. 





1909] 



HARRIS— LEAVES OF PODOPHYLLUM 



443 



Spanish chestnut, mixed, veins in leaves. 591 



Beech, Buckinghamshire, veins in leaves 570 



Spanish chestnut, Buckinghamshire, veins in leaves 466 



Ash, Monmouthshire, leaflets on leaves 405 



Ash, Dorsetshire, leaflets on leaves 396 



Ash, Buckinghamshire, leaflets on leaves 374 



Holly, Somersetshire, prickles on leaves 355 



Wild ivy, mixed, leaf-indices , 273 



Some of these are slightly higher and some slightly lower than 

 our coefficients; but when the probable errors attached to all con- 

 stants are borne in mind, I think we cannot assert that our values 

 are very different from those obtained by English biometricians 

 for other leaf characters. Furthermore Pearson shows reasons for 

 considering some of his values too high and some too low for true 

 homotypic relationships. For instance, ceterach is said by botanists 

 to be largely influenced by growth and environment. 3 



There still remains one possible reason for thinking that the real 

 correlation between the number of lobes on the leaves of the same 

 flowering stalk may be somewhat higher than is indicated by these 

 constants. The 



May 



My 



plants from both habitats were taken from quite a wide stretch 

 of woods, but a considerable number of the plants are doubtless 

 vegetatively related. I do not believe this has a very large influence 

 in my series, but it is proper to mention the point. 



3 From the arithmetical side there are also difficulties. I did not apply Sheppard's 

 correction for the second moment in calculating my standard deviations. Perhaps 

 this should have been done, but until some mathematician works out the theory, 

 biologists will not know what rule to follow in the case of integral variates. In the case 

 of a range of variability so narrow as we have here, Sheppard's correction would 

 make a considerable difference, raising the coefficient of correlation by lowering the 

 standard deviations. So perhaps our values should be a little higher. 



There is also the question of leaves which fall on the borderline between n and p*+i 

 lobes. In the present study I carefully tried to throw these into the class to which they 

 most nearly belonged, just as one would have to do in the case of real integral variates. 

 But after all, the lobing of the leaf of Podophyllum is not a case of discrete variation, 

 and if I were repeating the work I would divide questionable cases between adjoining 

 grades. Probably this would not make a very great difference in the end result. 



The reader will note, too, that I am discussing " homotypic" correlation on series 

 of material which I have just demonstrated to be differentiated. But I think I am 

 quite justified in treating the material as I have done, for lower and upper leaves 

 have always been kept separate. There has been no mixing of heterogeneous 



material. 



