The enquirer. [volume] (Richmond, Va.) 1804-1815, 1809-05-16


Therefore &c. q f.. ID.
| The same may be demonstrated gcornetri
catly without the c, cioid by the laws of mott,
on. Let the wheel be supposed to- be station
AIRY; b.tto revoive as a NH wheei-Tl,en
the motion of & may be supposed TO be CON
pounded OF two motions, one in the 6irecti
| Oh at CE, and the other in the direction of
! CA. In like manner the motion of A may
| be resolved into two motions, one i'm the di-
rection OF AE, and the o.her in the tlirecti-
ON or AT, a tangent to the circle ut A.--But
! ct aud AT being eIlal and Contrary tn each
ether. the wheel neither has progressive
motion or a rctrcgadc motion; but merely n
rotatory notion. Again if the wheel be not
stationary; but urged by q horizontal force
along the plane ABA, at The same time it
revovss ioui.., it's axis. Each of the points
& and n is urged bv the same force in the
SAME direction; but being at the same time
actlatc,' by the two equal and opposite forces
Cd and AT /; the nloupn OF E. along the plane
IL more progressive than A--Therefore {
moves swifter than A or A move, with less
velocity than c. '-,
| Cor. LIST. If the wheel be supposed to
have progressive motion from A 20 q, and
| at the same time to revoive about its axis
III contrary direction Of carriage wheel
| and In a plan. Perpendicular TO the Hori-
ION Then the under point X will move
with more velocity than the upper point G..
| :. Cor. I'd. If a. wheel move from South to
North III plane parallel 10 the Horizon.
ana at the Same time revolve ABOUT its axis
from East TO North. Then all the points of
the western Semicircle will move slower
| than the points of .hs Eastern semicircie
Cor. 3. If q wheel move from South to
| North, in plane parallel TO the Horizon. &
at The same time revoivc about its axis, from
west to North then All the points OF the
western ssmicircie wi!iinove swiFter than ali
the points OF the eastern seincircie.
| Cor 4th. II II wheel has a progressive moti-
on from South to North and at the me time
| reVolve about its axis in plane pertiendicus
| lar to the horizon, either from East to West
or from West to East-Then ali the points of
| the wheel Will move with equal veiocitv.-
with respect to what proportion the veloci-
tyof a bears to the velocity of G., in differ
ent points OF the quadrant A G.; I found from
a calculation BY the method of Fluxions ; that
the velocity OF the upper point G, is to the
velocity OF the under point A, as twice the
chord OF the arch of the circle, over which
or may have moved, to the difference
between twice the. diameter, and twice the
chord OF the supplement- of that arch.
a very remarkable corollary is therefore
deduced; and which may be supposed at
hrstto contradict the truth of the proposi,i-
1
moves slower than its corresponding point in
the upper semicircle.
l L he corolary is this, that the velocity of
at the point of contact with the plane, is
actually the same with the velocity of it's
opposite Z but IN the smallest arch which A
afterwards describes, the velocity changes
FOR before A describes any arch, there can
be no chord-Therefore the two ratios are
equal. Wherefore it may be demonstrated
hot . nx., L
seinicircie ID A F. while its opposite point
moves over: the opposite semicircle, that
the greatest difference in their velocities will
De III the points bisecting the quatirants ID
and 4 + but exactly at the points A
and Z, their velocitics will be equal
1 shall now proceed to apply these princi
pies to the motion of the earth round the
sun IN the plane of the ecliptc and to point
out, generally, the various phenomena which
must necessarily result and will demon
strate, thatnot only the tides, but the storms
at the eqninox-the trade winds and other
wlnds-the rains, as also animal and vege-
table life, are considerably affected BY the
difference ofvelocity in the two hemispheres
of the globe.
Z In the first place, with respect to the mo-
ton OF the earth round the sun,-Althoueh
every point OF a wheel describes, as it re-
VoiVes along plane, the curve called the
common cycloid; yet the points of the earth
decsribe curves different from the common
c, cloid; but of the cycloidaI species.-In the
common cycloid, the base is equal to the
circumference Of the generating circle and
the axis is equal to the diameter of the ge-
neratlng circle; But those cycloids which
the points OF the earth describe are different
he proportion between their axis and base,
depends upon the proportion between that
space OF the earth's orbit, over which she
meves IN twenty four hours, and the circmin-
ference OF the globe; and as this proportion
I varies In different points of her orbit, the
species OF cycloid generated, must also vary
but that species, which the earth de.
scriDes, are of the most elongated kind for
the circumference of the earth's orbit is
nearly hive h1ndrcd and seventy millions of
miles; and the circumference of the earth
itsclf only twenty four thousand eight hun
dred and sixty-three miles. Therefore up
on calculation, the proportion between the
axis and base of these cycloids, which the
earth describes, will be found to be nearly
as TO So
Inc difference of Velocity in the two He
miSpheres OF the Globe; during her diurn al
rotation, varies considerably from another
cause The axis of the Earth is neither
perpendicular or horizontal to the plane of
the Eehptlc but makes an angle with it. of
about 90 deg. 80 sec.--Also the axis ALWAYS
remains directed to the same ar4while the
Earth describes an Ellipsis round the sun
But to ascertain the change in the difference
of velocity from, thiS ause rso,,;,o. -otc,,i.