New volumes of the Encyclopædia Britannica > Volume 30, K-MOR

MODELS
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a distance, however, were conceived as differing from
those of the Newtonian law of attraction, in that they
could explain the properties not only of solid elastic
bodies, but also those of fluids, both liquids and gases.
The phenomena of heat were explained by the motion of
minute particles absolutely invisible to the eye, while to
explain those of light it was assumed that an impalpable
medium, called luminiferous ether, permeated the whole
universe; to this were attributed the same properties as
were possessed by solid bodies, and it was also supposed
to consist of atoms, although of a much finer composition.
To explain electric and magnetic phenomena the assump¬
tion was made of a third species of matter—electric fluids
which were conceived of as being more of the nature of
fluids, but still consisting of infinitesimal particles, also
acting directly upon one another at a distance. This first
phase of theoretical physics may be called the direct one, in
that it took as its principal object the investigation of the
internal structure of matter as it actually exists. It is
also known as the mechanical theory of nature, in that it
seeks to trace back all natural phenomena to motions of
infinitesimal particles, i.e.,to purely mechanical phenomena.
In explaining magnetic and electrical phenomena it
inevitably fell into somewhat artificial and improbable
hypotheses, and this induced Maxwell, adopting the ideas
of Faraday, to propound a theory of electric and magnetic
phenomena which was not only new in substance, but also
essentially different in form. If the molecules and atoms
of the old theory were not to be conceived of as exact
mathematical points in the abstract sense, then their true
nature and form must be regarded as absolutely unknown,
and their groupings and motions, required by theory,
looked upon as simply a process having more or less
resemblance to the workings of Nature, and representing
more or less exactly certain aspects incidental to them.
With this in mind, Maxwell propounded certain physical
theories which were purely mechanical so far as they
proceeded from a conception of purely mechanical pro¬
cesses. But he explicitly stated that he did not believe
in the existence in Nature of mechanical agents so
constituted, and that he regarded them merely as means
by which phenomena could be reproduced, bearing a
certain similarity to those actually existing, and which
also served to include larger groups of phenomena in a
uniform manner and to determine the relations that held
in their case. The question no longer being one of ascer¬
taining the actual internal structure of matter, many
mechanical analogies or dynamical illustrations became
available, possessing different advantages ; and as a matter
of fact Maxwell at first employed special and intricate
mechanical arrangements, though later these became more
general and indefinite. This theory, which is called that
of mechanical analogies, leads to the construction of
numerous mechanical models. Maxwell himself and his
followers devised many kinematic models, designed to
afford a representation of the mechanical construction of
the ether as a whole as well as of the separate mechanisms
at work in it: these resemble the old wave-machines, so far
as they represent the movements of a purely hypothetical
mechanism. But while it was formerly believed that it
was allowable to assume with a great show of probability
the actual existence of such mechanisms in Nature, yet
nowadays philosophers postulate no more than a partial
resemblance between the phenomena visible in such
mechanisms and those which appear in Nature. Here
again it is perfectly clear that these models of wood,
metal, and cardboard are really a continuation and
integration of our process of thought •, for, according to
the view, in question, physical theory is merely a mental
construction of mechanical models, the working of which
we make plain to ourselves by the analogy of mechanisms
we hold in our hands, and which have so much in common
with natural phenomena as to help our comprehension of
the latter.
Although Maxwell gave up the idea of making a
precise investigation into the final structure of matter as
it actually is, yet in Germany his work, under Kirchhoff’s
lead, was carried still farther. Kirchhoff defined his own
aim as being to describe, not to explain, the world of
phenomena; but as he leaves the means of description
open his theory differs little from Maxwell’s, so soon as
recourse is had to description by means of mechanical
models and analogies. Now the resources of pure
mathematics being particularly suited for the exact
description of relations of quantity, Kirchhoff’s school
laid great stress on description by mathematical expres¬
sions and formulae, and the aim of physical theory came
to be regarded as mainly the construction of formulae by
which phenomena in the various branches of physics
should be determined with the greatest approximation to
the reality. This view of the nature of physical theory is
known as mathematical phenomenology; it is a presenta¬
tion of phenomena by analogies, though only by such as
may be called mathematical.
Another phenomenology in the widest sense of the term,
maintained especially by Mach, gives less prominence to
mathematics, but considers the view that the phenomena
of motion are essentially more fundamental than all the
others to have been too hastily taken. It rather
emphasizes the prime importance of description in the
most general terms of the various spheres of phenomena,
and holds that in each sphere its own fundamental law
and the notions derived from this must be employed.
Analogies and elucidations of one sphere by another, e.g.,
heat, electricity, &c., by mechanical conceptions, this theory
regards as mere ephemeral aids to perception, which are
necessitated by historical development, but which in
course of time either give place to others or entirely
vanish from the domain of science.
All these theories are opposed by one, called in Germany
Energetics (in the narrower sense), which looks upon the
conception of energy, not that of matter, as the funda¬
mental notion of all scientific investigation. It is in the
main based on the similarities energy displays in its
various spheres of action, but at the same time it takes
its stand upon an interpretation or explanation of
natural phenomena by analogies which, however, are
not mechanical, but deal with the behaviour of energy
in its various modes of manifestation.
A distinction must be observed between the models
which have been described and those experimental models
which present on a small scale a machine that
is subsequently to be completed on a larger, so Bxperi-
as to afford a trial of its capabilities. Here Models
it must be noted that a mere alteration in
dimensions is often sufficient to cause a material altera¬
tion in the action, since the various capabilities depend in
various ways on the linear dimensions. Thus the weight
varies as the cube of the linear dimensions, the surface of
any single part and the phenomena that depend on such
surfaces are proportionate to the square, while other effects,
such as friction, expansion, and conduction of heat, &c.,
vary according to other laws. Hence a flying machine,
which when made on a small scale is able to support its
own weight, loses its power when its dimensions are
increased. The theory, initiated by Newton, of the
dependence of various effects on the linear dimensions, is
treated at length in the text-books of mechanics. Under
simple conditions it may often be affirmed that in com¬
parison with a large machine a small one has the same