422 G. S. WILSON 



effect of overcrowding in the determination of the numerical 

 development of colonies in plates. However, in considering this 

 question it must be realized that two factors are concerned. 

 The first may be called the error of sampling, the second the error 

 of overcrowding. 



a. The error of sampling. It is clear that if three tubes are 

 put up from an emulsion containing a comparatively small num- 

 ber of bacilli, the chances of obtaining a representative sample 

 must be smaller than if an emulsion be employed which contains 

 a much larger number of bacilli. Similarly with the tubes them- 

 selves. If only a few bacilli are introduced, the chances of ob- 

 taining a correct idea of the exact number are smaller than if a 

 large number of bacilli are introduced. Thus the greater the 

 number of colonies per tube, the less is the error of sampling. 

 That this is not a mere theoretical consideration is shown from an 

 examination of the data accumulated during the progress of his 

 work. Thus to quote from the actual figures of an experiment. 

 Three tubes were put up from a particular emulsion : in the first, 

 7; in the second, 12; and in the tliird, 15 colonies developed. The 

 arithmetic mean of these three is 11.33, and the percentage mean 

 deviation is 25.5 per cent. Or again; in a series of three tubes 

 inoculated from the same dilution, the number of colonies de- 

 veloping was 434, 454 and 470. The arithmetic mean of these is 

 452.7, and the percentage mean deviation is 2.75 per cent. From 

 these two examples it is seen that the percentage deviation of 

 each individual tube from the arithmetic mean was considerably 

 greater in the case when a small number of colonies developed 

 than in the case when a large number of baciUi were inoculated. 

 In other words the sampling error in the former instance was 

 large, in the latter comparatively small. Recognizing however, 

 the fallacies of a single experiment, a large number of experiments 

 were reviewed in which viable counts were put up by means of 

 three tubes each; the aritlimetic mean of each of these counts 

 was worked out, and the percentage deviation of each count from 

 the arithmetic mean estimated. The percentage mean deviation 

 was calculated for tubes in which to 50 colonies developed, and 

 again for those in which 50 to 100, 100 to 200, 200 to 400, 400 to 



