Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

196 MATHEMATICAL PHILOSOPHY
In this conception of natural law and the consequent
conception of natural science as having for its aim discovery of invariant relations among the things that appear and
disappear in the flowing pageant of the world, there is, I
believe, nothing new except its setting and its manner.
Rankine, for example, in a paper presented before the Glasgow Philosophical Society in I867, said: "One of the chief
objects of mathematical Physics is to ascertain, by the
help of experiment and observation, what physical quantities are conserved." And among invariants thus found
he instances mass, resultant momentum, total energy, and
other things. More embracing are the words of Major
MacMahon in his address to the Mathematical Section
of the British Association in go19. " In any subject of
inquiry there are," he says, " certain entities, the mutual
relations of which, under various conditions, it is desirable
to ascertain. A certain combination of these may be
found to have an unalterable value where the entities are
submitted to certain processes or are made the subject
of certain operations. The theory of invariants in its
evident scientific meaning determines these combinations,
elucidates their properties, and expresses results when
possible in terms of them. Many of the general principles
of political science can be expressed by means of invariantive relations connecting the factors which enter as entities into the special problems. The great principle of
chemical science which asserts that when elementary or
compound bodies combine with one another, the total
weight of the material is unchanged, is another case in
point. Again, in Physics, a given mass of gas under the
operation of varying pressure and temperature has the
well-known invariant, pressure multiplied by volume and
divided by absolute temperature." You doubtless know