MOVING FORCE. 
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5S 
to be as the quantity of matter into the velocity*. In that he 
agrees with .Mr, Smeaton ; but he afterwards concludes, that 
neither of the measures of force are capable of general appli- 
cation, and that for one class of the etfects of force, we have 
no proper measure. 
^ After discussing various examples of force, lie proceeds as 
peimanont e- follows : " But the truth is, the principle (of permanent quan- 
liiimeration of . . . 
force cannot obtains not according to either ol the measures, except 
be had t)y ci 
thcr of tlic 
measures. 
in particular cases, which may be demonstrated as the other 
properties of forces are from the general laws or axioms. 
Instances. ' “ Jo the rectilinear motion of bodies, accelerated from qui- 
escence, or retarded until they are at rest, the permanency of 
any given quantify of motion is demonstrated from the axioms, 
whether that motion be estimated by one measure or the other. 
“ In bodies which revolve round fixed axes, the principle 
obtains, without exception, when the momentum is measured 
by the quantity of maUer into the square of the velocity, but 
fails when measured by the quantit] of matter into the velocity^ 
a given quantity of motion thus estimated being alterable in 
any assigned ratio. 
" In the communication of motion to bodies by collision, 
when the direction of the stroke passes through the centre of 
gravity, the principle in question holds universally, according 
to the measure of the mass into its velocity, but fails wl.en the 
momenta are estimated by the mass into the square of the ve- 
locity in every case, except when both bodies are perfectly 
elastic. Of one iierfectly elastic, and the other perfectly hard, 
“ Lastly, when motion is communicated to bodies by im- 
pact, the direction of vvbicli passes not through the centres of 
gravity, the quantity of motion communicated, whether esti- 
mated by one measure or the other, preserves neither equality, 
nor any constant proportion to the quantity of motion im- 
pressedf." 
These conclusions appear to be rather paradoxical, but they 
are neither new nor uncommon. 
• Trralisp on Rc< tiiinear and Rotatory Motion. Preface, p. 10. 
t Ibid, p, S66 — 368, 
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