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 
