632 Proceedings of the Royal Society of Edinburgh. [Sess. 
4. The Law of the Epidemic. — It is not necessary to discuss this again 
fully. In my two communications to this Society (2), I have shown that 
the decline of infectivity of an organism must follow very closely a geo- 
metrical progression. 
5. The Loss of Protective Power of Vaccination against Small-pox . — 
This is the only example in which the data are in the least sufficient to 
permit of the calculation of the rate of loss of acquired immunity. The 
subject, however, is specially difficult. It is not sufficient to take the case 
rate for each age period of population and examine that, as has been done 
in previous instances. For, in the first place, both vaccinated and 
unvaccinated are specially susceptible to small-pox at the ages of 10-15, 
and, in the second place, old age confers a very real immunity against 
small-pox. In one instance alone do data exist which permit the elimina- 
tion of these factors, namely, the epidemic in Sheffield in 1887-88 (7), 
discussed in a former paper. In this case a census of the vaccinated and 
un vaccinated was made, so that for each age period we have the numbers 
of both vaccinated and unvaccinated, and the numbers of cases of small-pox 
occurring among each. 
This permits the calculation of the coefficients of correlation showing 
the degree of protection present (8). The values of these coefficients and 
of the geometrical progression fitted to them are given in the accompanying 
diagram (Diagram II.). As will be seen, the correspondence is very fairly 
close. Certain of the values are obviously too low, and certain others too 
high. When these are adjacent it will be noted that the curve almost 
exactly bisects the distance between them. The fit is as good as might be 
expected when the condition of spread of small-pox in a large town is 
considered, and there is sufficient correspondence of the facts with the 
theory to make the interpretation given here at least probable. 
As a general commentary on what has been said, it may be remarked in 
the first case that young children are more easily killed by certain 
organisms than older children. This susceptibility to death is related 
quantitatively to age, and this relation requires explanation. It may be 
explained if we assume that the young child has some substance present 
which affords a means of foothold to the attacking organism. This 
substance disappears with age in the manner of the mono-molecular 
chemical reaction. We then have a case of athreptic * immunity, that 
is, an immunity due to lack of nourishing substance in the attacked 
organisms. 
The second and third cases may be considered together. As the death- 
* Ehrlich’s “atreptic” in the barbarous German spelling. 
