MOVING WITH DIFFERENT VELOCITIES. 969 
respectively, and this will be the case whether the elastic or attractive force be constant 
or variable. Hence, if the orbital motions of a satellite and its primary were destroyed, 
they would approach their common centre of gravity with forces directly as their veloci- 
ties and inversely as their masses (see p. 361) ; and if another body were placed at their 
point of meeting, such body would receive a shock from the satellite as much greater 
than that received from the primary, as the velocity of the satellite was greater than that 
of the primary, or as the mass of the primary was greater than that of the satellite. 
Hence in all those operations in the arts by which the form of unelastic bodies is 
changed by collision or percussion, as in the action of the hammer or axe, the effi- 
ciency of'the instrument depends upon the inertia of the body against which it acts. 
Thus, if a block or anvil be suspended by a chain, or made to rest upon a spring, and 
a piece of lead or any soft and unelastic body be placed against or upon it and struck 
by a hammer, the force of the hammer will be divided between the lead and the bed or 
anvil; that is, in changing the form of the lead, and in giving motion to it and the 
anvil; and the distribution of the force, or the proportions which go to the different 
bodies involved in the action, may be found as follows : — 
Let the mass of the hammer = m. 
Its velocity before the blow = v. 
Its velocity after the blow aia, 
The mass of the bodies struck — m’. 
Velocity after the stroke . = v”. 
Then the force of the hammer before the stroke will be m vg. Of this force there will 
remain in the motion of the masses after the stroke 
m v? + m v? 
and m v? — m v? — m v"? must be absorbed in changing the form of the lead. 
If we neglect entirely the effect of elasticity, which we may do for most practical 
purposes, in both masses, then when m and m’ are equal, one quarter of the force will 
remain in the motion of m, one quarter will be communicated to produce motion in m’, 
and one half will go to change the form of the soft body. So, if the mass of m be 
infinitely greater than that of m, or, not being greater, if m' be made to move in a 
direction opposite to the motion of m, and with a velocity such that » and m remain 
at rest after the collision, then the whole force will be absorbed in changing the form 
of the soft body. | 
What is here stated may be applied to the whole subject of percussion or col- 
lision. ox gt 
VOL. VIII. 48 a 
