146 THE SCIENTIFIC MONTELY
an operation as a verb function, then o* will denote the operation of
raising a quantity to the nth power, when [o*]a5=fl:*, and since o*
is unity, [ao^ + fto* + co^'\x=a'\' bx + cx\ In all this. Boss mod-
estly regards himself as an amateur, but he believes that Newton him-
self may have adapted Dary's principle in devising his own method of
obtaining the roots of equations by approximation. In Boss's operative
division, each term of the quotient operates on the whole divisor instead
of being multiplied into it, as in ordinary algebraic or arithmetical
division. The rest of Boss's mathematical work has been concerned
with *' pathometry,*' a term of his invention signifying the quantitative
study of parasitic invasion and infection in individuals or groups of
individuals. He has investigated, for instance, the variations of mos-
quito-density in relation to time and place, the relation of mosquito
output to extent of breeding surface and the relations of mosquito-
density to the rate and extent of malaria-incidence in a given locality;
also the relation of malaria-rate to such factors as parasite-rate, spleen-
rate (number of malarial cases with enlarged spleen), fever-rate, and
the proportion of people who are constantiy ill from malarial fever, all
of which are lessened by '^ mosquito reduction." This work on mos-
quito distribution is said to have been the inspiration of the mathemat^
ical memoir of Pearson and Blakeman on random migration. Lat-
terly, Colonel Boss has occupied himself with the study of epidemic
curves, that is, the graphs predicting the course and probable duration
$t an epidemic from its initial data, which were first investigated by
the English statistician. Dr. William Farr, in 1866. Work of this
kind has been attempted only within the last sixty years, the explana-
tion being that there have been few vital and medical statistics covering
large averages until recent times. In the eighteenth century, Daniel
Bemouilli applied the calculus of probabilities to smallpox epidemics
and got an equation giving the number of survivors who have not had
the disease in terms of the number surviving at a given age out of a
given number, the number attacked and the number not attacked in a
year. The recent aim has been to discover the law of which an epi-
demic, in relation to space and time, is to be regarded as an expression.
In other words, while the hygienist aims to influence and limit the
course of the epidemic by such coefficients as vaccines, sera, destruction
of insects or animals carrying the disease, or other aggressive sanitary
measures, the aim of the modern epidemiologist is statistical prognosis
or the prognosis of infectious disease on a grand scale. The strong
point made by Farr was that the theoretical curve of an epidemic in
space and time is a normal curve. The generic idea is that all recur-
rent natural phenomena, e. g., the weekly ratio of illegitimacy to the
normal birthrate in a large city, tend to acquire a certain uniformity.
Farr^s law states the general epidemiological principle that subsidence
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