774 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
55. Instead of H and C being plates with gas between them, let them be earthen 
batteries of unlimited length, and suppose that guns are distributed at uniform intervals 
along those batteries; suppose, also, that all the shot fired from H bury themselves 
in the earth of C, and vice versa. 
Then, in the first place, it is obvious that since on firing a shot the momentum 
imparted to the gun is equal and opposite to the momentum given to the shot, every 
shot fired from H will exercise the same force to move the battery H away from C as 
the shot will exercise to move C away from H ; and in the same way the recoil of the 
guns on C will exercise the same tendency to move C away from H as the shot will 
exercise to move H away from C. And this will be the case whether the guns are 
supposed to be pointed straight across the interval between the batteries, or, as I shall 
suppose, are pointed with various degrees of obliquity. 
Since, then, the result of every shot, whether fired from H or C, causes equal and 
opposite forces on the two batteries, the result of all the firing, no matter how much 
harder one battery may bombard than the other, must be to cause an equal force on each 
battery, the batteries being of unlimited length. 
This case will be seen to be strictly analogous to the effect of the gas between two 
plates of unlimited extent to cause equal pressures on the plates, no matter what may 
be the differences in the temperature of the plates. 
If now we consider the batteries of limited extent, then, owing to the obliquity of 
the guns, some of the shot from H may pass beyond the ends of C, and vice versa; 
and in this case the force of recoil on the battery which fires will no longer be 
balanced by the stopping of the shot on the other battery. So that supposing the 
directions of firing to be similar, that battery which fires the hardest will be subject 
to the greatest tendency to move back. 
The battery which fires the hardest corresponds with the hottest plate; and hence 
we perceive by analogy that, if of limited extent, the hottest plate will experience 
the greatest pressure from the gas between the plates. 
56. The analogy between the batteries and the plates is rendered more strict if we 
suppose the batteries H and C to be two limited batteries, each placed in front of a 
battery of unlimited extent, and that these unlimited batteries are pounding away hi 
an exactly similar manner. 
The effect of the shot from these unlimited batteries on H and C will be analogous 
to the effect of the gas outside and beyond the plates. And it is at once seen that 
these unlimited batteries will produce similar effects on H and C respectively, and 
that the effect of the firing between H and C will be uninfluenced by the batteries 
behind, and therefore, as before, that battery will be subject to the greatest tendency 
to move back which fires the hardest. 
To make the analogy between the two cases complete, suppose that H and C, in 
addition to pounding away at each other, are exactly returning the fire of the batteries 
from behind, and that the mean rate at which H fires at C and C at II are exactly 
