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It IS written in plain english. No one -- or rather -- I do not object to
specialized vocabulary (chord, bisected, etc.) where needed.<br>
<br>
Joanna<br>
<br>
Chris Doss wrote:<br>
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cite="mid20051119160627.49387.qmail@web30203.mail.mud.yahoo.com">
<pre wrap="">
--- Bill Bartlett <a class="moz-txt-link-rfc2396E" href="mailto:billbartlett@dodo.com.au"><billbartlett@dodo.com.au></a> wrote:
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<pre wrap="">its a class thing. This style of writing, in other
words, is a
systematic form of exclusion. It could be written in
plain English,
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<pre wrap=""><!---->
It could? Write this in plain English:
Let the spherical bodies A, B be suspended by the
parallel and equal strings AC, BD, from the centres C,
D. About these centres, with those intervals, describe
the semicircles EAF, GBH, bisected by the radii CA,
DB. Bring the body A to any point R of the arc EAF,
and (withdrawing the body B) let it go from thence,
and after one oscillation suppose it to return to the
point V: then RV will be the retardation arising from
the resistance of the air. Of this RV let ST be a
fourth part, situated in the middle, to wit, so as RS
and TV may be equal, and RS may be to ST as 3 to 2
then will ST represent very nearly the retardation
during the descent from S to A. Restore the body B to
its place: and, supposing the body A to be let fall
from the point S, the velocity thereof in the place of
reflexion A, without sensible error will be the same
as if it had descended in vacuo from the point T. Upon
which account this velocity may be represented by the
chord of the arc TA. For it is a proposition well
known to geometers, that the velocity of a pendulous
body in the lowest point is as the chord of the arc
which it has described in its descent. After
reflexion, suppose the body A comes to the place s,
and the body B to the place k. Withdraw the body B,
and find the place v, from which if the body A, being
let go, should after one oscillation return to the
place r, st may be fourth part of rv, so placed in the
middle thereof as to leave rs equal to tv, and let the
chord of the arc tA represent the velocity which the
body A had in the place A immediately after reflexion.
For t will be the true and correct place to which the
body A should have ascended, if the resistance of the
air had been taken off. In the same way we are to
correct the place k to which the body B ascends, by
finding the place l to which it should have ascended
in vacuo. And thus everything may be subjected to
experiment, in the same manner as if we were really
placed in vacuo. These things being done, we are to
take the product (if I may so say) of the body A, by
the chord of the arc TA (which represents its
velocity), that we may have its motion in the place A
immediately before reflexion; and then by the chord of
the arc tA, that we may have its motion in the place A
immediately after reflexion. And so we are to take the
product of the body B by the chord of the arc Bl, that
we may have the motion of the same immediately after
reflexion. And in like manner, when two bodies are let
go together from different places, we are to find the
motion of each, as well before as after reflexion; and
then we may compare the motions between themselves,
and collect the effects of the reflexion. Thus trying
the thing with pendulums of ten feet, in unequal as
well as equal bodies, and making the bodies to concur
after a descent through large spaces, as of 8, 12, or
16 feet, I found always, without an error of 3 inches,
that when the bodies concurred together directly,
equal changes towards the contrary parts were produced
in their motions, and, of consequence, that the action
and reaction were always equal. As if the body A
impinged upon the body B at rest with 9 parts of
motion, and losing 7, proceeded after reflexion with
2, the body B was carried backwards with those 7
parts. If the bodies concurred with contrary motions,
A with twelve parts of motion, and B with six, then if
A receded with 2, B receded with 8; to wit, with a
deduction of 14 parts of motion on each side. For from
the motion of A subducting twelve parts, nothing will
remain; but subducting 2 parts more, a motion will be
generated of 2 parts towards the contrary way; and so,
from the motion of the body B of 6 parts, subducting
14 parts, a motion is generated of 8 parts towards the
contrary way. But if the bodies were made both to move
towards the same way, A, the swifter, with 14 parts of
motion, B, the slower, with 5, and after reflexion A
went on with 5, B likewise went on with 14 parts; 9
parts being transferred from A to B. And so in other
cases. By the congress and collision of bodies, the
quantity of motion, collected from the sum of the
motions directed towards the same way, or from the
difference of those that were directed towards
contrary ways, was ever changed. For the error of an
inch or two in measures may be easily ascribed to the
difficulty of executing everything with accuracy. It
was not easy to let go the two pendulums so exactly
together that the bodies should impinge one upon the
other in the lowermost place AB; nor to mark the
places s and k, to which the bodies ascended after
congress. Nay, and some errors, too, might have
happened from the unequal density of the parts of the
pendulous bodies themselves, and from the irregularity
of the texture proceeding from other causes.
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