358 Method of estimating Bacterial Density 



(2) For any considerable body of records of sets of parallel plates, 

 agreement with this theoretical distribution may be tested by means of 

 the index of dispersion 



where x is the mean, and x any individual number of colonies counted 

 on a plate (see Section 5). 



(3) From an examination of several large bodies of data we conclude 

 that accurate conformity with the theoretical distribution, though rare, 

 is not unattainable. In particular with a carefully improved technique, 

 and a relatively simple bacterial flora, we believe that the conditions have 

 probably been fulfilled by Breed and Stocking; secondly, by the aid of a 

 specially adapted medium Cutler and Thornton have shown that these 

 conditions have been accurately reproduced, in the great majority of 

 cases, even with the mixed bacterial flora of the soil. 



(4) Any signijicani departure from the theoretical distribution is a sign 

 that the mean may he wholly unreliable. 



(5) Excessive variance may be produced by the occurrence of certain 

 soil organisms, which have been isolated, and which exert a toxic influence 

 on other forms, and in one case disturb the counts by multiple colony 

 formation. 



(6) Subnormal variance is in our experience indicative of some defect 

 in tlie composition of the medium. 



REFERENCES 



(1) PoissoN (1837). Recherches sur la probabilite des Jugonents. Paris. 



(2) ■"Student" (1907). On the error of counting with haomocytometer. Biometrikn, 



V. 351. 



(3) Fisher, R. A. ( 1921 ). On the mathematical foundations of theoretical statistics. 



Phil. Trans. A. ccxxii. 309. 



(4) Eldekton, p. (1902). Tables for testing goodness of fit. Biometrika, i. 155. 



(5) Peahson, K. (1914). Tables for statisHcians and bionielricians. Camb. Univ. 



Press. 



(6) FiSHEK, R. A. (1922). On the interpretation of ;!^- from contingency tables, 



and the calculation of P. .J.R.S.S. lxxxv. 87. 



(7) SoPER, H. E. (1914). Tables of Poisson's exponential binomial hmit. Bio- 



metrika, x. 25. 



(8) Whitaker, L. (1914). On the Poisson law of small numbers. Biometrika, x. 



36. 



(9) Bateman, H. (1910). Xote on the probabihty distribution of a particles. Phil. 



Mag. Series vi. vol. xx. p. 704. 

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