26 



The small size of the Pennsylvania farms makes rather intensive 

 farming necessary there, so that the large herds of dairy cows kept 

 must be fed mainly from field crops. As corn produces more feed 

 per acre than any other crop commonly grown in that region, the 

 acreage of corn increases as the live stock increase in numbers. In 

 the Illinois locality, on the other hand, the area of corn increases 

 as live stock decrease in numbers, the corn being grown for sale. 

 It is also important to notice that the variation in intensity of 

 stocking is very slight in Illinois in the groups based on tilled crop 

 area, so that difference in the amount of manure available has less 

 influence here than in Table III. In the first two columns of 

 Table IV we find the crop index increasing and the intensity of 

 stocking slightly on the decrease as the tilled crop area increases. 

 Beyond a point between 28.4 and 43.3 per cent of tilled area both 

 decrease as tilled crop area increases. In this case the influence 

 of tillage seems to be more important than that of the animals kept 

 for the crop index increases in spite of decreasing live stock up to 

 the point at which we may assume that tillage becomes excessive, 

 beyond which humus appears to be burned up too fast and the crop 

 index falls off. 



Apparently in both these tables the optimum percentage of in- 

 tertilled crops is about the same, and is in the vicinity of 35 to 40 

 per cent. 



In the above illustration we are able to evaluate the factor of 

 tillage although its results are mixed up with the results of varia- 

 tion in the amount of available manure, for the reasons (1) that the 

 effect of the manure is known in advance and can thus be dis- 

 counted; (2) the effect of the two factors is not the same through- 

 out the series of averages. The same result could be arrived at 

 by comparing only farms with the same intensity of stocking, but 

 on account of the relation between number of animals and area of 

 corn it would require a very large number of farms to render this 

 possible. 



Recapitulation. In studying the relation between two factors, 

 the variation of one of which is supposed to be a direct cause of 

 variations in the other, the farms should always be grouped on the 

 basis of the causal factor and each group averaged on the basis of 

 the resultant factor. If each of two factors bears a causal relation 



