Royal Society. ^§8 



ceptible shock. When, however, the bladder containing the stone 

 rested upon the hand, during the act of disintegration a smart im- 

 pulse was felt. 



On the whole, I am of opinion that the electrical force applied in 

 the manner indicated, will be found quite as efficient for the disin- 

 tegration of calculi in the bladder as the more formidable analogous 

 operation of lithotrity, occasionally practised. And, as regards sim- 

 plicity and security, the electrical apparatus certainly appears pre- 

 ferable to the instruments used for crushing the stone by ordinary 

 mechanical force. 



" The Attraction of Ellipsoids considered generally." By Mathew 

 Collins, Esq., B.A. 



The author commences by stating, that the attraction of an ellip- 

 soid ^on a point on its surface or within it, in a direction perpendi- 

 cular to one of its principal planes, is proportional to the distance of 

 the attracted point from that plane. 



This general proposition, which is an extension to ellipsoids of 

 those already given for spheroids in Airy's Tract ** On the Figure of 

 the Earth," Prop. 8 and 10, and in MacLaurin's 4th Lemma, " De 

 causa physica Fluxus et Refluxus Maris," he demonstrates — 



1 . In the case when the attracted point is on the surface of the 

 ellipsoid. 



The demonstration of this is much like those given by the above- 

 named authors for the less general case of spheroids, and its final 

 step is effected by Cor. 1 to Prop. 87 of the first book of the Prin- 

 cipia. 



2. When the attracted point is within the ellipsoid. 



The demonstration in this case is effected by showing that an 

 ellipsoidal shell, bounded by two similar and similarly placed ellip- 

 soidal surfaces, exerts no attraction on a point situated anywhere 

 within it or upon its interior surface. 



The foregoing proposition shows that the attraction of an ellip- 

 soid on any point on its surface, or within it, can be got at once from 

 the attraction of the same ellipsoid on a point placed at the extre- 

 mity of an axis, and the author proceeds to show how the latter 

 attraction can be found and reduced to elliptic functions. He then 

 gives this proposition : 



Let a, h, c be the semiaxes of a homogeneous fluid ellipsoid, and 

 A, B, C the forces acting on points at the extremities of a, b, c, 

 caused partly by the ellipsoid's own attractions on its parts, and 

 partly by centrifugal forces of revolution about an axis (2c), or by 

 the action of an extraneous force directed towards its centre, and 

 varying as the distance from the centre, then the ellipsoid will pre- 

 serve its form if Aa=Bb = Cc. 



The last proposition stated in the paper is thus given : let R and r 

 be the radii of two homogeneous concentric spheres ; A and a the 

 attractions of each on a point on the surface of the other, then 



A a 



-— =— , whatever be the law of attraction as a function of the di- 



stance. 



