53] ON THE ATTRACTION OF AN INDEFINITELY THIN SHELL. 425 



be 



Hence 8X = kirpx - 



a 



v A c f"i 



. ' . A 477003 - 



a o 



ttj, 6 1} Cj are the semi-axes of the ellipsoid confocal with the outer given 

 ellipsoid and passing through the attracted point. 



Oj s 1 



,, , r and -4 = 



therefore y = 47rpy r 

 ^ J a- } 



and Z=ktrpz |< 



r a- j 



a' 



u 3 du 



u'du 



If in place of u we make X the independent variable where 



Su SX 



and so - = 



then X = 2irpxabc , 



I \ I ( ri~ 4- X V //i 2 



with similar expressions for Y and Z, where 



Xj = / a 2 = 6/ b' = c 1 2 c 2 . 



54 



