190 W. F. Magie — Method of Measuring 



surface tension divided by the specific gravity, the height of 

 the summit of the drop above the plate, the radius of the great- 

 est section of the drop, and the contact angle between the drop 

 and the plate. The formula holds, without any change, for a 

 bubble of air formed in a liquid under a level plate. 



If we transform this formula to get a value of a we obtain 



k 

 a= 



GO ,00 „ „ 00 



^2 cos - mV 2 cos J 3l V 2 cos 2 



(x-sio-f), 



where k is the height of the bubble, w the contact angle, and 

 /j. the radius of curvature of the summit of the bubble. The 

 symbol V is defined by the equation l'=l+(y/2 — l)a, where 

 lis the radius of the greatest section of the bubble. If the bub- 

 ble considered be large, that is, if it have a radius of 30 mm. or 

 over, the value of fi, as determined by an equation given by 

 Poisson on p. 216, is so great that the term containing it may 

 be neglected, and the surface of the bubble at the centre treated 

 as plane. If we measure the height of the bubble and know 

 the contact angle of the liquid and the plate, we get a first 

 approximation to the value of a by the use of the first term of 

 the formula. By substitution of this value in the remaining 

 term, we proceed to a second approximation, which in the case 

 of large bubbles is usually sufficient. 



When the liquid is of such a nature that it wets the plate 

 under which the bubble is formed, it is usual to assume that 

 the contact angle is zero. The formula then becomes simply 



_ h c e 



Doubts have, however, been thrown on the validity of this 

 assumption by the work of Wilhelmy,* Quincke, f TraubeJ and 

 others, and it cannot yet be considered as justified by experi- 

 ment. It can only be verified by a careful comparison of the 

 results obtained for the value of the constant a by the use of 

 different methods of measurement. It was for use in such a 

 comparison that the method described in this note was con- 

 trived. 



In place of the telescope of an ordinary cathetometer was 

 placed an arm carrying at one end a vertical microscope. In 

 the center of the object glass of the microscope was fastened a 

 small piece of white paper. It was brightly illuminated by 

 the rays from an incandescent electric lamp, which were con- 

 centrated by a lens, and reflected upon the paper from a small 

 mirror. The bubble to be measured was formed under a glass 



*Pogg. Ann., cxix, 171. f Pogg. Ann., cxxxix, 1. 



\ Journ. fur prakt. Chem., new series, xxxi, 514. 



