32 
Mr. Ivory on the Method of computing 
method ? On this question I shall confine myself to the two 
following remarks. 
In the first place the method we are speaking of is entirely 
unfit for finding a priori by a direct analysis all the possible 
figures compatible with a state of permanent equilibrium : for 
it is exclusively confined to spheroids whose radii are rational 
and integral functions of three rectangular co-ordinates of a 
point in the surface of a sphere, and it can only be employed 
to detect such figures belonging to that class as will satisfy 
the required conditions. On this account the anal} r sis in No. 
25, Liv. 3e, cannot be admitted as satisfactory : and indeed 
from the words in the beginning of No. 2 6, we may infer that 
the author himself was not perfectly satisfied with the strict- 
ness and universality of his investigation. 
But, in the second place, although it cannot be granted that 
the method of Laplace is general for all spheroids that nearly 
approach the spherical figure, it is nevertheless very extensive, 
and is applicable to a great variety of cases comprehending 
figures of revolution as well as others to which that character 
does not belong. In the class of spheroids that falls within 
the scope of the method, the algebraic expression of the radius 
may contain an indefinite number of terms and arbitrary co- 
efficients ; on which account that class may be considered as 
embracing within its limits all round figures that differ little 
from spheres, if not exactly, at least as nearly as may be re- 
quired. In this point of view therefore the real utility and 
value of Laplace’s solution of the problem of attractions will 
not be much diminished by its failing in that degree of gene- 
rality which its author conceived it to possess. 
In concluding this discourse, I have only farther to recom- 
