Change of Incidence of Small-Pox. 123 



the death rate at different ages at the time when previous 

 attacks by small-pox conferred the only immunity from 

 future attacks. And if the death rate on the vaccinated 

 community taken in the proportion of about 1 1 to i had 

 been at the same rate, up to the age of 20, the death rate 

 at the ages beyond, even if we do not lower it on the plea of 

 immunity conferred by small-pox, would not appear un- 

 reasonably large. 



Since 1880 the Registrar General's Returns have 

 separated the deaths from small-pox under the heads 

 Vaccinated, Unvaccinated, and No Statement, and these 

 returns show the same kind of progression as I have illus- 

 trated by the table above, and I know no reason why these 

 should not be taken as representing the general features of 

 the incidence of small-pox on the vaccinated and unvac- 

 cinated when equally exposed to it as during the said years 

 in London. 



It seems desirable to apply some amount of calculation 

 to make the comparison more obvious, and to that I now 

 proceed. 



My attention was called by Dr. Bottomley to a Memoir 

 by Daniel Bernoulli among the Memoires de I'Academie 

 Royale des Sciences for the year 1760, entitled "Essaid'une 

 nouvelle analyse de la mortalite causee par la petite Verole," 

 &c., which is very interesting both on account of the at- 

 tempt to find a mathematical expression for the death rate 

 from small-pox, and as giving a good idea of the virulence 

 of the disease and its incidence at different ages at that 

 date. As it may interest members of the Society, and will 

 certainly illustrate the change of the incidence of the dis- 

 ease between that date and this, I ask leave to add this 

 note to my paper lately read. 



Two short passages I will quote at length : — 



"J'ai dit d'abord que la petite verole naturelle enleve la 

 huitieme ou la septieme partie de ceux qui en sont malades. 



