16 



KAEL PEAESON 



Hence, by Table V, 

 and 



Here log x'= 1-9614, 



Xa, = X.,= 1-2566, 



rr V V XY ="0439. 



" ' 71294^"^^'^ 



Interpolating from Table IV we have for „o-,= "0439, 



r = 0-3, logx'=l"7596, 



r = 0-4, log x' = 2-0025. 



Hence log x'= 1-9614, r=-38. 



Had we treated "Temper" as a continuous variate of Gaussian distribution, 



we find 



r=-32±-03. 



Mr Soper's abac gives us at once r = -38, and saves the labour of the second 

 interpolation. 



Illustration II. The following table gives the relation between deaths or 

 recoveries from smaU-pox and the presence of a vaccination cicatrix (Phil. Trans. 

 Vol. 195 a, p. 43). 



SmaU-pox 



o 



Here log x' = 2-2549, 



^(1 + a,) = -9346, -J (1+ a,) = -7708. 

 Hence, by Table V^ Xa,= l'9437, Xa, = l"3869, 



and „^,. = ^xx,xx, = -0590. 



Interpolating from Table IV we have for oO-,.= -0590, 



r=0-6, logx' = 2-1090, 

 r = 0-7, log x' = 2-3088. 

 Hence for log x' = 2-2549, r=-67, 



precisely the value read off beforehand from the abac. 



Had we treated Cicatrix and Eecovery or Death as Gaussian variates, the 

 correlation would be 



r=-60±-03. 



