PROPAGATION OF LONGITUDINAL WAVES—MACGREGOR. 91 
If we correct the slip in substitution referred to above, it will 
be obvious that Maxwell should have deduced from equation (6), 
not equation (7), but the equation 
D—p, = Q’ (vu—), 
from which it would have followed that 
p—Q’v = const, 
and consequently, that as an increase of pressure produces an 
increase of volume in no known substance, the form of wave 
under consideration was not possible in actual substances. 
In later editions of the Theory of Heat there is substituted for 
equation (6) the equation 
Pi—P2 = Q (ui—w), 
and from this equation it follows that 
p + Q’v = const.; 
but no reason is given for this modification of equation (6). 
Now, if the Second Law of Motion is applicable in the way in 
which Maxwell has applied it, equation (6) is correct in the 
earlier editions and incorrect as given in the later editions. For 
p.—p, is the value of the resultant force, in the direction of the 
propagation of the wave, acting on the portion of the substance 
between A and B, and Q (u,—w.) is the rate of increase of the 
momentum in the same direction of the substance between A 
and B. Hence, if the Second Law is applicable in this way the 
conclusion should be drawn that waves of this kind eannot be 
propagated by actual substances. 
But the Second Law of Motion seems to be inapplicable in the 
present case. That law asserts that the resultant force acting 
on «@ body is equal to the rate of increase of the momentum of 
the body in the direction of the force, but not that the resultant 
force on the portion of a moving substance enclosed by certain 
bounding planes is equal to the rate of increase of the momen- 
tum of the substance thus enclosed. And hence the earlier 
form of equation (6) is not legitimately established. 
Some other method must therefore be adopted of obtaining a 
relation between p,v and Q. The following method gives us 
the required relation: Let A and B be indefinitely near one 
another. Then the mass entering the space between A and B 
