642 
Journal of Agricultural Research 
Vol. V, No. 14 
The results of the least-square reductions are presented graphically in 
figures 21 and 22. In all cases, the vertical component of the radiation 
has been employed rather than the radiation on a surface normal to the 
sun's rays. The reason for this will be apparent from an inspection of 
the radiation and transpiration charts, where it will be seen that during 
the early morning hours the slope of the radiation graph is much greater 
than that of the transpiration graph for rye, alfalfa, and amaranthus. 
In other words, the transpiration rate does not increase nearly as rapidly 
as the normal component of the radiation during the early daylight hours. 
In a field of grain or alfalfa, considered as a whole, it is evident that the 
vertical component of the radiation would alone be effective. In the 
case of an isolated pot of plants standing on the transpiration scale, the 
horizontal component would also be effective. The extent to which this 
enters can not be directly determined, however, and in the following 
discussion the vertical component has been used throughout. 1 
TRANSPIRATION AS DETERMINED BY RADIATION AND TEMPERATURE 
The observed and computed transpiration graphs, the latter based on 
the assumption that the vertical component of the radiation and the air 
temperature are the primary controlling factors in transpiration, are 
given in figure 21. The computed equations are as follows: 
For rye.0.384 0.642 Q=T; 
For alfalfa..0.514 i^+0.539 0=T; 
For amaranthus.0.546 0.443 6 =T; 
in which 
R v is the vertical component of radiation, 
6 is the temperature rise, and 
T is the transpiration. 
In the above equations and in those which follow the hourly values for 
each term are expressed as a percentage of the maximum. In other 
words, the general dimensionless equation is of the form: 
R‘ 
R i 
+ 6 
e'-e* 
T' 
nr _ nr 
u max u o 
in which the primed quantities represent observed values. 
1 Calculation of the vertical component of radiation. —If R represents the normal component of the radiation 
of the sun, Rv the vertical component, and h the altitude—i. e., the angular distance of the sun above the 
horizon—then: sin A. 
Expressing the altitude in terms of declination and hour angle (Smithsonian Institution. 1894, p. Ixviii), 
we have sin A=sin 0 sin 54 -cos 0 cos 5 cos f, 
in which 
0=the latitude of the place of observation; 
5 = the declination of the sun—i. e., the angular distance above or below the Equator (from U. S. Navy 
Dept., 1912); and § 
#=*the hour angle—i. e., the angle between the meridian plane through the place and the meridian plane 
through the sun. 
Substituting, we have: 
Rv=*R (sin 0 sin 54 -cos 0 cos 5 cos t). 
The daily observations are expressed on the basis of mean sun time, which introduces a slight error in 
the calculation of the vertical radiation component. 
