LOClober, 
486 On Scientific Method. 
proceeds, indeed, upon mathematical principles in calculating 
the number of the combinations of the things proposed ; 
but by the conclusions that are obtained by it the sagacity of 
the natural philosopher, the exactness of the historian, the 
skill and the judgment of the physician, and the prudence 
and foresight of the politician may be assisted, because the 
business of all these important professions is but to form 
reasonable conjectures concerning the several objects which 
engage their attention, and all wise conjectures are the results 
of a just and careful examination of the several different 
effects that may possibly arise from the causes that are 
capable of producing them.” 
When we apply this theory to faCts we are astonished at 
the results. Speaking of “ the variety of logical relations 
which may exist between a certain number of terms,” Prof. 
W. Stanley Jevons* says : — “ Four terms give 16 combina- 
tions, and no less than 65,536 possible selections from these 
combinations . for six terms the corresponding numbers 
are 64 and 18,446,744,073,709,551,616. Considering that it 
is the most common thing in the world to use an argument 
involving six objects or terms, it may excite some surprise 
that the complete investigation of the relations in which six 
such terms may stand to each other should involve an almost 
inconceivable number of cases. Yet those numbers of pos- 
sible logical relations belong only to the second order of 
combinations.” 
If the faCts of Nature be so numerous we can never hope 
to know them all. PerfeCt knowledge is for us impossible : 
how, then, are we to make the most of that partial know- 
ledge which we can alone attain to ? How can we measure 
the extent of our knowledge of any subject? By means of 
the theory of probability. 
Although perfect knowledge is impossible, yet we cannot 
be content with the accumulation of mere isolated faCts. 
We attempt to group faCts together, to form theories, and to 
apply these to the explanation of newly discovered faCts. 
The theory of probability must guide the mind in guaging 
its knowledge of any group of faCts. And the theory of 
probability is, as Laplace has said, “ good sense reduced to 
calculation.” 
Suppose it be required to determine the atomic weight of 
an element, we devise various methods of measurement, we 
repeat the measurements again and again, but there are 
nevertheless errors inherent in each method, errors in the 
* Principles of Science, vol. i., p. 223. 
