Spread of Liquids on Solid Bodies. 323 



The laws established formerly* by me, relative to the surface 

 common to two or three fluids, may, if the foregoing consi- 

 derations are just, be henceforth extended also to the case 

 where one fluid is replaced by a solid body. 



Let the three common surfaces of a solid body 1 and of two 

 fluids 2 and 3 intersect in a curved line ; then, upon a particle 

 P in the intersecting line there act three forces lying in the 

 plane normal to the element P of the curved line of intersec- 

 tion under consideration. These forces are equal to the capil- 

 lary constants or surface-tensions of the three capillary surfaces, 

 and are in equilibrium ; consequently they fulfil the conditions 

 of the equation 



a-12 _ ^31 _ <*2 3 /i\ 



sin w 3 sin w 2 sin w{ 



In this equation iv ly w 2 , w z represent the angles which are re- 

 spectively subtended at the point P by the mutually intersect- 

 ing elements of arc of the curved capillary surfaces whose 

 directions coincide with the directions of the forces a 12 , «2 3> a 3i« 

 The symbol a 12 represents the surface-tension or capillary con- 

 stant of the surface common to the solid body 1 and the fluid 

 2, &c. 



If a triangle be drawn (Plate XII. fig. 5) whose three sides 

 are proportional to the capillary constants or surface-tensions 

 of the bounding surfaces common to the solid body 1 and to 

 the fluids 2 and 3, and which meet in a point P, then the ex- 

 terior angles of this triangle give, for this point P, the edge- 

 angles of the surfaces considered. 



The triangle is possible, and has real exterior angles, only 

 if the sum of two sides be greater than the third, or when 



«12< a 31 + «23 (2) 



If this condition is not fulfilled, a spread of one of the fluids 

 will take place upon the surface of the solid body. 



Let us call 6 3 the acute edge-angle which the surface com- 

 mon to the two fluids makes with the surface common to the 

 solid and to fluid 3 ; then 



«2 i -.2 ^2 



COS 6/ 3 = = yd) 



^ a 31 a 2 3 



When the magnitudes a 31 , a 23 , and « 12 are independent of the 

 geometrical form of the surfaces, and depend only on the 

 nature of the fluids 2 and 3 of the solid body, then the edge- 

 angle 6 3 is also independent of the geometrical position of the 



* Pogg. Ann. cxxxix. pp. 58, 59 (1870). Phil. Mag. [IV. 1 vol. xli. 

 No. 275 (June 1871), pp. 454-476. 



Y2 



