DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
515 
where, in finding the value of dp/de, we suppose v to be constant, and w is the 
mean potential energy of the system. 
If £ 77 , £... be the number of equivalent molecules of the substances A, B, C. . . in 
the solution, then, since L must be stationary when the system is in equilibrium, we 
have 
with as many equations of a similar type as there are independent variables. We 
can experimentally determine the way in which 0 p/ 8 e and or vary with the quantities 
of the various substances in the solution ; and, if we have sufficient data to express these 
quantities as functions of f 77 , ... , the equations of the type (74) will enable us to find 
the values of f, 77 , . . . when there is equilibrium. The part of dw/d£ which depends 
upon the chemical affinity of the substances for each other can be measured by the 
heat developed when the chemical action which causes the diminution of the number 
of equivalents of the substance A by one goes on. But, just as in the case of the more 
dilute solutions, part of w may be the energy due to surface-tension, electrification, 
compression, &c., and the presence of this energy will affect the state of equilibrium. 
The Velocity of Chemical Change. 
§ 20. It is much easier in many cases to measure the rate at which chemical change 
takes place than to determine the final state of equilibrium. It seems desirable, 
therefore, in order to facilitate the comparison of theory with experiment, to endeavour 
to deduce some expression for the velocity of chemical change. 
Let us suppose that, as before, we have a number of substances which can act 
chemically on each other. Let 77 , £ ... be the number of equivalents of these 
substances : these will be connected by various equations ; let us choose ^ 77 ... as 
independent variables. Then, since when there is equilibrium dh/d£ = 0, dL/dy = 0, 
we conclude that these quantities have something to do with the velocity with which 
chemical change goes on. Now the approach of a mixture of various reagents to its 
state of equilibrium is not like the approach of a vibrating body resisted by a frictional 
force to its position of equilibrium, for after the mixture has got to its position of 
equilibrium it stays there instead of vibrating about it like the ordinary dynamical 
system. Thus the mixture behaves like a system in which inertia is absent or com¬ 
paratively unimportant ; we may, therefore, suppose that the accelerations f 77 , &c., 
are absent from the equations of motion of the mixture, and we may assume, at any 
rate when dL/d£, dLjdy, are small, that 
9 
dt 
drj 
dt 
A dL' 
= A -r 
d% 
= B 
dL 
dr) 
3 u 2 
(75) 
