Contact- Angle of Liquids and Solids. 169 



it may be easily shown that the distance in air from the object 

 mounted on the end of the object-glass to a point seen clearly 

 and in good focus, which distance, in this method of obser- 

 vation, is taken as a constant, is expressed by 



71 — 1 f 



2. The second correction arises from the fact that in the 

 second observation the rays from the object pass twice through 

 the thick lens, once before and once after reflexion at the 

 surface of the bubble. By the use of the formulas given by 

 Grauss *, if we represent further by 



N, the distance of the object from the lens in the second 



observation, and by 

 h, the distance from the centre of the concave surface of 



the lens to the bottom of the bubble, 



we may express the same constant distance between object 

 and sharply focused point by 



This expression is an approximation obtained by neglecting 

 terms containing the second and higher powers of N//. 

 From these formulas the value of h is found to be 



/(=A _ N _ • .i±pl 2 _ Nfr+MHK'+ay (IIt) 



n— 1 / / 



3. To obtain the value of k, the value of h must be 

 diminished by the distance from the centre of the concave 

 face of the lens to the horizontal plane containing the circle 

 of contact. This is the height of the arc of which the chord 

 is the diameter of the circle of contact. This diameter was 

 found by diminishing the measured diameter of the greatest 

 horizontal section of the bubble by a constant found by 

 observation for each liquid. 



To calculate these corrections a knowledge is necessary of 

 the thickness and index of refraction of the lens, and of the 

 radius of curvature of its concave face. The thickness of the 

 lens used in the experiments was determined with a sphero- 

 meter to be 7*859 millim. The index of refraction of the 

 lens was found from its polarizing-angle to be 1*539. By the 

 use of the concave face as a mirror, its radius of curvature 



* Gauss, Dinjt. Unter8. } Werke, vol. v. p. 2G1. 



