![In what times the
Planets would fall to
the Sun by the
power of gravity.
The prodigious
attraction of the
Sun and Planets.
cause them to ascend again towards the higher parts of their Orbits;
during which time, the Sun’s attraction acting so contrary to the
motions of those bodies, causes them to move slower and slower,
until their projectile forces are diminished almost to nothing; and
then they are brought back again by the Sun’s attraction, as before.
157. If the projectile forces of all the
Planets and Comets were destroyed at their
mean distances from the Sun, their
gravities would bring them down so, as that
Mercury would fall to the Sun in 15 days 13 hours; Venus in 39 days
17 hours; the Earth or Moon in 64 days 10 hours; Mars in 121 days;
Jupiter in 290; and Saturn in 767. The nearest Comet in 13 thousand
days; the middlemost in 23 thousand days; and the outermost in 66
thousand days. The Moon would fall to the Earth in 4 days 20 hours;
Jupiter’s first Moon would fall to him in 7 hours, his second in 15, his
third in 30, and his fourth in 71 hours. Saturn’s first Moon would fall
to him in 8 hours; his second in 12, his third in 19, his fourth in 68
hours, and the fifth in 336. A stone would fall to the Earth’s center, if
there were an hollow passage, in 21 minutes 9 seconds. Mr. Whiston
gives the following Rule for such Computations. “[31]
It is
demonstrable, that half the Period of any Planet, when it is
diminished in the sesquialteral proportion of the number 1 to the
number 2, or nearly in the proportion of 1000 to 2828, is the time
that it would fall to the Center of it’s Orbit.” This proportion is, when
a quantity or number contains another once and a half as much
more.
158. The quick motions of the Moons of
Jupiter and Saturn round their Primaries,
demonstrate that these two Planets have
stronger attractive powers than the Earth has. For, the stronger that
one body attracts another, the greater must be the projectile force,
and consequently the quicker must be the motion of that other body,
to keep it from falling to it’s primary or central Planet. Jupiter’s
second Moon is 124 thousand miles farther from Jupiter than our](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-16-320.jpg)
![Archimedes’s
Problem for raising
the Earth.
Moon is from us; and yet this second Moon goes almost eight times
round Jupiter whilst our Moon goes only once round the Earth. What
a prodigious attractive power must the Sun then have, to draw all
the Planets and Satellites of the System towards him; and what an
amazing power must it have required to put all these Planets and
Moons into such rapid motions at first! Amazing indeed to us,
because impossible to be effected by the strength of all the living
Creatures in an unlimited number of Worlds, but no ways hard for
the Almighty, whose Planetarium takes in the whole Universe!
159. The celebrated Archimedes affirmed
he could move the Earth if he had a place
to stand on to manage his machinery[32]
.
This assertion is true in Theory, but, upon examination, will be found
absolutely impossible in fact, even though a proper place and
materials of sufficient strength could be had.
The simplest and easiest method of moving a heavy body a little
way is by a lever or crow, where a small weight or power applied to
the long arm will raise a great weight on the short one. But then,
the small weight must move as much quicker than the great weight
as the latter is heavier than the former; and the length of the long
arm of the lever to the length of the short arm must be in the same
proportion. Now, suppose a man pulls or presses the end of the long
arm with the force of 200 pound weight, and that the Earth contains
in round Numbers 4,000,000,000,000,000,000,000 or 4000 Trillions
of cubic feet, each at a mean rate weighing 100 pound; and that the
prop or center of motion of the lever is 6000 miles from the Earth’s
center: in this case, the length of the lever from the Fulcrum or
center of motion to the moving power or weight ought to be
12,000,000,000,000,000,000,000,000 or 12 Quadrillions of miles;
and so many miles must the power move, in order to raise the Earth
but one mile, whence ’tis easy to compute, that if Archimedes or the
power applied could move as swift as a cannon bullet, it would take
27,000,000,000,000 or 27 Billions of years to raise the Earth one
inch.](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-17-320.jpg)
![The Planets disturb
one another’s
motion.
The consequences
thereof.
The World not
eternal.
carry off the Planets in straight lines from those parts of their Orbits
where Gravity left them. But, the Planets being once put into motion,
there is no occasion for any new projectile force, unless they meet
with some resistance in their Orbits; nor for any mending hand,
unless they disturb one another too much by their mutual
attractions.
163. It is found that there are
disturbances among the Planets in their
motions, arising from their mutual
attractions when they are in the same
quarter of the Heavens; and that our years
are not always precisely of the same
length[33]
. Besides, there is reason to believe that the Moon is
somewhat nearer the Earth now than she was formerly; her
periodical month being shorter than it was in former ages. For, our
Astronomical Tables, which in the present Age shew the times of
Solar and Lunar Eclipses to great precision, do not answer so well
for very ancient Eclipses. Hence it appears, that the Moon does not
move in a medium void of all resistance, § 174; and therefore her
projectile force being a little weakened, whilst there is nothing to
diminish her gravity, she must be gradually approaching nearer the
Earth, describing smaller and smaller Circles round it in every
revolution, and finishing her Period sooner, although her absolute
motion with regard to space be not so quick now as it was formerly:
and therefore, she must come to the Earth at last; unless that Being,
which gave her a sufficient projectile force at the beginning, adds a
little more to it in due time. And, as all the Planets move in spaces
full of æther and light, which are material substances, they too must
meet with some resistance. And therefore, if their gravities are not
diminished, nor their projectile forces increased, they must
necessarily approach nearer and nearer the Sun, and at length fall
upon and unite with him.
164. Here we have a strong philosophical
argument against the eternity of the World.
For, had it existed from eternity, and been left by the Deity to be](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-20-320.jpg)
![The amazing
smallness of the
particles of light.
The dreadful effects
that would ensue
from their being
larger.
CHAP. VIII.
Of Light. It’s proportional quantities on the different
Planets. It’s Refractions in Water and Air. The
Atmosphere; it’s weight and properties. The
Horizontal Moon.
165. Light consists of exceeding small
particles of matter issuing from a luminous
body; as from a lighted candle such particles
of matter continually flow in all directions. Dr. Niewentyt
[34]
computes,
that in one second of time there flows
418,660,000,000,000,000,000,000,000,000,000,000,000,000,000
particles of light out of a burning candle; which number contains at
least 6,337,242,000,000 times the number of grains of sand in the
whole Earth; supposing 100 grains of sand to be equal in length to an
inch, and consequently, every cubic inch of the Earth to contain one
million of such grains.
166. These amazingly small particles, by
striking upon our eyes, excite in our minds
the idea of light: and, if they were so large
as the smallest particles of matter
discernible by our best microscopes, instead of being serviceable to
us, they would soon deprive us of sight by the force arising from their
immense velocity, which is above 164 thousand miles every
second[35]
, or 1,230,000 times swifter than the motion of a cannon
bullet. And therefore, if the particles of light were so large, that a
million of them were equal in bulk to an ordinary grain of land, we](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-22-320.jpg)
![How objects
become visible to
us.
PLATE II.
The rays of Light
naturally move in
straight lines.
A proof that they
hinder not one
another’s motions.
Fig. XI.
In what proportion
durst no more open our eyes to the light than suffer sand to be shot
point blank against them.
167. When these small particles, flowing
from the Sun or from a candle, fall upon
bodies, and are thereby reflected to our
eyes, they excite in us the idea of that body
by forming it’s picture on the retina[36]
. And
since bodies are visible on all sides, light must be reflected from them
in all directions.
168. A ray of light is a continued stream
of these particles, flowing from any visible
body in straight lines. That they move in
straight, and not in crooked lines, unless
they be refracted, is evident from bodies not
being visible if we endeavour to look at
them through the bore of a bended pipe;
and from their ceasing to be seen by the interposition of other
bodies, as the fixed Stars by the interposition of the Moon and
Planets, and the Sun wholly or in part by the interposition of the
Moon, Mercury, or Venus. And that these rays do not interfere, or
jostle one another out of their ways, in flowing from different bodies
all around, is plain from the following Experiment. Make a little hole
in a thin plate of metal, and set the plate upright on a table, facing a
row of lighted candles standing by one another; then place a sheet of
paper or pasteboard at a little distance from the other side of the
plate, and the rays of all the candles, flowing through the hole, will
form as many specks of light on the paper as there are candles
before the plate, each speck as distinct and large, as if there were
only one candle to cast one speck; which shews that the rays are no
hinderance to each other in their motions, although they all cross in
the hole.
169. Light, and therefore heat so far as it
depends on the Sun’s rays (§ 85, towards
the end) decreases in proportion to the](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-23-320.jpg)
![light and heat
decrease at any
given
distance from the
Sun.
PLATE II.
Why the Planets
appear dimmer
when viewed thro’
telescopes than by
the bare eye.
squares of the distances of the Planets from
the Sun. This is easily demonstrated by a
Figure which, together with it’s description, I
have taken from Dr. Smith’s Optics[37]
. Let the
light which flows from a point A, and passes
through a square hole B, be received upon a
plane C, parallel to the plane of the hole; or, if you please, let the
figure C be the shadow of the plane B; and when the distance C is
double of B, the length and breadth of the shadow C will be each
double of the length and breadth of the plane B; and treble when AD
is treble of AB; and so on: which may be easily examined by the light
of a candle placed at A. Therefore the surface of the shadow C, at
the distance AC double of AB, is divisible into four squares, and at a
treble distance, into nine squares, severally equal to the square B, as
represented in the Figure. The light then which falls upon the plane
B, being suffered to pass to double that distance, will be uniformly
spread over four times the space, and consequently will be four times
thinner in every part of that space, and at a treble distance it will be
nine times thinner, and at a quadruple distance sixteen times thinner,
than it was at first; and so on, according to the increase of the
square surfaces B, C, D, E, built upon the distances AB, AC, AD, AE.
Consequently, the quantities of this rarefied light received upon a
surface of any given size and shape whatever, removed successively
to these several distances, will be but one quarter, one ninth, one
sixteenth of the whole quantity received by it at the first distance AB.
Or in general words, the densities and quantities of light, received
upon any given plane, are diminished in the same proportion as the
squares of the distances of that plane, from the luminous body, are
increased: and on the contrary, are increased in the same proportion
as these squares are diminished.
170. The more a telescope magnifies the
disks of the Moon and Planets, they appear
so much dimmer than to the bare eye;
because the telescope cannot magnify the
quantity of light, as it does the surface; and,
by spreading the same quantity of light over a surface so much larger](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-24-320.jpg)
![Fig. VIII.
Refraction of the
rays of light.
than the naked eye beheld, just so much dimmer must it appear
when viewed by a telescope than by the bare eye.
171. When a ray of light passes out of one
medium[38]
into another, it is refracted, or
turned out of it’s first course, more or less,
as it falls more or less obliquely on the
refracting surface which divides the two mediums. This may be
proved by several experiments; of which we shall only give three for
example’s sake. 1. In a bason FGH put a piece of money as DB, and
then retire from it as to A, till the edge of the bason at E just hides
the money from your sight: then, keeping your head steady, let
another person fill the bason gently with water. As he fills it, you will
see more and more of the piece DB; which will be all in view when
the bason is full, and appear as if lifted up to C. For, the ray AEB,
which was straight whilst the bason was empty, is now bent at the
surface of the water in E, and turned out of it’s rectilineal course into
the direction ED. Or, in other words, the ray DEK, that proceeded in a
straight line from the edge D whilst the bason was empty, and went
above the eye at A, is now bent at E; and instead of going on in the
rectilineal direction DEK, goes in the angled direction DEA, and by
entering the eye at A renders the object DB visible. Or, 2dly, place the
bason where the Sun shines obliquely, and observe where the
shadow of the rim E falls on the bottom, as at B: then fill it with
water, and the shadow will fall at D; which proves, that the rays of
light, falling obliquely on the surface of the water, are refracted, or
bent downwards into it.
172. The less obliquely the rays of light fall upon the surface of any
medium, the less they are refracted; and if they fall perpendicularly
thereon, they are not refracted at all. For, in the last experiment, the
higher the Sun rises, the less will be the difference between the
places where the edge of the shadow falls, in the empty and full
bason. And, 3dly, if a stick be laid over the bason, and the Sun’s rays
be reflected perpendicularly into it from a looking-glass, the shadow](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-25-320.jpg)
![The Atmosphere.
The Air’s
compression and
rarity at different
heights.
of the stick will fall upon the same place of the bottom, whether the
bason be full or empty.
173. The denser that any medium is, the more is light refracted in
passing through it.
174. The Earth is surrounded by a thin
fluid mass of matter, called the Air, or
Atmosphere, which gravitates to the Earth,
revolves with it in it’s diurnal motion, and
goes round the Sun with it every year. This
fluid is of an elastic or springy nature, and
it’s lowermost parts being pressed by the weight of all the Air above
them, are squeezed the closer together; and are therefore densest of
all at the Earth’s surface, and gradually rarer the higher up. “It is well
known[39]
that the Air near the surface of our Earth possesses a space
about 1200 times greater than water of the same weight. And
therefore, a cylindric column of Air 1200 foot high is of equal weight
with a cylinder of water of the same breadth and but one foot high.
But a cylinder of Air reaching to the top of the Atmosphere is of equal
weight with a cylinder of water about 33 foot high[40]
; and therefore if
from the whole cylinder of Air, the lower part of 1200 foot high is
taken away, the remaining upper part will be of equal weight with a
cylinder of water 32 foot high; wherefore, at the height of 1200 feet
or two furlongs, the weight of the incumbent Air is less, and
consequently the rarity of the compressed Air is greater than near the
Earth’s surface in the ratio of 33 to 32. And having this ratio we may
compute the rarity of the Air at all heights whatsoever, supposing the
expansion thereof to be reciprocally proportional to its compression;
and this proportion has been proved by the experiments of Dr. Hooke
and others. The result of the computation I have set down in the
annexed Table, in the first column of which you have the height of
the Air in miles, whereof 4000 make a semi-diameter of the Earth; in
the second the compression of the Air or the incumbent weight; in
the third it’s rarity or expansion, supposing gravity to decrease in the
duplicate ratio of the distances from the Earth’s center. And the small](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-26-320.jpg)
![It’s weight how
found.
PLATE II.
numeral figures are here used to shew what number of cyphers must
be joined to the numbers expressed by the larger figures, as 0.17
1224
for 0.000000000000000001224, and 2695615
for
26956000000000000000.
Air’s
Height. Compression. Expansion.
0 33 1
5 17.8515 1.8486
10 9.6717 3.4151
20 2.852 11.571
40 0.2525 136.83
400 0.17
1224 2695615
4000 0.105
4465 73907102
40000 0.192
1628 26263189
400000 0.210
7895 41798207
4000000 0.212
9878 33414209
Infinite. 0.212
6041 54622209
From this Table it appears that the Air in proceeding upwards is
rarefied in such manner, that a sphere of that Air which is nearest the
Earth but of one inch diameter, if dilated to an equal rarefaction with
that of the Air at the height of ten semi-diameters of the Earth,
would fill up more space than is contained in the whole Heavens on
this side the fixed Stars, according to the preceding computation of
their distance[41]
.” And it likewise appears that the Moon does not
move in a perfectly free and un-resisting medium; although the air at
a height equal to her distance, is at least 34000190
times thinner than
at the Earth’s surface; and therefore cannot resist her motion so as to
be sensible in many ages.
175. The weight of the Air, at the Earth’s
surface, is found by experiments made with
the air-pump; and also by the quantity of
mercury that the Atmosphere balances in](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-27-320.jpg)
![A common mistake
about the weight of
the Air.
Without an
Atmosphere the
Heavens would
always appear dark,
and we should have
no twilight.
the barometer; in which, at a mean state; the mercury stands 291
⁄2
inches high. And if the tube were a square inch wide, it would at that
height contain 291
⁄2 cubic inches of mercury, which is just 15 pound
weight; and so much weight of air every square inch of the Earth’s
surface sustains; and every square foot 144 times as much, because
it contains 144 square inches. Now as the Earth’s surface contains
about 199,409,400 square miles, it must be of no less than
5,559,215,016,960,000 square feet; which, multiplied by 2016, the
number of pounds on every foot, amounts to
11,207,377,474,191,360,000; or 11 trillion 207 thousand 377 billion
474 thousand 191 million and 360 thousand pounds, for the weight
of the whole Atmosphere. At this rate, a middle sized man, whose
surface may be about 14 square feet, is pressed by 28,224 pound
weight of Air all round; for fluids press equally up and down and on
all sides. But, because this enormous weight is equal on all sides, and
counterbalanced by the spring of the internal Air in our blood vessels,
it is not felt.
176. Oftentimes the state of the Air is
such that we feel ourselves languid and dull;
which is commonly thought to be occasioned
by the Air’s being foggy and heavy about us. But that the Air is then
too light, is evident from the mercury’s sinking in the barometer, at
which time it is generally found that the Air has not sufficient
strength to bear up the vapours which compose the Clouds: for, when
it is otherwise, the Clouds mount high, the Air is more elastic and
weighty about us, by which means it balances the internal spring of
the Air within us, braces up our blood-vessels and nerves, and makes
us brisk and lively.
177. According to [42]
Dr. Keill, and other
astronomical writers, it is entirely owing to
the Atmosphere that the Heavens appear
bright in the day-time. For, without an
Atmosphere, only that part of the Heavens
would shine in which the Sun was placed:
and if an observer could live without Air, and should turn his back](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-28-320.jpg)
![It brings the Sun in
view before he
rises, and keeps
him in view after he
sets.
Fig. IX.
PLATE II.
towards the Sun, the whole Heavens would appear as dark as in the
night, and the Stars would be seen as clear as in the nocturnal sky.
In this case, we should have no twilight; but a sudden transition from
the brightest sunshine to the blackest darkness immediately after
sun-set; and from the blackest darkness to the brightest sun-shine at
sun-rising; which would be extremely inconvenient, if not blinding, to
all mortals. But, by means of the Atmosphere, we enjoy the Sun’s
light, reflected from the aerial particles, before he rises and after he
sets. For, when the Earth by its rotation has withdrawn the Sun from
our sight, the Atmosphere being still higher than we, has his light
imparted to it; which gradually decreases until he has got 18 degrees
below the Horizon; and then, all that part of the Atmosphere which is
above us is dark. From the length of twilight, the Doctor has
calculated the height of the Atmosphere (so far as it is dense enough
to reflect any light) to be about 44 miles. But it is seldom dense
enough at two miles height to bear up the Clouds.
178. The Atmosphere refracts the Sun’s
rays so, as to bring him in sight every clear
day, before he rises in the Horizon; and to
keep him in view for some minutes after he
is really set below it. For, at some times of
the year, we see the Sun ten minutes longer above the Horizon than
he would be if there were no refractions: and about six minutes every
day at a mean rate.
179. To illustrate this, let IEK be a part of
the Earth’s surface, covered with the
Atmosphere HGFC; and let HEO be the[43]
sensible Horizon of an observer at E. When the Sun is at A, really
below the Horizon, a ray of light AC proceeding from him comes
straight to C, where it falls on the surface of the Atmosphere, and
there entering a denser medium, it is turned out of its rectilineal
course ACdG, and bent down to the observer’s eye at E; who then
sees the Sun in the direction of the refracted ray edE, which lies](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-29-320.jpg)
![Our imagination
cannot judge rightly
of the distance of
inaccessible objects.
horizontal refractions are near a third part less at the Equator than at
Paris, as mentioned by Dr. Smith in the 370th remark on his Optics,
where the following account is given of an extraordinary refraction of
the sun-beams by cold. “There is a famous observation of this kind
made by some Hollanders that wintered in Nova Zembla in the year
1596, who were surprised to find, that after a continual night of three
months, the Sun began to rise seventeen days sooner than according
to computation, deduced from the Altitude of the Pole observed to be
76°: which cannot otherwise be accounted for, than by an
extraordinary quantity of refraction of the Sun’s rays, passing thro’
the cold dense air in that climate. Kepler computes that the Sun was
almost five degrees below the Horizon when he first appeared; and
consequently the refraction of his rays was about nine times greater
than it is with us.”
184. The Sun and Moon appear of an oval figure as FCGD, just
after their rising, and before their setting: the reason is, that the
refraction being greater in the Horizon than at any distance above it,
the lowermost limb G appears more elevated than the uppermost.
But although the refraction shortens the vertical Diameter FG, it has
no sensible effect on the horizontal Diameter CD, which is all equally
elevated. When the refraction is so small as to be imperceptible, the
Sun and Moon appear perfectly round, as AEBF.
185. We daily observe, that the objects
which appear most distinct are generally
those which are nearest to us; and
consequently, when we have nothing but our
imagination to assist us in estimating of distances, bright objects
seem nearer to us than those which are less bright, or than the same
objects do when they appear less bright and worse defined, even
though their distance in both cases be the same. And as in both
cases they are seen under the same angle[44]
, our imagination
naturally suggests an idea of a greater distance between us and
those objects which appear fainter and worse defined than those
which appear brighter under the same Angles; especially if they be](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-32-320.jpg)
![Nor always of those
which are
accessible.
The reason
assigned.
PLATE II.
Fig. XII.
such objects as we were never near to, and of whose real
Magnitudes we can be no judges by sight.
186. But, it is not only in judging of the
different apparent Magnitudes of the same
objects, which are better or worse defined
by their being more or less bright, that we may be deceived: for we
may make a wrong conclusion even when we view them under equal
degrees of brightness, and under equal Angles; although they be
objects whose bulks we are generally acquainted with, such as
houses or trees: for proof of which, the two following instances may
suffice.
First, When a house is seen over a very
broad river by a person standing on low
ground, who sees nothing of the river, nor
knows of it beforehand; the breadth of the
river being hid from him, because the banks seem contiguous, he
loses the idea of a distance equal to that breadth; and the house
seems small, because he refers it to a less distance than it really is
at. But, if he goes to a place from which the river and interjacent
ground can be seen, though no farther from the house, he then
perceives the house to be at a greater distance than he imagined;
and therefore fancies it to be bigger than he did at first; although in
both cases it appears under the same Angle, and consequently
makes no bigger picture on the retina of his eye in the latter case
than it did in the former. Many have been deceived, by taking a red
coat of arms, fixed upon the iron gate in Clare-Hall walks at
Cambridge, for a brick house at a much greater distance[45]
.
Secondly, In foggy weather, at first sight,
we generally imagine a small house, which is
just at hand, to be a great castle at a distance; because it appears so
dull and ill defined when seen through the Mist, that we refer it to a
much greater distance than it really is at; and therefore, under the
same Angle, we judge it to be much bigger. For, the near object FE,
seen by the eye ABD, appears under the same Angle GCH, that the
remote object GHI does: and the rays GFCN and HECM crossing one](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-33-320.jpg)
![Fig. IX.
Why the Sun and
Moon appear
biggest in the
Horizon.
another at C in the pupil of the eye, limit the size of the picture MN
on the retina; which is the picture of the object FE, and if FE were
taken away, would be the picture of the object GHI, only worse
defined; because GHI, being farther off, appears duller and fainter
than FE did. But if a Fog, as KL, comes between the eye and the
object FE, it appears dull and ill defined like GHI; which causes our
imagination to refer FE to the greater distance CH, instead of the
small distance CE which it really is at. And consequently, as mis-
judging the distance does not in the least diminish the Angle under
which the object appears, the small hay-rick FE seems to be as big as
GHI.
187. The Sun and Moon appear bigger in
the Horizon than at any considerable height
above it. These Luminaries, although at
great distances from the Earth, appear
floating, as it were, on the surface of our
Atmosphere HGFfeC, a little way beyond the
Clouds; of which, those about F, directly over our heads at E, are
nearer us than those about H or e in the Horizon HEe. Therefore,
when the Sun or Moon appear in the Horizon at e, they are not only
seen in a part of the Sky which is really farther from us than if they
were at any considerable Altitude, as about f; but they are also seen
through a greater quantity of Air and Vapours at e than at f. Here we
have two concurring appearances which deceive our imagination, and
cause us to refer the Sun and Moon to a greater distance at their
rising or setting about e, than when they are considerably high as at
f: first, their seeming to be on a part of the Atmosphere at e, which is
really farther than f from a spectator at E; and secondly, their being
seen through a grosser medium when at e than when at f; which, by
rendering them dimmer, causes us to imagine them to be at a yet
greater distance. And as, in both cases, they are seen[46]
much under
the same Angle, we naturally judge them to be biggest when they
seem farthest from us; like the above-mentioned house § 186, seen
from a higher ground, which shewed it to be farther off than it](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-34-320.jpg)
![PLATE IV.
Fig I.
The Moon’s
horizontal Parallax,
what.
The Moon’s distance
determined.
CHAP. IX.
The Method of finding the Distances of the Sun, Moon, and
Planets.
190. Those who have not learnt how to take the
[47]
Altitude of any Celestial Phenomenon by a common
Quadrant, nor know any thing of Plain Trigonometry, may pass over the first Article
of this short Chapter, and take the Astronomer’s word for it, that the distances of
the Sun and Planets are as stated in the first Chapter of this Book. But, to every
one who knows how to take the Altitude of the Sun, the Moon, or a Star, and can
solve a plain right-angled Triangle, the following method of finding the distances of
the Sun and Moon will be easily understood.
Let BAG be one half of the Earth, AC it’s semi-diameter,
S the Sun, m the Moon, and EKOL a quarter of the Circle
described by the Moon in revolving from the Meridian to the Meridian again. Let
CRS be the rational Horizon of an observer at A, extended to the Sun in the
Heavens, and HAO his sensible Horizon; extended to the Moon’s Orbit. ALC is the
Angle under which the Earth’s semi-diameter AC is seen from the Moon at L, which
is equal to the Angle OAL, because the right lines AO and CL which include both
these Angles are parallel. ASC is the Angle under which the Earth’s semi-diameter
AC is seen from the Sun at S, and is equal to the Angle OAf because the lines AO
and CRS are parallel. Now, it is found by observation, that the Angle OAL is much
greater than the Angle OAf; but OAL is equal to ALC, and OAf is equal to ASC. Now,
as ASC is much less than ALC, it proves that the Earth’s semi-diameter AC appears
much greater as seen from the Moon at L than from the Sun at S: and therefore the
Earth is much farther from the Sun than from the Moon[48]
. The Quantities of these
Angles are determined by observation in the following manner.
Let a graduated instrument as DAE, (the larger the
better) having a moveable Index and Sight-holes, be fixed
in such a manner, that it’s plane surface may be parallel to
the Plan of the Equator, and it’s edge AD in the Meridian:
so that when the Moon is in the Equinoctial, and on the
Meridian at E, she may be seen through the sight-holes
when the edge of the moveable index cuts the beginning of the divisions at o, on
the graduated limb DE; and when she is so seen, let the precise time be noted.](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-37-320.jpg)
![The Sun’s distance
cannot be yet so
exactly determined
as the
Moon’s;
How near the truth
it may soon be
determined.
Now, as the Moon revolves about the Earth from the Meridian to the Meridian again
in 24 hours 48 minutes, she will go a fourth part round it in a fourth part of that
time, viz. in 6 hours 12 minutes, as seen from C, that is, from the Earth’s center or
Pole. But as seen from A, the observer’s place on the Earth’s surface, the Moon will
seem to have gone a quarter round the Earth when she comes to the sensible
Horizon at O; for the Index through the sights of which she is then viewed will be
at d, 90 degrees from D, where it was when she was seen at E. Now, let the exact
moment when the Moon is seen at O (which will be when she is in or near the
sensible Horizon) be carefully noted[49]
, that it may be known in what time she has
gone from E to O; which time subtracted from 6 hours 12 minutes (the time of her
going from E to L) leaves the time of her going from O to L, and affords an easy
method for finding the Angle OAL (called the Moon’s horizontal Parallax, which is
equal to the Angle ALC) by the following Analogy: As the time of the Moon’s
describing the arc EO is to 90 degrees, so is 6 hours 12 minutes to the degrees of
the Arc DdE, which measures the Angle EAL; from which subtract 90 degrees, and
there remains the Angle OAL, equal to the Angle ALC, under which the Earth’s
Semi-diameter AC is seen from the Moon. Now, since all the Angles of a right-lined
Triangle are equal to 180 degrees, or to two right Angles, and the sides of a
Triangle are always proportional to the Sines of the opposite Angles, say, by the
Rule of Three, as the Sine of the Angle ALC at the Moon L is to it’s opposite side AC
the Earth’s Semi-diameter, which is known to be 3985 miles, so is Radius, viz. the
Sine of 90 degrees, or of the right Angle ACL to it’s opposite side AL, which is the
Moon’s distance at L from the observer’s place at A on the Earth’s surface; or, so is
the Sine of the Angle CAL to its opposite side CL, which is the Moon’s distance from
the Earth’s centre, and comes out at a mean rate to be 240,000 miles. The Angle
CAL is equal to what OAL wants of 90 degrees.
191. The Sun’s distance from the Earth is found the
same way, but with much greater difficulty; because his
horizontal Parallax, or the Angle OAS equal to the Angle
ASC, is so small as, to be hardly perceptible, being only 10
seconds of a minute, or the 360th part of a degree. But
the Moon’s horizontal Parallax, or Angle OAL equal to the
Angle ALC, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at
it’s mean state; which is more than 340 times as great as
the Sun’s: and therefore, the distances of the heavenly bodies being inversely as
the Tangents of their horizontal Parallaxes, the Sun’s distance from the Earth is at
least 340 times as great as the Moon’s; and is rather understated at 81 millions of
miles, when the Moon’s distance is certainly known to be 240 thousand. But
because, according to some Astronomers, the Sun’s horizontal Parallax is 11
seconds, and according to others only 10, the former Parallax making the Sun’s
distance to be about 75,000,000 of miles, and the latter 82,000,000; we may take it
for granted, that the Sun’s distance is not less than as deduced from the former, nor
more than as shewn by the latter: and every one who is accustomed to make such](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-38-320.jpg)
![Why the celestial
Poles seem to keep
still in the same
points of the
Heavens,
notwithstanding the
Earth’s motion
round the Sun.
Relative mean distances from the Sun.
38710 72333 100000 152369 520096 954006
From these numbers we deduce, that if the Sun’s horizontal Parallax be 10ʺ, the
real mean distances of the Planets from the Sun in English miles are
31,742,200 59,313,060 82,000,000 124,942,580 426,478,720 782,284,920
But if the Sun’s Parallax be 11ʺ their distances are no more than
29,032,500 54,238,570 75,000,000 114,276,750 390,034,500 715,504,500
Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax
2,709,700 5,074,490 7,000,000 10,665,830 36,444,220 66,780,420
195. These last numbers shew, that although we have the relative distances of
the Planets from the Sun to the greatest nicety, yet the best observers have not
hitherto been able to ascertain their true distances to within less than a twelfth part
of what they really are. And therefore, we must wait with patience till the 6th of
June, A. D. 1761; wishing that the Sky may then be clear to all places where there
are good Astronomers and accurate instruments for observing the Transit of Venus
over the Sun’s Disc at that time: as it will not happen again, so as to be visible in
Europe, in less than 235 years after.
196. The Earth’s Axis produced to the Stars, being
carried [50]
parallel to itself during the Earth’s annual
revolution, describes a circle in the Sphere of the fixed
Stars equal to the Orbit of the Earth. But this Orbit, though
very large in itself, if viewed from the Stars, would appear
no bigger than a point; and consequently, the circle
described in the Sphere of the Stars by the Axis of the
Earth produced, if viewed from the Earth, must appear but as a point; that is, it’s
diameter appears too little to be measured by observation: for Dr. Bradley has
assured us, that if it had amounted to a single second, or two at most, he should
have perceived it in the great number of observations he has made, especially upon
γ Dragonis; and that it seemed to him very probable that the annual Parallax of this
Star is not so great as a single second: and consequently, that it is above 400
thousand times farther from us than the Sun. Hence the celestial poles seem to
continue in the same points of the Heavens throughout the year; which by no](https://image.slidesharecdn.com/88948-250705053555-5a54abac/85/Wiley-Encyclopedia-of-Computer-Science-and-Engineering-5-Volume-Set-1st-Edition-Benjamin-W-Wah-40-320.jpg)
Wiley Encyclopedia of Computer Science and Engineering 5 Volume Set 1st Edition Benjamin W. Wah
- 1. Wiley Encyclopedia of Computer Science and Engineering 5 Volume Set 1st Edition Benjamin W. Wah download pdf https://ebookultra.com/download/wiley-encyclopedia-of-computer-science- and-engineering-5-volume-set-1st-edition-benjamin-w-wah/ Discover thousands of ebooks and textbooks at ebookultra.com download your favorites today!
- 2. Here are some recommended products for you. Click the link to download, or explore more at ebookultra.com Wiley Encyclopedia of Forensic Science Five Volume Set 1st Edition Allan Jamieson https://ebookultra.com/download/wiley-encyclopedia-of-forensic- science-five-volume-set-1st-edition-allan-jamieson/ Encyclopedia of Environment and Society 5 Volume Set 1st Edition Paul Robbins https://ebookultra.com/download/encyclopedia-of-environment-and- society-5-volume-set-1st-edition-paul-robbins/ Encyclopedia of Ecology Five Volume Set Volume 1 5 1st Edition S.E. Jorgensen https://ebookultra.com/download/encyclopedia-of-ecology-five-volume- set-volume-1-5-1st-edition-s-e-jorgensen/ Junior Worldmark Encyclopedia of Physical Geography 5 Volume Set 1st Edition Susan B. Gall https://ebookultra.com/download/junior-worldmark-encyclopedia-of- physical-geography-5-volume-set-1st-edition-susan-b-gall/
- 3. Encyclopedia of Membrane Science and Technology 3 Volume Set 1st Edition Hoek M.V. Erik https://ebookultra.com/download/encyclopedia-of-membrane-science-and- technology-3-volume-set-1st-edition-hoek-m-v-erik/ Encyclopedia of Imaging Science Technology 2 volume set 1st Edition Joseph P. Hornak https://ebookultra.com/download/encyclopedia-of-imaging-science- technology-2-volume-set-1st-edition-joseph-p-hornak/ Encyclopedia of Grain Science Three Volume Set Vol 1 3 1st Edition Harold Corke https://ebookultra.com/download/encyclopedia-of-grain-science-three- volume-set-vol-1-3-1st-edition-harold-corke/ The Social History of Crime and Punishment in America An Encyclopedia 5 Volume Set 1st Edition Wilbur Miller https://ebookultra.com/download/the-social-history-of-crime-and- punishment-in-america-an-encyclopedia-5-volume-set-1st-edition-wilbur- miller/ The Science and Simulation of Human Performance Volume 5 Advances in Human Performance and Cognitive Engineering Research 1st Edition James W Ness https://ebookultra.com/download/the-science-and-simulation-of-human- performance-volume-5-advances-in-human-performance-and-cognitive- engineering-research-1st-edition-james-w-ness/
- 5. Wiley Encyclopedia of Computer Science and Engineering 5 Volume Set 1st Edition Benjamin W. Wah Digital Instant Download Author(s): Benjamin W. Wah ISBN(s): 9780471383932, 0471383937 Edition: 1 File Details: PDF, 47.57 MB Year: 2009 Language: english
- 7. Wiley Encyclopedia of Computer Science and Engineering FullTitle of Book: Wiley Encyclopedia Of Computer Science And Engineering Editor(s): Wah Publisher: Wiley-interscience YearPublished: Nov., 2008 ISBN-10: 0471383937 ISBN-13: 978-0471383932 Size& Format: 2362 pages
- 8. • Applications • Computer Vision • Computing Milieux • Data • Foundation and Theory • Hardware and Architecture • Image Processing and Visualization • Intelligent Systems • IS • Parallel and Distributed Systems • Software
- 9. A ASYNCHRONOUS TRANSFER MODE NETWORKS Asynchronous transfer mode, or ATM, is anetwork transfer technique capable of supporting a wide variety of multi- media applications with diverse service and performance requirements. It supports traffic bandwidths ranging from a few kilobits per second (e.g., a text terminal) to several hundred megabits per second (e.g., high-definition video) and traffic types ranging from continuous, fixed-rate traffic (e.g., traditional telephony and file transfer) to highly bursty traffic (e.g., interactive data and video). Because of its support for such a wide range of traffic, ATM was designated by the telecommunication standardization sec- tor of the International Telecommunications Union (ITU-T, formerly CCITT) as the multiplexing and switching tech- nique for Broadband, or high-speed, ISDN (B-ISDN) (1). ATM is a form of packet-switching technology. That is, ATM networks transmit their information in small, fixed- length packets called cells, each of which contains 48 octets (or bytes) of data and 5 octets of header information. The small, fixed cell size was chosen to facilitate the rapid processing of packets in hardware and to minimize the amount of time required to fill a single packet. This is particularly important for real-time applications such as voice and video that require short packetization delays. ATM is also connection-oriented. In other words, a virtual circuit must be established before a call can take place, where a call is defined as the transfer of information between two or more endpoints. The establishment of a virtual circuit entails the initiation of a signaling process, during which a route is selected according to the call’s quality of service requirements, connection identifiers at each switch on the route are established, and network resources such as bandwidth and buffer space may be reserved for the connection. Another important characteristic of ATM is that its network functions are typically implemented in hardware. With the introduction of high-speed fiber optic transmis- sion lines, the communication bottleneck has shifted from the communication links to the processing at switching nodes and at terminal equipment. Hardware implementa- tion is necessary to overcome this bottleneck because it minimizes the cell-processing overhead, thereby allowing the network to match link rates on the order of gigabits per second. Finally, as its name indicates, ATM is asynchronous. Time is slotted into cell-sized intervals, and slots are assigned to calls in an asynchronous, demand-based man- ner. Because slots are allocated to calls on demand, ATM can easily accommodate traffic whose bit rate fluctuates over time. Moreover, in ATM, no bandwidth is consumed unless information is actually transmitted. ATM also gains bandwidth efficiency by being able to multiplex bursty traffic sources statistically. Because bursty traffic does not require continuous allocation of the bandwidth at its peak rate, statistical multiplexing allows a large number of bursty sources to share the network’s bandwidth. Since its birth in the mid-1980s, ATM has been fortified by a number of robust standards and realized by a signifi- cant number of network equipment manufacturers. Inter- national standards-making bodies such as the ITU and independent consortia like the ATM Forum have developed a significant body of standards and implementation agree- ments for ATM (1,4). As networks and network services continue to evolve toward greater speeds and diversities, ATM will undoubtedly continue to proliferate. ATM STANDARDS The telecommunication standardization sector of the ITU, the international standards agency commissioned by the United Nations for the global standardization of telecom- munications, has developed a number of standards for ATM networks. Other standards bodies and consortia (e.g., the ATM Forum, ANSI) have also contributed to the develop- ment of ATM standards. This section presents an overview of the standards, with particular emphasis on the protocol reference model used by ATM (2). Protocol Reference Model The B-ISDN protocol reference model, defined in ITU-T recommendation I.321, is shown in Fig. 1(1). The purpose of the protocol reference model is to clarify the functions that ATM networks perform by grouping them into a set of interrelated, function-specific layers and planes. The refer- ence model consists of a user plane, a control plane, and a management plane. Within the user and control planes is a hierarchical set of layers. The user plane defines a set of functions for the transfer of user information between communication endpoints; the control plane defines control functions such as call establishment, call maintenance, and call release; and the management plane defines the opera- tions necessary to control information flow between planes and layers and to maintain accurate and fault-tolerant network operation. Within the user and control planes, there are three layers: the physical layer, the ATM layer, and the ATM adaptation layer (AAL). Figure 2 summarizes the functions of each layer (1). The physical layer performs primarily bit- level functions, the ATM layer is primarily responsible for the switching of ATM cells, and the ATM adaptation layer is responsible for the conversion of higher-layer protocol frames into ATM cells. The functions that the physical, ATM, and adaptation layers perform are described in more detail next. Physical Layer The physical layer is divided into two sublayers: the phy- sical medium sublayer and the transmission convergence sublayer (1). 1 Wiley Encyclopedia of Computer Science and Engineering, edited by Benjamin Wah. Copyright # 2008 John Wiley & Sons, Inc.
- 10. Physical Medium Sublayer. The physical medium (PM) sublayer performs medium-dependent functions. For example, it provides bit transmission capabilities including bit alignment, line coding and electrical/optical conversion. The PM sublayer is also responsible for bit timing (i.e., the insertion and extraction of bit timing information). The PM sublayer currently supports two types of interface: optical and electrical. Transmission Convergence Sublayer. Above the physical medium sublayer is the transmission convergence (TC) sublayer, which is primarily responsible for the framing of data transported over the physical medium. The ITU-T recommendation specifies two options for TC sublayer transmission frame structure: cell-based and synchronous digital hierarchy (SDH). In the cell-based case, cells are transported continuously without any regular frame struc- ture. Under SDH, cells are carried in a special frame structure based on the North American SONET (synchro- nous optical network) protocol (3). Regardless of which transmission frame structure is used, the TC sublayer is responsible for the following four functions: cell rate decou- pling, header error control, cell delineation, and transmis- sion frame adaptation. Cell rate decoupling is the insertion of idle cells at the sending side to adapt the ATM cell stream’s rate to the rate of the transmission path. Header error control is the insertion of an 8-bit CRC in the ATM cell header to protect the contents of the ATM cell header. Cell delineation is the detection of cell boundaries. Transmis- sion frame adaptation is the encapsulation of departing cells into an appropriate framing structure (either cell- based or SDH-based). ATM Layer The ATM layer lies atop the physical layer and specifies the functions required for the switching and flow control of ATM cells (1). There are two interfaces in an ATM network: the user- network interface (UNI) between the ATM endpoint and the ATM switch, and the network-network interface (NNI) between two ATM switches. Although a 48-octet cell pay- load is used at both interfaces, the 5-octet cell header differs slightly at these interfaces. Figure 3 shows the cell header structures used at the UNI and NNI (1). At the UNI, the header contains a 4-bit generic flow control (GFC) field, a 24-bit label field containing virtual path identifier (VPI) and virtual channel identifier (VCI) subfields (8 bits for the VPI and 16 bits forthe VCI), a2-bit payloadtype (PT) field,a 1-bit cell loss priority (CLP) field, and an 8-bit header error check (HEC) field. The cell header for an NNI cell is identical to that for the UNI cell, except that it lacks the GFC field; these four bits are used for an additional 4 VPI bits in the NNI cell header. The VCI and VPI fields are identifier values for virtual channel (VC) and virtual path (VP), respectively. A virtual channel connects two ATM communication endpoints. A virtual path connects two ATM devices, which can be switches or endpoints, and several virtual channels may be multiplexed onto the same virtual path. The 2-bit PT field identifies whether the cell payload contains data or control information. The CLP bit is used by the user for explicit indication of cell loss priority. If the value of the CLP is 1, then the cell is subject to discarding in case of congestion. The HEC field is an 8-bit CRC that protects the contents of the cell header. The GFC field, which appears only at the UNI, is used to assist the customer premises network in controlling the traffic flow. At the time of writ- ing, the exact procedures for use of this field have not been agreed upon. Figure 1. Protocol reference model for ATM. Figure 2. Functions of each layer in the protocol reference model. 2 ASYNCHRONOUS TRANSFER MODE NETWORKS
- 11. ATM Layer Functions The primary function of the ATM layer is VPI/VCI transla- tion. As ATM cells arrive at ATM switches, the VPI and VCI values contained in their headers are examined by the switch to determine which outport port should be used to forward the cell. In the process, the switch translates the cell’s original VPI and VCI values into new outgoing VPI and VCI values, which are used in turn by the next ATM switch to send the cell toward its intended destination. The table used to perform this translation is initialized during the establishment of the call. An ATM switch may either be a VP switch, in which case it translates only the VPI values contained in cell headers, or it may be a VP/VC switch, in which case it translates the incoming VPI/VCI value into an outgoing VPI/VCI pair. Because VPI and VCI values do not represent a unique end- to-end virtual connection, they can be reused at different switches through the network. This is important because the VPI and VCI fields are limited in length and would be quickly exhausted if they were used simply as destination addresses. The ATM layer supports two types of virtual connec- tions: switched virtual connections (SVC) and permanent, or semipermanent, virtual connections (PVC). Switched virtual connections are established and torn down dyna- mically by an ATM signaling procedure. That is, they exist only for the duration of a single call. Permanent virtual connections, on the other hand, are established by network administrators and continue to exist as long as the admin- istrator leaves them up, even if they are not used to trans- mit data. Other important functions of the ATM layer include cell multiplexing and demultiplexing, cell header creation and extraction, and generic flow control. Cell multiplexing is the merging of cells from several calls onto a single trans- mission path, cell header creation is the attachment of a 5- octet cell header to each 48-octet block of user payload, and generic flow control is used at the UNI to prevent short- term overload conditions from occurring within the net- work. ATM Layer Service Categories The ATM Forum and ITU-T have defined several distinct service categories at the ATM layer (1,4). The categories defined by the ATM Forum include constant bit rate (CBR), real-time variable bit rate (VBR-rt), non-real-time variable bit rate (VBR-nrt), available bit rate (ABR), and unspecified bit rate (UBR). ITU-T defines four service categories, namely, deterministic bit rate (DBR), statistical bit rate (SBR), available bit rate (ABR), and ATM block transfer (ABT). The first of the three ITU-T service categories correspond roughly to the ATM Forum’s CBR, VBR, and ABR classifications, respectively. The fourth service cate- gory, ABT, is solely defined by ITU-T and is intended for bursty data applications. The UBR category defined by the ATM Forum is for calls that request no quality of service guarantees at all. Figure 4 lists the ATM service categories, their quality of service (QoS) parameters, and the traffic descriptors required by the service category during call establishment (1,4). The constant bit rate (or deterministic bit rate) service category provides a very strict QoS guarantee. It is targeted at real-time applications, such as voice and raw video, which mandate severe restrictions on delay, delay variance (jitter), and cell loss rate. The only traffic descriptors required by the CBR service are the peak cell rate and the cell delay variation tolerance. A fixed amount of band- width, determined primarily by the call’s peak cell rate, is reserved for each CBR connection. The real-time variable bit rate (or statistical bit rate) service category is intended for real-time bursty applica- tions (e.g., compressed video), which also require strict QoS guarantees. The primary difference between CBR and VBR-rt is in the traffic descriptors they use. The VBR-rt service requires the specification of the sustained (or aver- age) cell rate and burst tolerance (i.e., burst length) in addition to the peak cell rate and the cell delay variation Figure 3. ATM cell header structure. Figure 4. ATM layer service categories. ASYNCHRONOUS TRANSFER MODE NETWORKS 3
- 12. tolerance. The ATM Forum also defines a VBR-nrt service category, in which cell delay variance is not guaranteed. The available bit rate service category is defined to exploit the network’s unused bandwidth. It is intended for non-real-time data applications in which the source is amenable to enforced adjustment of its transmission rate. A minimum cell rate is reserved for the ABR connection and therefore guaranteed by the network. When the network has unused bandwidth, ABR sources are allowed to increase their cell rates up to an allowed cell rate (ACR), a value that is periodically updated by the ABR flow control mechanism (to be described in the section entitled ‘‘ATM Traffic Control’’). The value of ACR always falls between the minimum and the peak cell rate for the connection and is determined by the network. The ATM Forum defines another service category for non-real-time applications called the unspecified bit rate (UBR) service category. The UBR service is entirely best effort; the call is provided with no QoS guarantees. The ITU-T also defines an additional service category for non- real-time data applications. The ATM block transfer ser- vice category is intended for the transmission of short bursts, or blocks, of data. Before transmitting a block, the source requests a reservation of bandwidth from the network. If the ABT service is being used with the immedi- ate transmission option (ABT/IT), the block of data is sent at the same time as the reservation request. If bandwidth is not available for transporting the block, then it is simply discarded, and the source must retransmit it. In the ABT service with delayed transmission (ABT/DT), the source waits for a confirmation from the network that enough bandwidth is available before transmitting the block of data. In both cases, the network temporarily reserves bandwidth according to the peak cell rate for each block. Immediately after transporting the block, the network releases the reserved bandwidth. ATM Adaptation Layer The ATM adaptation layer, which resides atop the ATM layer, is responsible for mapping the requirements of higher layer protocols onto the ATM network (1). It oper- ates in ATM devices at the edge of the ATM network and is totally absent in ATM switches. The adaptation layer is divided into two sublayers: the convergence sublayer (CS), which performs error detection and handling, timing, and clock recovery; and the segmentation and reassembly (SAR) sublayer, which performs segmentation of conver- gence sublayer protocol data units (PDUs) into ATM cell- sized SAR sublayer service data units (SDUs) and vice versa. In order to support different service requirements, the ITU-T has proposed four AAL-specific service classes. Figure 5 depicts the four service classes defined in recom- mendation I.362 (1). Note that even though these AAL service classes are similar in many ways to the ATM layer service categories defined in the previous section, they are not the same; each exists at a different layer of the protocol reference model, and each requires a different set of func- tions. AAL service class A corresponds to constant bit rate services with a timing relation required between source and destination. The connection mode is connection- oriented. The CBR audio and video belong to this class. Class B corresponds to variable bit rate (VBR) services. This class also requires timing between source and desti- nation, and its mode is connection-oriented. The VBR audio and video are examples of class B services. Class C also corresponds to VBR connection-oriented services, but the timing between source and destination needs not be related. Class C includes connection-oriented data transfer such as X.25, signaling, and future high-speed data ser- vices. Class D corresponds to connectionless services. Con- nectionless data services such as those supported by LANs and MANs are examples of class D services. Four AAL types (Types 1, 2, 3/4, and 5), each with a unique SAR sublayer and CS sublayer, are defined to support the four service classes. AAL Type 1 supports constant bit rate services (class A), and AAL Type 2 sup- ports variable bit rate services with a timing relation between source and destination (class B). AAL Type 3/4 was originally specified as two different AAL types (Type 3 and Type 4), but because of their inherent similarities, they were eventually merged to support both class C and class D services. AAL Type 5 also supports class C and class D services. AAL Type 5. Currently, the most widely used adaptation layer is AAL Type 5. AAL Type 5 supports connection- oriented and connectionless services in which there is no timing relation between source and destination (classes C and D). Its functionality was intentionally made simple in order to support high-speed data transfer. AAL Type 5 assumes that the layers above the ATM adaptation layer can perform error recovery, retransmission, and sequence numbering when required, and thus, it does not provide these functions. Therefore, only nonassured operation is provided; lost or corrupted AAL Type 5 packets will not be corrected by retransmission. Figure 6 depicts the SAR-SDU format for AAL Type 5 (5,6). The SAR sublayer of AAL Type 5 performs segmenta- tion of a CS-PDU into a size suitable for the SAR-SDU payload. Unlike other AAL types, Type 5 devotes the entire 48-octet payload of the ATM cell to the SAR-SDU; there is no overhead. An AAL specific flag (end-of-frame) in the Figure 5. Service classification for AAL. Figure 6. SAR-SDU format for AAL Type 5. 4 ASYNCHRONOUS TRANSFER MODE NETWORKS
- 13. ATM PT field of the cell header is set when the last cell of a CS-PDU is sent. The reassembly of CS-PDU frames at the destination is controlled by using this flag. Figure 7 depicts the CS-PDU format for AAL Type 5 (5,6). It contains the user data payload, along with any necessary padding bits (PAD) and a CS-PDU trailer, which are added by the CS sublayer when it receives the user information from the higher layer. The CS-PDU is padded using 0 to 47 bytes of PAD field to make the length of the CS- PDU an integral multiple of 48 bytes (the size of the SAR- SDU payload). At the receiving end, a reassembled PDU is passed to the CS sublayer from the SAR sublayer, and CRC values are then calculated and compared. If there is no error, the PAD field is removed by using the value of length field (LF) in the CS-PDU trailer, and user data is passed to the higher layer. If an error is detected, the erroneous information is either delivered to the user or discarded according to the user’s choice. The use of the CF field is for further study. AAL Type 1. AAL Type 1 supports constant bit rate services with a fixed timing relation between source and destination users (class A). At the SAR sublayer, it defines a 48-octet service data unit (SDU), which contains 47 octets of user payload, 4 bits for a sequence number, and a 4-bit CRC value to detect errors in the sequence number field. AAL Type 1 performs the following services at the CS sublayer: forward error correction to ensure high quality of audio and video applications, clock recovery by monitoring the buffer filling, explicit time indication by inserting a time stamp in the CS-PDU, and handling of lost and misinserted cells that are recognized by the SAR. At the time of writing, the CS- PDU format has not been decided. AAL Type 2. AAL Type 2 supports variable bit rate services with a timing relation between source and desti- nation (class B). AAL Type 2 is nearly identical to AAL Type 1, except that it transfers service data units at a variable bit rate, not at a constant bit rate. Furthermore, AAL Type 2 accepts variable length CS-PDUs, and thus, there may exist some SAR-SDUs that are not completely filled with user data. The CS sublayer for AAL Type 2 performs the following functions: forward error correction for audio and video services, clock recovery by inserting a time stamp in the CS-PDU, and handling of lost and misinserted cells. At the time of writing, both the SAR-SDU and CS-PDU for- mats for AAL Type 2 are still under discussion. AAL Type 3/4. AAL Type 3/4 mainly supports services that require no timing relation between the source and destination (classes C and D). At the SAR sublayer, it defines a 48-octet service data unit, with 44 octets of user payload; a 2-bit payload type field to indicate whether the SDU is at the beginning, middle, or end of a CS-PDU; a 4-bit cell sequence number; a 10-bit multiplexing identifier that allows several CS-PDUs to be multiplexed over asingle VC; a 6-bit cell payload length indicator; and a 10-bit CRC code that covers the payload. The CS-PDU format allows for up to 65535 octets of user payload and contains a header and trailer to delineate the PDU. The functions that AAL Type 3/4 performs include seg- mentation and reassembly of variable-length user data and error handling. It supports message mode (for framed data transfer) as well as streaming mode (for streamed data transfer). Because Type 3/4 is mainly intended for data services, it provides a retransmission mechanism if neces- sary. ATM Signaling ATM follows the principle of out-of-band signaling that was established for N-ISDN. In other words, signaling and data channels are separate. The main purposes of signaling are (1) to establish, maintain, and release ATM virtual con- nections and (2) to negotiate (or renegotiate) the traffic parameters of new (or existing) connections (7). The ATM signaling standards support the creation of point-to-point as well as multicast connections. Typically, certain VCI and VPI values are reserved by ATM networks for signaling messages. If additional signaling VCs are required, they may be established through the process of metasignaling. ATM TRAFFIC CONTROL The control of ATM traffic is complicated as a result of ATM’s high-link speed and small cell size, the diverse service requirements of ATM applications, and the diverse characteristics of ATM traffic. Furthermore, the configura- tion and size of the ATM environment, either local or wide area, has a significant impact on the choice of traffic control mechanisms. The factor that most complicates traffic control in ATM is its high-link speed. Typical ATM link speeds are 155.52 Mbit/s and 622.08 Mbit/s. At these high-link speeds, 53- byte ATM cells must be switched at rates greater than one cell per 2.726 ms or 0.682 ms, respectively. It is apparent that the cell processing required by traffic control must perform at speeds comparable to these cell-switching rates. Thus, traffic control should be simple and efficient, without excessive software processing. Such high speeds render many traditional traffic control mechanisms inadequate for use in ATM because of their reactive nature. Traditional reactive traffic control mechanisms attempt to control network congestion by responding to it after it occurs and usually involves sending Figure 7. CS-PDU format, segmentation and reassembly of AAL Type 5. ASYNCHRONOUS TRANSFER MODE NETWORKS 5
- 14. feedback to the source in the form of a choke packet. However, a large bandwidth-delay product (i.e., the amount of traffic that can be sent in a single propagation delay time) renders many reactive control schemes ineffec- tive in high-speed networks. When a node receives feed- back, it may have already transmitted a large amount of data. Consider a cross-continental 622 Mbit/s connection with a propagation delay of 20 ms (propagation-bandwidth product of 12.4 Mbit). If a node at one end of the connection experiences congestion and attempts to throttle the source at the other end by sending it a feedback packet, the source will already have transmitted over 12 Mb of information before feedback arrives. This example illustrates the inef- fectiveness of traditional reactive traffic control mechan- isms in high-speed networks and argues for novel mechanisms that take into account high propagation-band- width products. Not only is traffic control complicated by high speeds, but it also is made more difficult by the diverse QoS require- ments of ATM applications. For example, many applica- tions have strict delay requirements and must be delivered within a specified amount of time. Other applications have strict loss requirements and must be delivered reliably without an inordinate amount of loss. Traffic controls must address the diverse requirements of such applica- tions. Another factor complicating traffic control in ATM net- works is the diversity of ATM traffic characteristics. In ATM networks, continuous bit rate traffic is accompanied by bursty traffic. Bursty traffic generates cells at a peak rate for a very short period of time and then immediately becomes less active, generating fewer cells. To improve the efficiency of ATM network utilization, bursty calls should be allocated an amount of bandwidth that is less than their peak rate. This allows the network to multiplex more calls by taking advantage of the small probability that a large number of bursty calls will be simultaneously active. This type of multiplexing is referred to as statistical multiplex- ing. The problem then becomes one of determining how best to multiplex bursty calls statistically such that the number of cells dropped as a result of excessive burstiness is balanced with the number of bursty traffic streams allowed. Addressing the unique demands of bursty traffic is an important function of ATM traffic control. For these reasons, many traffic control mechanisms developed for existing networks may not be applicable to ATM networks, and therefore novel forms of traffic control are required (8,9). One such class of novel mechanisms that work well in high-speed networks falls under the heading of preventive control mechanisms. Preventive control attempts to manage congestion by preventing it before it occurs. Preventive traffic control is targeted primarily at real-time traffic. Another class of traffic control mechan- isms has been targeted toward non-real-time data traffic and relies on novel reactive feedback mechanisms. Preventive Traffic Control Preventive control for ATM has two major components: call admission control and usage parameter control (8). Admis- sion control determines whether to accept or reject a new call at the time of call set-up. This decision is based on the traffic characteristics of the new call and the current net- work load. Usage parameter control enforces the traffic parameters of the call after it has been accepted into the network. This enforcement is necessary to ensure that the call’s actual traffic flow conforms with that reported during call admission. Before describing call admission and usage parameter control in more detail, it is important to first discuss the nature of multimedia traffic. Most ATM traffic belongs to one of two general classes of traffic: continuous traffic and bursty traffic. Sources of continuous traffic (e.g., constant bit rate video, voice without silence detection) are easily handled because their resource utilization is predictable and they can be deterministically multiplexed. However, bursty traffic (e.g., voice with silence detection, variable bit rate video) is characterized by its unpredictability, and this kind of traffic complicates preventive traffic control. Burstiness is a parameter describing how densely or sparsely cell arrivals occur. There are a number of ways to express traffic burstiness, the most typical of which are the ratio of peak bit rate to average bit rate and the average burst length. Several other measures of burstiness have also been proposed (8). It is well known that burstiness plays a critical role in determining network performance, and thus, it is critical for traffic control mechanisms to reduce the negative impact of bursty traffic. Call Admission Control. Call admission control is the process by which the network decides whether to accept or reject a new call. When a new call requests access to the network, it provides a set of traffic descriptors (e.g., peak rate, average rate, average burst length) and a set of quality of service requirements (e.g., acceptable cell loss rate, acceptable cell delay variance, acceptable delay). The net- work then determines, through signaling, if it has enough resources (e.g., bandwidth, buffer space) to support the new call’s requirements. If it does, the call is immediately accepted and allowed to transmit data into the network. Otherwise it is rejected. Call admission control prevents network congestion by limiting the number of active con- nections in the network to a level where the network resources are adequate to maintain quality of service guar- antees. One of the most common ways for an ATM network to make a call admission decision is to use the call’s traffic descriptors and quality of service requirements to predict the ‘‘equivalent bandwidth’’ required by the call. The equivalent bandwidth determines how many resources need to be reserved by the network to support the new call at its requested quality of service. For continuous, constant bit rate calls, determining the equivalent band- width is simple. It is merely equal to the peak bit rate of the call. For bursty connections, however, the process of deter- mining the equivalent bandwidth should take into account such factors as a call’s burstiness ratio (the ratio of peak bit rate to average bit rate), burst length, and burst interarri- val time. The equivalent bandwidth for bursty connections must be chosen carefully to ameliorate congestion and cell loss while maximizing the number of connections that can be statistically multiplexed. 6 ASYNCHRONOUS TRANSFER MODE NETWORKS
- 15. Random documents with unrelated content Scribd suggests to you:
- 16. In what times the Planets would fall to the Sun by the power of gravity. The prodigious attraction of the Sun and Planets. cause them to ascend again towards the higher parts of their Orbits; during which time, the Sun’s attraction acting so contrary to the motions of those bodies, causes them to move slower and slower, until their projectile forces are diminished almost to nothing; and then they are brought back again by the Sun’s attraction, as before. 157. If the projectile forces of all the Planets and Comets were destroyed at their mean distances from the Sun, their gravities would bring them down so, as that Mercury would fall to the Sun in 15 days 13 hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours; Mars in 121 days; Jupiter in 290; and Saturn in 767. The nearest Comet in 13 thousand days; the middlemost in 23 thousand days; and the outermost in 66 thousand days. The Moon would fall to the Earth in 4 days 20 hours; Jupiter’s first Moon would fall to him in 7 hours, his second in 15, his third in 30, and his fourth in 71 hours. Saturn’s first Moon would fall to him in 8 hours; his second in 12, his third in 19, his fourth in 68 hours, and the fifth in 336. A stone would fall to the Earth’s center, if there were an hollow passage, in 21 minutes 9 seconds. Mr. Whiston gives the following Rule for such Computations. “[31] It is demonstrable, that half the Period of any Planet, when it is diminished in the sesquialteral proportion of the number 1 to the number 2, or nearly in the proportion of 1000 to 2828, is the time that it would fall to the Center of it’s Orbit.” This proportion is, when a quantity or number contains another once and a half as much more. 158. The quick motions of the Moons of Jupiter and Saturn round their Primaries, demonstrate that these two Planets have stronger attractive powers than the Earth has. For, the stronger that one body attracts another, the greater must be the projectile force, and consequently the quicker must be the motion of that other body, to keep it from falling to it’s primary or central Planet. Jupiter’s second Moon is 124 thousand miles farther from Jupiter than our
- 17. Archimedes’s Problem for raising the Earth. Moon is from us; and yet this second Moon goes almost eight times round Jupiter whilst our Moon goes only once round the Earth. What a prodigious attractive power must the Sun then have, to draw all the Planets and Satellites of the System towards him; and what an amazing power must it have required to put all these Planets and Moons into such rapid motions at first! Amazing indeed to us, because impossible to be effected by the strength of all the living Creatures in an unlimited number of Worlds, but no ways hard for the Almighty, whose Planetarium takes in the whole Universe! 159. The celebrated Archimedes affirmed he could move the Earth if he had a place to stand on to manage his machinery[32] . This assertion is true in Theory, but, upon examination, will be found absolutely impossible in fact, even though a proper place and materials of sufficient strength could be had. The simplest and easiest method of moving a heavy body a little way is by a lever or crow, where a small weight or power applied to the long arm will raise a great weight on the short one. But then, the small weight must move as much quicker than the great weight as the latter is heavier than the former; and the length of the long arm of the lever to the length of the short arm must be in the same proportion. Now, suppose a man pulls or presses the end of the long arm with the force of 200 pound weight, and that the Earth contains in round Numbers 4,000,000,000,000,000,000,000 or 4000 Trillions of cubic feet, each at a mean rate weighing 100 pound; and that the prop or center of motion of the lever is 6000 miles from the Earth’s center: in this case, the length of the lever from the Fulcrum or center of motion to the moving power or weight ought to be 12,000,000,000,000,000,000,000,000 or 12 Quadrillions of miles; and so many miles must the power move, in order to raise the Earth but one mile, whence ’tis easy to compute, that if Archimedes or the power applied could move as swift as a cannon bullet, it would take 27,000,000,000,000 or 27 Billions of years to raise the Earth one inch.
- 18. Hard to determine what Gravity is. If any other machine, such as a combination of wheels and screws, was proposed to move the Earth, the time it would require, and the space gone through by the hand that turned the machine, would be the same as before. Hence we may learn, that however boundless our Imagination and Theory may be, the actual operations of man are confined within narrow bounds; and more suited to our real wants than to our desires. 160. The Sun and Planets mutually attract each other: the power by which they do so we call Gravity. But whether this power be mechanical or no, is very much disputed. We are certain that the Planets disturb one another’s motions by it, and that it decreases according to the squares of the distances of the Sun and Planets; as light, which is known to be material, likewise does. Hence Gravity should seem to arise from the agency of some subtile matter pressing towards the Sun and Planets, and acting, like all mechanical causes, by contact. But on the other hand, when we consider that the degree or force of Gravity is exactly in proportion to the quantities of matter in those bodies, without any regard to their bulks or quantity of surface, acting as freely on their internal as external parts, it seems to surpass the power of mechanism; and to be either the immediate agency of the Deity, or effected by a law originally established and imprest on all matter by him. But some affirm that matter, being altogether inert, cannot be impressed with any Law, even by almighty Power: and that the Deity must therefore be constantly impelling the Planets toward the Sun, and moving them with the same irregularities and disturbances which Gravity would cause, if it could be supposed to exist. But, if a man may venture to publish his own thoughts, (and why should not one as well as another?) it seems to me no greater absurdity, to suppose the Deity capable of superadding a Law, or what Laws he pleases, to matter, than to suppose him capable of giving it existence at first. The manner of both is equally inconceivable to us; but neither of them imply a contradiction in our ideas: and what implies no contradiction is
- 19. within the power of Omnipotence. Do we not see that a human creature can prepare a bar of steel so as to make it attract needles and filings of iron; and that he can put a stop to that power or virtue, and again call it forth again as often as he pleases? To say that the workman infuses any new power into the bar, is saying too much; since the needle and filings, to which he has done nothing, re-attract the bar. And from this it appears that the power was originally imprest on the matter of which the bar, needle, and filings are composed; but does not seem to act until the bar be properly prepared by the artificer: somewhat like a rope coiled up in a ship, which will never draw a boat or any other thing towards the ship, unless one end be tied to it, and the other end to that which is to be hauled up; and then it is no matter which end of the rope the sailors pull at, for the rope will be equally stretched throughout, and the ship and boat will move towards one another. To say that the Almighty has infused no such virtue or power into the materials which compose the bar, but that he waits till the operator be pleased to prepare it by due position and friction, and then, when the needle or filings are brought pretty near the bar, the Deity presses them towards it, and withdraws his hand whenever the workman either for use, curiosity or whim, does what appears to him to destroy the action of the bar, seems quite ridiculous and trifling; as it supposes God not only to be subservient to our inconstant wills, but also to do what would be below the dignity of any rational man to be employed about. 161. That the projectile force was at first given by the Deity is evident. For, since matter can never put itself into motion, and all bodies may be moved in any direction whatsoever; and yet all the Planets both primary and secondary move from west to east, in planes nearly coincident; whilst the Comets move in all directions, and in planes so different from one another; these motions can be owing to no mechanical cause of necessity, but to the free choice and power of an intelligent Being. 162. Whatever Gravity be, ’tis plain that it acts every moment of time: for should it’s action cease, the projectile force would instantly
- 20. The Planets disturb one another’s motion. The consequences thereof. The World not eternal. carry off the Planets in straight lines from those parts of their Orbits where Gravity left them. But, the Planets being once put into motion, there is no occasion for any new projectile force, unless they meet with some resistance in their Orbits; nor for any mending hand, unless they disturb one another too much by their mutual attractions. 163. It is found that there are disturbances among the Planets in their motions, arising from their mutual attractions when they are in the same quarter of the Heavens; and that our years are not always precisely of the same length[33] . Besides, there is reason to believe that the Moon is somewhat nearer the Earth now than she was formerly; her periodical month being shorter than it was in former ages. For, our Astronomical Tables, which in the present Age shew the times of Solar and Lunar Eclipses to great precision, do not answer so well for very ancient Eclipses. Hence it appears, that the Moon does not move in a medium void of all resistance, § 174; and therefore her projectile force being a little weakened, whilst there is nothing to diminish her gravity, she must be gradually approaching nearer the Earth, describing smaller and smaller Circles round it in every revolution, and finishing her Period sooner, although her absolute motion with regard to space be not so quick now as it was formerly: and therefore, she must come to the Earth at last; unless that Being, which gave her a sufficient projectile force at the beginning, adds a little more to it in due time. And, as all the Planets move in spaces full of æther and light, which are material substances, they too must meet with some resistance. And therefore, if their gravities are not diminished, nor their projectile forces increased, they must necessarily approach nearer and nearer the Sun, and at length fall upon and unite with him. 164. Here we have a strong philosophical argument against the eternity of the World. For, had it existed from eternity, and been left by the Deity to be
- 21. governed by the combined actions of the above forces or powers, generally called Laws, it had been at an end long ago. And if it be left to them it must come to an end. But we may be certain that it will last as long as was intended by it’s Author, who ought no more to be found fault with for framing so perishable a work, than for making man mortal.
- 22. The amazing smallness of the particles of light. The dreadful effects that would ensue from their being larger. CHAP. VIII. Of Light. It’s proportional quantities on the different Planets. It’s Refractions in Water and Air. The Atmosphere; it’s weight and properties. The Horizontal Moon. 165. Light consists of exceeding small particles of matter issuing from a luminous body; as from a lighted candle such particles of matter continually flow in all directions. Dr. Niewentyt [34] computes, that in one second of time there flows 418,660,000,000,000,000,000,000,000,000,000,000,000,000,000 particles of light out of a burning candle; which number contains at least 6,337,242,000,000 times the number of grains of sand in the whole Earth; supposing 100 grains of sand to be equal in length to an inch, and consequently, every cubic inch of the Earth to contain one million of such grains. 166. These amazingly small particles, by striking upon our eyes, excite in our minds the idea of light: and, if they were so large as the smallest particles of matter discernible by our best microscopes, instead of being serviceable to us, they would soon deprive us of sight by the force arising from their immense velocity, which is above 164 thousand miles every second[35] , or 1,230,000 times swifter than the motion of a cannon bullet. And therefore, if the particles of light were so large, that a million of them were equal in bulk to an ordinary grain of land, we
- 23. How objects become visible to us. PLATE II. The rays of Light naturally move in straight lines. A proof that they hinder not one another’s motions. Fig. XI. In what proportion durst no more open our eyes to the light than suffer sand to be shot point blank against them. 167. When these small particles, flowing from the Sun or from a candle, fall upon bodies, and are thereby reflected to our eyes, they excite in us the idea of that body by forming it’s picture on the retina[36] . And since bodies are visible on all sides, light must be reflected from them in all directions. 168. A ray of light is a continued stream of these particles, flowing from any visible body in straight lines. That they move in straight, and not in crooked lines, unless they be refracted, is evident from bodies not being visible if we endeavour to look at them through the bore of a bended pipe; and from their ceasing to be seen by the interposition of other bodies, as the fixed Stars by the interposition of the Moon and Planets, and the Sun wholly or in part by the interposition of the Moon, Mercury, or Venus. And that these rays do not interfere, or jostle one another out of their ways, in flowing from different bodies all around, is plain from the following Experiment. Make a little hole in a thin plate of metal, and set the plate upright on a table, facing a row of lighted candles standing by one another; then place a sheet of paper or pasteboard at a little distance from the other side of the plate, and the rays of all the candles, flowing through the hole, will form as many specks of light on the paper as there are candles before the plate, each speck as distinct and large, as if there were only one candle to cast one speck; which shews that the rays are no hinderance to each other in their motions, although they all cross in the hole. 169. Light, and therefore heat so far as it depends on the Sun’s rays (§ 85, towards the end) decreases in proportion to the
- 24. light and heat decrease at any given distance from the Sun. PLATE II. Why the Planets appear dimmer when viewed thro’ telescopes than by the bare eye. squares of the distances of the Planets from the Sun. This is easily demonstrated by a Figure which, together with it’s description, I have taken from Dr. Smith’s Optics[37] . Let the light which flows from a point A, and passes through a square hole B, be received upon a plane C, parallel to the plane of the hole; or, if you please, let the figure C be the shadow of the plane B; and when the distance C is double of B, the length and breadth of the shadow C will be each double of the length and breadth of the plane B; and treble when AD is treble of AB; and so on: which may be easily examined by the light of a candle placed at A. Therefore the surface of the shadow C, at the distance AC double of AB, is divisible into four squares, and at a treble distance, into nine squares, severally equal to the square B, as represented in the Figure. The light then which falls upon the plane B, being suffered to pass to double that distance, will be uniformly spread over four times the space, and consequently will be four times thinner in every part of that space, and at a treble distance it will be nine times thinner, and at a quadruple distance sixteen times thinner, than it was at first; and so on, according to the increase of the square surfaces B, C, D, E, built upon the distances AB, AC, AD, AE. Consequently, the quantities of this rarefied light received upon a surface of any given size and shape whatever, removed successively to these several distances, will be but one quarter, one ninth, one sixteenth of the whole quantity received by it at the first distance AB. Or in general words, the densities and quantities of light, received upon any given plane, are diminished in the same proportion as the squares of the distances of that plane, from the luminous body, are increased: and on the contrary, are increased in the same proportion as these squares are diminished. 170. The more a telescope magnifies the disks of the Moon and Planets, they appear so much dimmer than to the bare eye; because the telescope cannot magnify the quantity of light, as it does the surface; and, by spreading the same quantity of light over a surface so much larger
- 25. Fig. VIII. Refraction of the rays of light. than the naked eye beheld, just so much dimmer must it appear when viewed by a telescope than by the bare eye. 171. When a ray of light passes out of one medium[38] into another, it is refracted, or turned out of it’s first course, more or less, as it falls more or less obliquely on the refracting surface which divides the two mediums. This may be proved by several experiments; of which we shall only give three for example’s sake. 1. In a bason FGH put a piece of money as DB, and then retire from it as to A, till the edge of the bason at E just hides the money from your sight: then, keeping your head steady, let another person fill the bason gently with water. As he fills it, you will see more and more of the piece DB; which will be all in view when the bason is full, and appear as if lifted up to C. For, the ray AEB, which was straight whilst the bason was empty, is now bent at the surface of the water in E, and turned out of it’s rectilineal course into the direction ED. Or, in other words, the ray DEK, that proceeded in a straight line from the edge D whilst the bason was empty, and went above the eye at A, is now bent at E; and instead of going on in the rectilineal direction DEK, goes in the angled direction DEA, and by entering the eye at A renders the object DB visible. Or, 2dly, place the bason where the Sun shines obliquely, and observe where the shadow of the rim E falls on the bottom, as at B: then fill it with water, and the shadow will fall at D; which proves, that the rays of light, falling obliquely on the surface of the water, are refracted, or bent downwards into it. 172. The less obliquely the rays of light fall upon the surface of any medium, the less they are refracted; and if they fall perpendicularly thereon, they are not refracted at all. For, in the last experiment, the higher the Sun rises, the less will be the difference between the places where the edge of the shadow falls, in the empty and full bason. And, 3dly, if a stick be laid over the bason, and the Sun’s rays be reflected perpendicularly into it from a looking-glass, the shadow
- 26. The Atmosphere. The Air’s compression and rarity at different heights. of the stick will fall upon the same place of the bottom, whether the bason be full or empty. 173. The denser that any medium is, the more is light refracted in passing through it. 174. The Earth is surrounded by a thin fluid mass of matter, called the Air, or Atmosphere, which gravitates to the Earth, revolves with it in it’s diurnal motion, and goes round the Sun with it every year. This fluid is of an elastic or springy nature, and it’s lowermost parts being pressed by the weight of all the Air above them, are squeezed the closer together; and are therefore densest of all at the Earth’s surface, and gradually rarer the higher up. “It is well known[39] that the Air near the surface of our Earth possesses a space about 1200 times greater than water of the same weight. And therefore, a cylindric column of Air 1200 foot high is of equal weight with a cylinder of water of the same breadth and but one foot high. But a cylinder of Air reaching to the top of the Atmosphere is of equal weight with a cylinder of water about 33 foot high[40] ; and therefore if from the whole cylinder of Air, the lower part of 1200 foot high is taken away, the remaining upper part will be of equal weight with a cylinder of water 32 foot high; wherefore, at the height of 1200 feet or two furlongs, the weight of the incumbent Air is less, and consequently the rarity of the compressed Air is greater than near the Earth’s surface in the ratio of 33 to 32. And having this ratio we may compute the rarity of the Air at all heights whatsoever, supposing the expansion thereof to be reciprocally proportional to its compression; and this proportion has been proved by the experiments of Dr. Hooke and others. The result of the computation I have set down in the annexed Table, in the first column of which you have the height of the Air in miles, whereof 4000 make a semi-diameter of the Earth; in the second the compression of the Air or the incumbent weight; in the third it’s rarity or expansion, supposing gravity to decrease in the duplicate ratio of the distances from the Earth’s center. And the small
- 27. It’s weight how found. PLATE II. numeral figures are here used to shew what number of cyphers must be joined to the numbers expressed by the larger figures, as 0.17 1224 for 0.000000000000000001224, and 2695615 for 26956000000000000000. Air’s Height. Compression. Expansion. 0 33 1 5 17.8515 1.8486 10 9.6717 3.4151 20 2.852 11.571 40 0.2525 136.83 400 0.17 1224 2695615 4000 0.105 4465 73907102 40000 0.192 1628 26263189 400000 0.210 7895 41798207 4000000 0.212 9878 33414209 Infinite. 0.212 6041 54622209 From this Table it appears that the Air in proceeding upwards is rarefied in such manner, that a sphere of that Air which is nearest the Earth but of one inch diameter, if dilated to an equal rarefaction with that of the Air at the height of ten semi-diameters of the Earth, would fill up more space than is contained in the whole Heavens on this side the fixed Stars, according to the preceding computation of their distance[41] .” And it likewise appears that the Moon does not move in a perfectly free and un-resisting medium; although the air at a height equal to her distance, is at least 34000190 times thinner than at the Earth’s surface; and therefore cannot resist her motion so as to be sensible in many ages. 175. The weight of the Air, at the Earth’s surface, is found by experiments made with the air-pump; and also by the quantity of mercury that the Atmosphere balances in
- 28. A common mistake about the weight of the Air. Without an Atmosphere the Heavens would always appear dark, and we should have no twilight. the barometer; in which, at a mean state; the mercury stands 291 ⁄2 inches high. And if the tube were a square inch wide, it would at that height contain 291 ⁄2 cubic inches of mercury, which is just 15 pound weight; and so much weight of air every square inch of the Earth’s surface sustains; and every square foot 144 times as much, because it contains 144 square inches. Now as the Earth’s surface contains about 199,409,400 square miles, it must be of no less than 5,559,215,016,960,000 square feet; which, multiplied by 2016, the number of pounds on every foot, amounts to 11,207,377,474,191,360,000; or 11 trillion 207 thousand 377 billion 474 thousand 191 million and 360 thousand pounds, for the weight of the whole Atmosphere. At this rate, a middle sized man, whose surface may be about 14 square feet, is pressed by 28,224 pound weight of Air all round; for fluids press equally up and down and on all sides. But, because this enormous weight is equal on all sides, and counterbalanced by the spring of the internal Air in our blood vessels, it is not felt. 176. Oftentimes the state of the Air is such that we feel ourselves languid and dull; which is commonly thought to be occasioned by the Air’s being foggy and heavy about us. But that the Air is then too light, is evident from the mercury’s sinking in the barometer, at which time it is generally found that the Air has not sufficient strength to bear up the vapours which compose the Clouds: for, when it is otherwise, the Clouds mount high, the Air is more elastic and weighty about us, by which means it balances the internal spring of the Air within us, braces up our blood-vessels and nerves, and makes us brisk and lively. 177. According to [42] Dr. Keill, and other astronomical writers, it is entirely owing to the Atmosphere that the Heavens appear bright in the day-time. For, without an Atmosphere, only that part of the Heavens would shine in which the Sun was placed: and if an observer could live without Air, and should turn his back
- 29. It brings the Sun in view before he rises, and keeps him in view after he sets. Fig. IX. PLATE II. towards the Sun, the whole Heavens would appear as dark as in the night, and the Stars would be seen as clear as in the nocturnal sky. In this case, we should have no twilight; but a sudden transition from the brightest sunshine to the blackest darkness immediately after sun-set; and from the blackest darkness to the brightest sun-shine at sun-rising; which would be extremely inconvenient, if not blinding, to all mortals. But, by means of the Atmosphere, we enjoy the Sun’s light, reflected from the aerial particles, before he rises and after he sets. For, when the Earth by its rotation has withdrawn the Sun from our sight, the Atmosphere being still higher than we, has his light imparted to it; which gradually decreases until he has got 18 degrees below the Horizon; and then, all that part of the Atmosphere which is above us is dark. From the length of twilight, the Doctor has calculated the height of the Atmosphere (so far as it is dense enough to reflect any light) to be about 44 miles. But it is seldom dense enough at two miles height to bear up the Clouds. 178. The Atmosphere refracts the Sun’s rays so, as to bring him in sight every clear day, before he rises in the Horizon; and to keep him in view for some minutes after he is really set below it. For, at some times of the year, we see the Sun ten minutes longer above the Horizon than he would be if there were no refractions: and about six minutes every day at a mean rate. 179. To illustrate this, let IEK be a part of the Earth’s surface, covered with the Atmosphere HGFC; and let HEO be the[43] sensible Horizon of an observer at E. When the Sun is at A, really below the Horizon, a ray of light AC proceeding from him comes straight to C, where it falls on the surface of the Atmosphere, and there entering a denser medium, it is turned out of its rectilineal course ACdG, and bent down to the observer’s eye at E; who then sees the Sun in the direction of the refracted ray edE, which lies
- 30. Fig. IX. The quantity of refraction. above the Horizon, and being extended out to the Heavens, shews the Sun at B § 171. 180. The higher the Sun rises, the less his rays are refracted, because they fall less obliquely on the surface of the Atmosphere § 172. Thus, when the Sun is in the direction of the line EfL continued, he is so nearly perpendicular to the surface of the Earth at E, that his rays are but very little bent from a rectilineal course. 181. The Sun is about 321 ⁄4 min. of a deg. in breadth, when at his mean distance from the Earth; and the horizontal refraction of his rays is 333 ⁄4 min. which being more than his whole diameter, brings all his Disc in view, when his uppermost edge rises in the Horizon. At ten deg. height the refraction is not quite 5 min. at 20 deg. only 2 min. 26 sec.; at 30 deg. but 1 min. 32 sec.; between which and the Zenith, it is scarce sensible: the quantity throughout, is shewn by the annexed table, calculated by Sir Isaac Newton. 182. A Table shewing the Refractions of the Sun, Moon, and Stars; adapted to their apparent Altitudes. Appar. Alt. Refraction. Ap. Alt. Refraction. Ap. Alt. Refraction. D. M. M. S. D. M. S. D. M. S. 0 0 33 45 21 2 18 56 0 36 0 15 30 24 22 2 11 57 0 35 0 30 27 35 23 2 5 58 0 34 0 45 25 11 24 1 59 59 0 32 1 0 23 7 25 1 54 60 0 31 1 15 21 20 26 1 49 61 0 30 1 30 19 46 27 1 44 62 0 28 1 45 18 22 28 1 40 63 0 27 2 0 17 8 29 1 36 64 0 26 2 30 15 2 30 1 32 65 0 25 3 0 13 20 31 1 28 66 0 24
- 31. PLATE II. The inconstancy of Refractions. A very remarkable case concerning refraction. 3 30 11 57 32 1 25 67 0 23 4 0 10 48 33 1 22 68 0 22 4 30 9 50 34 1 19 69 0 21 5 0 9 2 35 1 16 70 0 20 5 30 8 21 36 1 13 71 0 19 6 0 7 45 37 1 11 72 0 18 6 30 7 14 38 1 8 73 0 17 7 0 6 47 39 1 6 74 0 16 7 30 6 22 40 1 4 75 0 15 8 0 6 0 41 1 2 76 0 14 8 30 5 40 42 1 0 77 0 13 9 0 5 22 43 0 58 78 0 12 9 30 5 6 44 0 56 79 0 11 10 0 4 52 45 0 54 80 0 10 11 0 4 27 46 0 52 81 0 9 12 0 4 5 47 0 50 82 0 8 13 0 3 47 48 0 48 83 0 7 14 0 3 31 49 0 47 84 0 6 15 0 3 17 50 0 45 85 0 5 16 0 3 4 51 0 44 86 0 4 17 0 2 53 52 0 42 87 0 3 18 0 2 43 53 0 40 88 0 2 19 0 2 34 54 0 39 89 1 1 20 0 2 26 55 0 38 90 0 0 183. In all observations, to have the true altitude of the Sun, Moon, or Stars, the refraction must be subtracted from the observed altitude. But the quantity of refraction is not always the same at the same altitude; because heat diminishes the air’s refractive power and density, and cold increases both; and therefore no one table can serve precisely for the same place at all seasons, nor even at all times of the same day; much less for different climates: it having been observed that the
- 32. Our imagination cannot judge rightly of the distance of inaccessible objects. horizontal refractions are near a third part less at the Equator than at Paris, as mentioned by Dr. Smith in the 370th remark on his Optics, where the following account is given of an extraordinary refraction of the sun-beams by cold. “There is a famous observation of this kind made by some Hollanders that wintered in Nova Zembla in the year 1596, who were surprised to find, that after a continual night of three months, the Sun began to rise seventeen days sooner than according to computation, deduced from the Altitude of the Pole observed to be 76°: which cannot otherwise be accounted for, than by an extraordinary quantity of refraction of the Sun’s rays, passing thro’ the cold dense air in that climate. Kepler computes that the Sun was almost five degrees below the Horizon when he first appeared; and consequently the refraction of his rays was about nine times greater than it is with us.” 184. The Sun and Moon appear of an oval figure as FCGD, just after their rising, and before their setting: the reason is, that the refraction being greater in the Horizon than at any distance above it, the lowermost limb G appears more elevated than the uppermost. But although the refraction shortens the vertical Diameter FG, it has no sensible effect on the horizontal Diameter CD, which is all equally elevated. When the refraction is so small as to be imperceptible, the Sun and Moon appear perfectly round, as AEBF. 185. We daily observe, that the objects which appear most distinct are generally those which are nearest to us; and consequently, when we have nothing but our imagination to assist us in estimating of distances, bright objects seem nearer to us than those which are less bright, or than the same objects do when they appear less bright and worse defined, even though their distance in both cases be the same. And as in both cases they are seen under the same angle[44] , our imagination naturally suggests an idea of a greater distance between us and those objects which appear fainter and worse defined than those which appear brighter under the same Angles; especially if they be
- 33. Nor always of those which are accessible. The reason assigned. PLATE II. Fig. XII. such objects as we were never near to, and of whose real Magnitudes we can be no judges by sight. 186. But, it is not only in judging of the different apparent Magnitudes of the same objects, which are better or worse defined by their being more or less bright, that we may be deceived: for we may make a wrong conclusion even when we view them under equal degrees of brightness, and under equal Angles; although they be objects whose bulks we are generally acquainted with, such as houses or trees: for proof of which, the two following instances may suffice. First, When a house is seen over a very broad river by a person standing on low ground, who sees nothing of the river, nor knows of it beforehand; the breadth of the river being hid from him, because the banks seem contiguous, he loses the idea of a distance equal to that breadth; and the house seems small, because he refers it to a less distance than it really is at. But, if he goes to a place from which the river and interjacent ground can be seen, though no farther from the house, he then perceives the house to be at a greater distance than he imagined; and therefore fancies it to be bigger than he did at first; although in both cases it appears under the same Angle, and consequently makes no bigger picture on the retina of his eye in the latter case than it did in the former. Many have been deceived, by taking a red coat of arms, fixed upon the iron gate in Clare-Hall walks at Cambridge, for a brick house at a much greater distance[45] . Secondly, In foggy weather, at first sight, we generally imagine a small house, which is just at hand, to be a great castle at a distance; because it appears so dull and ill defined when seen through the Mist, that we refer it to a much greater distance than it really is at; and therefore, under the same Angle, we judge it to be much bigger. For, the near object FE, seen by the eye ABD, appears under the same Angle GCH, that the remote object GHI does: and the rays GFCN and HECM crossing one
- 34. Fig. IX. Why the Sun and Moon appear biggest in the Horizon. another at C in the pupil of the eye, limit the size of the picture MN on the retina; which is the picture of the object FE, and if FE were taken away, would be the picture of the object GHI, only worse defined; because GHI, being farther off, appears duller and fainter than FE did. But if a Fog, as KL, comes between the eye and the object FE, it appears dull and ill defined like GHI; which causes our imagination to refer FE to the greater distance CH, instead of the small distance CE which it really is at. And consequently, as mis- judging the distance does not in the least diminish the Angle under which the object appears, the small hay-rick FE seems to be as big as GHI. 187. The Sun and Moon appear bigger in the Horizon than at any considerable height above it. These Luminaries, although at great distances from the Earth, appear floating, as it were, on the surface of our Atmosphere HGFfeC, a little way beyond the Clouds; of which, those about F, directly over our heads at E, are nearer us than those about H or e in the Horizon HEe. Therefore, when the Sun or Moon appear in the Horizon at e, they are not only seen in a part of the Sky which is really farther from us than if they were at any considerable Altitude, as about f; but they are also seen through a greater quantity of Air and Vapours at e than at f. Here we have two concurring appearances which deceive our imagination, and cause us to refer the Sun and Moon to a greater distance at their rising or setting about e, than when they are considerably high as at f: first, their seeming to be on a part of the Atmosphere at e, which is really farther than f from a spectator at E; and secondly, their being seen through a grosser medium when at e than when at f; which, by rendering them dimmer, causes us to imagine them to be at a yet greater distance. And as, in both cases, they are seen[46] much under the same Angle, we naturally judge them to be biggest when they seem farthest from us; like the above-mentioned house § 186, seen from a higher ground, which shewed it to be farther off than it
- 35. Their Diameters are not less on the Meridian than in the Horizon. appeared from low ground; or the hay-rick, which appeared at a greater distance by means of an interposing Fog. 188. Any one may satisfy himself that the Moon appears under no greater Angle in the Horizon than on the Meridian, by taking a large sheet of paper, and rolling it up in the form of a Tube, of such a width, that observing the Moon through it when she rises, she may, as it were, just fill the Tube; then tie a thread round it to keep it of that size; and when the Moon comes to the Meridian, and appears much less to the eye, look at her again through the same Tube, and she will fill it just as much, if not more, than she did at her rising. 189. When the full Moon is in perigeo, or at her least distance from the Earth, she is seen under a larger Angle, and must therefore appear bigger than when she is Full at other times: and if that part of the Atmosphere where she rises be more replete with vapours than usual, she appears so much the dimmer; and therefore we fancy her to be still the bigger, by referring her to an unusually great distance; knowing that no objects which are very far distant can appear big unless they be really so. Plate IIII.
- 36. J. Ferguson delin. J. Mynde Sculp.
- 37. PLATE IV. Fig I. The Moon’s horizontal Parallax, what. The Moon’s distance determined. CHAP. IX. The Method of finding the Distances of the Sun, Moon, and Planets. 190. Those who have not learnt how to take the [47] Altitude of any Celestial Phenomenon by a common Quadrant, nor know any thing of Plain Trigonometry, may pass over the first Article of this short Chapter, and take the Astronomer’s word for it, that the distances of the Sun and Planets are as stated in the first Chapter of this Book. But, to every one who knows how to take the Altitude of the Sun, the Moon, or a Star, and can solve a plain right-angled Triangle, the following method of finding the distances of the Sun and Moon will be easily understood. Let BAG be one half of the Earth, AC it’s semi-diameter, S the Sun, m the Moon, and EKOL a quarter of the Circle described by the Moon in revolving from the Meridian to the Meridian again. Let CRS be the rational Horizon of an observer at A, extended to the Sun in the Heavens, and HAO his sensible Horizon; extended to the Moon’s Orbit. ALC is the Angle under which the Earth’s semi-diameter AC is seen from the Moon at L, which is equal to the Angle OAL, because the right lines AO and CL which include both these Angles are parallel. ASC is the Angle under which the Earth’s semi-diameter AC is seen from the Sun at S, and is equal to the Angle OAf because the lines AO and CRS are parallel. Now, it is found by observation, that the Angle OAL is much greater than the Angle OAf; but OAL is equal to ALC, and OAf is equal to ASC. Now, as ASC is much less than ALC, it proves that the Earth’s semi-diameter AC appears much greater as seen from the Moon at L than from the Sun at S: and therefore the Earth is much farther from the Sun than from the Moon[48] . The Quantities of these Angles are determined by observation in the following manner. Let a graduated instrument as DAE, (the larger the better) having a moveable Index and Sight-holes, be fixed in such a manner, that it’s plane surface may be parallel to the Plan of the Equator, and it’s edge AD in the Meridian: so that when the Moon is in the Equinoctial, and on the Meridian at E, she may be seen through the sight-holes when the edge of the moveable index cuts the beginning of the divisions at o, on the graduated limb DE; and when she is so seen, let the precise time be noted.
- 38. The Sun’s distance cannot be yet so exactly determined as the Moon’s; How near the truth it may soon be determined. Now, as the Moon revolves about the Earth from the Meridian to the Meridian again in 24 hours 48 minutes, she will go a fourth part round it in a fourth part of that time, viz. in 6 hours 12 minutes, as seen from C, that is, from the Earth’s center or Pole. But as seen from A, the observer’s place on the Earth’s surface, the Moon will seem to have gone a quarter round the Earth when she comes to the sensible Horizon at O; for the Index through the sights of which she is then viewed will be at d, 90 degrees from D, where it was when she was seen at E. Now, let the exact moment when the Moon is seen at O (which will be when she is in or near the sensible Horizon) be carefully noted[49] , that it may be known in what time she has gone from E to O; which time subtracted from 6 hours 12 minutes (the time of her going from E to L) leaves the time of her going from O to L, and affords an easy method for finding the Angle OAL (called the Moon’s horizontal Parallax, which is equal to the Angle ALC) by the following Analogy: As the time of the Moon’s describing the arc EO is to 90 degrees, so is 6 hours 12 minutes to the degrees of the Arc DdE, which measures the Angle EAL; from which subtract 90 degrees, and there remains the Angle OAL, equal to the Angle ALC, under which the Earth’s Semi-diameter AC is seen from the Moon. Now, since all the Angles of a right-lined Triangle are equal to 180 degrees, or to two right Angles, and the sides of a Triangle are always proportional to the Sines of the opposite Angles, say, by the Rule of Three, as the Sine of the Angle ALC at the Moon L is to it’s opposite side AC the Earth’s Semi-diameter, which is known to be 3985 miles, so is Radius, viz. the Sine of 90 degrees, or of the right Angle ACL to it’s opposite side AL, which is the Moon’s distance at L from the observer’s place at A on the Earth’s surface; or, so is the Sine of the Angle CAL to its opposite side CL, which is the Moon’s distance from the Earth’s centre, and comes out at a mean rate to be 240,000 miles. The Angle CAL is equal to what OAL wants of 90 degrees. 191. The Sun’s distance from the Earth is found the same way, but with much greater difficulty; because his horizontal Parallax, or the Angle OAS equal to the Angle ASC, is so small as, to be hardly perceptible, being only 10 seconds of a minute, or the 360th part of a degree. But the Moon’s horizontal Parallax, or Angle OAL equal to the Angle ALC, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at it’s mean state; which is more than 340 times as great as the Sun’s: and therefore, the distances of the heavenly bodies being inversely as the Tangents of their horizontal Parallaxes, the Sun’s distance from the Earth is at least 340 times as great as the Moon’s; and is rather understated at 81 millions of miles, when the Moon’s distance is certainly known to be 240 thousand. But because, according to some Astronomers, the Sun’s horizontal Parallax is 11 seconds, and according to others only 10, the former Parallax making the Sun’s distance to be about 75,000,000 of miles, and the latter 82,000,000; we may take it for granted, that the Sun’s distance is not less than as deduced from the former, nor more than as shewn by the latter: and every one who is accustomed to make such
- 39. The Sun proved to be much bigger than the Moon. The relative distances of the Planets from the Sun are known to great precision, though their real distances are not well known. observations, knows how hard it is, if not impossible, to avoid an error of a second; especially on account of the inconstancy of horizontal Refractions. And here, the error of one second, in so small an Angle, will make an error of 7 millions of miles in so great a distance as that of the Sun’s; and much more in the distances of the superiour Planets. But Dr. Halley has shewn us how the Sun’s distance from the Earth, and consequently the distances of all the Planets from the Sun, may be known to within a 500th part of the whole, by a Transit of Venus over the Sun’s Disc, which will happen on the 6th of June, in the year 1761; till which time we must content ourselves with allowing the Sun’s distance to be about 81 millions of miles, as commonly stated by Astronomers. 192. The Sun and Moon appear much about the same bulk: And every one who understands Geometry knows how their true bulks may be deduced from the apparent, when their real distances are known. Spheres are to one another as the Cubes of their Diameters; whence, if the Sun be 81 millions of miles from the Earth, to appear as big as the Moon, whose distance does not exceed 240 thousand miles, he must, in solid bulk, be 42 millions 875 thousand times as big as the Moon. 193. The horizontal Parallaxes are best observed at the Equator; 1. Because the heat is so nearly equal every day, that the Refractions are almost constantly the same. 2. Because the parallactic Angle is greater there as at A (the distance from thence to the Earth’s Axis being greater,) than upon any parallel of Latitude, as a or b. 194. The Earth’s distance from the Sun being determined, the distances of all the other Planets from him are easily found by the following analogy, their periods round him being ascertained by observation. As the square of the Earth’s period round the Sun is to the cube of it’s distance from him, so is the square of the period of any other Planet to the cube of it’s distance, in such parts or measures as the Earth’s distance was taken; see § 111. This proportion gives us the relative mean distances of the Planets from the Sun to the greatest degree of exactness; and they are as follows, having been deduced from their periodical times, according to the law just mentioned, which was discovered by Kepler and demonstrated by Sir Isaac Newton. Periodical Revolution to the same fixed Star in days and decimal parts of a day. Of Mercury Venus The Earth Mars Jupiter Saturn 87.9692 224.6176 365.2564 686.9785 4332.514 10759.275
- 40. Why the celestial Poles seem to keep still in the same points of the Heavens, notwithstanding the Earth’s motion round the Sun. Relative mean distances from the Sun. 38710 72333 100000 152369 520096 954006 From these numbers we deduce, that if the Sun’s horizontal Parallax be 10ʺ, the real mean distances of the Planets from the Sun in English miles are 31,742,200 59,313,060 82,000,000 124,942,580 426,478,720 782,284,920 But if the Sun’s Parallax be 11ʺ their distances are no more than 29,032,500 54,238,570 75,000,000 114,276,750 390,034,500 715,504,500 Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax 2,709,700 5,074,490 7,000,000 10,665,830 36,444,220 66,780,420 195. These last numbers shew, that although we have the relative distances of the Planets from the Sun to the greatest nicety, yet the best observers have not hitherto been able to ascertain their true distances to within less than a twelfth part of what they really are. And therefore, we must wait with patience till the 6th of June, A. D. 1761; wishing that the Sky may then be clear to all places where there are good Astronomers and accurate instruments for observing the Transit of Venus over the Sun’s Disc at that time: as it will not happen again, so as to be visible in Europe, in less than 235 years after. 196. The Earth’s Axis produced to the Stars, being carried [50] parallel to itself during the Earth’s annual revolution, describes a circle in the Sphere of the fixed Stars equal to the Orbit of the Earth. But this Orbit, though very large in itself, if viewed from the Stars, would appear no bigger than a point; and consequently, the circle described in the Sphere of the Stars by the Axis of the Earth produced, if viewed from the Earth, must appear but as a point; that is, it’s diameter appears too little to be measured by observation: for Dr. Bradley has assured us, that if it had amounted to a single second, or two at most, he should have perceived it in the great number of observations he has made, especially upon γ Dragonis; and that it seemed to him very probable that the annual Parallax of this Star is not so great as a single second: and consequently, that it is above 400 thousand times farther from us than the Sun. Hence the celestial poles seem to continue in the same points of the Heavens throughout the year; which by no
- 41. Welcome to our website – the ideal destination for book lovers and knowledge seekers. With a mission to inspire endlessly, we offer a vast collection of books, ranging from classic literary works to specialized publications, self-development books, and children's literature. Each book is a new journey of discovery, expanding knowledge and enriching the soul of the reade Our website is not just a platform for buying books, but a bridge connecting readers to the timeless values of culture and wisdom. With an elegant, user-friendly interface and an intelligent search system, we are committed to providing a quick and convenient shopping experience. Additionally, our special promotions and home delivery services ensure that you save time and fully enjoy the joy of reading. Let us accompany you on the journey of exploring knowledge and personal growth! ebookultra.com