604 RICE ART. L 



that no physical or chemical changes take place in the wall, 

 and no energy changes so caused are therefore involved, but 

 the perimeter of the dividing surface may move along the wall 

 (the creeping of the meniscus in a capillary tube up or down is a 

 familiar example) and the condition above must then be written 



f(ai8Ti + CX28T2 + azbTz)Dl = , 



where 8T1 is the tangential motion (normal to Dl) in the dividing 

 surface, 8T2 the tangential motion in the surface between the 

 single accent phase and the wall, dTs that in the surface between 

 the double accent phase and the wall, and o-j, cr2, 0-3 are respec- 

 tively the three free surface energies between the two phases, 

 and between each phase and the wall. This means that at any 

 point of the perimeter 



(T18T1 + 0-25^2 + (Ts8Ts = , 



and this is the well-known condition 



ci cos a + 0-2 — o"3 = , 



where a is the contact angle between the dividing surface and 

 the wall. Actually, in the general case of several homogeneous 

 phases and dividing surfaces, the condition is interpreted in a 

 similar way for a number of surfaces of discontinuity (at least 

 three) meeting in one line, as is shown at the bottom of page 281 

 of Gibbs' treatise. 



The constants Mi, M2 are the potentials at the level from 

 which z is measured (positive if vertically upwards). It follows 

 that p', p", 0-, r are functions of t, Mi, M2, z. If determined by 

 experiment these functions enable us to turn [613] into a differ- 

 ential equation for the surface of tension as shown in pages 

 282-283. Equation [620] is an approximate form of this 

 differential equation. We refer the reader to the short note on 

 curvature (this volume, p. 14) for an explanation of the left- 

 hand side of it. 



