334 Mr. G. H. Knibbs : Mathematical Analysis of 



3. Theory of Evaporation from Circular Tank 

 of Limited Dimensions, 

 Under similar circumstances regarding the elements which 

 affect diffusion, the rate at which the vapour is given off 

 from a liquid depends on the absolute temperature. Accord- 

 ing to Stefan's investigation (AbJtandl. Akad. Wien, 1881 ; 

 Journ. de Phys. 1882, p. 202) the rate of formation of vapour 

 in a circular vessel of small dimensions is proportional, how- 

 ever, to the lineal and not to the areal dimensions of the 

 surface. The lines of flow of the vapour are a system of 

 hyperbolas, the foci of which are on the bounding edge of 

 the liquid, and the orthogonal trajectories of which (ellip- 

 soids) constitute the surfaces of equal pressure. Since these 

 are closest together at the margin of the liquid and least 

 close directly over its centre, the flow is greatest at the edge,, 

 and least immediately over the middle. 



These results represent what would take place where therfr 

 was no physical motion of the air over the liquid. In all 

 actual cases, however, apart from the vortical disturbances 

 of the air due to the motion generated by the sources of 

 heat, there are other air disturbances ; and even when these 

 are moderate, there can be no doubt that the conditions are 

 completely changed, and the theory in its integrity becomes 

 inapplicable. Thus A. Winkelmann's (Wied. Ann. xxxiiL 

 & xxxv., 1888) attempt at experimental verification was not 

 successful, though he regarded the failure as not attributable 

 to defect in Stefan's theory. This theory of Stefan's leads 

 to the formula 



F-p 



t-p' 



where E is the quantity evaporated per unit of time, k is a 

 constant, r is the radius of the surface, P is the atmospheric 

 pressure, p' that of the vapour at the surface, and p" that at 

 a considerable distance, say the ordinary pressure in the air 

 of the vapour. That is, under the conditions supposed the 

 quantity varies as the diameter, not (as one might suppose) 

 as the area. It is obvious, however, that with considerable 

 air-disturbance the rate of evaporation will more nearly 

 approach the ratio of area, since the diffusion conditions 

 become more nearly similar for each unit of surface-area. 



4. Application to Human Body. 



The equipotential surfaces about a human body in still air 

 would be very complex in form ; and if they could be treated: 

 by mathematical theory, that theory would furnish result* 



E = 4irlog e 4 r -S-, (7) 



