88 Prof. Maxwell, On a Paradox in the [Mar. 12, 



and if the lengtii of a diameter parallel to the given chord is 2c?, 

 then the value of y for any point of the chord is 



y = l^d (16). 



Hence if p = Cp"'^ (17), 



a particle placed at any point of the disk will be in equilibrium 

 under the action of any pair of sectors formed by chords intersect- 

 ing at that point, and therefore it will be absolutely in equi- 

 librium. 



When as in the case of electricity, w = 2, 



P=Cp-' (18), 



the known law of distribution of density. 



If the repulsion were inversely as the distance, the fluid would 

 be accumulated in the circumference of the disk, leaving the rest 

 entirely empty. 



If the force were inversely as the cube of the distance, the 

 density would be uniform over the surface of the disk. 



Lastly, let us consider a solid ellipsoid, the equation of the 

 surface being 



a' h' & ' 



and at any point within it let 



. r v' r 



¥ 



=f 



At any point of a chord drawn parallel to a diameter whose 

 length is 2c^ the value of y is 'pd. 



If we consider a double cone of small angular aperture whose 

 vertex is at a given point, and whose axis is this chord, the sec- 

 tions at two corresponding elements are in the ratio of the squares 

 of the distances of the elements from the given point, and therefore 

 in the ratio of the values of p^ at these elements. Hence the con- 

 dition to be satisfied is 



p^*~" = C^ a constant. 



If this condition be fulfilled the fluid will be in equilibrium at 

 every point of the ellipsoid. 



If w = 2, p = (7p-' 



is the condition of equilibrium. But if C is finite the whole mass 

 of the fluid in the ellipsoid if distributed according to this law of 



