Manchester Memoirs, Vol. Ixv. (1921), No. 4 13 



has used drops varying from 07 to 1*25 cm. in radius, calculating the 

 contact angle from the equation — 



k 2 = 4a 2 sin 2 - 

 2 



in which even the first order correction term of (xii) is neglected. For a 



drop 1 cm. in radius - in the case of water is about 0-27 and -5 about 



0*075, an d neither of these quantities can be called small in comparison 

 with unity. It would be far safer to use larger drops, measure both q and 

 k independently, and so obtain the values of a and <o for the actual drop 

 or bubble under investigation. Such a procedure involves no special 

 difficulties, and the necessary observations may be made either photo- 

 graphically or by cathetometer measurements. 1 



I do not propose to discuss here the development of equations (xi) and 

 (xii). In the paper just cited I have given a simple investigation of the 

 problem 2 which is conducted on principles similar to those laid down for 

 the capillary tube problem. The analysis of the anchor ring problem 3 

 (number 4 in the "genealogical tree") follows much the same lines as the 

 large bubble problem, and the approximations involved are of the same 

 order. 



The Measurement of the Tension in a Liquid-Liquid Surface. 



This problem is, for the colloid chemist, one of pressing importance, 

 and the attempts made, up to the present, to forward its solution are of 

 very doubtful value. The discussion of the agreement between theory 

 and experiment in the case of the Gibbs-Thomson adsorption formula is 

 pointless unless we have an experimental method which is above suspicion. 

 At present the agreement is apparently considered good if the observed 

 and calculated results differ by less than 100 per cent., while some sub- 

 stances may show adsorption from 20 to 100 times greater than that cal- 

 culated from the formula. 4 It is sheer waste of time to discuss reasons 

 for these differences so long as the experimental methods are open to 

 suspicion. 



The great majority of the figures for interfacial tensions are obtained 

 by some modification of the drop-weight method, in which, instead of 

 finding the weight of a given number of the drops, one determines the 

 number of drops formed by a given quantity of liquid. 



Let Fig. 1 d represent a drop of liquid of density 0, pendent, in another 

 liquid of density p, from a tube of radius r. The drop is conventionally 

 assumed cylindrical at AB. The equation of equilibrium of the portion 

 ABCA is 



2?rrT + I (J> - gp'y)2irxdx = (p H \-n-r 2 + mg, 



1 Magie, Phil. Mag., Aug., 1888 ; Ferguson, Phil. Mag., April, 1913, p. 507. 



2 L.c, pp. 508 seqq. 3 Cantor, Wied. Ann., 47, 399 (i8g2). 



4 Willows and Hatschek, " Surface Tension and Surface Energy " {Churchill, 1919), 

 pp. 51 seqq. 



