332 H. A. Blair 



between this latent injury and the clinical syndrome, but this has not yet been 

 established. The advantages of developing non-lethal methods for detecting 

 latent injury will be mentioned later. 



It should also be remembered in what follows that the minimal lethal injury 

 to an animal may not initially be manifest clinically at all, and that death occurs 

 only after many days during which clinical signs develop. Because most 

 mammals, if they are going to die from irradiation, do so within three or four 

 weeks, it is customary to describe the lethal dose as that one which will kill 

 one-half the experimental group within thirty days and to designate it LD50 or 

 LD5Q 30 days. The events which happen between the time of exposure, when 

 presumably a lethal threshold for primary injury must be reached, or exceeded, 

 if death is to occur, and actual death, are outside the scope of this discussion. 



The LD50 for most mammals using whole body exposure is within the 

 range of 400 to 800 roentgens for the young adult. 



In accord with the above hypotheses, the rate of development of injury / 

 under exposure at constant dose rate y is 



f =^7-^(/-oc}'0 (1) 



in which /> is the rate of recovery per unit injury and A and a are constants. 



Integration of equation (1) gives for the level of injury after exposure for 



time t 



(^ — a) „, 



I = ^^—^y{\--e-f^^) + y.yt (2) 



If the time of exposure is sufficiently short that no significant recovery 

 occurs during exposure, as is usual in determining the acute median lethal 

 dose or LD50, e"''' may be replaced by 1 — /:»/ so that equation (2) becomes 



/ = Ayt = Aot. 

 a being the total dose. 



If, now, a is the LD50, the injury / is the lethal injury and according to postu- 

 late (e) 



I=A(x^ So- S (3) 



in which 5*0 is the normal life expectancy of the animal and S is its age at 

 radiation death. The constant of proportionality associated with Sq — S 

 is taken arbitrarily as unity 



For animals irradiated at daily constant rates for periods of some months 

 e~^^ may be neglected. This reduces equation (2) to 



. (A - a) 



r + ay/ (4) 



or, on using equation (3), to 



5*0 — 5" A — a 



+ a/ (5) 



Because nearly all chronic radiation experiments are begun on the young 

 adult animal and also because postulate (e) catmot possibly be valid in very 

 young animals in which the lethal dose rises instead of diminishes with age, 



