DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
309 
i.e., one which only enters into the expression for the kinetic energy through its 
differential coefficient with respect to the time, so that the kinetic energy is not an 
explicit function of this coordinate, but only of its rate of change ; the other coordinate 
is of a geometrical kind. This way of fixing the intensity of magnetisation is the 
mathematical analogue of Ampere’s theory of magnetism, which supposes that 
electrical currents flow round the molecules of bodies, and that a body is magnetised 
when its molecules are so arranged that the normals to the planes of the currents 
which flow round them are not distributed uniformly in all directions. Thus the 
kinosthenic coordinates would be the ones fixing the molecular currents, and the 
geometrical ones those fixing the arrangement in space of the normals to the planes 
of the currents. We shall call the kinosthenic coordinate £, and the geometrical one 77 , 
and suppose they are chosen so that the intensity of magnetisation is rji; where £ is 
the generalised component of momentum of the type £. 
We must now consider how to represent the temperature of a body so as to bring 
it within the power of dynamical methods. In the ordinary kinetic theory of gases 
the temperature is taken to be the mean kinetic energy of translation of the molecules 
of the gas, and there are reasons for believing that a similar thing may be true for 
bodies in the solid and liquid as well as in the gaseous state. We shall therefore 
suppose that the temperature is represented by that part of the kinetic energy in unit 
of volume which involves the squares and products of the velocities of a system of 
coordinates denoted by the symbols u x , u z ... , u m . A moment’s consideration will 
show that the As must be kinostenic coordinates, i.e., that the kinetic energy is a 
.function of the differential coefficients of these quantities with respect to the time 
and not of the quantities themselves; and since the kinetic energy cannot be altered 
if we reverse the motion of the system whose kinetic energy is supposed to be 
measured by the temperature, the expression for the kinetic energy cannot contain 
any terms which involve the product of a “ u ” velocity with one of the type x, y, z, 
or w. We may therefore take u x , u % . . . , u m to be principal coordinates, and suppose 
that that part of the kinetic energy per unit of volume which depends upon the 
squares of their velocities, and which we shall call ©, is given by the equation 
©=MK w i] w i 3 +[%%]V+- • •} 
or if v l3 ... be the momenta corresponding to u x , % . . . 
( 1 ) 
0 = 4 - 
( 2 ) 
and this form is more convenient for some purposes than the preceding one. Since 
the temperature can be fixed by one coordinate when it is uniform, we must suppose, 
MDCCCLXXXV. 2 S 
