356 MR. S. M. JACOB ON 



Now it is clear that we want as far as possible to correlate the amount of 

 matured crop as nearly as may be with the actual rain which reaches the land on 

 which the crop is grown, and the problem at once arises whether it would be 

 desirable to interpolate, or rather to extrapolate, from the values of the rain- 

 fall at the Tahsil Towns, and so to obtain a measure of the rainfall over each of 

 the areas in question. But the problem of determining the best interpolation 

 and extrapolation formula is in itself a task of some magnitude, and simply to 

 weight the rainfalls at the Tahsil Towns by their scalar mean or centroidal mean 

 distances is not a process which can be confidently adopted until it is found to be 

 justifiable. 



Consequently, no attempt has been made to find the probable value of the rain- 

 fall over the selected areas, and the correlations of the matured area of crop have 

 been made simply with the rainfall at the chief town of the Tahsil in which the 

 villages are situated. 



Some measure of the differences between the true mean rainfall over the areas 

 chosen and the actual adopted value of the rainfall will be given by an examination 

 of the differences in the rainfall where it has been measured, viz., at Sialkot, 

 Zafarwal, Raya, Pasrur and Daska. 



The total rainfall for each year for the 6 months April to September, both 

 inclusive, and for the 6 months October to March, both inclusive, have been formed 

 for each Tahsil Town, and taking the rainfall at Sialkot as a standard, the differences 

 between the rainfall there and the four other Tahsil Towns have been calculated. 

 These differences were squared, their mean value taken, and then the square root of 

 this mean value. The results are given in the table below : — 



Table showing the root-mean-square of the differences between the rainfall in Sialkot 

 Town and the places mentioned below for the years 1887-8 to 1906-7. 







Daska. 



Pasrur. 



Zafarwal. 



Raya. 



I. 



For the 6 months 













April to September 



. . 8"-io 



7"-oi 



8 ,, -87 



7-64 



II. 



For the 6 months 













October to March 



. . 2"- 4 2 



i"-6 3 



i"-88 



2"-56 



Now the standard deviations of the rainfall in each of these places is : — 



I. For the 6 months 



April to September . . 8"-670 7"'043 o/'^gS 7""4 6 5 



II. For the 6 months 



October to March . . 3"-i26 4 ,/, 300 4""575 3""35o 



Thus we see that the root-mean-square of the differences of rainfall as we pass 

 from Sialkot to the four places mentioned is as large as the standard deviation in these 



