GROWTH 529 



and the last is {xn_i -}- 2a-„)/3. If further smoothing is desired, a 

 five-day instead of a three-day running average may be used, and it is 

 computed in a corresponding manner. Phelps (1934) gives an example 

 of the running average plot. 



In many of the earlier studies, the culture medium was inadequate, and 

 after a time the division rate approached zero. Unless the animals were 

 transferred to a favorable medium, the strain then died out. Such a 

 growth period has been termed a "cycle" by Calkins. During a cycle, 

 or, with some Protozoa during periods of nearly constant growth, small 

 fluctuations in the growth rate occur. These minor variations are termed 

 "rhythms" (Woodruff, 1905; Woodruff and Baitsell, 1911). Rhythms 

 are associated with cellular reorganization (endomixis). The constant 

 culture of Didinium nasutum without rhythms led Beers (1928) to be- 

 lieve that rhythms were due to food, temperature, and the condition of the 

 culture medium. Rhythms may have a function in some species and be 

 merely effects of the environment in others. 



That the Calkins cycle depends on the adequacy of the culture medium 

 has been demonstrated by a number of experimenters, e.g.. Woodruff 

 and Baitsell (1911a), Mast (1917), Beers (1928b), Darby (1930a), 

 and Gerstein ( 1937) . A medium that may be adequate for a few weeks 

 may not be suitable for long periods. Dawson's Parameciujn and Blepha- 

 risma showed gradual negative trends during the three years of the cul- 

 ture. At this rate the cycle would not end for several years (Richards 

 and Dawson, 1927) and, in the meantime, some slight change in the 

 medium might reverse the trend by supplying the cultural inadequacy, 

 thus prolonging the cycle. Competition may bring out more rapidly the 

 effects of the environment with populations than with individuals. The 

 study of Protozoa, maintained for some time in an effectively constant 

 culture medium, should add materially to our knowledge of growth. 

 Peters (1901) gives useful methods; yeast techniques are summarized 

 by Richards (1934). 



Dawson kept pedigreed isolation cultures of Histrio complanatus, 

 Blepharisjna undulans, and a mutant P. aureUa for three years. A sta- 

 tistical analysis of the division rates removed the long-time trends, and 

 established a seasonal cycle, with a maximum division rate in the sum- 

 mer and a minimum rate in winter (Richards and Dawson, 1927). The 

 statistical methods used were those used in economics in the study of 



