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II. ON THE ATTRACTION OF ELLIPSOIDS, WITH A NEW 

 DEMONSTRATION OF CLAIRAUT'S THEOREM, 

 BEING AN ACCOUNT OF THE LATE PROFESSOR 

 MAC CULLAGH'S LECTURES ON THOSE SUBJECTS. 

 COMPILED EY GEORGE JOHNSTON ALLMAN, LL.D., 

 OF TRINITY COLLEGE, DUBLIN. 



[Transactions of the Royallrish Academy, VOL. xxn. p. 379. Read June 13, 1853.] 



PROPOSITION I. 



If P be any point on the surface of an ellipsoid, and PCi be 

 drawn perpendicular to an axis 00, and an ellipsoid be described 

 through Ci concentric, similar, and similarly placed to the given 

 ellipsoid ; then the component of the attraction of the given ellipsoid 

 on P in a direction parallel to 00 is equal to the attraction of the 

 inner ellipsoid on the point Ci. 



This theorem is an extension of that given by Mac Laurin* 

 relating to the attraction of a spheroid on a point placed on its 

 surface. It may, moreover, be established by means of the same 

 geometrical proposition from which Mac Laurin deduced his 

 theorem. 



Through the point P let a chord PP' of the given ellipsoid 

 be drawn parallel to the axis 00. Now, suppose both ellipsoids 

 to be divided into wedges by planes parallel to each . other, and 

 passing respectively through this chord and the parallel axis of 

 the inner ; and suppose the wedges to be divided into pyramids, 

 the common vertex of one set "being at P, and of the other at d. 



* De caus. Phys. Flux, et Eefl. Mar is, sect. 3 ; or see Airy's Tract on the 

 Figure of the Earth, Prop. 8. 



