567 
NOTES AND REFERENCES. 
173. I attach some value to this analysis and development of Laplace’s Method, 
showing how it leads to the actual expression for the Potential of an Ellipsoid upon 
an exterior point in a series of terms of the form ^a 2 + /3 2 ^ + 7 2 
being in fact the series deduced by me in the year 1842 from a result of Lagrange’s; 
see vol. I., Notes and References 2 and 3. 
191. The theorem obtained at the end of the paper is a very peculiar one; the 
only paper that I know of in anywise relating to the theory is Donkin, “ On an 
application of the Calculus of Operations to the transformation of Trigonometric Series,” 
Quart. Math. Jour. t. ill. (1860), pp. 1—15, where (pp. 13—15) my theorem is referred 
to and a more general theorem involving two arbitrary functions <f>, F, is arrived at. 
194. In connexion herewith see the Memoir, Donkin, “ On the Analytical Theory 
of the Attraction of Solids bounded by Surfaces of a hypothetical Class including the 
Ellipsoid,” Phil. Trans, t. 150 (1860), pp 1—11. The author referring to my Note 
remarks that I there showed that if two of the principal theorems of attraction (in 
the case of the ellipsoid) be given the rest follow very simply and are common to 
all the surfaces of which these two can be predicated: but that the demonstration of 
the two assumed theorems constitute the most essential part of the analytical problem, 
and that it was his present object to show that they and the others connected with 
them are implied in the two partial differential equations 
and 
: and he accordingly derives the whole 
satisfied by the function 
a+h b+h c+h 
theory, and in particular the theorems v. and vi. (equivalent to my assumed theorems) 
from these two partial differential equations.