DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
483 
Now, if we consider the molar coordinates, w T e shall see that they are of two 
kinds : the first kind, which I called in my first paper kinosthenic coordinates, only 
enter into the expressions for the energy through their differential coefficients, and 
do not occur explicitly themselves ; the molar coordinates of the second kind enter 
explicitly into the expressions for the energies, and do not occur merely as differential 
coefficients. 
A good example of the two classes of coordinates is afforded by the coordinates 
required to fix the position of a rod suspended by one extremity. We may fix it by 
the angle 6 which the rod makes with the vertical, and the azimuth (f> of the plane 
through the rod and the vertical line through its fixed extremity. The expression 
for the kinetic energy of the rod in terms of these coordinates is of the form 
Ad 3 + B sin 3 9ff> 2 ; 
the potential energy is of the form 
C cos 0, 
where A, B, C, are constants. We see that (f) is a coordinate of the first kind, since it 
only enters the expression for the kinetic energy through its differential coefficient, 
while 0 is a coordinate of the second kind, as functions of 0 occur in the expressions 
for the kinetic and potential energies. When the system is in a steady state the 
velocity of the first kind of coordinate is constant, while that of the second kind is 
zero. In the variations which we shall suppose L to suffer we shall suppose that the 
velocities of the kinosthenic coordinates remain unaltered, while the coordinates 
of the second kind are varied. In calculating the mean value of L for a system in 
a steady state, we may suppose that all the terms in the kinetic energy which involve 
a differential coefficient of a coordinate of the second kind are omitted, since in the 
steady state these differential coefficients vanish. We may, therefore, for our purpose, 
without loss of generality, suppose that dh/dq 2 = 0, where q 2 is a molar coordinate 
of the second kind. 
The equation 
8L = t 
: 
may conveniently be written 
SL = t 
clL 
dq\ 
/0 
where q x and q 2 are molar coordinates of the first and second kinds respectively, and 
q% is a molecular coordinate. We may disregard the last term by the reasoning, due 
3 Q 2 
