1901.] NATUKAL SCIKMCES OF PHILADELPHIA. 319 



that the obliquity of the leaf is occasioned by its fitting itself to 

 utilize the space at its disposal. 



Summary and Conclusion. 



1. This study of the limits of variations in plants was under- 

 taken as, in part, a contribution to the problem of species. 



2. Moreover, this study was undertaken to provide statistical 

 data which would throw light upon the difficulty, from an evolu- 

 tionary standpoint, of small or initial variations. 



3. Considerable vai'iation in the size and shape of leaves is evi- 

 dent, and the amount of the variation was determined statistically; 

 the weight and volume of fruits were calculated ; the number of 

 seeds was determined. 



4. The quantitative amount of variation in the juvenile, arrpsted 

 and transformed leaves of a number of plants was also determined 

 and tabulated. 



5. In Liriodendrontulljjifera, Sanguinaria canadensis, and Ailan- 

 thus glandulosa it was ascertained that variation in the size and 

 configuration of the leaves of these plants is in part due to t he 

 persistence of juvenile forms, to the arrested development of such 

 leaves, to their evolution and transformation to higher forms. The 

 amount of these diflereuces Avas also tabulated. 



6. In conclusion, it may be stated that these changes in most 

 cases are due to two causes: the internal hei^editary impulse deter- 

 mining, as in Ailanthus glandulosa, the asymmetry of the lateral 

 paired leaflets, and the direct environmental influence fitting 

 the leaf to utilize the space at its disposal, and thus enabling it 

 to present the largest amount of leaf surface to light action. We 

 have, therefore, in the tables an exact mathematical expression 

 of the influence of the various operating factors which determine 

 plant form. 



