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Proceedings of the Royal Society of Edinburgh. [Sess. 
its power of infecting thereafter at a rate corresponding to a geometrical 
progression. Miss Chick (3), in some experiments on disinfection, came to 
a like conclusion, finding that, in the application of a germicide to spore- 
bearing organisms, the number of survivors at the end of each period of 
time obeyed the same law. Miss Chick’s problem is, however, fundamentally 
different from mine : their relationships will be discussed later. Such 
observations suggested a search through the records of disease for analogous 
examples. Five such in all have been discovered up to the present — 
1. The decline of the death-rate in children’s zymotic diseases from 
birth to the age of ten years. 
2. The increase of mortality in zymotic diseases of adults with 
increase of age. 
3. The general increase of mortality with old age (Gompertz’ Law). 
4. The course of epidemics. 
5. The loss of protective power of vaccination against small-pox. 
1. In this group three diseases are included — measles, whooping-cough, 
and scarlet fever (4). All are specially fatal to young children. During 
the first year of life the mortality varies in a manner which is not 
susceptible to any simple explanation ; but by the time the age of one year 
is reached there is evidence that a certain chemical stability is attained. 
From this age to the age of ten years the population may be taken 
as homogeneous. The patients are mostly children born in the city. 
Above ten years immigration introduces a serious error, as the patients 
suffering from these diseases at high ages are largely country born, and 
therefore susceptible to an attack of greater severity. It is to be noted 
(Table I.) that in measles and scarlet fever the death-rate diminishes in 
a geometrical progression almost uniformly. Where the fitted geometrical 
progression deviates largely from the actual figures, it is only at one age 
that this deviation occurs. In the case of measles it is at the age of four 
years. In the case of scarlet fever it is at the age of six in Glasgow and at 
that of three in Manchester. When the fitting of these curves is tested by 
Pearson’s method of estimating goodness of fit the value of P is fairly large, 
but in each case at least two-thirds of the value of x 2 is due to one year, 
and in each case a different year. We may, then, hold it probable that the 
deviation is accidental. The case of whooping-cough is somewhat different, 
but the selection for admission in this case is much more stringent : 
specially ill children only are chosen, or those whose home circumstances 
are very bad, so that at the higher ages there will be a larger proportion 
of severe cases. Thus a priori a concordance of fact with theory should 
