The spirit of the age. [volume] (Woodstock, Vt.) 1840-1844, 1841-10-22
Communication.
the Editor of The Spirit Of The .Age,

To the Editor Of The Spiritcf The .age,
Sir:-The following communication was pre-
pared for publication several months since, but on
being submitted to Professor of Mathematics in
one of our colleges, it was objected to
|. On the ground of the apparent ignorance Of
the writer of the " famous controversy respecting
the measure of the forces Of bodies in motion"
g Because mathemacians are united ut last
in the opinion that lime ought 10 be regarded in
the measurement of forces
g. Because " to make the square of the velocity
Of moving body the measure of its force, would
be the reviying of an exploded error"
4. Because "lhe writer suggests n difficulty
which has been the cause of so much controversy,
as though he supposed it were ncw.'
In regard to the first and last objections, which
are similar, would say, that were the writer as
ignorant Of the history of the famous controver-
sy" as the objecor suspects, this historical 'snor-
ance would in no way affect the truth Of what he
asserts as facts, or the correctness Of his deduc-
tons, nasnuch as they are based Oh much oet-
ter foundation than that Of historical evidence.
was not, however, ignorant that it had been
whether the momena of moving bodies, their guam
titles being equal, were in the ratio Of their veoci-
ties, or the square of their yeocities.
In compendium Of the arguments, which is all
that have seen or wish to see, | saw nothing to
support the former POSITION either in the Facts and
experiments adduced, or in the arguments drawn
thereliom, so long as the true and commonly re-
ceived definition Of the terms, momentum, or
forces OF bodies in notion" were adhered TO. Let
no one refer me to the familiar and futile expert
ments with balls Of soft clay, till they can first ac-
coun, for the force which is expended in compress
ing the balls in the experiment, or in the drl-
wing of one of the pins to greater distance than
the other, in the other experiment.
Nor let it be supposed that an argument sustain
ing the former position, can be grounded on the
fact, that the centrifugal forces Of equal bodies,
revolving in the same periodical time, but in orbits
of different diameters, are in the same ratio as the
dametcrs of their orbits, and consequently in the
same ratio as their velocites. For equal bodies,
revolving with equal veloctes, but in orbits OF
different dmmeters, have not equal centrifugal for
ces because in the larger orbit, the resultant curve
varies less. in any given distance, from the tangent
ine and consequently less centrpetal force Is re-
CURED to produce such resultant curve.
But equal bodies, revolving in the same orbits
with different veloci,ies, will have their centrifugal
forces in The same ratio as the squares Of their We
loces, and will also have their con;ripetal aud
tangent forces in the same ratio, otherwise the same
resultant cure would not be produced.
Now the cenlripetalheing equal 10 the centrifugal,
and the tangent forces being in the same ratio rs
the cen,ripea the tangent forces must be as the
squares of the velocties, as must also be the mo-
men,a; for the tangent forces would become the
momen,a of the bodies moving in Alright line, were
the ccn,ripeta force 10 cease.
But lest it may be suspected that this controvers,
has been maintained in consequence OF the dlfe'
ent meanings attached to the terms, momentum
or the forces Of bodies in notion will here de
fine the term as used throughout this communica
ton. The momentum of body in motion is it
power to overcome impedments. II is the reserv
ed power which body in motion posse ses, whcl
must be expended, before the body will be brough
TO a state Of rest.
Now the merest tyro in mechanics knows tina
the power Of water or steam is estimated ant