130 Mr. Gwvtiier on the 



may, therefore, consider that, as far as adults are considered, 

 the extent to which they are now Hable to attacks of small- 

 pox during an epidemic is approximately expressed by the 

 formula of Bernoulli's first theorem, in which x is now to 

 stand for the number of years during which they have been 

 exposed to small-pox In an epidemic form. If, for instance, 

 a person aged 35 now has passed through a smaller number 

 of years of epidemic than a person aged 35 forty years ago, 

 we may reasonably suppose that his chance of taking small- 

 pox is greater, and that the ratio may be expressed in some 

 way similar to that of Theorem I. As far as infantile 

 small-pox is concerned the law of Incidence Is altered 

 altogether, and I do not know where we are to look for the 

 cause except in our system of vaccination. Much light 

 might be thrown on this subject by a comparison with the 

 similar statistics of the German Empire, if their present 

 system of vaccination has been carried on long enough to 

 give comparable results, and this, I think, must be the case, 

 as it is during the action of the cause that we can but 

 estimate its effect. 



If, as I have assumed, vaccination has only a protective 

 influence for a limited time, and if its effect is to reduce the 

 number of small-pox cases up to adolescence and then lose 

 its virtue. Its secondary effect must be to leave a larger 

 number subject to small-pox at adult ages, according to 

 Theorem II. And that this effect is operating would seem 

 to be the evidence given by my tables. On this point we 

 may see Bernoulli's answer to certain doctors who objected 

 that Inoculation might form a continuous source of infection, 

 each case communicating the infection to ten others, and 

 these again In the same ratio, thus c^ulckly arriving at a 

 number exceeding the total population of the world. Tlie 

 objection in this form was absurd, but Bernoulli's answer 

 was that perhaps it might be better for the human race if 

 the malady was in this way endemic, and that possibly the 



