of Edinburgh, Session 1882-83. 
17 
Thus, even when there is a transformation of the energy of the 
system, the results of § 9 still hold good. And it is to be observed 
that if one of the masses, sa}'' m.j,, is enormously greater than the 
other, the equation 
'^\ 9 \ + '^2/^2 ^ 
shows that is excessively small, and the visible change of motion 
is confined to the smaller mass. Carrying this to the limit, we 
have the case of motion about a (so-called) “ fixed centre.” In such 
a case it is clear that though the momenta of the two masses relative 
to their centre of inertia are equal and opposite, the kinetic energy 
of the greater mass vanishes in comparison with that of the smaller. 
These results are then extended to any self-contained system of 
free particles, and the principle of Varying Action follows at once. 
It is thus seen to be a general expression of the three propositions 
of § 2 above. 
(12) So far as we have yet gone, nothing has been said as to how 
the mutual potential energy of two particles depends on their 
distance apart. If we suppose it to be enormously increased by a 
very small increase of distance, w^-. have; practically the case of two 
particles connected by an inextensible string — as a chain-shot. But 
from this point of view such cases, like those of connection by an 
extensible string, fall under the previous categories. 
The case of impact of two particles falls under the same rules, so 
far as motion of the centre of inertia, and moment of momentum 
about that centre, are concerned. The conservation of energy, in 
such cases, requires the consideration of the energy spent in perma- 
nently disfiguring the impinging bodies, setting them into internal 
vibration, or heating them. But the first and third of these, at 
least, are beyond the scope of abstract dynamics. 
(13) The same may be said of constraint by a curve or surface, 
and of loss of energy by friction or resistance of a medium. Thus 
a constraining curve or surface must be looked upon (like all physical 
bodies) as deformable, but, if necessary, such that a very small 
deformation corresponds to a very great expenditure of energy. 
(14) To deal with communications of energy from bodies outside 
the system, ah we need do is to include them in the system. Treat 
as before the whole system thus increased, and then consider only 
VOL. XIL 
B 
