1886.] on Capillary Attraction. 489 



by multiplying tlie sum * of the curvatures in two mutually-perpen- 

 dicular normal sections, by the amount of the force per lineal centi- 

 metre. In any place where the surface is concave the effect of the 

 surface tension is to suck outwards — that is to say, in mathematical 

 language, to exert negative pressure inwards. Now, suppose in an 

 instant the rigidity to be annulled, and the piece of glass which you 

 see, still undisturbed by gravity, to become water. The instantaneous 

 effect of these unequal pressures over its surface will be to set it 

 in motion. If it were a perfect fluid it would go on vibrating for 

 ever with wildly-irregular vibrations, starting from so rude an initial 

 shape as this which I hold in my hand. Water, as any other liquid, 

 is in reality viscous, and therefore the vibrations will gradually 

 subside, and the piece of matter will come to rest in a spherical 

 figure, slightly warmed as the result of the work done by the forces 

 of mutual attraction by which it was set in motion from the initial 

 shape. The work done by these forces during the change of the 

 body from any one shape to any other is in simple proportion to the 

 diminution of the whole surface area ; and the configuration of 

 equilibrium, when there is no disturbance from gravity, or from 

 any other solid or liquid body, is the figure in which the surface 

 area is the smallest possible that can enclose the given bulk of 

 matter. 



I have calculated the period of vibration of a sphere of water "f 

 (a dew-drop !) and find it to be I a^, where a is the radius measured 

 in centimetres : thus — 



The dynamics of the subject, so far as a single liquid is concerned, 

 is absolutely comprised in the mathematics without symbols which I 

 have put before you. Twenty pages covered with sextuple integrals 

 could tell us no more. 



Hitherto we have only considered mutual attraction between the 

 parts of two portions of one and the same liquid — water for instance. 

 Consider, now, two different kinds of liquid : for instance, water and 

 carbon disulphide (which, for brevity, I shall call sulphide). Deal 

 with them exactly as we dealt with the two pieces of water. I need 



* This sum for brevity I henceforth call simply " the curvature of the surface " 

 at any point. 



t See paper by Lord Kayleigh in Proceedings of the Koyal Society, No. 196, 

 May 5, 1879. 



