304 PROCEEDINGS OF THE ACADEMY OF [April, 



statistical method in the study of variation/ and it appears to the 

 writer that this method is the only accurate and scientific one that 

 can be employed. Several plants, therefore, were chosen, because 

 of their easy procurement, and measurements were made of their 

 several parts and these measurements tabulated. Several striking 

 facts were brought out during the course of the statistical inquiry, 

 and these are referred to in their proper place throughout the 

 paper. 



The following common plants were chosen for a somewhat 

 detailed measurement of the parts mentioned, viz. : Fruits of the 

 May apple {Podophyllum j^e/tofwju), leaves of the tulip poplar 

 {Liriodendron tulipifera), leaves of the Japanese ivy {Ampelop.m 

 VeitchW), fruits of white oak (Quercus alba), fruits of the swamp 

 chestnut oak (Qaercus prinus paludris), leaves of the moon-seed 

 {MenUpermum eanadense), entire plants of Indian turnip {Ari- 

 scema triphyllum), leaves of bloodroot (^Sanguinaria canadensis), 

 leaves of the tree of heaven (^Ailanthus glandxdosa) — the latter 

 plant not being studied statistically, but in a comparative way to 

 bring out some peculiarities of its pinnation. The material was 

 used either in the green condition or it was used in the preserved 

 state (dry or alcoholic). In all cases where leaves were taken, 

 careful tracings were made by a sharp-pointed lead pencil upon 

 ordinary drawing or raanila paper, and these tracings were after- 

 ward accurately measured. The character of the material, 

 whether fresh, dry or alcoholic, is mentioned in connection with 

 the subjoined tables. Prof. Halsted' has shown that leaves suffer 

 in drying, but in drying, as they all maintain the same relative 

 size, the results which are mainly comparative do not seem 

 to be vitiated. 



The measurement of the linear dimensions of the leaves and 

 parts of the plants was made by a standardized boxwood scale 

 manufactured by Keuffel & Essler Co., New York, which ruler 

 was divided into centimeters, millimeters and half-millimeters, the 

 length of the scale being twenty centimeters in all. Superficial 

 dimensions, in order to be accurate and expressive of the real size 

 of the leaf or other part, require a detailed trigonometrical calcu- 



' 1900, Botanical Qazette, " Account of the International Botanical Con- 

 gress,'' XXX, p. 405. 



^Halsted, Bulletin lorrey Botanical Club, xxi, p. 127. 



