386 MR. S. M. JACOB ON 



The notation is the same as that previously adopted, R K being the total mean- 

 rainfall of April to September, both inclusive; and R P of October to March, both inclu- 

 sive ; and r denotes the correlation of R K with the following R P . 



N denotes the number of years to which the data extend. 



Of the 8 coefficients of correlation, 5 are positive, and 3 negative, and not one of 

 them is but just over twice its probable error. It is doubtful if any one of them is 

 gnificant. 



If the diagrams given below, which show the product moment for each year, 

 be examined, it becomes clear that for a few years a positive correlation is possible, but 

 that on the whole the positive and negative moments alternate in such a way that no 

 correlation results. 



Thus the Lahore data exhibit a very striking alternation. From 1862 to 1876 the 

 correlation is on the whole positive, for 1877 to 1889 it is markedly negative, and 

 from 1890 to 1906 it is again positive. 



Thus the reason for the high correlations given above for four stations in the Sialkot 

 district is that the years for which the calculation was based included the last of the 

 periods mentioned, and not the previous one. The inclusion ol the first of the 

 periods in the Lahore data has had the effect of making the correlation positive ; but 

 it would certainly seem that previous to i860 a period of negative correlation had 

 probably existed, the inclusion of which would cause all positive correlation to dis- 

 appear. At any rate the results for the whole period 1862— 1906 are suggestive of 

 some such conclusion. 



It is clear, therefore, that no linear equation of regression will suffice to predict 

 the value of the -rainfall in October to March from the given April to September 

 rainfall preceding. Direct attack of this problem by this method does not apparently 

 promise much success. 



If, however, we take the system of points which give the value of the product 

 moment, and plotting these as ordinates to the corresponding years as abscissae, join 

 the points for successive years, as has been done in the diagrams below, in certain 

 cases there seems to be an alternation of the sign and magnitude of the product 

 moment which is roughly simple harmonic. 



This is a very wide field of speculation, and my investigations are not sufficiently 

 extended either in time or space to enable the existence of periodic alternations to be 

 definitely asserted. 



In the case of three of the places taken — Peshawar, Nagpore, and Jubbulpore — 

 the alternations are such that no simple harmonic curves can be fitted to them by 

 inspection. In the remaining five cases a sine curve, or, as in the case of Lahore, a 

 double sine curve has been fitted to the data. 



As neither the method of moments or of least squares has been adopted for the 

 fitting, it is not possible to assert that the curves given will best represent the given 

 points. To do this and to apply the proper tests for goodness of fit are problems which 

 must be made the subjects for future enquiry. 



The following are the constants for the sine curves chosen: — 



