100 J. W. SHIVE AND B. E. LIVINGSTON 



to enquire how much is added to the soil moisture residue for 

 each doubhng of the evaporation rate, the equation becomes, 



y_ 



X = 2". In the present instance it is desired to find the value 

 of a which satisfies this equation and brings the curve in question 

 to pass through the first two main averages of the graph {x = 0.3, 

 y = 4.30, and x = 1.5, y = 5.48). It is clear that the value 

 4.30 must be considered zero, thus passing the axis of abscissas 

 through this point. Referring to the axes of the general curve 

 above given, the two points to be considered become (0.3. 0) 



y 



and (1.5, 1.18). Now if the curve, x = 2", passes through 







these two points, it follows that the two equations, 0.3 = 2", 



1.18 



and 1.5 = 2 « , must be simultaneous. Dividing each member 



1.18 o 



of the second by the corresponding member of the first, 5=2" " 



— . . 1 18 



or 5 = 2 ° . The last equation is the same as, log 5 = — — log 2, 



a 



l.lSloff 2 , 



or 



a = — ^- — , from which it appears that a = 0.504. 



log 5 



The curve actually shown in figure 1 has the constant difference 



(a) taken as 0.50, the constant ratio as 2, and it passes through 



the first two points designated by heavy circles. It is clear at 



once that this theoretical curve, derived from the first two main 



averages, very nearly passes through the points representing 



y 

 the three remaining averages. From the equation log x = — log 2, 



0.5 



may be found the value y for any given value of x. The 

 agreement between the ordinates of the last three averages and 

 the corresponding ordinates thus calculated is very close, so close 

 that there is left no doubt that the given logarithmic curve repre- 

 sents the relation sought. It may therefore be stated that, for 

 the present series, each doubling of the evaporating power of the 

 air as here measured is accompanied by an arithmetical increase 

 equal to about 0.5 per cent, of the dry weight of the soil, in 

 the soil moisture residue remaining at permanent wilting. 



On the graph of figure 1 the calculated value (from the Briggs 



