The Attraction of Ellipsoids considered geometrically. 401 



Finally, the author observes with regard to the application of 

 the Bonenberger apparatus which he had first pointed out {An- 

 nalen, June 1851, p. 308), " M. Person has lately made the just 

 remark {Comptes Rendus, 1853, Sept. 27 and Oct. 18), that in 

 order to withdraw it completely from the influence of the rota- 

 tion of the earth, the apparatus must be placed with its principal 

 axis parallel to the earth^s axis ; since (in strictness) the motion 

 of the whole apparatus round an axis, which does not coincide 

 with one of the three axes contained in it, must alter the rotation 

 of the ball." 



And he suggests, that in the experiment the whole should be 

 furnished with the means of rapid rotation about a vertical axis, 

 and so that the rotatory axis of the ball might have any i-equired 

 position given to it with respect to the new axis. 



LXIV. The Attraction of Ellipsoids considered geometrically . By 

 Matthew Collins, B.A., Senior Moderator in Mathematics 

 and Physics, and Bishop Law's Mathematical Prizeman, Trin. 

 Coll. Dublin; Professor of Mathematics in the Mechanics' 

 Institute, Liverpool"^. 



THE attraction of an ellipsoid A on a point P on its surface, 

 or within it in a direction perpendicular to one of its 

 principal planes B, is proportional to the distance of the attracted 

 point P from that principal plane. 



1 . When P is on the surface. Draw PP' a chord of A perpen- 

 dicular to B, and through P and P' draw planes parallel to B 

 cutting the principal axis CC perpendicularly in p and p' ; then 

 describe through p and p' an ellipsoid a, concentric, similar, and 

 similarly placed to A, and its attraction on p will be equal to the 

 attraction of A on P in a direction perpendicular to B. 



For through PP' draw two planes E, F containing a very small 

 angle, and ihrongh pp' draw two planes e,/parallel to the former; 

 then let a cone of revolution, whose axis is PP' and vertex P cut 

 E, F along the straight Unes PE, PE', PF, PF', and let another 

 such cone very close to the former, and having the same axis 

 and vertex, also cut E, F along PE^ PE', PF, PF'„ and through 

 p draw, in the planes e,f, the straight lines pe pe' pf pf and 

 pe, pef, pfi pfl respectively parallel to the foregoing ; then as the 

 sections of the two similar ellipsoids A and a by the parallel 

 planes E, e are necessarily similar ellipses, and as the chord PP' 

 parallel to an axis (CC) of the greater ellipse is = to the homo- 

 logous axis pjj' of the less, .-. by Airy's Tract on the Figure of the 

 Earth, Props. 2 and 3, PE + PE' =pe +pe' ; and .-. by Airy's 4th 



* Communicated by the Author. 

 Phil Mag, S. 4. Vol. 7. No. 47. June 1854. 2 E 



