Virginia Argus. [volume] (Richmond, Va.) 1796-1816, 1809-05-16

the centre f, draw the line c X ID parallel
to the tangent at A or at right angles to BA
emitting the paths of A & B in a and b.
lis propos tion we known in geometry.
that each ofthe curves A N, s. BIB Il, isa
semcycloid equal to twice tn. tiare,er
n of the generating circle: Therefore
these semlcycloids are equal to each other.
or he points A * b during half a revolution
of the wheel, have moved over equal spa
COS. But the space B b, which B has ies-
cribed in quarter of a revolution, IS grea.
ter than the space a, which A has des-
described IN the same gu rter. For 10 n B
ID, then by property of the cyclod (V. Hut
ton's Mathenat'c Al Dictionary, Emerson,
"M'Laurins and Cavallo) A or b b is e.
qua to twice B ID, and twi 3 ID is great.
er than twice + the radius of the wheel,
or than A the diameter, but A a Il il
equal to twice B n, there ore A a is less
than B A and 1t has been proved that B
bis greater rhan n, therefore A n is less
than b a, that is the point A has moved
over less space than the point B during a
Quarter OF revolution, wherefore A has
moved with less velocity than B, during the
first quadrant Of it's motion, and in the
same manner it may he demonstrated that
any other point in tn. lower sem'circle,
moves slower than any o,her poin, in the
EI- ".
The same may be demonstrated geome-
trcally without the cyclod by the law of
motion. Let the wheel A c B ID be sup
posed to be stationary; but 90 We volve as
mill wheel. Then the motion OF b may
We supposed to be compounded of two mo-
tons, one in the direction of T., and tina
other in the direction Of B II a tangent to
The circle Ut h. In like manner the mo.
ton of may be resolved into two motions,
one in the direction of A +, and the other
in the direction of A F, tangent to the
/ circle at A But B II and A F being equal
and contrary to each 9th +, the wheel nei-
ther has progressive motion, or retro
gade motion, but merely rotatory motion.
Again, If the wheel be not stationary, but
urged by a horizontal force along the yAane
a 3, at the same time it revolves ronnd
its axis from b to ID. Each of the points
and a IS urged by the same force IN the
same direction, but being at the same time
actuated by the two equal and opposite for
ces b II and A F the mouon of along
the plane rs more progressive than A,
therefore B moves swifter than A.
! Cor. 1st. IL the wheel A d be sup
posed to have a progressive motion from A
to -, and at the same time to revolve about
its axis from B 10 G n a contrary direc-
! ton OF a carriage wheel; and in a plane
perpendicular TO the horizon, then the
under point a will move with more velo.
city than the upper point B.
! Cor. Cd. If a wheel move IRON South Tn
North IN plane parallel TO the horizon.
and at the same time reyolve about IT'S
axis from East TO North, then all The
points of the WesterA semicrcie W |! move
slower than the points OF the Eastern SEMI
circle.
Cor. Sd. If wheel move from South to
North in a plane parallels TO the HORIZON,
| and at the same time revolve about IT'S
axis from West to North. then all the
points of the Western se,nicircle will move
swittcr than the points of the Eastern SCI
micircle.
! Cor. 9TH. If wheel has progressive
motion from South to North, and at the
same time revoive abou, it's axis in pl me
perpendicular to the horizon, either from
East to West, or from West to East, then
all points of the wheel wall move with G..
quail velocity.
With respect to the proportion, which
the velocity Of A bears to tie velocity Of Is,
| IN different points of the quadrant A c
\ fouud from A calculation by the method
{ OF fuxions, that the velocity of the upper
point b, IS to the velocity Of the un.ier
point a; as twice the chord of the arch Of
the circle, over which A or Is NAV hay.
moved, to the difference between twice the
diameter, and twice the chord Of the sup
plement of that arch.
A very remarkable corolIary is there
tore deduced and which may be supposed
at brst to contradict the trutn of the pro-
position, that every point in the under SCI
miclrcle moves slower than it's correspon-
dlng point in the upper semcirce. The
coroiiary is this; that the vcloc " of A at
the point OF contact with the plane is ac-
tuaiiy the same with the velocity of it's
! opposite b but the smallest arch which
"A afterwards describes, the velocity chan
ges. For before A describes any arch,
there can be no chord therefore the two
ratios are equal. Wherefore it may be
emonstrated that if the point d moves
round the under semisirc.e - A G, while
IT'S opposite pc MT moves over the oppo-
site semcircle that the greatest difsr.
ence in their veiocites will b. in the points
oisectlng the quadFants d A and A'C but
exactly at the points a and Is their veloci-
ties will be equal.
shall now proceed to apply these prin-
cipies, to the motion of the earth round the
sun IN the plane of the elliptic and To
point out generally the various phenome-
ma which must necessarily result and will
demonstrate that noe only the tides, but the
/ storms f,c he n