CROP ROTATION IN RELATION TO SOIL PRODUCTIVITY 7 
The above method is subject to criticism, because two assump- 
tions are involved. First, in arriving at the values of the effects of 
rotation (r) and manure (J) when acting independently of each other, 
it is assumed that the effects of cultivation are the same when con- 
joined with rotation or manure as when it is acting alone. The same 
assumption is made in evaluating the conjoint effects of rotation and 
manure. This assumption, in all probability, does not distort the 
true values of rotation and manure very much one way or another, 
since cultivation is the one factor which is involved in all the yields 
compared; and, moreover, there seems to be no way to determine 
whether or not the effects of cultivation represent the same value 
in all the comparable yields. 
The second assumption made is that the effect of rotation (R) when 
conjoined with manure is the same as when it is acting independ- 
ently of manure. It seems reasonable to believe that rotation must 
exert some effect on manure, and that manure, in turn, must have 
some effect on the efficiency of rotation. In other words, it seems 
highly probable, as analysis seems to show, that there is an inter- 
action between rotation and the use of manure when these practices 
are combined. 
If the formula cfr — cr (47.73 — 37.5) is correct in arriving at a value 
of 10.2 bushels of increase for manure (F) when conjoined with rota- 
tion, it is just as logical and correct to use the formula cfr — cf 
(47.7—37.1) to arrive at a value of 10.6 bushels for the effects of rota- 
tion (R) when this practice is conjoined to the use of manure. In a 
previous paragraph, the effect of rotation has been evaluated at 15.1 
bushels of increase when conjoined with manure, or the same as 
when rotation acts in the absence of manure. According to the 
second formula, the rotation value is not the same, but less by 4.5 
bushels. 
It is a fact that must be accepted that the conjoint effects of rota- 
tion and manure resulted in an increase, in this particular experi- 
ment, of 25.3 bushels over cultivation alone. In arriving at this 
value no assumptions are made. However, it can not be deter- 
mined just how much of this total increase should be credited to 
rotation or to manure. According to the above analysis the value 
for rotation (R), when joined to the use of manure, must lie some- 
where between 10.6 bushels and 15.1 bushels; and the value for the 
use of manure (F), when joined to rotation, between 10.2 bushels 
and 14.7 bushels. 
SECOND METHOD 
Another method that suggests itself in this study is to consider 
the effects of cultivation, rotation, and fertilizers from the point of 
view of farm practices, and to evaluate their effects on crop yields 
in terms of the differences in the average yields obtained. Thus, 
taking the same Missouri results with manure on corn, as used for 
illustration, the practice of cultivation alone resulted in an average 
yield of 22.4 bushels per acre; of combining the use of manure with 
cultivation, 37.1 bushels; of combining rotation of crops with culti- 
vation, 37.5 bushels; and of combining all three practices, 47.7 
bushels per acre. Since in these evaluations no assumptions are 
involved, this second method is the first of two methods used in 
this study. 
