free Path of the Molecu les. 17 1) 



When the surface is spherical, each element of the path 



offers an obstruction expressed by , . T — r for the parts 



S6 cos (<£-£*) ^ r 



below », and by 7 , , ; — c- for those above, a is the angle 



r ' J cos(^> + i«) 6 



between the radius of curvature at the point p and that to the 

 other end of the path; <£— \u is the mean value of the angle 

 between the direction of path and the normals to the sur- 

 faces of equal density for the parts below p } and <j> + ^a the 

 corresponding angle for those above p. 

 Integrating, 



/i-p'o =J:= P'o-P'2 , 

 cos(<£ — \a) cos(0 + Ja) 



This shows that, whereas the difference in density above and 

 below was the same for a plane surface, in the case of a sphe- 

 rical surface the pressure from below is greater, and that up- 

 ward less. Or the pressure from below is greater and that 

 from above greater. This must cause a greater density at p. 

 The tendency of a particle to move from the liquid into the 

 surrounding atmosphere is due to the difference in density of 

 the liquid and of its vapour. For small changes in the density, 

 the change in this tendency may be assumed as proportional 

 to the change of density. It must be found what change of 

 density takes place at p. As the change of density is due to 

 an increase of pressure on p, this increase must be equal in all 

 directions. So it is only necessary to consider one direction. 

 Take the direction tangent to the curved surface at p. The 

 increase in pressure is therefore proportional to the difference 

 in density of the layer through/ and that through h, or to the 

 length fh. It is evident that 



fh = ih j 

 h r 



where h is the free path, and r the radius of curvature of the 

 surface. Hence we have 



the change in tension -J/2 



the tension of vapour at plane surface "" r 



Sir William Thomson has shown that the change in ten- 

 sion at a curved surface is equal to the pressure of a column 

 of the vapour of the height to which the liquid would rise in a 

 capillary tube of a diameter of twice the radius of curvature 

 of the surface. 



In a tube of diameter 1'294 millim. water rises to a height 



