484 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
to Clausius, which we have already given on page 474, and we have just seen that 
we may suppose dL/dq 2 = 0, so that the equation becomes 
SL = 2 
5 
but, since the motion is steady, dL/dq 1 is constant, so that this may be written 
8E = s f;( 8si); ' 
Now we have supposed that the variation is of such a kind that q x remains 
unaltered ; in this case $q L remains constant throughout the motion, and therefore 
vanishes, so that we have 
S L = 0, .(13) 
or L has a stationary value for all changes which leave the velocities unchanged. 
It is convenient to work with the mean values of L, because, as we shall see later 
on, it is possible in many cases involving the motion of great numbers of molecules 
to calculate L from data given by experiment, when it would not be possible to 
calculate L. 
The expression for the energy of a system consisting of a great number of molecules 
will contain terms of three kinds : (1) terms depending entirely on molar coordinates; 
(2) terms depending partly upon molar and partly upon molecular coordinates ; and 
(3) terms depending entirely upon molecular coordinates. The energy expressed by 
the terms of the first kind can be entirely converted into mechanical work, while that 
expressed by the terms (2) and (3) can only be partially converted, the extent of the 
conversion depending on the distribution of kinetic energy throughout the system. 
Yon Helmholtz* calls the first kind of energy free energy, the other he calls bound 
energy. 
Since the velocities are supposed to remain constant in the variations we con¬ 
template in equation (13), it is evident that the only terms in the kinetic energy 
which are affected are those which involve the coordinates themselves. The energy 
expressed by such terms we may call the positional kinetic energy, and it is the only 
part of the kinetic energy which we need consider, or which has any influence on the 
way in which any transformation of energy takes place. We shall now go on to 
apply the principle that 
8 L = 0 
to some special cases. 
* Von Helmholtz, “ Die Thermodynamik cliemischer Vorgdnge,” ‘ Wissenschaftliclie Abliandlungen,* 
vol. 2, p. 958. 
