\Q Harris, \ quantitative study of fche Factors influencing etc. 



base of the pod, the sigmas denoting thc Standard deviationa aud 

 the bars the means, wo find for thc two lots: 



NU Seriös 



4 ovules. w = 9.456 + .212 p 



5 ovules. w = 9.131 -f- .152 p 



6 ovules. w = 8.840 + .162 p 



7 ovules. w = 8,743 + .081 p 



GG Series 



4 ovules. w = 16.289 + .387 p 



5 ovules. w = 16.873 + .263 p 



6 ovules. w — 16.821 -4- .198 p 



7 ovules. w = 16.658 -f- .171 p 



8 ovules. w = 17.441 + .120 p 



These lines and the empirical means are shown graphically 

 in Diagrams 3 and 4. For both series the increase in weight 

 froni the base towards the tip of the pod is unmistakeable. It 

 would be hazardous to say that any curve of a higher order would 

 describe the rate of change for the GG series better than a straight 

 line. For the NH series, the straight line is clearly inadequate 

 — the empirical means forming beantifully regulär curves. At 

 first, the rate of increase is more rapid than is indicated by the 

 straight line, later, it falls off and finally may actually decrease. 

 The mean distal weight is in all four cases greater than the mean 

 proximal. 



To test this matter of the form of the regression line 

 somewhat more critically, the correlation ratio, rj, which measures 

 the intensity of interdependence bctween the magnitude of two 

 characters when the y character (seed weight) does not increase 

 at a linear rate with the x character (position in the pod). 



From the table it appears that the correlation ratio is some- 

 times materially larger than the coefficient of correlation, but in 

 general there is not much choice between them as descriptions of 

 the interrelationship between the two characters. Blake man's 

 test for linearity of regression 1 ) 



v- 1 e 



]/ 1+ (l — ri*)*— (1 ■ r*)' 



Xi 



where I = >f 2 — r 2 and xi = • 67449 / \ N, applied to these individual 

 values of r and rj enables us to say whether or not the ratio of 

 change may be regarded as uniform (within the limits of the errors 

 of sampling) from the base to the tip of the pod. Apparently, in 

 most cases (e. g., in GG w T here the conclusiou from ßlakeman's 

 test is amply substantiated by the diagram) the straight line may 



>) Blakeman, J., Biometrika. Vol. 4. 1905. p. 332—350. 



