W. F. SlIKPPARD 



179 



of J.V, or iV.j arc nsiiully irregulär. Thus, calculating tlie valiu-s uf ,r für A' = 14-05 

 anil 141.') by ineans of tlio first ditilbreiico alonc, aiul thence cak-ulatiiig i ( l + «) 

 froni Table I. (remeinberiiig tliat x und a are negative), wo get the l'ulluwiag 

 results, as compared with the actual obscrvations : — 



It is (jiiite possiblo tliat the discrepancy between the ealculati'd and the actual 

 values is mainly due to the errors of random selection of the 11 8 individuals lying 

 between X = 13-95 and X = 14-25. 



7. Certain Special Cases. The mcthod is especially uscful (r/) where the 

 difterence.s in A' are irregulär or are large in comparison with the Standard 

 deviation, and (6) in dealing with tho " arrays " in cases of normal or nearly 

 normal correlation. As an example of the former, Prof. Pearson has jirovided 

 nie with the following rcsnlts obtained by Miss C. D. Fawoett. 



Muttlimj of Mimulus Liitens. 



A' = Numbei- of splotches Less thau 50 öO to Ol i'yi to 71 

 Number of individuals 18 43 Hl 



More than 71 

 5G 



Total 

 204 



This eives three values of *■ in terms of A', viz : — 



X 49^ Gl^ 



X - 1-352 + ■084 - -527 + 002 



+ -599 ± -ÜG3 



The differenccs in .r are -825 and 11 2G, whereas the differences in A' are in the 

 i-atio of 6 : 5. Having regard to the probable errors, it is very doubtful whether 

 the distribution can be treated as normal. If it can be, the truo values of .-« may 

 be somewhat as follows : — 



A 49i 



x (corrected) — 1-503 



Ratio of correction to P. E. — 18 



These would give a meaii of GGGl, and a Standard deviation of ir05, the 

 probable errors being re-spectively + 52 antl + -37. 



23—2 



