126 Mr. Gwyther on the 



The rate of death from small-pox calculated from it he 

 thinks relatively too high for children under one year, and 

 proposes to account for it as a difference rather moral than 

 physical and attributes it to the slight communication which 

 such children have with the outside world. As the difference 

 would relatively now seem to be in the other direction, we 

 may have to consider a change of manners as partially 

 accounting for it. To return, it is obvious from the method 

 of obtaining the equation above that it would only be true 

 even approximately for a disease in an endemic and not an 

 epidemic form, and therefore if v/e are going to lay any 

 weight on Halley's Tables, with which Bernoulli compares 

 his formula, it must be on the hypothesis that, although in 

 places small-pox might be epidemic, the general character 

 of its incidence upon the peoples from whose death rate the 

 tables were founded was, on the average, that of an endemic 

 disease. The results drawn from it would neither agree 

 with modern tables nor yet with such tables as those given 

 by Dr. McVail in the paper quoted above, though they 

 would agree with the latter in limiting the excessive inci- 

 dence of small-pox to youth. 



Comparing the death rates in the first and the second 

 years as found from this formula, they appear to be in the 

 ratio of 13-1 to 12-4, and, as I stated before, Bernoulli is 

 forced to consider the first too high. It is so certainly if 

 we may compare it with the Kilmarnock death rate ; but at 

 present the ratio in England appears to be about 3:1, and 

 the heaviest death rate appears to be compressed into the 

 first half-year of life, during part of which children are in 

 no way protected. Considering further the death rate from 

 small-pox during the first five years of life, Bernoulli con- 

 cludes that he is not far wrong in considering it about one- 

 tenth of the total death rate during those years. A similar 

 comparison during the years 187 1-2 gives us about one- 

 thirtieth, which is certainly very heavy ; but on the average 

 of the last twenty years we find it is a very small fraction. 



