THE DOCTRINE OF MOTION.
1. _Pure Mechanism._--THE doctrine of Motion, of which we
have here to speak, is that in which motion is considered
quite independently of its cause, force; for all
consideration of force belongs to a class of ideas entirely
different from those with which we are here concerned. In
this view it may be termed the _pure_ doctrine of motion,
since it has to do solely with space and time, which are the
subjects of pure mathematics. (See c. i. of this book.)
Although the doctrine of motion in connexion with force,
which is the subject of mechanics, is by far the most
important form in which the consideration of motion enters
into the formation of our sciences, the Pure Doctrine of
Motion, which treats of space, time, and velocity, might be
followed out so as to give rise to a very considerable and
curious body of science. Such a science is the science of
Mechanism, independent of force, and considered as the
solution of a problem which may be thus enunciated: 'To
communicate any given motion from a first mover to a given
body.' The science which should have for its object to solve
all the various cases into which this problem would ramify,
might be termed _Pure Mechanism_, in contradistinction to
_Mechanics Proper_, or _Machinery_, in which Force is taken
into consideration. The greater part of the machines which
have been constructed for use in manufactures have been
practical solutions of some of the cases of this problem. We
have also important contributions to such a science in the
works of Mathematicians; for example, the various
investigations and demonstrations which have been published
respecting the form of the Teeth {157} of Wheels, and Mr.
Babbage's memoir[15\2] on the Language of Machinery. There
are also several works which contain collections of the
mechanical contrivances which have been invented for the
purpose of transmitting and modifying motion, and these
works may be considered as treatises on the science of Pure
Mechanism. But this science has not yet been reduced to the
systematic simplicity which is desirable, nor indeed
generally recognized as a separate science. It has been
confounded, under the common name of _Mechanics_, with the
other **science, Mechanics Proper, or Machinery, which
considers the effect of _force_ transmitted by Mechanism
from one part of a material combination to another. For
example, the _Mechanical Powers_, as they are usually
termed, (the Lever, the Wheel and Axle, the Inclined Plane,
the Wedge, and the Screw,) have almost always been treated
with reference to the relation between the _Power_ and the
_Weight_, and not primarily as a mode of changing the
velocity and kind of the motion. The science of pure motion
has not generally been separated from the science of motion
viewed with reference to its causes.
[Note 15\2: _On a Method of expressing by Signs the action
of Machinery._ _Phil. Trans._ 1826, p. 250.]
Recently, indeed, the necessity of such a separation has
been seen by those who have taken a philosophical view of
science. Thus this necessity has been urged by M. Ampère, in
his _Essai sur la Philosophie des Sciences_ (1834): 'Long,'
he says, (p. 50,) 'before I employed myself upon the present
work, I had remarked that it is usual to omit, in the
beginning of all books treating of sciences which regard
motion and force, certain considerations which, duly
developed, must constitute a special science: of which
science certain parts have been treated of, either in
memoirs or in special works; such, for example, as that of
Carnot upon Motion considered Geometrically, and the essay
of Lanz and Betancourt upon the Composition of Machines.' He
then proceeds to describe this science nearly as we have
{158} done, and proposes to term it _Kinematics_
(_Cinématique_), from κίνημα, motion.
2. _Formal Astronomy._--I shall not attempt here further to
develop the form which such a science must assume. But I may
notice one very large province which belongs to it. When men
had ascertained the apparent motions of the sun, moon, and
stars, to a moderate degree of regularity and accuracy, they
tried to conceive in their minds some mechanism by which
these motions might be produced; and thus they in fact
proposed to themselves a very extensive problem in
_Kinematics_. This, indeed, was the view originally
entertained of the nature of the science of astronomy. Thus
Plato in the seventh Book of his _Republic_[16\2], speaks of
astronomy as the doctrine of the motion of solids, meaning
thereby, spheres. And the same was a proper description of
the science till the time of Kepler, and even later: for
Kepler endeavoured in vain to conjoin with the knowledge of
the motions of the heavenly bodies, those true mechanical
conceptions which converted formal into physical
astronomy[17\2].
[Note 16\2: P. 528.]
[Note 17\2: _Hist. Induc. Sc._ ii. 130.]
The astronomy of the ancients admitted none but uniform
circular motions, and could therefore be completely
cultivated by the aid of their elementary geometry. But the
pure science of motion might be extended to all motions,
however varied as to the speed or the path of the moving
body. In this form it must depend upon the doctrine of
limits; and the fundamental principle of its reasonings
would be this: That velocity is measured by the Limit of the
_space_ described, considered with reference to the _time_
in which it is described. I shall not further pursue this
subject; and in order to complete what I have to say
respecting the Pure Sciences, I have only a few words to add
respecting their bearing on Inductive Science in general.
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