THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 361 



The question, therefore, which arises is — ' Is the type distribution of the rainfall the 

 same for the two periods April — September and October— March ? ' By type here I 

 mean simply the average distribution and the deviations therefrom. Though the en- 

 quiry will need great extension yet some grounds for answering this question in the 

 negative is given in Part II of this paper, where it appears that in a certain instance 

 the skewness of the distribution has opposite signs in the two cases. 



Again, is the high value of r P as it were factitious, since the Rabi harvest is largely 

 dependent on the rainfall of April — September, which for the 20 years considered is 

 correlated with the rainfall of the succeeding October to March ? But calculated for 

 longer periods this correlation of the rainfall in the two periods becomes insignifi- 

 cant (v. Part III), so that may be r P too would be reduced if found from a greater 

 range of values. Finally, in the case of the Kharif harvest are we not correlating the 

 crop with a rainfall more widely differing from the true mean rainfall than is the case 

 for the Rabi harvest, as seems probable from inspection of the correlations of local 

 rainfall ? 



I put these questions to show what points have to be considered before any de- 

 duction can be made from the differing values of the coefficient of correlation for the 

 two harvests. At present I must leave them unanswered. 



As to the function for which the value <p has been adopted, it appears to be de- 

 sirable to tabulate it, but it cannot be fully discussed till it has been evaluated for a 

 number of cases. 



Since the regression equation of crop on rain is 



C—C= — r (R—R) 



C C — 



we have — =r— = <p (R — R). 



Thus <P is the ratio which the excess of the probable crop obtained from a rain- 

 fall one unit above the average, over the average crop bears to the average crop. So 

 that if, for instance, the average crop is 1 acre, t represents the added or diminished 

 acreage due to every inch above or below the average rainfall. 



Thus for the 120 villages considered here, whilst one inch of rain above the 

 average in the months April to September increases the probable Kharif crop 

 by about -fcth, the Rabi crop may be expected to have about -^ 5 -th added to 

 its mean crop by each additional inch of rain in the months October to March : 

 or from this point of view an inch of rain in October to March has about 

 five times the crop-producing value of an inch of rain in the months April to 

 September. 



Taking each of the Tahsils separately the distribution of rain and crop will be 

 shown by diagrams which will also exhibit the regression lines. 



