Prof. Tait on the Laws of Motion. 443 
2. Conservation of energy. 
3. That property (those properties ?) of matter, in virtue of 
which it is the necessary vehicle, or, as the case may be, the 
storehouse- of energy. 
(3) The third of these alone presents any difficulty. So 
long as energy is obviously kinetic, this property is merely 
our old friend inertia. But the mutual potential energy of 
two gravitating ir asses, two electrified bodies, two currents, 
or two magnets, is certainly associated (at least in part, and 
in some as yet unknown way) with matter, of a kind not yet 
subjected to chemical scrutiny, which occupies the region 
in which these masses &c. are situated. And even when 
the potential energy obviously depends on the strain of a 
portion of ordinary matter, as in compressed air, a bent spring, 
a deformed elastic solid, &c, we can, even now, only describe 
it as due to " molecular action," depending on mechanism of 
a kind as yet unknown to us : — though in some cases, such 
as the kinetic gas theory, at least partially guessed at. 
(4) The necessity for the explicit assumption of the third 
principle, and a hint at least of the limits within which it must 
be extended, appear when we consider the very simplest case 
of motion, viz. that of a lone particle moving in a region in 
which its potential energy is the same at every point. For 
the corservation of energy tells us merely that its speed is 
unaltered. We know, however, that this is only part of the 
truth : the velocity is constant. It will be seen later that this has 
most important dynamical consequences in various directiors. 
(The remarkable discussion of this point by Clerk-Maxwell 
is then referred to, in which it is virtually shown that, were 
things otherwise, it would be possible for a human mind to 
have knowledge of absolute position and of absolute velocity.) 
(5) But Maxwell's reasoning is easily seen to apply equally 
to any component of the velocity. Hence, when we come to 
the case in which the potential energy depends on the posi- 
tion, the only change in the particle's motion at any instant 
is a change of the speed in the normal to the equipotential 
surface on which the particle is at that instant situated. The 
conservation of energy assigns the amount of this change, and 
thus the motion is completely determined. If V be the poten- 
tial energy of unit mass at the point p, we have at once 
p = -W, 
from which the circumstances of the motion can be deduced. 
In fact, this problem is precisely the same as was that of the 
motion of a luminous corpuscle in a non-homogeneous medium, 
the speed of passing through any point of the medium being 
assigned. 
