THERMODYNAMICS OF CHANGE OF STATE, ETC. 317 



Putting p=l and T = 80 



eo_ 160 1 

 gc to'~l-25xl0 9 ' r 



1-28x10-7 



to 1-28x10-7 

 logl ^ 2-30 xr 



56 x 10-7 



If r=10- 5 cm. "=1-013 



CO 



r=10-cm. -,= 1-138 



CO 



r= 10-7 cm. = 3-631 



CO 



or it is only when the drop is of the order of a millionth of a centi- 

 metre that its vapour-pressure is sensibly greater than that from a plane 

 surface, and if the dust particles are greater than this, a very small 

 excess above normal saturation may make drops form on them. 



If no dust particles are present, we may perhaps still see how drops 

 are formed if the pressure is great enough (chap. x.). For there may 

 be groups of the vapour molecules formed here and there by collisions 

 which are virtually small liquid masses. Now the radius of the sphere 

 of action of a molecule is of the order 10 ~ 8 (chap, ix.), so that if a group 

 of size 10~ 7 is formed it may find the space saturated if the pressure is 

 three or four times its normal value and it may continue to grow. 



The Connection between Alteration of Vapour-Pressure by 

 Pressure on the Liquid and the Change in Melting-Point by 



Pressure. An alteration in the hydrostatic pressure to which a liquid 

 or a solid is subjected, affects the vapour-pressure, whether the altera- 

 tion is produced by capillarity, as in the rise or fall of a liquid in a 

 tube, or by increasing or decreasing the atmospheric pressure on the 

 surface, as when ice or water is contained in a vessel into which more or 

 less air may be pumped. 



If we have a mixture of ice and water in such a vessel with their 

 vapour only above the mixture, then their equilibrium point is the 

 triple point. But if air be pumped in till the pressure is P, the equili- 

 brium temperature of the ice and water falls by 



where v l is the volume of 1 gm. of ice, v 2 that of 1 gm. of water, and L' 

 is the latent heat of fusion. 



