490 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
but 
so that 
and equation (21) becomes 
cli; = — 47ror<x da, 
da 1 
d % A.ira?a 
A0 + no log ^ - ue + no p - c ,e - - e% - Wl + w 2 + 
® p a 1 a dd 1 1 
aa 
= 0 . 
Comparing this with equation (17), we see that, if S p be the change in the vapour- 
pressure due to the curvature, 
-R0^ + Rd^ + — =0, 
p a aa 
or 
R 0 Sp = -^-~ .(23) 
This coincides with the formula given by Sir William Thomson (‘ Proceedings of' the 
Royal Society of Edinburgh,’ Feb. 7, 1870 ; quoted in Maxwell’s ‘ Theory of Heat,’ 
p. 290). 
We can also prove that the density of the saturated vapour will be altered by 
charging drops of the liquid with electricity. For suppose the drop to be spherical 
and charged with a quantity e of electricity. The potential energy due to the 
electrification of the drop is ^ ; subtracting this from the value previously given 
for L, we may easily prove, in the same way as before, that the change §p in the 
vapour-density, due to the electrification, is given by the equation 
( 21 ) 
did Sp = 
1 c 2 
87t a 4 a — p 
assuming that as the drops evaporate the electricity remains behind on the drop. 
This seems to be proved by Blake’s experiments on the evaporation of electrified 
liquids (Wiedemann’s ‘ Lehre von der Elektricitat,’ vol. 4, p. 1212). We see from 
equation (24) that electrification diminishes the density of the saturated vapour, so 
that moisture might condense on a drop of water when electrified, though the same 
drop would evaporate if not charged with electricity. This would tend to make 
electrified drops of rain larger than unelectrified ones, and would probably tend to 
increase the size of the rain drops in a thunderstorm. 
The maximum value of e/a 2 in air at atmospheric pressure is about 130 C.G.S. 
units in electrostatic measure, so that the maximum change in the density of the 
saturated vapour is given by the equation 
