200 Prof. J. V. Jones. Calculation of the Coefficient of 



This result afforded a sufficiently satisfactory proof of the accuracy of 

 the calculations, seeing that the result in 8 was obtained by the 

 application of equations (3) and (5), and that it approximated so 

 closely to the result just given. The approximation would be still 

 closer if we had taken account of the neglected terms of the series, 

 K 8 and K 9 . 



11. To find corresponding general expressions for the rates of 

 variation of Me with A, a, and x it is simplest to revert to the 

 expression 



A f* 



_ -^ a \ 



P Jo 



We have dM& - _M? +:^ f * cos 



dx ' ~ x x \ v/ 



(putting p a?/), 



= _ + p 



x x 



,,, ,.- /-2or A , 



aM@ M , A a cos 

 ~7T~ == "7 Aa cos0 2 ., ^ 



A cos a 



= -Aa 



where F and II have the same significations as in equation (6). 

 Similarly d ~ = ck | F ~^^ ( 1? - n ) } 



1 





It is readily deducible from equations (7) that 



+ r + s = 1. 



