1166 REPORT—1885. 
this difference is not accidental? It is shown that the answer depends upon a 
certain constant, or co-efficient, which might be calculated from life-tables. This 
constant enables us to find the probability that the mean age at death of a hundred 
(or a thousand) persons taken at random, would deviate to an assigned extent 
from the mean age at death of the general population. This all-important con- 
stant may be defined as one or other of the following correlated quantities : the 
precision, the probable error, the modulus, or (as the writer proposes to call the 
square of the modulus) the fluctuation. 
Two problems in vital statistics, in the case of which the discovery of the requi- 
site constant presents peculiar difficulties, form the special subject of this study. 
I. Suppose out of a population, resident in the same place in the same year, 
there are taken at random several groups, and the death-rates calculated for each 
of those groups; according to what modulus would these figures fluctuate? It is 
required to elicit this answer from the Registrar-General’s returns, which give 
only death-rates for different years and different places. The answer to this problem 
may be used to verify inferences concerning the relative unhealthiness of different 
occupations. Buta wider utility attends the solution of the problem. The fact 
that the different methods by which it may be attacked lead to the same result is 
calculated to give us confidence in handling the mathematical instruments of 
statistics, We realise that to each class of phenomenon there appertains in 
general a tolerably constant co-efficient of fluctuation ; which, having been obtained 
by observation, we shall be able to employ this datum of past experience to test 
future statistical inductions. 
II. The second problem exemplified is to determine whether a given series of 
statistical returns indicates progress. Consider a set of figures representing the 
mortality of a certain population for several consecutive years. The theory of the 
modulus can determine whether an appearance of increase or decrease in these re- 
turns corresponds to a real difference in the conditions of life. The indications 
afforded by scientific method are apt to differ considerably from the guesswork of 
common sense.’ 
4. On the Application of Biology to Economics. By Patrick Guppes. 
Since the progress of any order of ideas proceeds mainly from within, even 
heresies arising by a reversal of former beliefs, it is not to be wondered at if 
economists of all schools, orthodox or heterodox alike, are little attracted by the 
proposal to translate the propositions they debate from the time-honoured vernacular 
into the language of scientific specialists. Yet to point to this round-about way 
of simplifying matters is the object of the present paper. Not only, however, does 
biology owe much to economics—witness such a principle as the physiological 
division of labour—but the author of the ‘ Origin of Species’ has traced its direct 
filiation to Malthus’ theory of population. 
A classic account of this relation is to be found in Mr. Spencer's well-known 
popular work ‘On the Study of Sociology,’ and the importance of the subject has 
often been insisted upon—witness Dr. Ingram’s memorable presidential address of 
1878, or his recent article ‘ Political Economy.’ But as a recent reviewer scorn- 
fully asks, what have physics or biology to do with land-tenure, with taxation, 
the depreciation of silver, the rate of wages, the thousand and one problems of the 
economist ?—hbut the reply is easy: what biology seeks to deal with are the funda- 
mental conceptions of the subject, not their application to concrete details. Thus 
the biologist, while as yet at least wholly shrinking from interference with matters 
too high for him, will in no wise be restrained from claiming what the economist 
lumps as ‘ competition’ as a form of the general struggle for existence, and seeking 
to analyse it, or, dissatisfied with the loose and popular notion of ‘ progress,’ 
endeavouring to distinguish whether it means evolution or degeneration of popu- 
lation and their surroundings in each special case. When this is done the air 
becomes clearer: we see how, for instance, the dispute preceding the passing of 
1 Printed im extenso in the Journal of the Statistical Society for January, 1886, 
a_i. 2 
