Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

460 REASONING AND DEDUCTIVE EVIDENCE.
nected with these affections, we are not liable to be disturbed
by those physical accidents, which, in the other applications of
mathematical science, necessarily render the result more or
less at variance with the theory. In measuring the height of a
mountain, or in the survey of a country, if we are at due pains
in ascertaining our data, and if we reason from them with mathematical strictness, the result may be depended on as accurate
within very narrow limits; and as there is nothing but the incorrectness of our data by which the result can be vitiated, the
limits of possible error may themselves be assigned. But in
the simplest applications of mathematics to mechanics or to
physics, the abstractions which are necessary in the theory, must
always leave out circumstances which are essentially connected
with the effect. In demonstrating, for example, the property
of the lever, we abstract entirely fiom its own weight, and consider it as an inflexible mathematical line; - suppositions with
which the fact cannot possibly correspond; and for which, of
course, allowances (which nothing but physical experience can
enable us to judge of) must be made in practice.
Next to practical geometry, properly so called, one of the
feet, or of any part or multiple of a foot. This known length, by being
multiplied or divided, is sufficient to give us a distinct idea of any length
whatsoever.
" Izeproper quantity is that which cannot be nmeaslured by its oznel kind, but to
which we assign a measure in some proper quantity that is related to it.
Thus velocity of motion, when we consider it by itself, cannot be measured.
~We may perceive one body to move faster, another slower, but we can perceive no proportion or ratio between their velocities, without taking in
some quantity of another kind to measure them by. Having therefore
observed, that by a greater velocity, a greater space is passed over in the
same time, by a less velocity a less space, and by an equal velocity an
equal space; we hence learn to measure velocity by the space passed over in
a given time, and to reckon it to be in exact proportion to that; and having once assigned this measure to it, we can then, and not till then, conceive one velocity exactly double, or triple, or in any proportion to another.
We can then introduce it into mathematical reasoning, without danger of
error or confusion; and may use it as a measure of other improper
quantities."