204 Leaf-Product [402 



the corresponding leaflet breadth was measured at the point 

 of greatest width, at right angles to the long axis of the 

 leaflet. Since soy-bean leaflets are approximately elliptical 

 in form and since the area of an ellipse is proportional to 

 the product of its axes, the leaflet-product (length times 

 breadth) of any leaflet should be nearly proportional to the 

 area of that leaflet. Whether this relation may hold during 

 the growth of the leaflet under different sets of climatic con- 

 ditions depends upon how nearly the elliptical form is re- 

 tained. The sum of the individual leaflet-products of any 

 plant, which is the total leaf -product for that plant, should 

 be approximately proportional to the total leaf area of the 

 plant, if the relation given above holds. In the discussion 

 that follows it will be shown that such an approximate propor- 

 tionality does exist in the case of the four-week soy-bean 

 plants. 



In order to find out whether the actual area of the leaves 

 in these cultures was proportional to the leaf-products, the 

 ratio of the two quantities was worked out for a number of 

 the stations. It was found that the leaf -product divided by 

 the leaf area gives a number that varies only slightly from the 

 value 1.28. In other words, if we measure the two diameters 

 of the leaflets of a four-week soy-bean plant, multiply these 

 two numbers, and add the products, a number is obtained 

 which, when divided by 1.28, closely approximates the actual 

 leaf area of that plant. Instead of using the sum of the 

 products of length and breadth as an index of the area per 

 plant we may use the sum of the squares of the lengths of 

 the leaflets or the sum of the squares of the breadths of the 

 leaflets of the plant. The numbers thus secured do not, how- 

 ever, bear as nearly constant a ratio to the actual leaf area 

 as does the total leaf-product, and hence neither is as satis- 

 factory an index of the area as is the leaf -product itself. 



One of the most interesting properties of the four-week 

 soy-bean plant is that the dry weight of stem and leaves is 

 proportional, approximately, to the total leaf area. Having, 

 therefore, a means by which the leaf area may be conveniently 



