THE CORRELATIONS OF AREAS OE MATURED CROP AND THE RAINFALL. 373 



Further let P be the position of an individual value of a single observation, then 

 the single observations are grouped about c with a frequency F(£) U } say, and it is 

 necessary to find the grouping of the P's about c' . 



The frequency of a deviation X of p from c' , where X = t-x, is clearly 



-foo 

 &X\ F(t)f(x)dx. 

 -co 



S 



+ 00 



f{x) dx. 



— 00 



+00 

 8 X\ F(X +x) f{x) dx. 



— CO 



J 



+ CO 



f(x) dx 



— 00 



where X is a constant for the integration. 



Suppose the distribution of the c' s' and of the individuals about c to be ' normal 

 and of the form 



X* 



y = y c e =f{x) 



X2 



y =yt e =F(x) 



then the distribution of the individuals about c' is 





1 



.+00 



(X + X)i 



Xi 



yo 



y<\ 



1 



-co 



2 



e 



«p 



2<r c 2 , 



dx 









r +<» 





#2 







yc 



'-00 



e 



2^ C 2 , 



dx 



y c yi-~==e 2{°c*+°i*) 



'. ".• 



yc js/z* « c 



X" 





