MOVING WITH DIFFERENT VELOCITIES. 365 
the force of the inertia of motion. This conception, while it violates no fact or result 
of experiment, will aid us in explaining them all. pr. 
-= The question now is, How much of this force has gone to A, and how much to 
B? Or,What is the force of A and of B respectively, at the instant they are discharged 
from the spring? One party in the controversy, who array themselves under the great 
name of Newton, determine the force of each by multiplying its mass by its velocity, 
simply, and find A, mass 10, multiplied by its velocity 1, to be 10; and B, mass 1, 
multiplied by its velocity 10, to be 10. That is, the force of the spring is equally dis- 
tributed between the two bodies. They hold that this must be so of necessity; for the 
spring during its action pressed equally to the right and to the left, equally against 
the bodies A and B. This pressure was continued an equal time upon both bodies, 
namely, during all the time of the spring's action. How is it possible then, say they, 
that a greater effect has been produced in one direction than in the other ? 
This affirmation that the action is equal upon both bodies may be held as 
not merely derived from, but as constituting the substance of, Newton’s Third Law, 
which asserts that “to every action there is always opposed an equal reaction: or the 
mutual actions of two bodies upon each other are always equal, and directed to con- 
trary parts" ; and it is not to be denied that, so far as pressure constitutes action, this 
has been fully established by his citation of instances under this Third Law. But it 
by no means follows, because the spring maintains a like pressure by both its ends 
during the act of extending itself, that therefore its force is transferred equally to both 
bodies. The velocity with which this pressure overcomes the resistance opposed to it 
must be regarded, as well as the pressure itself; and indeed the whole controversy lies 
in determining the value that belongs to the velocity as one of the factors by which the 
force is produced; that is, whether this factor shall be taken in its simple form, a value 
clearly assigned, to it by Newton in the Corollaries and Scholium of his Third Law; 
or whether a higher value, as its square, shall be given to it, as was first proposed by 
Leibnitz. Let us then see if, by tracing the course in which the spring elongates itself 
under different conditions, we can increase our knowledge of the transference of its 
force. By an examination of this subject, we shall find that the spring acts upon each 
body with a velocity proportional to the resistance that it receives from the opposite body ; 
and we shall find that, as we increase the mass of either body, the effect produced upon the 
opposite body will be increased. Thus, if we add to the mass of D, until it becomes 
equal to that of A, and let the spring expand as before, the velocities of A and B 
wil be equal; the velocity of A being more than double (as y5.5 to y1) what it 
was before the size of B was increased. The force expended, namely, the elastic force 
