lotka: discontinuous evolution 59 



for New York City. The supposition of a stationary popula- 

 tion and an equilibrium condition of the disease is quite unwar- 

 ranted here, but in the absence of more suitable material, and in 

 view of the great uncertainty of the figures obtainable, we shall 

 have to rest content with this very crude illustration. 



In 1909 the total population of New York was about 4.5 mil- 

 lions. The total number of consumptives at the time has been 



Ni 

 estimated at about 45,000. Hence — = 0.01. The death rate 



N 



per head, per annum, from all causes, was 0.016; that from tuber- 

 culosis alone 0.002. Hence 



s =.0.016 

 7 s = 0.002 

 7 = 0.125 



The coefficient r represents a measure of the "deadliness" 

 of the disease, i.e., it expresses what fraction of the persons once 

 struck with the disease untimately die therefrom. It is difficult 

 to obtain any kind of estimate of the value of r. We will assume 

 that r = 0.8 



We then have by (30) 



L _ 0,01 xQ,8 _ 1 

 0,002 ' 



In view of the crudity of the data on which it is based, this 

 calculation must be regarded purely as an illustration of the prin- 

 ciples involved, and not in any sense as an attempt to determine 

 L, although the endeavor has been made to preserve at least the 

 right order of magnitude in the example given. 



The mathematical treatment of the phenomena presented by 

 infectious diseases has been developed in some detail by Sir 

 Ronald Ross, especially with respect to insect-carried diseases, 

 in his book The Prevention of Malaria, 4 and, quite recently, in 

 a paper published in Nature.' 



4 Published by Murray, 1910; Second Edition, 1911. 



5 "Some Quantitative Studies in Epidemiology," Nature, Oct. 5, p. 466. 1911. 



