T 11 K O U BIT U F U 11 A X U S. 11 



***) 



, + ! 



consequently we have for the derivatives of A from formulae (8) 



!a* ,* -|- a 1 ,' )-f- etc. 



(9) 



'' '-1 / r'i'i" <9 ! 6 ( .\ / (9i ( , ^ftf ^i^X 



= (0) ( a v |- a* ,- ) -f- (1) ( a f- 3a* 1 1- a* - - j-j- etc. 



The derivatives of A being formed in this way, those of h are immediately 

 deduced from the equations 



hen a is equal to |, A is of the form 



a OTt + (!) ^L + (2)V fL + etc.} 

 ^a ^a* 



'1'lie quantity within parentheses is of the same form with A, in the case of * = |. 

 If we represent it by A we shall have 



PA dA' 



^ ^ 



4' being the same form with A, the derivatives : - and ^-^- will be of the form 



(9), substituting | for the index J, and (0)', (1)', etc., for (0), (1), etc. 



IP the case of = | the derivatives are obtained in the same way, which is too 

 simple to need elucidation. 



We have now to pass from the derivatives of A to those of -, the coefficients 



i 



of the perturbative function. The form of these derivatives will depend not on 

 whether the planet is disturbing or disturbed, but on whether it is an outer or 



