STATISTICAL TREATMENT 



243 



probability paper, or by using specially prepared logarithmic probability 

 paper. In either of these cases we have a quick and reasonably accurate 

 method of arriving at the value of the lethal dose. 



The method just outlined is satisfactory when it is possible to use a 

 large number of animals for the determination of each percentage. But 

 when we are limited to a few animals, an approximate determination of 

 lethal dose will have to be made and the procedure given in the follow- 

 ing illustration will usually be found satisfactory for summing up the 

 evidence contained in the observations. In Table 7 is presented a series 

 of observations made by Russ et al. (7) for the determination of the 

 dosage of penetrating X-rays necessary to kill the cat. The total number 

 of animals used was 27, and these animals in groups, varying in size 

 from 2 to 10 were subjected to dosages over a range from 0.22 Ti to 1.1 Tx. 



Table 7. — Mortality of Cats Subjected to X-ray Radiation 



Inspection of Table 7 shows that it is obviously impossible to deter- 

 mine the percentage dying at each of the various dosages, but we can 

 make an approximation to the lethal curve by making use of the two 

 following assumptions: (a) All animals tested at any given dosage and 

 found to survive would have survived if subjected to a smaller dosage. 

 (6) All animals tested at a given dosage and found to die would have 

 died if subjected to a larger dosage. Applying these two assumptions to 

 the observations in the table, we can set up the columns headed m, 

 implicit survivals, and /;, implicit deaths. From the probability theorem 

 that if an event has happened n times and has failed to happen m times, 

 then the probability that on the next trial the event will happen is given 

 by (n + l)/(m -f n + 2), we may arrive at a figure indicating the likeli- 

 hood that a cat will die at each of the dosages tried. Plotting these 

 probabilities against the dosages on arithmetic probability paper, drawing 

 a straight line through the points, and reading the dosage corresponding 



