Contact-Angle of Liquids and Solids. 165 



constant a. In the experiments with water, given by Dr. 

 Traube, the radius of the tube . employed was 1*72 millim., 

 and the value of a may be taken as about 3'87. In the 

 cases of the other liquids employed, for which the value of 

 a is in every case less than that for water, the ratio of the 

 radius to the value of a is almost unity. Clearly in these cases 

 the approximation is no longer applicable. A calculation by 

 Poisson's formulas of the height of the meniscus formed by 

 water in a tube of radius 1*72 millim., gives as that height 

 1*51 millim. The height observed by Dr. Traube was 1*45 

 millim. The agreement of the calculated and observed results 

 is such that the difference may be explained as due, perhaps, 

 partly to the difficulty of observation noticed by Laplace, 

 partly to the inadequacy of the approximation in tubes of such 

 a diameter, and not necessarily to the existence of a finite 

 contact-angle. The diminution in the height of the meniscus 

 as the temperature rises may be explained from the well- 

 known fact that the value of a 2 decreases as the temperature 

 rises, and does not demonstrate the existence of a variable 

 contact-anode. 



Method. — The method employed in the investigation here 

 presented was, in general, that used by Prof. Quincke*. It 

 consists in the comparison of the values of a 2 , for the different 

 liquids examined, determined by two independent methods. 

 One of the methods is independent of any assumption about 

 the contact-angle, and the other involves the assumption that 

 the contact-augle is zero. The formulas show that, in case 

 this assumption is untrue, the value of a 2 given by the latter 

 method should be less than that given by the other; while the 

 results of the two methods should be in substantial agreement 

 if the assumption is justifiable. 



Both methods employed were based upon measurements of 

 the dimensions of large air-bubbles formed in the liquid under 

 a horizontal glass plate. In the first method the distance 

 measured was the vertical distance from the bottom of the 

 babble to the horizontal plane containing the greatest section 

 of the bubble. This distance, in the subsequent formulas and 

 tables, is called q. In the second method the distance measured 

 was the vertical distance from the bottom of the bubble to the 

 horizontal plane containing the circle in which the bubble- 

 surface is in contact with the glass plate. This distance is 

 called k. In both cases a measurement of the diameter of the 

 greatest horizontal section of the bubble, designated by /, was 



* Pogg. Ann, cxxxix. p. 1 M^7<">). 



