ARTICLES 607 



in such cases the dividing cells are more vulnerable to the 

 rays than are the growing cells, then it will be a matter of first 

 importance to arrange that the majority of the cells forming 

 the tumour shall for some period during the exposure be in 

 the act of division. It will be seen later that in order to 

 secure this, some information must be gained of the average 

 rate of growth of the tumour and of the intensity of radiation 

 which is necessary to produce some retarding effect upon the 

 growth of the constituent cells. 



On the simplest assumptions of cell growth and prolifera- 

 tion, mathematical expressions may be obtained [vide Appendix) 

 which represent the numbers (N and n) of growing and 

 dividing cells, at any time subsequent to inoculation. If \ x 

 and X 2 ar e two constants which characterise the rapidity with 

 which the whole cycle of division, growth to maturity, and 

 division again occurs, then the numerical values of these two 

 constants for any strain of tumour may be obtained, pro- 

 vided (1) that frequent measurements of the rate of growth 

 are made, and (2) that an estimate is made by microscopical 

 observations of the relative proportions of the growing and 

 dividing cells. These two constants tell us what fraction of 

 the growing cells are reaching the dividing stage per second, 

 and what fraction of the dividing cells are passing over to 

 the growing stage per second. 



Now the rate at which a tumour is progressing is propor- 

 tional to Xi and Xa ; the larger these are the quicker the growth. 



Confining our attention to one strain of tumour, if it be 



observed, say, that the tumour decreases in its rate of growth, 



then the ratio of N to n will remain exactly the same if Xi 



and X 2 are altered in the same proportion as one another. 



If, however, when the rate of growth is diminished it be due to 



an unequal decrease in \ x and X2, this will show itself when 



the ratio of N to n is found experimentally. 



N 

 In other words if we examine how — varies for a tumour 



n 



strain growing at different rates, we may be able to say whether 



the decreased rate is due to a retardation of the mytotic process 



or of the actual growth of the cells. This has been put to the 



test in the case of the Jensen rat sarcoma, which has been 



cultivated in the Cancer Research Laboratories of the Middlesex 



Hospital for the last seven years. 



