676 RICE ART. L 



change of free surface energy of amount (Tbs — (Tas — <^ab cos a. 

 For equilibrium this must be positive or zero, and so 



(Tbs — (Tas '^ Oab COS a. 

 Similarly 



(Tab — (Tbs "^ ctab COS /3, 



where (8 is the angle QXP. If A and B are in contact with a 

 single face, a and jS are supplementary angles, and the signs of 

 inequality must be removed since the two statements would 

 be contradictory in that case; thus we obtain [672]. A very 

 good account of the measurement of contact angles is given in 

 Adam's book on the Physics and Chemistry of Surfaces, Chap- 

 ter VI, where, in addition to the well-known troubles due to 

 contamination, the effect produced by a movement of the 

 liquid along the surface of the solid is discussed, an effect 

 which is not sufficiently recognized in much of the literature. 

 The contact angle gives a very good idea of the relative mag- 

 nitudes of the adhesions of different liquids to a given solid. 

 The measure of such an adhesion is the energy per unit area re- 

 quired to separate the solid and liquid from contact. Thus if 

 (tla is the surface tension of the liquid in contact with air, 

 csA that of the solid in contact with air and (Tls that of the 

 interface between solid and liquid, this "work of adhesion" is 

 equal to (Tla + (Tsa — (tls- If now a is the contact angle at 

 which the liquid-air interface meets a wall of the solid (measured 

 in the liquid) we have from [672] 



(Tla cos a = (Xsa — (Tls- 



Therefore the work of adhesion, being measured as above, is 

 equal to 



(tlaO- + cos a). 



If the contact angle is zero the work of adhesion is equal to 

 2(rLA, which is the energy required to separate the liquid 

 from itself (since such a separation produces two surfaces in 

 contact with air, where there were none previously), and so if 



