1 877.] 
On Scientific Method, 
485 
probably find ourselves — like the alchemists — spending our 
years in useless labour, searching in the labyrinth of detached 
fadts without any guide, and, like them, we shall arrive at no 
true results. 
The dodtrine or theory of combinations enables us to deter- 
mine the possible number of ways in which a given set of fadts 
or circumstances may be grouped together. This theory is of 
the utmost importance in enabling us to form just concep- 
tions of the nature of the task set before him who would 
investigate Nature. The- importance of the dodtrine of com- 
binations is thus insisted on by James Bernouilli :* — “ It is 
easy to perceive that the prodigious variety which appears 
both in the works of Nature and in the adtions of man, and 
which constitutes the greatest part of the beauty of the 
Universe, is owing to the multitude of different ways in 
which its several parts are mixed with, or placed near, each 
other. But because the number of causes that concur in 
producing a given event, or effedt, is oftentimes so immensely 
great, and the causes themselves are so different one from 
another, that it is extremely difficult to reckon up all the 
different ways in which they may be arranged or combined 
together, it often happens that men, even of the best under- 
standings and greatest circumspection, are guilty of that 
fault in reasoning which the writers on logic call the insuffi- 
cient or imperfect enumeration of parts or cases ; insomuch that I 
will venture to assert that this is the chief and almost the only 
source of the vast number of erroneous opinions — and these, 
too, very often in matters of great importance — which we 
are apt to form on all the subjects we refledt upon, whether 
they relate to the knowledge of Nature, or the merits and 
motives of human add; ions. It must therefore be acknowledged 
that that art which affords a cure to this weakness or defedt 
of our understandings, and teaches us to enumerate all the 
possible ways in which a given number of things may be 
mixed and combined together, and that we may be certain 
that we have not omitted any one arrangement of them that 
can lead to the objedt of our enquiry, deserves to be consi- 
dered as most eminently useful and worthy of our highest 
esteem and attention, And this is the business of the art or 
doctrine of combinations. Nor is this art or dodtrine to be 
considered merely a branch of the mathematical sciences, 
for it has a relation to almost every species of useful know- 
ledge that the mind of man can be employed upon. It 
* Da Arte Conje&andi, translated by Baron Maseres (London, 1795, 
p. 353) » quoted by Jevons in Principles of Science, vol. i., pp. 198 — 200. 
