Th eory of Surface Forces . 467 



The general problem was treated -p. .., 



by Young by means of superficial To 

 tensions, which must balance when 



resolved parallel to the surface of z ^^fT^ 1 



the solid, though not in the perpen- ^r—* q^ ** 



dicular direction. In this way 23 a 12 

 Young found at once 



T 31 cos0+T 12 = T 23 ; (51) 



or rather, in terms of the more special hypothesis, 



{a l ^a,) 2 co?>e+{a 1 -cT 2 Y={a 2 -<T z Y. . . (52) 



From this we deduce 



cos^ 2 ^-" 1 -" 3 , (53) 



0-1-0-3 



in agreement with what we found above for a special case. 

 The equation may also be written 



cr 1 cos 2 i6> + o- 3 sin 2 i^ = o- 2 ; .... (54) 

 or if, as we may suppose without real loss of generality, 



cr 3 = 0, 



o^cos 2 ±0 = <t 2 , (55) 



a form given by Laplace. In discussing the equation (53) 

 with cr 3 :=0, Young* remarks: — "Supposing the attractive 

 density of the solid to be very small, the cosine will approach 

 to —1, and the angle of the liquid to two right angles ; and on 

 the other hand, when cr 2 becomes equal to g- } , the cosine will 

 be 1, and the angle will be evanescent, the surface of the 

 liquid coinciding in direction with that of the solid. If the 

 density o 2 be still further increased, the angle cannot undergo 

 any further alteration, and the excess of force will only tend 

 to spread the liquid more rapidly on the solid, so that a thin 

 film would always be found upon its surface, unless it were 

 removed by evaporation, or unless its formation were pre- 

 vented by some unknown circumstance which seems to lessen 

 the intimate nature of the contact of liquids with dry solids." 

 The calculation of the angle of contact upon these lines is 

 thus exceedingly simple, but I must admit that I find some 

 difficulty in forming a definite conception of superficial 

 tension as applied to the interface of a solid and a fluid. It 

 would seem that interfacial tension can only be employed in 

 such cases as the immediate representative of interfacial energy y 



* Works, vol. i, p. 464. I have introduced an insignificant change in 

 the notation. 



