_ Moving Force. 109 
the. principle obtains, without exception, when 
the, momentum is measured by the quantity of 
‘matter, into the square, of the velocity, but 
fails when. measured by the quantity of matter 
into the velocity,;.a given quantity of motion 
thus estimated. being alterable in any assigned 
ratio. hat ) 
., “In the communication of motion to bodies 
by collision, when the direction of the stroke 
passes through ths centre of gravity, the prin- 
ciple in, question holds universally, according 
to the measure of the mass into its velocity, 
but fails when the momenta are estimated by 
the, mass into the square of .the velocity, in 
every case, except when both bodies are per- 
fectly, elastic, or one perfectly elastic, and the 
other perfectly hard. 
és Lastly, when motion is communicated to 
bodies by impact, the  direction,,ef which 
passes not through the centres of gravity, the 
quantity of motion communicated, whether 
_ estimated, by one measure or the other, pre- 
serves neither equality nor any constant pro- 
portion to the quantity of motion impressed.”* 
These conclusions appear to be rather para- 
doxical, but they are. neither new nor jun- 
common. 
* Treatise on Rectil. and Rotat. Motion, p. 366—368, 
