June 19, 1921 mohler and foote: soft x-rays 273 



are those in x, not X, for in bacterial phenomena the population must 

 be taken into account. The logarithm of the number of bacteria, 

 and not the number itself, should therefore be used for routine pur- 

 poses. 



SUMMARY 



The chance {Pc) of finding C bacteria in a cc. of water containing 

 X bacteria per cc. is 



Pc = —^ exp. (- aX) 



This theorem is applied to the "per cent negative" (100 Po) method of 

 counting bacteria and to the method of counting positive plates. 



It is shown that the variability in samples containing more than ten 

 bacteria is small, so that differences between the arithmetic and 

 geometric means cannot be due to fluctuations of sampling. 



The extreme variability usually found in bacteriology is due to 

 differences of locality and time. In any case where the data vary very 

 widely, a few very large values, representing perhaps less than one 

 per cent of the results, may double the value of the arithmetic mean ; 

 their effect upon the geometric mean is but slight. This renders the 

 arithmetic mean practically valueless. 



Bacteriological frequency distributions usually possess not only 

 wide variability, but positive skewness. In such cases the geometric 

 mean is more probable than the arithmetic mean, but the most impor- 

 tant reason for preferring the geometric mean is its stability as an 

 average. 



PHYSICS. — Soft characteristic X-rays from arcs in gases and vapors.^ 

 F. L. MoHLER and Paul D. Foote, Bureau of Standards. 



If an electron current is maintained by a potential V between a hot 

 cathode and anode in a vapor at low pressure, then as V is increased 

 successive changes occur in the spectrum excited by electron impact. 

 The highest frequency v of each additional group of lines is related to 

 the least potential required to excite the group by the quantum equa- 

 tion Ve = hv. 



The authors have studied the stages in the discharge by measuring 

 the photo-electric effect of the radiation on two other electrodes en- 

 tirely shielded from ions produced in the arc. This photo-electric 

 current plotted as a function of the exciting voltage shows nearly a 

 linear relation with changes of slope at critical potentials. In this 



1 Received June 15, 1921. 



