258 Proceedings of Boyal Society of Ediribiirgh. [sess. 
Hence we get the known expression for the pressure due to the 
total charge Q, 
1 Q2 E2 
where R is the resultant electric force at the surface of the sphere. 
If we suppose electric energy to be stored in the medium, we see 
that QYSttC^ or R^/Stt is also the expression for the energy per unit 
of volume at the surface. 
V. Electrification and Vajpoiir-Pressure . — Let E be the electrical 
energy contained in a liquid sphere of radius C and density cr. We 
have 
_ J_ Q! 
dC~ “y C^' 
If m represents the mass of the vapour we have 
dm= -IttCWC. 
Also we have 
r/E , cTEj dO) n 7 j j 
dm = — — — dm — — ^^^—dm=dvdv. 
dm dO dm {SttCV 
But dv = 
dm, p being the vapour density. 
Hence 
dp= - 
1 p 
87t O' — p 
which agrees with J. J. Thomson’s result. 
VI. Surface-Tension and Vapour-Pressure . — Let T and S repre- 
sent respectively the surface-tension and the surface of a drop of 
liquid, and let the other quantities he indicated as in the pre- 
vious case. We get - dpdv = 0. How = SttCc^C = - 
1 ^pdv 
C cr — p 
Hence 
dp = ^ 
dT 
P 
cr-p 
or, summing from T = 0 to T = T, 
P-To = 
9^ P 
C O’ — p 
where p and p^ represent respectively the equilibrium-pressure of 
