348 MR. S. M. JACOB ON 



most effective for approaching the problems which arise when the relationship is to be 

 expressed numerically. 



In this paper the correlation coefficient ' r ' has been calculated for a number of 

 cases, the correlated variables, so far as the main purpose of the paper is concerned, 

 being the total rainfall in certain groups of months and the total harvested area in 

 chosen localities for the harvests which mature subsequently to these months. 



The results obtained seem to be of some interest and of practical importance. 

 For the autumn harvest the correlation coefficient has a value of about -4 to -5, and 

 for the spring harvest, from -6 to -8. 



Even the high probable errors of these coefficients do not rob them of their sig- 

 nificance. 



Other fundamental constants of the modern theory of statistics, e.g., the 

 " coefficient of variation, " l( standard deviation " are calculated in a number of cases, 

 and in the light of this theory it may be said that a knowledge of these constants is 

 essential to a proper description of the chief facts of Agriculture and Meteorology. 



So far as the author is aware these constants have not been previously calcu- 

 lated for India, except for certain rainfall data by Blanford, who has given the 

 'probable deviations' in certain cases. 1 



Apart from the fact that the data of this paper differ from those considered by 

 Blanford, the special object has been to find equations which will predict within 

 certain limits of error the amount of a crop from the rainfall on which it depends. 

 These equations are the well-known regression equations, and in forming them the 

 author believes that at any rate a first approximation to scientific prediction is 

 attained. 



In each case diagrams are given from which the probable extent of a crop can 

 be found from the antecedent rainfall for the localities considered. 



In this part of the paper there is also a theoretical discussion of the way in which 

 the regression equations are modified by errors of measurement such as certainly 

 occur for agricultural statistics and to a less extent in rainfall data. 



Part II. — Here the distribution of rainfall, a fundamental problem both for 

 agriculture and meteorology is considered by the method of curve fitting developed 

 by Prof. Karl Pearson. The 'Gaussian' and 'normal' curve 



2^2 



y = y e 

 and the skew curve 



P 



X 



/ X\<- a 



1 Since this paper was written, Dr. Gilbert T. Walker, F.R.S., Director-General of Observatorines in India, has very 

 kindly shown me his calculations in manuscript of a very large number of coefficients of correlations of rainfall and 

 pressure and other meteorological variables, which he has made the basis of a wide-reaching treatment of the problem of 

 monsoon prediction. — S. M. J. 14-8-09. 



