300 



<f> (r) be such a him-timi of r thatF(r) is its differential 

 coefficient with respect to r, and let 



the in- n<lrd so as to include, all tli< 



ments b"<ly ; then will 



dU .. ,ir <UT 



JL = -J- , 2 = jr- . /j j . 



da (//> ac 



therefore A' = - p - dxdydz 



_dU_ 

 ~ da ' 



Similarly, the equations Y = - andZ=-' maybe 

 established. 



It may be observed that if in any case, for example that 

 of an infinite solid, the integral U becomes infinite, but the 



differential coefficients , - . . '^ are finite, the prcced- 

 aa do ac 



ing values of A", Y, Z will still be correct. 



For suppose we tike a finite portion of the pnlid ; the com- 



ponents of its attraction will have for values the differential 



coefficients of U. Suppose now that we extend without limit 



the portion of the mass considered, the. components of the 



:i will always be 



dU _ _ 



" da ' '" db' 9 " </< ' 



whether U increase without limit or not. Hence, if these 

 three expressions tend to limits, those limits will be the com- 



