THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 349 



are fitted to the data by the ' method of moments ' , and the results are exhibited 

 graphically. This discussion forms a connecting link between the problems of Part 

 I and that of 



Part III , in which the change of a rainfall from year to year is considered. It 



is shown that if we take the deviations of rainfall from its mean value for the two 



periods April— September, October — March, and form their product for each period of 



12 months, we get a series of points which are found to indicate a marked oscillatory 



sine 

 change, which can be roughly described by the help of harmonic — : — curves 



G cosine 



where periods are about 19 years and some simple ratio of this period. The oscilla- 

 tion of 19 years periods appears to be sufficiently characteristic in certain cases, 

 though in others it may perhaps be marked by oscillations of different period and 

 amplitude. 



The matter is one which demands a thorough harmonic analysis, but it seems that 

 some light may be thrown in this way on the nature of the saecular changes in 

 climatic conditions; though it is possible that random sampling may explain away all 

 the variations. The subject is still one for speculation; but apart from that, certain 

 definite facts are established, and they may perhaps be suggestive of future paths of 

 enquiry. Since the paper was written the following results for the total unirrigated 

 harvests of Sialkot, Zafarwal and Daska Tahsils have been obtained, and a table is 

 annexed showing what the predicted value of these areas was as calculated from the 

 appropriate regression equations : — 



Sialkot. Zafarwal. Daska. 



Prediction based on April — 



August rainfall .. 56,200 + 7000 52,000 + 6200 



Prediction based on April — 



September rainfall .. 59,963+6718 54,376 + 6068 26,656+5089 



Actual measured area in acres 61,333 55>534 35,&°7 



The predictions for Sialkot and Zafarwal based on April — September rainfall 

 are only about 2 % in error, which is certainly smaller than the error of measurement 

 itself. 



For Daska the error is large. Such an error might indeed be attributed to a defect 

 in the process applied, but I had long since remarked (v. p. 355) that the Daska 

 statistics seemed to require correction. As, however, the Daska Tahsil regression 

 equations had been calculated it was thought well to give the predicted area of matured 

 crop, even although it differed from the value given by official measurement. It 

 would be completely unscientific to conceal a discrepancy of this kind. 



The object of this paper is to investigate to a first approximation only the 

 interdependence and correlations which subsist between certain of the fundamental 

 data in the statistics of Agriculture and Meteorology. 



