SHORTER ARTICLES AND DISCUSSION 



THE TABULATION OF FACTORIAL VALUES 1 



In Science for January 23 2 Dr. Ellis L. Michael discusses the 

 validity of the ordinary system of tabulation in the determina- 

 tion of the probable number of bacteria in an emulsion. He 

 argues in favor of the use of the logarithms of the measurements 

 instead of the direct measurements because the former give a 

 symmetrical distribution, while the latter give one that is dis- 

 tinctly asymmetrical. As Dr. Michael has invited discussion it 

 may be of interest to mention briefly a similar method used dur- 

 ing the last two years in a study of the germinal and environ- 

 mental factors affecting eye facet number in the bar races of 

 DrosophUa. A report of the method was made at the St. Louis 

 meeting of the American Society of Zoologists and the results of 

 its application to the particular problems in hand are being pub- 

 lished in a series of papers. 3 



In working up the data it became evident that the demands of 



arrangement in classes with equal fact numbers. The wide 

 range in individual stocks and the still wider differences between 

 different races made it desirable to express relations directly in 

 terms of factorial units affecting .facet number rather than in 

 facet numbers. In dealing with a stock averaging 30 facets as 

 compared with one averaging 300 facets it became evident that a 

 one facet change at the mean in a 30 facet stock represents the 

 same factorial value as a ten facet change at the mean in a 300 

 facet stock and that a corresponding principle applies within the 

 range of a single stock. Accordingly the classes were arranged 



2 "Concerning Application of the Probable Error in Cases of Extremely 

 Asymmetrical Frequency Curves," Science, N. S., 51: 89-91. 



8"A Change in the Bar Gene of Drosophila Involving Further Decrease 

 69-71. J. Exp. Zool., 1920, 30: 293-324. ' °* Phjsiol, 1919, 2 

 358 



