206 WILBER BROTHERTON, JR., AND H. H. BARTLETT 
Summary 
The mathematical formulation of the results of size inheritance 
according to the multiple factor hypothesis should be paralleled by a 
biological analysis, the object of which is the identification of the 
several factors concerned. In such a biological analysis, it will inevit- 
ably be found that quantitative variations may be correlated with 
variation in either the number or the size of the constituent cells of 
the organisms or organs involved. Still other variations involve both 
cell number and cell size. 
In the investigation of quantitative variations of a hereditary 
nature, it seems likely that the study by the histological method of 
reactions to the environment and of the obscure reaction known as 
"vigor of heterozygosis" will afford a means of correcting for these 
disturbing factors. 
In connection with genetical studies in Phaseolus, we Have made 
some studies of fluctuating variation due to the effect of light, one of 
the most disturbing factors concerned in size inheritance. The results 
are of considerable interest in themselves, and may be summarized as 
follows : 
1. In Phaseolus muUiflorus, growth in darkness results in the elonga- 
tion of the internodes to 3.6 times the length of normal internodes 
grown in the light. 
2. This increase in length is accounted for to the extent of 34 per- 
cent by increase in the number of divisions taking place in the primary 
meristem, the remainder of the increase being due to increase in length 
of the cell or group of cells derived from each primary division. 
3. It is possible to recognize the group of secondary cells formed by 
division of a primary cell during its extension, since the outline of the 
primary cell is pointed at the ends, whereas the subsequently formed 
cross walls are approximately perpendicular. 
4. There appears to be a specific mean length for division of the 
primary epidermal cells, with a value of about 0.140 mm., which is 
independent of light or darkness. 
5. In consequence of the fact that the length for division is attained 
in a larger number of primary cells in the etiolated than in the normal 
internode, it is necessary, in appraising the relative importance of the 
cell number and cell size factors, to discriminate carefully between 
primary and secondary epidermal cells. 
