36 The Rev. Brice Bronwin on the TJieonj of Planetary Disturbance. 



tlierefore, 



7rf|\ _ d^ ^nr dr^ 



\dT)~dt~l^d^' (^) 



The preceding are all the formula of this kind that are really wanted ; but 

 I shall give some others, on the ground that they may possibly be some time 

 found useful. If we could change t into t in liigher differentials than the first, 

 we might, perhaps, by differentiating the fundamental theorems, or any of the 

 others, relative to t or t, and then changing t into t, find some new theorems 

 which might be made available for simplification, or some way useful. 



From (2), section (1), or -^ =TT2-^^ putting t + for ^, we have 



d:±__^d^ Therefore 

 d-^~ h,edr- -I'lereiore, 



or by (7), 



dr-J ~ hj'\d 



^di^J A/ dt^h]^' dz - ^^> 



Equation (4), section (1), gives immediately 



And from (2), referred to above, after putting t + ^ for f, and differentiating 

 relative to t, we have 



d'^ _ 1 dh 2A dj 



drdt ~ A,$- dt hfi^ dt ' 



or, by substitution from (6), 



\ 1 dh Snh d(r'-\ 



(10) 



I might extend this list, but not without some difficulty ; and as I am not 

 sure of its utility, I shall here leave it. 



