482 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
The Application of Dynamical Principles to Phenomena which are in a Steady State. 
§ 5. The most convenient principle for this purpose is the Hamiltonian one, 
according to which, if i be constant, 
S 
'i 
Jo 
Ldt = t 
( 12 *) 
where q is one of tire coordinates helping to fix the configuration of the system, and 
L the Lagrangian function or PlOUTh’s modification of it, according as it is or is not 
expressed entirely in terms of the velocities of the coordinates. 
If 
and if S be expressed in terms of i, and the coordinates at the tunes 0 and i, then, if q 
be a coordinate at the time i, we see from equation (12*) that 
and, by Lagrange’s equation, 
hence we see that the momentum corresponding to any coordinate and the rate 
of change of the momentum can both be expressed as the differential coefficients 
of functions with respect to that coordinate. 
We shall now proceed to show that for Steady Motion 
dT _ dS 
dq dq 
4 S' = -f (T - Y); 
dl dq dq ' 
where L is the mean value of L, and where S is to be interpreted in the following 
way. 
Adi, or nearly all, the systems we shall have to deal with are those which consist of 
a large number of molecules, and we may conveniently for our purpose divide the 
coordinates, fixing the configuration of such a system into two kinds : — 
(а) Molar coordinates, which fix the configuration of the system as a whole, and 
whose value we may by various physical processes alter at our pleasure. When we 
say that the system is in a steady state, all that we mean is that the configuration as 
fixed by the molar coordinates is steady. 
(б) Molecular coordinates, which fix the position of individual molecules. The 
values of these coordinates are quite beyond our control. 
