Reduction of Transpiration Observations . 
243 
An examination of his tabulated results shows that such agreement 
as exists is purely fortuitous — for some values of a one formula shows 
fair agreement, for other values the other formulae are invoked. The 
figures show that the agreement, for example, of the values calculated 
from CttR 2 does not necessarily represent any physical fact, but is simply 
an expression of the mathematical fact that two quite unrelated curves 
may approximately coincide for a small portion of their length. 
The figures obtained from the formula expressing the linear law and^ 
those obtained from the formula expressing the area law may be so different 
that the errors introduced by reduction according to the erroneous formula 
may be large enough to rob the results of any meaning. 
Thus, in the laboratory experiment to determine the relation between 
the amount of evaporation per unit time from a leaf surface and from a water 
surface of equal area, Detmer 1 gives the figures for an actual experiment 
which yields the result 
Water lost by 100 sq. cm. of water surface __ 11*3 _ ^ 
Water lost by 100 sq. cm. of leaf surface ~~ 1*99 ^ 
This result was obtained by reducing the experimental figures according to 
the ‘ area ’ law. If we assume Stefan’s law for the evaporation from the 
water surface, and assume further (as Detmer does) that the evaporation 
from the leaf surface is proportional to its area, the above ratio becomes 
2*53 — an error of about 120 per cent. ! It is not too much to assert that, 
until reasonable certainty exists as to the true law connecting the evaporation 
from a water surface with its area, such figures possess no quantitative 
significance whatever. 
Certain deductions from Stefan’s law have been subjected to the test of 
experiment by Winkelmann 2 and by v. Pallich. 3 Apart from the closely 
analogous experiments on diffusion carried out by Brown and Escombe 4 
and more recently by Renner, 5 we are not acquainted with, however, any 
results which give the laws connecting E and a under various c everyday ’ 
conditions ; and the experiments detailed below are offered as a contribution 
towards the establishment of such laws. 
2. Algebraic Statement of Law of Evaporation from 
Circular Surfaces. 
We assume then that the law of evaporation from a circular basin of 
water or other liquid is given by an equation of the type 
E = Ka n ...( i), 
1 Detmer : Practical Plant Physiology. (Eng. Translation by Moor, 1909, p. 212.) 
2 Winkelmann : Ueber die Verdampfung von den einzelnen Theilen einer kreisformigen freien 
Oberflache. Wied. Ann., xxxv, 1888, p. 401. 
3 J. v. Pallich : Uber Verdunstung aus einem offenen kreisformigen Becken. Berlin. Akad., 
Sitz., 106, p. 384, 1897, and Sci. Abs., i, p. 203, 1898. 
4 Loc. cit. , p. 223. 
5 Loc. cit. 
