BETWEEN LIMITS BY SUMMATION. 



609 



The equations are 



Op 



The solution of these equations gives 



p= 0-5855571, 

 g= 0-9294971, 

 r= 0-57969554, 



The positions of the thirteen points are given in the annexed figure. 



R R 



Q R 



R 



R 



TRIPLE INTEGRATION. 



In extending this method to triple integration we meet with the curious 

 result, that in certain cases the solution indicates that we are to employ 

 values of the function some of which correspond to values of the variables 

 outside the limits of integration. 



VOL. II. 77 



