352 MR. S. M. JACOB ON 



is entered in the Government papers as three-quarters of an acre of matured 

 crop. 



It is the areas of the crops so estimated, which form the closest measure of 

 the real outturn at present obtainable, with which we are here concerned. 



The accuracy of these estimates is, as will be seen from the above, very limited : 

 errors of 5, 10 or even, 15 % are by no means improbable and greater ones are possible. 



The most serious errors will arise from a want of constancy in the 'personal 

 equation 'of the estimator from harvest to harvest, and to a less extent in passing 

 from field to field : and even if the f personal equation ' were constant for a single in- 

 dividual, discrepancies would arise wherever one estimating official was substituted 

 for another owing to their c relative personal equation. ' It is of the utmost importance 

 then, if the data are to be relied on as approximately accurate, that the 'personal 

 equation' should be as nearly as possible constant, and the 'relative personal equation' 

 small. 1 In practice I think these conditions hold good to a certain extent. The 

 estimating official has usually been born and reared in an agricultural community 

 which has a very shrewd insight into the quantity and quality of its means of sub- 

 sistence, and, unless deliberately falsified, the official's estimate must have a real 

 significance. 



Taking, then, the data so obtained, and going back as far as is possible, 2 in this 

 part of the paper the standard deviations, coefficients of variation and correlation 

 of rainfall and harvested areas will be examined for each of the two chief harvests 

 and for the months preceding them during which the rainfall has a determining effect 

 on them. 



If, as will prove to be the case, a substantial correlation is found to exist between 

 the amount of the matured crop in any harvest and the rainfall in the selected 

 period preceding, then the regression or prediction equations can be formed from 

 which it will be possible to forecast within stated limits of error the probable extent of 

 the matured crop for the locality for which the equations have been calculated, when- 

 ever the amount of rainfall in the months preceding that harvest is given. 3 



1 I have tested the ' relative personal equation ' of myself and another person over a considerable area, the 

 estimates being made quite independently and at different times. The agreement was on the whole within 3% and 

 rarely exceeded 6 or 7% of the total area. 



2 Unfortunately only 20 years' statistics have been available in the majority of instances. 



3 The prediction cannot, of course, be absolute for any individual harvest, since unless the correlation of cropped 

 area with the variable used for prediction be unity, the cropped area will not be the same even for the same rainfall. 

 What is predicted by the regression equations is the mean value of the various cropped areas which occur for a parti- 

 cular amount of rainfall. The value of any particular cropped area will vary about that mean in a way expressible, if 

 the correlation be ' normal,' in terms of the standard deviation of the crop and the coefficient of correlation. 



As a matter of fact in this paper it will be assumed that the correlation is 'normal ' throughout. For the purpose 

 of calculating the probable errors of the constants this assumption will be near enough to the truth ; but, should it 

 prove to be the case, as seems likely a priori, that the correlation is not only not ' normal' but not even 'linear', then 

 the regression equations would need modification when applied to extreme cases. Paucity of data do not justify the 

 consideration of this problem just at present, and it is not contended that the present investigation will lead to more 

 than a first approximation. 



Conformably, the coefficient used throughout is Galton's function '/', which it is perhaps necessary to define here.' 

 Let (x { , y { ) (x-2, y- 2 ) (x s , y :i ) ( x n y n ) ... be a system of pairs of associated variables, let x, y be the mean 



