GROWTH 527 



metical, until the final size of the colony is reached. The time interval 

 between cell divisions also gradually increases. 



The growth of Zoothamnium alternans depends on the common 

 stalk, according to Faure-Fremiet (1925). The cell initiating the colony 

 has a given component of granular material which is distributed un- 

 equally during division and, as it is used up, the growth of the colony 

 ceases through transformation of material into the stalk. This may be 

 analogous to the accumulation of nonliving material in multicellular 

 organisms, a phenomenon which some biologists believe results in the 

 limited growth of such organisms. The growth curves are sigmoid 

 (Faure-Fremiet, 1925, 1930), and the growth is believed to be auto- 

 catalyzed by the granular material. 



Pedigree Isolation Culture and Life Cycles 



The culture of a single cell in a drop of a suitable food and the iso- 

 lation of one of the divided cells, shortly after division, into a new drop 

 of medium, effectively maintains the environment constant, and the 

 growth is then potentially unlimited. With a constant medium and suit- 

 able bacterial food, the rate of growth is very nearly constant, as has 

 been demonstrated by Woodruff and Baitsell (1911), Darby (1930, 

 1930a, 1930b), Beers (1929), and others. If the growth curve for the 

 sum of the individuals be plotted on arithlog paper, a straight line will 

 result, because the growth (j) is exponential, y == yoc'"', when jo is the 

 amount of the seeding, or the growth at time, t = O and e, is the 

 Naperian base. The proportionality constant k = {In 2)/G.T., or 

 0.6^9 /G.T. The generation time {G.T.) is the time between divisions. 

 Tabel 5 summarizes the growth rates under fairly constant conditions for 

 certain Protozoa. 



The study of the variation in cell division has been obscured by the 

 unfortunate practice of plotting the division rates in the form of a histo- 

 gram. The bars of the plot commonly give the average division rate for 

 ten-day periods. The histogram is used properly to show unit events 

 which have no intermediate values, e.g., the results of tossing dice 

 which cannot assume a position intermediate between two of the num- 

 bered sides. The average division rate is no such discrete, mutually ex- 

 clusive attribute, but may take any fractional value within the limits of 

 the experiment. An example showing how information on the division 



