92 MORPHOLOGIC VARIATION 



the cells according to their area-length indices. The curves for 

 length show the increased variation in length during the period of 

 active growth which was previously observed with Bacillus megath- 

 erium. There is, however, not nearly so pronounced a skewness 

 in the curves and no tendency toward bimodality. The culture 

 studied, however, w^as relatively heavily seeded, and it is probable that 

 if further studies were made with this organism, with lightly seeded 

 cultures, as has been done in the case of Bacillus megatherium, simi- 

 lar increased variation and a tendency toward bimodality in the 

 distribution curves would be noted. The frequency distribution 

 curves for area-length index of the cells show nothing very striking, 

 save that during the period of active growth (at three hours) the 

 range was somewhat restricted and the variation in form is some- 

 what less. The negative correlation between size and area-length 

 index, then, is also evident in the distribution curves. 



The relation between size and form of the cells may be more 

 clearly seen in a correlation graph (Figure 27) in which the length 

 of the cells is plotted against the area-length index. For this graph 

 the data from the three-hour sample, as representative of the maxi- 

 mum growth phase; and from the eighteen-hour sample, as repre- 

 sentative of the resting phase, have been chosen. A curve has 

 been very roughly fitted to the data by simple inspection. This 

 curve is clearly hyperbolic, the ascending limb approaching as a 

 limit an area-length index of zero, i.e., a form in which the thick- 

 ness is infinitely small in proportion to the length; the descending 

 limb approaches as a limit a form in which the length equals the 

 thickness, i.e., a sphere. Such a hyperbolic curve would result if the 

 cells varied in length but remained constant in diameter. That 

 such is not the case is apparent from an inspection of Figure 24; 

 the three-hour cells are distinctly thicker than the others. But 

 proportionately to length, the increase in diameter is not great, and 

 consequently a hyperbolic curve results when length is plotted against 

 form. It is interesting in this connection to note that Minoux has 

 recently concluded from theoretical-mathematical considerations that 

 bacterial cells must grow much less in diameter than they do in 

 length. 



