MOVING FORCK. 
1237 
Is there not some inconsistency in supposing the spring to pro- Cases of 
Uuce motion in one case, but none in the other ? doet'r/nts of 
If, instead of the unequal pressure of a spring, an uniform nioTiug forte, 
pressure be applied, as in the Sth case, the various quantities of 
mechanical force expended at different periods of the operation, 
will be more distinctly shown j for, the pressure being con- 
stant, each portion of space through which it acts, will express 
the quantity of mechanical power which has been expeuded in 
that space. 
In its passage through a space=EH = J EF (6g. 8) an uni- 
form resistance lias been opposed to A, which would bring it 
to rest in a sjrace = EF. When it has arrived opposite to H, 
it has therefore lost half its velocity ; and B having arrived 
opposite to I by the action of an equal pressure through a 
V 
space = FI = ^ EF has acquired the velocity — ; and KH, 
'eqnal ^ EF, will consequently be the depth of the penetration 
of c into A. Now, if A be a nonclastic soft mass of clay, 
vfbr example, we know that it cannot be jx'netrated without 
iforce ; nor have we any reason to suppose, that the force which 
*has been expended in producing the penetration, can ever be 
restored. We therefore cannot expect to find in the motion of 
A and B, after collision, the same quantity of force which they 
had before collision. If, however, the pressure into the space 
tthrough which it acts be taken as the measure of the force, we 
'Shall find that a compound effect has been produced by A in its 
'passage through the space = EH, that only one-third of the 
iforce which A has lost has been communicated to B, and that 
the other two-thirds of that force has been spent in producing a 
cchange of figure in A. These proportions are obvious from 
the mere inspection of the diagram. We may suppose A to be 
.« ranch harder substance than clay, so that the space represented 
tby EF may be very small ; but the pressure being propor- 
tionally greater, the product of the pressure into the space will 
utill be the same, however small the penetration may be. 
Any explanation, however, which takes into consideration 
the force which is expended in proilucing a change of figure. 
II 
