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



air-motion, as influencing evaporation, may be supposed to 

 have a dual action, viz. : — 



(a) By disturbing the film of air saturated with aqueous 



vapour on the surface of the body it may ultimately 



render each unit of area equally potentially efficient 



in contributing to the total evaporation ; 



(V) It may directly influence the quantity of evaporation. 



Hence for (a) the formula must contain an expression 

 1 

 W", in which 2<n<3, 



and n must be a function of wind velocity Y say. In order 

 that in this expression n shall be between the limits 2 and 3, 

 we must have some such function as 



n = 2 + e~ mYC , (14) 



e being the base of the Napierian logarithms. The value of 

 this is 3 when V = 0, that is, when the saturated aqueous 

 vapour-film next to the body has to distribute itself by 

 diffusion. It also approaches 2 when V c is large. The 

 rapidity and characteristics of the rate of approach are 

 determined by the magnitude of the constants m and c. 



For (6) we may write l + ^r(Y), and must determine 

 the form of the function by experiment. Probably 



l + yjr(V) = l + kY-lV 2 .... (15) 



will be found satisfactory enough. This expression could be 

 made to express the conditions required, as far as they are 

 known, though its form cannot, in the nature of the case, 

 be quite general. A formula to make the increase for the 

 effect of wind velocity most rapid initially, and finally pro- 

 portional to the velocity, would require to be of some such 

 form as 



l + ^(V) = l + *{V + a(l -*-'*)} . . (16) 



(since the former expression can give only empirically the 

 desired results for a limited range). 



The constants Jc, a, b could be determined from the obser- 

 vations, and e is the base of the Napierian logarithms. The 

 constant a would be small as compared with large values 

 of V*. 



* For actual evaporation of water Professor C. F. Marvin believes 

 that the effect of wind is ultimately to give an increasing value for 

 d~E/dY, that is, the graph of the curve with velocities of wind as absciss;e 

 and evaporation as ordinates is concave upwards (see Monthly Weather 

 Review, February 1909, p. 59). This would require the formula to be 

 1 + &V— JV 2 +mV 3 , but such formula would probably apply to water- 

 surface only where wave disturbance was a feature. 



