682 INFECTION BY THE BLOOD PROTOZOA 



The members of this equation have not been measured exactly, but fairly accurate 

 conckisions have been made possible by determining the first and second terms and 

 evaluating the third (the author and L. G. Taliaferro [1922], the author [1924] on 

 trypanosomes, and L. G. Taliaferro [1925] on malaria). The first term (as previously 

 indicated) is obtained by making frequent parasite counts during the course of the 

 infection. The second term is obtained indirectly, since to be valid it must be inde- 

 pendent of both the first and third terms, and hence can in no way depend on number 

 counts. Because reproduction proceeds in cycles in malaria, whereas in trypanosome 

 infections it does not, a different method is used in the two groups, but each method 

 requires that sufficient parasites be in the blood to obtain a statistically valid sample. 



An approximate method of measuring the rate of reproduction independent of 

 the number of organisms destroyed is to ascertain the percentage of dividing forms. 

 This is the method used by Robertson (191 2) and has been used in all of our work as 

 a check on the following method which is considerably more exact. Throughout the 

 trypanosome infections fifty trypanosomes were drawn and measured at frequent 

 intervals and their variability in total length, as expressed in terms of the coefficient 

 of variation, compared. (The coefficient of variation was computed from the actual 

 measurements by means of the usual formula and expresses the variability in terms of 

 percentages of the mean size; the author and L. G. Taliaferro [1922].) For example, 

 in T. lewisi, a coefficient of variation of 30 per cent indicates a population in which 

 reproduction is at its height, whereas one of 3 per cent indicates a population of adults 

 in which there is no reproduction (see Fig. i). Relating this to the equation, it is 

 obvious that the number produced by reproduction in the first case would be very 

 high, and in the second case nil. The rationale of this method is based on the well- 

 known fact that a sample of organisms measured, on the one hand, from a population 

 undergoing rapid reproduction, with the constant production of young forms and 

 intermediate growth stages, will exhibit much greater variability in size than a sample 

 of organisms measured, on the other hand, from a population in which there is little 

 or no reproduction and in which all of the organisms are full-grown adults. (For a 

 fuller discussion of this method as well as a consideration of a number of its possible 

 fallacies see the author and L. G. Taliaferro [1922].) 



The coefficient of variation method is applicable to trypanosome infections be- 

 cause the organisms reproduce by binary fission with no periodicity. Thus, if re- 

 production is going on, a random sample at any time will include all stages of repro- 

 duction and growth. In the malarial infections, on the other hand, the asexual forms 

 grow up and sporulate nearly synchronously (Fig. 3). Thus, a sample at one time will 

 contain only small forms (merozoites) ; at another, only large forms (schizonts), etc. 

 The length of time it takes for the organisms to complete this cycle of growth and 

 sporulation is, however, actually an expression of how long it takes one merozoite 

 to become fifteen merozoites, and hence is a measure of the rate of reproduction of 

 the parasites, and should it vary, the rate of reproduction may be said to vary. Ac- 

 cordingly, fifty parasites were drawn and their mean size obtained at each two- to 

 four-hour interval during as much of the infection as possible. As can be seen from 

 Figure 10, the data obtained showed a series of cycles, each cycle consisting of a 

 gradual rise and abrupt fall in the mean size of the parasites. Comparing the time it 

 takes this cycle to be completed during the various stages of the infection (acute, 



