Similarly, the annual precipitation ;- on the boundary line between 

 the stepp and desert climate is given by 



r ^= t -[- 0- 



F. R. Falkner (1938), based on climatological study in Africa, expressed 

 the arid boundary by the following formulae 



r — ^ = 12 or r = /; + 12 

 This is the same form as Koppen's. 



Emm. de Martonne's aridity index D, the most famous formula, is 

 given hy 



^ = rfTo 



where P is the annual precipitation (millimetre), and t the annual mean 

 temperature (°c.). 



R. Rang's rain-factor (" Regenfaktor "), based on the pedological 

 point of view, is also the similar form 



--^ ■ ■ 



These two formulse are generallv expressed by 



and D ^ is considered to be a special case when ^ — O. 



Martonne considered that the outer limits of land utilization and 

 agriculture coincide with the line which connects the points where D 

 is 20. 



Hence if we express P by centimetres instead of millimetres, the 

 upper formula becomes 



P - 2 (^ + iS) 



which is the same as Koppen's. 



C. W. Thornthwaite called the ratio of precipitation to evaporation 

 by the name of " P-E ratio " and empirically expressed it b}' 



e = ^^-^(f-hTo) 



where P is the annual precipitation (inch) and F the annual mean 

 temperature (°F.). 



If we choose the unit of millimetre and centigrade instead of inch 

 and fahrenheit respectively 



E =«•" (TTm) 



Now we define the dry limit where the annual amount of precipitation 

 equals the annual evaporation, or P-E ratio is 1-0, the upper formulae 

 becomes 



P = 3-6 {t + 12-2) 



This is also similar in form to Koppen's, except that the numerical 

 constants differ a little. 



Hence the formula devised by many authorities reduce to the same 

 form. But the numerical constants must be different with respect to 

 the individual regions and not unique in the wide area of the world 



123 



