Thus, while work can be called a substance only in a limited sense,
since its conservation is limited only to perfect machines, we may call
energy a substance unqualifiedly, since in every instance of which we
know the principle has been maintained _that a quantity of any energy
never disappears unless an equivalent quantity of another energy
arises_. Accordingly, this law of the conservation of energy must be
taken as a fundamental law of the physical sciences. But not only do all
the phenomena of physics, including chemistry, occur within the limits
of the law of conservation, but until the contrary is proved the law of
conservation must also be regarded as operative in all the later
sciences, that is, in all the activities of organisms, so that all the
phenomena of life must also take place within the limits of the law of
conservation. This corresponds to the general fact, which I have
emphasized a number of times, that all the laws of a former science find
application in all the following sciences, since the latter can only
contain concepts which by specialization, that is, by the addition of
further characteristics, have sprung from the concepts of the former or
more general sciences.
=45. Mass and Matter.= It has been noted above that kinetic energy
depends upon another magnitude beside velocity. A conception of its
nature can be obtained when we try to put different bodies in motion.
In doing so the muscles of the arm perform certain quantities of work,
and we feel whether the quantities are greater or smaller. In this way
we obtain a clear consciousness of the fact that different bodies
require quite different quantities of work for the same velocity. The
property which comes into play here is called _mass_, and mass is
proportional to the work which the various bodies require to attain the
same velocity. Since the work and the velocity can be measured very
accurately by appropriate means, mass also lends itself to a
correspondingly accurate measurement.
All known ponderable bodies have mass. That means there is a regular
connection between the property which makes a body tend to the earth
with a certain definite force (called weight) and the property by virtue
of which a body assumes certain velocities under the influences of
motive causes. We can readily conceive that it is possible for us to
learn only of such bodies as are heavy, that is, bodies which are _held_
by the earth, since the others, if they exist at all, would naturally
have left the earth long ago. That all these bodies also have mass is to
be explained in a similar way. For a body of mass zero would at each
impulse assume infinitely great velocity, and could therefore never be
the object of our observation. Consequently, by reason of the physical
conditions obtaining on the earth's surface, the bodies known to us must
combine both properties, mass and weight.
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