276 
MR. LUBBOCK’S RESEARCHES 
A similar theorem exists with the quantity 
v d R 
° ’ dT’ 
and it will readily be seen 
that all the developments & R, l . r (^7)5 & • (77) and & • (77) maybe effected 
very easily by means of Table II. 
Similarly, if denote the variation due to the disturbance of the earth by 
the moon, 
I11 d R the terms which arise from 
d . $s 
are multiplied by the small quantity m. 
( d a 2 
J and R the terms multiplied byy^, 
r '(i?)= 2B ’ S.r'(**) = 2 »R> 
• • • • 
considering the terms multiplied by— j, 
a i 
r(^)= 3 R, *.^(|f)=S »* 
Hence the value of r (^37^ and e) . r (^77^ may at once be inferred from R 
and 5 R. 
I reserve the formation of these developments and of the final equations for 
determining the coefficients of the different inequalities to another opportunity. 
These equations are voluminous when all sensible quantities are taken into 
account ; but they are formed with so much facility by means of Table II., that 
error is not likely to arise in this part of the process. Error is more, I think, 
to be apprehended in the terms of R multiplied by the cubes and fourth powers 
of the eccentricities; the rest have been verified by an independent method. 
See p. 39 . 
