966 ON THE MEASURE OF THE FORCES OF BODIES 
of the spring, has been the same in both cases. Will it be said that it has been distrib- 
uted in the same proportion to the two bodies, when A, the mass of which has not 
been changed, has had its velocity increased in this essential degree? And yet the New- 
tonians would make it the same; namely, half to each body in both instances. 
We may, I think, obtain a clear conception of the action of the spring, if we con- 
- sider it as depending, for its effect on each body, upon the degree of.immobility which 
- it finds in the opposite body; and hence the force communicated to each body will de- 
pend upon the resistance of the inertia of the opposite body ; or, through the action of the ; 
spring, the inertia of rest in each body is transferred as an active force in the motion of 
the opposite body. In the case before us, the body A having an inertia 10 times as 
great as that of B, the force communicated to B by the spring is 10 times as great as 
the force communicated to A. To show this more clearly, let us attend to the exact 
course of the action of the spring. It will be found, if proper means be taken to 
mark the motion of the spring (Fig. 1) in its course of extending itself, that, during 
this extension, 10 of the rings of which it is composed open to the left, in the direc- 
tion of B's motion, and only one in the direction of A, while the point a (Fig. 2) hàs 
remained at rest. The spring has acted from a plane, passing through the point a, as 
from a base, to the right and to the left. Now will any one say, that, when 10 out of 
11 parts of the spring have acted wholly in the direction of B, the effect of the spring 
has been equally distributed between A and B? 
. Suppose we cut the spring in two at the point a, and fix the.cut end of the larger 
part to an immovable plane, as in Fig. 3, and, placing the ball B against it when com- 
Fig. 3. 
pressed, suffer it to extend itself against B. The velocity of motion that it will commu- 
nicate to B will be precisely equal to that produced under the conditions of Figs. 1 and 
.2; and if we take the remaining coil of the spring, and fix it to the opposite side of the 
plane, as in Fig. 3, and suffer it to extend itself, it will produce the same motion in A 
that was produced in the first experiment. Now it must be evident that the 10 rings 
of the spring contain 10 times as much elastic force as the. 1 ring, and that, as no - 
motion whatever is communicated to the plane by their action, all the force of each 
