77 
extensive Class of Spheroids, 
Before we pursue the investigation farther, we shall stop to 
demonstrate a property of the attractions of a shell of homo- 
geneous matter bounded by the surfaces of two ellipsoids, 
similar to one another and similarly placed, on a point within 
the shell. If we suppose k to denote the axis of the greater 
ellipsoid, and put h for the corresponding axis of the smaller 
one ; then the value of V relatively to the latter solid will be 
found merely by changing k into h in the last expression ; be- 
cause s contains no quantities but such as are common to the 
two solids : therefore the value of V, relatively to the shell 
of matter included between the two surfaces, will be equal to 
a quantity which is independent on the position of the attracted 
point : therefore the differential coefficients of V for any co- 
ordinates of the attracted point are evanescent ; and conse- 
quently so are the attractive forces parallel to the co-ordinates 
(No. 6). Therefore a material point within such a shell is 
attracted equally in opposite directions. 
Let us now investigate the value of 
put y> = £ -ff ( x — <? ) . uff ; q =/ -j- ( i — /) . [jS ; then s =-p . 
5 
