* 9 
the Attractions of Spheroids of every Description. 
positive and not less than unit, the proof of Laplace is not 
liable to much objection; and that his theorem is true to the 
full extent of the enunciation, or for all spheroids that differ 
but little from spheres, whatever be the function which ex- 
presses the thickness of the molecules in the excess of the 
spheroid above the sphere. 
Let us next examine what will happen when the exponent 
of the law of attraction is negative : for this purpose, write 
— n for n in the equation (F), and it will become 
n — 1 
( r ~f> 
n — 2 
C r ~p) 
n—i 
. dm 
| r % — 2rp . 
w -f- 1 
now, according to what has already been proved, the expres- 
sion under the sign of integration must be regarded as a 
finite quantity depending on the nature of the molecule dm : 
therefore, when n is greater than 2, the part of the function 
?) + 
n — I 
2 a 
. V, which is derived from the difference between 
the spheroid and sphere, will, on account of the infinite fac- 
tor, be infinitely great instead of being equal to nothing, as 
Laplace’s theorem would require it to be. 
The case of nature corresponds to the supposition of 11 = 2 
in the last formula ; in this case, after having multiplied by a> 
we shall find 
a 
ds 
dr ) "t" 2 5 
a 
( r—p ) . dm 
{ 
r — 2rp . 7 + p- 
1 
whence we get the value of that part of the function -L V-J- a . 
{“), which is derived from the difference between the sphe- 
roid and the sphere : but the value of the other part, which is 
derived from the sphere, is = — ~ . a 2 : consequently 
