which are neither Spherical nor Cylindrical. 25 



sequence of the inferior curvature, the radius of curvature M at 

 this extremity will also be greater than the radius of the circle. 

 But since, with respect to an arc of a cu.vve thus ])laced, the 

 radius of curvature and the normal have a like direction, and 

 consequently the same sign, it follows from the above that the 



quantity ^rf + i^ would be greater at the point where this arc 



rejoins the circle than at a point very close to the axis, a result 

 which is incompatible with the condition of equilibrium. If wc 

 were to suppose that the curvature diminishes from the axis 

 outwards, the same mode of reasoning would show that the 



quantity t? + ^ would be smaller at the point where the arc of 



the curve rejoins that of the circle than at a point very near the 

 axis. 



Equilibrium, therefore, is not possible unless the curvature be 

 constant and, at the same time, the meridian curve meet the 

 axis normally ; in other words, this meridian curve must be a 

 circle having its centre on the axis, or, in the case of an infinite 

 radius, a line perpendicular to the axis; hence the figure gene- 

 rated is necessarily either a sphere or a plane. 



From this principle, it follows that the meridian curves of 

 other equilibrium-figures either stretch to infinity or close out- 

 side the axis ; we shall afterwards find that the first of these 

 conditions is alone fulfilled. 



These points established, I proceed next to the examination of 

 the curves in question. An iron cylinder, say 15 centimetres 

 long and 2 in diameter, is maintained horizontally at a certain 

 height in the alcoholic mixture, and a mass of oil of suitable 

 volume is caused to adhere to the same. This mass spreads itself 

 over the surface of the cylinder so as to envelope a portion of 

 the length of the latter, and assumes the form of a figure of revo- 

 lution whose meridian curve, convex in the middle, changes the 

 nature of its curvature towards its extremities, where it becomes 

 tangential to the generating line of the cylinder*. 



The same figure formed entirely of oil, that is to say, without 

 having a solid cylindrical core, may be obtained by attaching a 

 mass of oil — at first in excess — to two vertical discs of the same 

 diameter as the above cylinder, and placed opposite one another 

 at a distance asunder equal to the length of the figure obtained 

 with the cylinder, and afterwards by removing, M'ith the small 

 syringe, as much liquid as is found necessary in order to make 

 the extreme elements of the meridian curve appear horizontal ; 



* M. Beer, in the memoir] above- raentionetl, suggests the same exjjeri- 

 ment as being suitable for the verification of one of the results of his eal- 

 culus; I hail, however, made the experiment long before. 



