THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 387 



The amplitude is measured in inches-squared, and the epoch represents the date 

 at which the amplitude is a maximum. The period is the time of a half oscillation, 

 that is from a maximum to a minimum. 





A 



mplitude 



Shahpur 





5 



Kohat (curve I) 





10 



„ (curve II) 





10 



Lahore (curve I) 





10 



,, (curve II) 





10 



Ajmere 





10 



Beawar 





2-5 



Period. 



Epoch. 



19 years 



1890 AD 



19 „ 



1890 „ 



19 » 



1895 „ 



I3'5 „ 



1900 ,, 



9 ,, 



1893 „ 



19 „ 



1895 „ 



19 ,, 



1890 ,, 



All these appear to be at any rate partial representations of the change in the 

 value of the product moment. 



In the case of Lahore a combination of the above two curves gives a better fit 

 than either of them alone. 



If y denote the product of the two deviations from the mean rainfall, the follow- 

 ing are the equations which gives its value as a rough approximation for the places 

 named. 



*(t - 1890) * ) 

 Shahpur y=$sm\ — ^ -+-J 



c rtt - 1890) , ■"■ 



Kohat v =10 sin 3 I-- 



l 19 2 



2*{t - 1900) »■ ) to sw 

 Lahore v = 10 s*w J — 2 — i + - f -f- 



^-189 3) ; 

 9 " 1_ 2| 



, "-(£-1895) *■ 



Aimere v = 10 sin < — — — - |- - 



19 2 



Beawar y = 2\5 sin 



^-1890) 

 19 " 



To predict the value of the rainfall of October to March from the known rainfall 

 in the preceding six months, we determine the value of y from the above, and have 



(Rk-Rk) {R P -R P )=y 



whence 



Rp = Rr 



y 



Rk — R* 



