-4194035 r 101 + 7-1997263 R 101 + 5-6956376 R 101 '} sin l 
+ {3-1744332 r 102 - 5-9693425 R 102 + 5-8838691 R 102 '} sin (t - x) 
+ {4-2060990 r, 03 - 4-3466666 R l03 - 2-5333440 R w3 ’ } sin (t + x) 
+ {- 4-32409291- 104 + 5-1933516 R 104 + 37101653 R 104 '} sin (<- 2 ) 
[2-4899904] 
[1-3488787] 
[2-3541741] 
[2-3383041] 
[1-3946097] 
[3-4147879] 
[1-3033627] 
[1-1626061] 
[5-3481901] 
[6-4098870] 
[3-4884264] 
[3-6803018] 
The preceding expressions serve to show the extent to which the approxima¬ 
tion must be carried in the calculation of the quantities X, R, &c. 
If we take the term 5-6361652 R 3 , since log. = 7*7464329, it is evident 
that in order not to neglect -01" in the value of the coefficient of 
cos (2 t—x) in the development of h R must be calculated exactly to the 
fifth place of decimals, but not beyond. The number 4-1857212 is the loga¬ 
rithm of the quantity ^ expressed in sexagesimal seconds, and 
serves to show in like manner how far the approximation must be carried in 
d R 
the calculation of xr. 
When the square of the disturbing force is neglected, 
R 2 
m t a 3 
2|*V 
R a = 
m t a 3 
8 jx af 
m, a 3 
2 ix a 3 
t" 2 — 3 r 0 
r K — 3 r 0 
c * — 1 + 3 r 0 
2m l a 3 _ j 7 m i a 3 
[x a t 3 . 2 [x a t 3 
The equation of p. 5, line 8, gives r 8 = 0. 
