﻿562 Dr. G. Bakker on the 



of Laplace, as we can show also immediately with the aid of 

 the formula of Laplace : 



where 



ty(z) = \ U{u)udu and Ii{u) = -f^ 





*■ o 



§ 5. Superficial tension. — This may be regarded as the 

 force in respect to the unit of length, exercised normally to 

 a line traced on the surface of the liquid; this is numerically 



2H. 



the coefficient H of the term -75- in the formula which 



expresses the surface-pressure of some spherical mass of liquid 

 enveloped in its vapour and supposed not to be weighty. In 

 this case the fundamental equation (3) becomes 



d 2 V 2 dV 2Tr , , , 



^ + ^^ V + 47r ^ «... (8) 



r being the distance from the point considered as the centre 

 of the sphere adopted as the origin of the coordinates. 



Let R be the radius of the spherical mass of liquid limited 

 by the capillary layer ; for all the points of this layer one 

 may write r = R + /<, h varying from zero to the thickness 

 of this layer; in this case equation (8) becomes, neglecting 

 h with respect to R : 



d 2 V 2 dV V , . - / 1\ 



aW + RTh=X> + ^ fp > { X = g} 



dV 

 If we multiply these two members by 2 — — and integrate, 



it becomes : 



1 dV a 

 pdh dh > 



in which j p -jr dh is exactly the surface-pressure K. 



ForR = co the last term vanishes; the difference in the 

 values of K for R = go and for a definite value R is therefore 



1 1 ( 2 (dy\' 7 _2R 

 whence 



H^f(S)"» « 



* See Rayleigh, Phil. Mag-. Oct. and Dec. 1890, p. 290. 



