382 MR. S. M. JACOB ON 



And the moments about the mean are : — 



v l =o 



m 2 =1-092 



^3= -I 'OS 



m 4 =5-220. 



N -—. " 458x * 



The Gaussian curve y = e 2a becomes y = 101*17 e 



with a standard deviation <>■ = 1-045. 



The diagram shows this curve and the original data. 



The mean and modal rainfall would have to occur together on July 30th, if this 

 curve is to be an adequate representation. 



One-fourth of the total rainfall will have fallen on an average by the 9th of July, 

 and three-fourths by the 18th August ; the former of these dates being roughly about 

 the time of the so-called breaking of the south-west monsoon. 



However, the diagram itself shows that a skew curve would probably be better 

 suited to represent the facts. 



2nd. The Gaussian curve will not fit the data of any frequency group within the 



limits of the errors of random sampling unless fi 2 ~ 3 is sensibly zero, where P 2 =— - • 

 In the case of the rainfall data of example I st , we have /3 2 - 3 = 1-38 which is 



many times greater than its probable error '67449 J — — ■ 



265 



Let us fit, therefore, a curve of the type y=y (l+-\ e~a X ' to * ne data, where 



a = 



i"2 3 



f-3" 



4 I 



V-2 



2 — 

 ^3 



M 2 3 

 fi= 4 I 



We find p =4-006, a— - 1-871, and the curve is 



o / ' x \ 4-006 



where the distance between mean and mode is -467, and the range ends at 2-338 

 from the mean, and 2-787 from the median line of July. 



