48 Mr. Ivory on the Attractions of an 
still greater weight ; it does not exhibit the several terms of 
the scries for the attractive force in separate and independent 
expressions: it only points out in what manner they may be 
derived successively, one after another ; in so much that the 
terms of the series near the beginning cannot be found with- 
out previously computing all the rest. This remark gave 
occasion to the following paper, in which it is my design to 
give a solution of the problem which is rot chargeable with 
the imperfections just mentioned : the analysis is direct, and 
every term of the series for the attractive force is deduced 
immediately from the radius of the spheroid. As the ellipsoid, 
which comprehends both sorts of elliptical spheroids of revo- 
lution, falls within the class of figures here treated of, I have 
derived, as a corollary from my investigation, the formulas 
for the attractions of that figure which are required in the 
theory of the earth : this paper therefore will contain all that 
is useful on the subject of the attractions of spheroids, as far 
as our knowledge at present extends, deduced by one uniform 
mode of analysis. 
Having mentioned the principal object of this discourse, I 
must likewise notice a subordinate purpose I have in view ; it 
is to put in a clear light the real grounds of Laplace’s me- 
thod, and of the equivalent method delivered in the following 
pages ; to the accomplishment of which nothing is likely to 
contribute so much, as a direct and rigorous analysis perspi- 
cuously conducted. To promote the same end still farther, by 
preserving greater order and perspicuity in treating a subject 
in its own nature very complicated, this paper will be divided 
into two principal sections : in the first section it is proposed 
