68 THE STRUGGLE FOR EXISTENCE 



Richards ('32), even in employing the super-centrifuge of Harvey one 

 can not succeed in obtaining a solid packing of the cells, and inter- 

 stices remain between them. If we draw our attention to the fact 

 that the size of the cells changes in the process of the growth of the 

 culture, and that in mixed populations of the two species we have to 

 deal with cells of different sizes then, theoretically, this must lead to 

 a very different degree of packing of the cells in different cases, and 

 the volume of the cells determined by centrifugation apparently does 

 not yet allow us to judge of their mass. However, the measurements, 

 some of which will be given further on, show that the errors which 

 actually arise are small, and that the centrifugation method is per- 

 fectly reliable for our purposes. 



In the study of the population growth of yeast it is difficult to carry 

 on observations upon the very same culture, as it is urgent to strictly 

 maintain the sterility of the medium and to avoid injury to the cells. 

 For this reason a great number of test tubes were inoculated at the 

 beginning of the experiment ; at certain fixed moments determinations 

 were made upon a group of test tubes which were then put aside and 

 further determinations were made upon new tubes. 



in 



(1) Having examined the technical details of cultivation of yeast 

 cells we can now pass to the problem which interests us first of all: 

 how does the multiplication of the yeast proceed in a microcosm with 

 a limited amount of energy, and what are the factors which check the 

 growth of the population? Let us begin by examining the kinetics 

 of growth under anaerobic conditions. Figure 9 represents the 

 growth of volume of the yeast Saccharomyces cerevisiae, according to 

 the data of one of our experiments in 1930. It is clearly seen that the 

 volume increases slowly at first, then faster, and finally slows down 

 on approaching a certain fixed value. The curve of growth is asym- 

 metrical, i.e., its concave part does not represent a reverse reflection 

 of the convex one (Richards, '28c, Gause, '32a). The first of them is 

 somewhat steep but the second comparatively inclined. This asym- 

 metry is, however, not sharply expressed, and it can be neglected if 

 we analyze the growth in a first approximation to reality. 



In experiments of this type immediately after the yeast cells are 

 inoculated an intensive multiplication begins. There is scarcely any 

 lag-period, or period of an extremely slow initial growth, while the 



