THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 381 



PART II. 



THE MEAN DISTRIBUTION OF RAINFALL AS EXPRESSED BY 

 CERTAIN TYPES OF FREQUENCY CURVES. 



§ 9. The problem of the mean distribution of the rainfall throughout the year or 

 other period is an important one, as when random variations have been eliminated, 

 there results a certain type-curve which will be characteristic for the given locality 

 and period. 



The curves do not, of course, express the actually occurring rainfall during any 

 given year, or other non-recurring cycle, as the ordinate representing the actual 

 rainfall will have a series of maxima and minima. It seems probable, however, that if 

 a sufficient number of recurring cycles are taken, their maxima and minma will not in 

 general coincide, and that the resultant curve will have but a few maxima and minima, 

 and be expressible by the help of the ordinary frequency curves of the types recently 

 investigated. If this be the case, then a given frequency curve will represent the 

 generic rainfall, from which the actual rainfall in any year will vary, but within 

 certain limits, as a species might vary from its genus in the animal kingdom. 



Further, the problem of the determination of the characteristic distribution of 

 the rainfall, interesting as it is in itself, has a most important bearing on the nature 

 and seasonal position of the crops which it affects. 



Example 1st. The rainfall data of Zafarwal (District Sialkot) fitted with a nor- 

 mal or ' Gaussian' frequency curve. 



The average rainfall in Zafarwal for the years 1887-1906 is as follows: — 



Month. 



Rain -^ 6 inches 



April 



6 



May 



8 



June 



..24 



July 



..87 



August 



..105 



September 



• • • 33 



October 



2 



Let us suppose each of the frequencies collected at the median line of the month 

 in which it occurs, and let us find the moments referred to the median line of July. 

 Properly the unequal lengths of the months should be allowed for, but the error intro- 

 duced is small. 



The moments are ^"f'449, "' 2 = i'377> "'a ="653, " / 4 =5 , 4o8, and using Shep- 

 hard's corrections ^ =-449, i>-\ =1-294, / 3 = -541, **' 4 =4749. Thus the mean is at 

 a point -449 beyond the median point of July, a month being the base unit. 



