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MR. J. J. THOMSON ON SOME APPLICATIONS OF 
at any rate when things are in a steady state, that there are (in— 1) linear relations 
between the m quantities u x , u 2 ... . We might easily alter the equations of motion 
so as to allow for this relation, or we might eliminate (in— 1) of the quantities 
u v u 2 ... , but it is more convenient to use the expressions for © given in equations 
(1) and (2) : the reason for this is that when any property of a body depends upon 
the temperature it does not depend upon the value of one of the us more than 
another, but only on the value of 0 : the As never occur except as parts of the 
expression ©. 
We have at present only considered kinetic energy and have not said anything about 
potential energy, but we shall see that if we give a sufficiently wide meaning to the 
term material system we can explain all the effects produced by potential energy by 
considerations about kinetic energy alone. There is an advantage gained by doing 
this, because kinetic energy appears to be a much more fundamental conception than 
potential energy. When we can explain any phenomenon as a property of the 
motion of bodies, we have got what may be called a physical explanation of the 
phenomenon, and any further explanation must be rather metaphysical than physical; 
it is not so, however, with regard to potential energy, the use of this quantity cannot 
in any ordinary sense of the word be said to explain any physical phenomenon, it 
does little more than embody the results of experiments in a form well adapted to 
mathematical investigation. An investigation similar to that given in Thomson and 
Tait’s ‘ Treatise on Natural Philosophy,’ vol. i., p. 320, 2nd edition, shows that the 
effects produced by the potential energy of a system (A) can be explained by changes 
in the kinetic energy of another system (B) connected with (A). We must suppose 
that there are portions of matter connected with the system (A) and capable of 
motion which are not fixed by any of the coordinates which we have already spoken 
about, viz., the geometric, electric, magnetic, elastic, and temperature coordinates, and 
that the coordinates fixing the position of these portions of matter enter the 
expression for the kinetic energy only through their different coefficients. An 
analogous case is that of a sphere surrounded by water ; in order to fix the con¬ 
figuration of the water it would be necessary to use an infinite number of coordinates, 
but these would enter the expression for the kinetic energy of the sphere and water 
only through their differential coefficients. For the sake of brevity we have called 
coordinates of this kind kinosthenic coordinates. 
The coordinates fixing the configuration of the portions of matter mentioned above 
are kinosthenic coordinates. We shall denote them by the letters Xi> X 2 • • • » X»* We 
shall suppose for the sake of simplicity that there are no terms containing the product 
of a differential coefficient of one of the y’s with a differential coefficient of one of 
the geometric, elastic, electric, magnetic, or temperature coordinates. 
Since yq, . . . do not enter into the expression for the kinetic energy T of the 
systems (A) and (B), we have by Lagrange’s equations 
