THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 355 



already remarked an absolutely definite value of C cannot (except in the case 

 of perfect correlation) be determined, and when the amount of crop i or other 

 variable is calculated from the regression equation, not only is the ordinate of 

 the regression line in error to an extent given by its probable error of equation (3), 

 but also no anticipation of the distance of C in excess and defect of the ordinate can 

 be made except by the statement of a probability, the prediction becoming closer as 

 °-c is reduced or as r approaches unity. 



This point will be further discussed at a later stage. 



§ 3 . It is now possible to consider the application of the theory to the statistics 

 chosen. The greater part of those in this part relate to the Sialkot District in 

 the Punjab, and these are taken first of all. 



Diagram I gives a map of the District with its 5 Tahsils — Sialkot, Zafarwal, Raya, 

 Pasrur and Daska. 



In each of these Tahsils 30 villages were chosen with especial reference 

 to their containing a large amount of unirrigated crop. It was found, however, that 

 the statistics for the 30 villages selected for the Daska Tahsil exhibited such a large 

 progressive increase in the amount of the matured crop, that it was evident that 

 either the villages in question had started additional cultivation on unirrigated 

 lands during the period under consideration, which fact would to some extent invali- 

 date the regression equations unless special modifications were introduced, 1 or that the 

 statistics themselves were seriously at fault. In either case the coefficients found 

 would be of little use and they were not evaluated. 



Lists of the villages chosen and the figures for the cropped areas of the 

 two harvests on unirrigated land will be found in the Appendix. 



The Diagram I shows the position of each of the villages in the 4 Tahsils : Sialkot, 

 Zafarwal, Raya and Pasrur. 



From inspection of the map the mean distances of the villages in each Tahsil 

 from the Tahsil town, that is from the point at which the rainfall is measured, were 

 found to be as follows : — 



Sialkot . . . . • • 5i miles. 



Zafarwal . . . . 9 ,, 



Pasrur . . . . . . 2| ,, 



Raya .. .. . . 15 „ 



These distances are intended to represent roughly not the distances of the 

 • centroids ' of the areas, but their mean scalar distance from the Tahsil Town. 

 Except in the case of Raya, where the villages all lie within bearings of N. and 

 N. E. of Raya Town itself, the 'centroidal' or vectorial mean distances of the 

 village areas will be considerably less than the above. 



1 The period is so short, that this would hardly be feasible. As a matter of fact the area sown is not cotfstant for 

 any of the villages, and a double regression equation based on both area cropped and area sown would probably give 

 better results. It is intended to make this extension, or one equivalent to it, later on. 



