lotka: discontinuous evolution 57 



drawn for one entire fundamental period, and the curve for y for 

 one-half-period. 



The significance to a biological kindred-group of such alter- 

 nating periods of prosperity and depression as are indicated in our 

 oscillating curve, representing a function of the form (24) is so 

 obvious as to call for no further comment. In particular, the 

 question suggests itself to our minds, whether the curve of growth 

 along which the human race is at present ascending, leads to a 

 maximum, to be followed by a downward incline. That we have 

 been living on our capital of natural resources is only too clear. 

 But we are awakening to a realisation of this fact, and are taking 

 stock, and looking ahead in preparation to meet such emergencies 

 as may arise. Our reflections here lead us to the consideration 

 of such topics as the preservation of our natural resources, the 

 production of nitrogen compounds from the air, and the exploita- 

 tion of the radiant energy received from the sun. These things 

 have been discussed at length in the current scientific and tech- 

 nical literature, and their mere mention here in their logical place 

 must suffice. 



As an example of a case of the type (1. b) (page 50), we will 

 consider a bacterial disease, such as pulmonary phthisis, which is 

 more or less constantly present in the population (i.e., not epi- 

 demic in its occurrence). Brief reflection shows that we can 

 apply to this case a mathematical treatment precisely analogous 

 to that of the growth of a population. For we may think of the 

 diseased part of the population as a separate aggregate, into which 

 new individuals are recruited by fresh infection, just as new indi- 

 viduals enter an ordinary population by births. On the other 

 hand members are continually eliminated from the aggregate, 

 firstly by deaths, and secondly by recoveries. On the basis of 

 these considerations formulae can without difficulty be estab- 

 lished to express a relation between the total and the diseased 

 population, which in this case is of more immediate interest than 

 the ratio of the total mass of the population to that of the bac- 

 teria. Such general furmulse however involve certain functions 

 which are unknown, and whose determination by statistical 

 methods would at best present great difficulties. The matter 



