242 
Thomas and Ferguson . — On the 
water surface ; 1 2 > 3 and, as the areas of the two evaporating surfaces are in 
general different, to reduce the observations by assuming that the evaporation 
from a free water surface is proportional to its area. This, except under 
certain special circumstances, is not even approximately true, and the 
present research was undertaken with the object of demonstrating the law 
actually followed, and of showing how the results obtained may be applied 
to place the figures acquired in transpiration experiments on a more 
consistent basis. 
It has been demonstrated theoretically by Stefan 4 * that the rate of 
evaporation of a circular liquid surface evaporating into an indefinite 
homogeneous atmosphere is given by the equation 
where V is the volume evaporated in unit time, a the radius of the surface, 
k the coefficient of diffusion, p Q and p x the pressure of the vapour at the 
surface and at an infinite distance from it respectively, and P the atmo- 
spheric pressure. If p x and p 0 be small with respect to P, this reduces to 
V = 4&a 
Renner 6 has made a series of experiments on the rate of evaporation of 
free water surfaces, and has compared the results obtained experimentally 
with the values calculated from the formula 
E = 4 k (ft — p 2 ) a, 
where E is the mass evaporated in unit time, a the radius of the surface, 
k the coefficient of diffusion, ft the density of saturated vapour at the given 
temperature, p 2 the vapour density of the surrounding atmosphere at the 
same temperature. This formula is of a different form from that given by 
Stefan, and it is to be remembered that, granted the proper conditions, 
Stefan’s formula provides an exact solution. Renner compares the experi- 
mental results with those calculated from three formulae, viz. C4R, Ca-ttR, 
and CttR 2 , where C^k (ft — ft) 60. 
1 Cf. Livingston : The Relation of Desert Plants to Soil Moisture and Evaporation. Carnegie 
Inst. Publications, No. 50, 1906. 
2 Shreve : The Daily March of Transpiration in a Desert Perennial. Carnegie Inst. Publications, 
No. 194, 1914* 
3 Yapp : On Calibration of Evaporimeters. Appendix to paper On Stratification in the Vegeta- 
tion of a Marsh, and its Relations to Evaporation and Temperature. Ann. Bot., 1909. 
4 Stefan: Ueber die Verdampfung aus einem kreisformig oder elliptisch begrenzten Becken. 
Wied. Ann., xvii, 1882, p. 550. 
6 This equation is misquoted by Brown and Escombe as 4 ka • 
■P—Po 
vol. cxciii, 1900, p. 251. 
6 Renner : Beitrage zur Physik der Transpiration. Flora, 1900, p. 485 et seq. 
Phil. Trans., B., 
