March 8, 1918] 



SCIENCE 



239 



anatomy and Dr. I. H. Goldberger, has been 

 appointed special lecturer of child hygiene in 

 the school for oral hygiene. 



Mr. Arthuk C. "Walton, M.A. (Northwest- 

 ern '15), M.A. (Harvard 'IG) has been made 

 acting professor of biology in the chair made 

 vacant by the death of Professor Umbach. 

 Mr. Walton holds a Harvard traveling fellow- 

 ship and had planned work in Sweden but 

 was prevented by the war. 



Fred G. Allen, of Erie, Pa., a graduate of 

 the University of Toronto, has been appointed 

 assistant professor in electrical engineering 

 at Lafayette College to take the place left 

 vacant by the resignation of E. D. Tanzer, 

 who has become assistant professor of elec- 

 trical engineering at the Georgia Institute of 

 Technology. 



Early in January Miss Margaret Heatley, 

 instructor in botany at Wellesley College, 

 sailed for South Africa to take charge of the 

 botanical department in Huguenot College of 

 Cape Colony during the absence on sabbatical 

 grant of Dr. Bertha Stoneman. Miss Alice 

 M. Ottley, who was absent on leave, has re- 

 turned to Wellesley College to fill the vacancy 

 in the botany department caused by Miss 

 Heatley's absence. 



DISCUSSION AND CORRESPONDENCE 



NOTE ON THE GEOMETRICAL MEAN AS A 

 B. COLI INDEX 



It is always a beneficial means of grace for 

 a scientist to wander into paths outside his 

 own domain; such excursions often reveal too 

 the lack of coordination between the various 

 sciences, although happily there has been great 

 progress within the past two decades in this 

 respect. These remarks are evoked by a read- 

 ing of the note by William Firth Wells : " The 

 Geometrical Mean as a B. Coli Index " in 

 Science for January 11. 



The first impression gained is the lack of 

 a clear presentation of the method. The 

 notion of a geometric mean is purely mathe- 

 matical, but it must be said that to a mathe- 

 matician, even to one fairly conversant with 

 the theory and methods of bacteriological 

 analysis, the theory on which this method 



rests is not at all in evidence, save only per- 

 hai)s in the remark that " the ordinary bac- 

 teriological dilution scale is in reality a log- 

 arithmic scale." It does not, however, follow 

 necessarily that the most probable number of 

 B. coli is the geometric mean as obtained by 

 Mr. Wells. In support of this contention, 

 see a thoroughly mathematical treatment of 

 the whole question by M. H. McCrady,' of the 

 laboratories of the board of health of the 

 Province of Quebec ; the formulas there de- 

 rived show that the logarithmic function is 

 more complicated than Mr. Wells perhaps has 

 in mind. His experimental data may, on the 

 other hand, show that his proposed method will 

 serve well as a " first approximation." 



The second impression coming from a study 

 of the article is the feeling that this method 

 merits a mathematical treatment. It seems to 

 be essentially as follows: Five sets of twenty 

 tubes each, containing portions of the sample 

 in powers (not " multiples ") of ten, are tested 

 for the presence of gas, indicating the presence 

 of B. coli. For the dilutions 10 c.c, 1 c.c, 

 .1 c.c, .01 c.c, .001 c.c, graded with the scale 

 numbers 0, 1, 2, 3, 4, respectively, the number 

 of tubes showing presence of B. coli was 20 

 18, 8, 1, 0, respectively, the experiment having 

 been extended from a dilution at which all 

 tubes gave positive results to one in which no 

 tube gave such a result. In going from the 

 weakest dilution to the next higher there was 

 a gain of one tube, next a gain of 7, then of 10, 

 then of 2. The scale numbers, which appear 

 to correspond to the logarithms of certain 

 hjiiothetical most probable numbers of B. coli 

 for the separate dilutions, are averaged with 

 the foregoing gains used as weights, i. e., 2, 

 10, 7, 1,0; and the weighted mean thus found 

 corresponds to the logarithm of the desired 

 most probable average number of B. coli. 

 In other words, the weighted geometric mean 

 of the above-mentioned hjTwthetical numbers 

 of B. coli is taken as the desired average. 



An immediate consequence of the mathe- 

 matics involved is that the same result is 



1 M. H. McCrady, ' ' The Numerical Interpreta- 

 tion of Fermentation-Tube Eesults, " Journal of 

 Infectious Diseases, Vol. 17, No. 1, January, 1915, 

 pp. 183-212. 



