Ill] A POPULATION OF YEAST 153 



The duplication-period thus determined is known to brewers as 

 the generation-time. 



Much care is taken to ensure the maximal growth. If the yeast 

 sink to the bottom of the vat only its upper layers enjoy unstinted 

 nutriment; a potent retardation-factor sets in, and the exponential 

 phase of the growth-curve degenerates into a premature horizontal 

 asymptote. Moreover, both the yeast and the bacteria differ in 

 this respect from the typical (or perhaps only simpHfied) case of 

 man, that they not only begin to suffer want as soon as there comes 

 to be a deficiency of any one essential constituent of their food*, but 

 they also produce things which are injurious to their own growth 

 and in time fatal to their existence. Growth stops long before the 

 food-supply is exhausted ; for it does so as soon as a certain balance 

 is reached, depending on the kind or quahty of the yeast, between 

 the alcohol and the sugar in the cellf. 



If we use the compound-interest law at all, we had better think 

 of Nature's interest as being paid, not once a year nor once an hour 

 as our elementary treatment of the yeast-population assumed, but 

 continuously; and then we learn (in elementary algebra) that in 

 time t, at rate r, a sum P increases to Pe'^\ or P< ^ ^o^^*. 



Applying this to the growth of our sample of 1360 yeast cells, 

 we have 



PtIPo = 2610, log 2610 = 3-417, which, multipHed by the modulus 

 2-303 = 7-868. Dividing by n = 35, the number of hours, 



7-868/35 = 0-225 = r. 



The rate, that is to say, is 22-5 per cent, per hour, continuous 

 compound interest. It becomes a well-defined physiological constant, 

 and we may call it, with V. H. Blackman, an index of efficiency. 

 Our former result, for interest at hourly intervals, was 25-4 per 



* According to Liebig's "law of the minimum." 



t T. Carlson, Geschwindigkeit und Grosse'der Hefevermehrung, Biochem. Ztschr. 

 Lvn, pp. 313-334, 1913; A. Slator, Journ. Chem. Soc. cxix, pp. 128-142, 1906; 

 Biochem. Journ. vii, p. 198, 1913; 0. W. Richards, Ann. of Botany, xlh, pp. 271-283, 

 1928; Alf Klem, Hvalradets Skrifter, nr. 7, pp. 55-91, Oslo, 1933; Per Ottestad, 

 ibid. pp. 30-54. For optimum conditions of temperature, nutriment, pB., etc. see 

 Oscar W. Richards, Analysis of growth as illustrated by yeast. Cold Spring Harbour 

 Symposia, ii, pp. 157-166, 1934. 



