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This mode of enunciating the direction of the attraction has 
the advantage of making known the level surfaces with respect, 
to the attraction of the shell on external points, 
Tn 1838, M. Chasles presented to the Academy of Sciences 
avery simple and elegant investigation, in which he arrives at 
Poisson’s results respecting the attraction of a shell on an exter- 
nal point, by a purely synthetical method, 
M. Chasles’ method is founded on Ivory’s well-known pro- 
perty of corresponding points on two confocal ellipsoids, and on 
some elementary propositions in the theory of the Potential. 
Struck by the simplicity and beauty of Steiner's method of 
finding the direction of the attraction of a shell on an external 
point, the author of the present paper was induced to think 
that by means of the same method of decomposing the shell 
into pairs of elements employed by Steiner, a correspondingly 
simple mode of determining the wtensity of the attraction 
might probably be found. The author has been fortunate 
enough to succeed in realizing this idea, and the result is the 
method contained in the first part of the present paper. 
This method is throughout quite elementary. It requires 
the knowledge of only the most simple properties of ellipsoids, 
including Ivory’s well-known property respecting corresponding 
points on two confocal ellipsoids, 
The proof of the theorem respecting the direction of the 
attraction differs from that given by Steiner, and harmonizes 
better with the method employed for determining the intensity 
of the force. No use is made in this method of the properties 
of the Potential. 
The second part of the present paper is devoted to what the 
author considers to be an improvement on M. Chasles’ method 
of determining the attraction of a shell on an external point. 
Its novelty consists in the mode in which the intensity of the 
attraction of the shell is found. M. Chasles first compares the 
attractions of two confocal shells on the same external point. 
