Contact- Angle of Liquids and Solids. 163 



angle I call, in distinction from the infinitesimal contact-angle 

 existing when a 2 is less than /3 2 , a finite acute contact-angle. 



It seems not unlikely that such a relation may exist in many 

 cases between the force-functions as will give rise to a finite 

 acute contact-angle. Even if the force-functions are not of 

 the same form, so that the proportionality assumed between 

 them and the constants a 2 and /3 2 does not exist, they are 

 probably of the same order of magnitude ; so that, for certain 

 relations between them, the constant a 2 will lie between the 

 limits 2/3- and /3 2 , and the contact-angle be finite and acute. 

 While there is thus no theoretical reason against the existence 

 of a finite acute contact-angle, yet no indubitable evidence 

 has, in my opinion, yet been presented of the existence of such 

 an angle. Such as has been given is based upon the use of 

 methods so open to objection that it cannot be accepted as 

 final. I have endeavoured, by the use of methods so modified 

 as to, as far as possible, remove those objections, to establish 

 the presence or absence of an acute finite contact-angle in the 

 cases of the liquids which were examined. For many of them 

 the investigations of Quincke and Traube have indicated the 

 possibility of the existence of such an angle. 



Prof. Quincke's conclusions were based upon the compa- 

 rison of the results of his measurements of the dimensions of 

 air-bubbles formed under a horizontal glass plate in the various 

 liquids examined with those of the measurements of the rise 

 of the same liquids in capillary tubes*. His observations and 

 methods of calculation have been criticised by Yolkmannf, 

 TTorthington f, Stieg§, and myself ||, and it will not be neces- 

 sary to discuss them here. A word may be said, however, in 

 reference to a recent paper by Prof. Quincke If, in which he 

 calls attention to his use of an empirical correction by which, 

 in his opinion, the defects of his earlier method of calculation 

 are removed. This correction is obtained by the measurement 

 of bubbles 100 millim. in diameter, and is based upon the 

 assumption that, at a point in the contour of the greatest 

 horizontal section of such a bubble, the radius of curvature 

 of that section is infinite in comparison with the radius of 

 curvature of the vertical section. The value of the capillary 

 constant a 2 , computed on this assumption, is used as the basis 

 for the correction of results obtained from the measurement 



* Quincke, Pogg. Ann. cxxxix. p. 1 (1870). 

 t Wied. Ann. xvii. p. 355 (1882). 

 X Phil. Mag. xx. p. 65 (IS 

 § Trans. Berlin. Phvs. Soc. Nov. 25, 1888. 

 || Wied. Ann. xxv. p. 429 (1885). 

 H Ibid, xxvii. p. 219(188 

 M2 



