166 Dr. W. F. Magie on the 



made for use in the correction -terms of the formulas ; and for 

 use in the second method, an .estimate of the difference between 

 that diameter and the diameter of the circle of contact of the 

 bubble with the glass was also necessary. The contact-angle 

 co was assumed to be 0. 



The formulas used in the computation of a 2 from these 

 measurements are slight modifications of those given by 

 Poisson*. They are 



^=^+^-£(2^/2-1), (L) 



a = 



V2cos-^ /is/ 2 cos— 3^2cos 2 -^- 



Z L — 



(l-sin 3 !). (Ik.) 



Formula (II a), on the supposition that o> = 0, becomes 



° = 72 + ^~WW ■ • ■ (I1 ^ 



In these formulas jjl denotes the radius of curvature at the 

 centre of the under surface of the bubble. Since the bubbles 

 used were in every case so large that their under surfaces 

 could be considered plane, the term containing \l could be 

 neglected in both formulas. The computation is made in both 

 cases by using the value of a 2 given by the first term of the 

 formula in the calculation of the correction-term. One such 

 approximation is usually sufficient. 



Apparatus. — The liquids examined were contained in a 

 tank, about 25 centim. square, formed of heavy plates of plate 

 glass, mounted in an iron frame furnished with levelling 

 screws. The tank and all parts of the apparatus that came 

 in contact with the liquids were carefully cleaned, first with 

 dilute nitric acid, next with a mixture of alcohol and a strong 

 solution of caustic potash, and lastly, with dilute hydrochloric 

 acid. They were also repeatedly washed under the tap, and 

 finally rinsed with distilled water. As this process was tedious 

 and did not seem to be in every case necessary, washing with 

 alcohol and ether was sometimes substituted for it. The 

 bubble was formed, in a way kindly suggested to me by Mr. 

 Worthington and recommended by Gauss f, under the slightly 

 concave face of a plano-concave lens. The lens was placed 

 on three small porcelain supports, and the liquid poured in 

 until its level was above the lower surface of the lens, yet so 

 that the upper plane surface of the lens was not covered. 



* Nouv. Th. de V Act. Cap. p. 217. 



t Gauss, Fig. Fluid., Werhe t vol. x. p. 77. 



