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SIR ISAAC NEWTON'S PRINCIPLES,
ADE EASY TO THOSE WHO HAVE NOT STUDIED MATHEMATICS.
TO WHICH ARE ADDED,
A PLAIN METHOD OF FINDING THE DISTANCES
OF ALL THE PLANETS FROM THE SUN,
TRANSIT OF VENUS OVER THE SUN'S DISC,
In the year 1761 :
AN ACCOUNT OF MR. HORROX's OBSERVATION
OF THE TRANSIT OF VENUS,
In the year 1639:
AND OF THE
DISTANCES OF ALL THE PLANETS FROM THE SUN*,
AS DEDUCED FROM OBSERVATIONS OF THE TRANSIT
In the year 1761,
BY JAMES FERGUSON, F. R. S.
Heb. xi. 3. The worlds were framed by the Word of God.
Job xxvi. 7. He liangeth the earth upon nothing.
13. By his Spirit he hath garnished the heavens.
THE SECOND AMERICAN, FROM THE LAST LONDON EDITION
REVISED, CORRECTED, AND IMPROVED,
BY ROBERT PATTERSON,
Professor of Mathematics, in the University of Pennsylvania.
PRINTED FOR AND PUBLISHED BY MATHEW CAREY,
1 7 OR SALE BY C. &. A. CONRAD &. CO. BRADFORD &. INSKEEP, HOPKINS
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Be it remembered. That on the thirteenth day of February, in the thirtieth
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thew Carey, of the said District, hith deposited in this office, the title of a book,
the right whereof he claims as Proprietor, in the words following, to wit :
u Astronomy explained upon Sir Isaac Newton's Principles, and made easy
to those who have not studied Mathematics. To which are added, a plain
method of finding the distances of all the planets from the sun, by the transit
of Ven'is over the sun's disc, in the year 1761 : an account of Mr. Horrox's
observation of the transit of Venus, in the year 1639 : and of the distances of
all the planets from the sun, as deduced from observations of the transit in
year 1761. By James Ferguson, F. R. S.
Heb. xi. 8. The worlds were framed by the Word of God.
Job xxvi. 7. H; hangf-th the earth upon nothing.
13, By his Spirit he hath garnished the heavens.
The first American edition, from the last London edition; revised, cor-
rected, and improved, by Robert Patterson, Professor of Mathematics, and
Teacher of Natural Philosophy, in the University of Pennsylvania."
In conformity to the Act of the Congress of the Ur-ited States, intituled,
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TO THE FIR3T AMERICAN EDITION.
THE well-established reputation of Fergusotfs As-
tronomy, renders any particular encomiums on the work,
at this time, altogether unnecessary.
The numerous editions through which this Treatise has
passed, and the increasing demand for it f "bear ample testi-
mony to its merit.
The Publisher submits to the candid acceptance of his
fellow-citizens, this correct American Edition; for which
he solicits, and flatters himself he shall obtain, their liberal
No cost or pains have been spared to render it worthy
of this patronage. In the text, a number of typographi-
cal errors, and grammatical inaccuracies, have been cor-
rected ; and a variety of notes, explanatory or corrective
of the text, which the numerous discoveries since our au-
thor's time had rendered necessary, have been occasionally
Besides, to this edition alone there is prefixed a copious
explanation of all the principal terms in astronomy, chro-
nology, and astronomical geography, occurring in the
work, arranged in alphabetical order; with such remarks
and examples interspersed, as were judged necessary for
illustration : together with Tables of the periodical times,
distances, magnitudes, and other elements, of all the plan-
ets, both primary and secondary, in the solar system ; ac-
cording to the latest observations.
This, it is presumed, cannot fail to be considered as a
valuable appendage to the work especially by the young
student of astronomy : as the glossary will tend greatly to
facilitate his progress, and the tables will present him with
a comprehensive view of the whole science the result of
the observations and researches both of past and present
Philadelphia, Feb. Utk, 1806.
Explanation of the principal Terms relating to As-
tronomy, Chronology \ and the astronomical
parts of Geography ; with occasional
Illustrations and Remarks.
Aberration of a star, is a small apparent motion, occasioned
by a sensible proportior between the velocity of light and
that of the earth in its annual orbit. From this cause,
every star will, in the course of a year, appear to describe
a small ellipsis in the heavens, whose greater axis = 40"
and its iesser axis, perpendicular to the ecliptic, = 40"
X cos. 01 star's -at. (co radius 1.) In astronomical calcu-
lations, v-'iei-fj f reat accuracy is required, and the place of
a st-ir concerned, a correction on account of aberration,
as \veil as oii ether accounts, ou^ht to be applied to the
star's place c<s found in the tables. This correction may
r. Lij ! >c iG'.in.' by the following theorems ; in which A
the star's riyht ascension, D = its declination, and S = the
.fen; i. ( .1.272 cos. (A S)) 4- r.os. D -f (0.055,
cos, (A + '">)) T- cos. D = aberr. in R. A. in seconds of
Theorem 2. 20 cos. A. sin. S. sin. D -f 18.346 sin.
A. cos. S. s'.n D 7.964 cos. S. cos. D aberr. in dec. in
seconds of u decree : observing that the sine, cosine, See.
of uli arches between 90 and 270 are to be considered as
negative i j.nd those of ail other arches as affirmative.
a the stc.r has south declination, let the sign of the
last term in the 2d theorem be changed.
dc'-'-i'-itiii'm (dkiinui) of a fixed star, is the difference be-
:C aiciuvcal and the mean solar day, which = 3'
6j".'j or c' DO" of mean time nearly ; and so much sooner
vi;i ony fixed star nse, culminate, or set, every day, than
on the pivocdin s clay A piaiict is said to be accelerated
in iis niO'ion, when its veiocitys in any part of its orbit, ex-.
ceeds its mean velocity; and this wiii always be the case
when its distance from the Sun is less than its mean dis-
( 8 )
, or e/ioch, any noted point of time, in chronology, from
which events are reckoned, or computations made. Dif-
ferent nations or people make use of different epochs :
as the Jews, that of the creation of the worjd ; the crris-
tian nations, that of the nativity of Christ, A. M. 4UC7 ;
the Mahometans, that of the Hegira, or flight of Maho-
met from Mecca, A. D. 622; the ircient Greeks, that of
the Olympiads, commencing B. C. 775 : the Romans, that
of the building of Rome, B. C. 752; the ancient Per-
sians and Assyrians, that of Nabonasser, &:c.
Altitude of a celestial body, is its elevation above the horizon,
measured on the arch of an. azimuth-circle intercepted be-
tween the body and the horizon. The apparent altitude,
or that measured by an instrument, re uires to be cor-
rected in order to obtain the true altitude 1. by subtract-
ing the refraction; 2. by adding the parallax; 3. by sub-
tracting the dip corresponding to the height of the ob-
server's eye above the surface of the earth ; and 4. when
the lower or upper limb of the sun or moon is observed,
by adding or subtracting the apparent semidiameter.
Altitude, meridian, is that of a body when on the meridian.
Amplitude of a celestial body, is an arch of the horizon inter-
cepted between the east or west points thereof, and that
point where the body rises or sets. The true amplitude
of a body may be found by the following proportion :
Racl : cos. lat. : : sin. dec. : sin. amp. which will be of
the same name (north or south) with the declination.
The difference between the true, and the magnetic am-
plitude of a body, or that observed by a compass furnished
with a magnetic needle, will be the -variation of the com-
Angle is the inclination of two converging lines meeting in
a point, called the angular point. A plane angle is that
-drawn on a plane surface. The measure of a plane angle
is the arch of a circle comprehended between the lines in-
cluding the angle, the angular point being the centre. A
spheric 'angle is that formed by the intersection of two
great circles on the surface of a sphere. The measure of
a spheric angle is the arch of a great circle comprehend-
ed between the two arches including the angle, the angu-
lar point being its pole. A right angle is one whose mea-
sure is an arch of 90. An acute angle is one less than
90. An obtuse angle, one greater than 90.
Anomaly is the angular distance of a planet from its aphelion.
It is distinguished into true,ex centric, and mean. True ano-
nialy of a planet, is the angle at the sun or focus of the
elliptical orbit; formed by the line of apses and radius vec-
( 9 )
lor. Excentric anomaly, is the angle at the centre of the
elliptical orbit, formed by the line of apses and a line drawn
to the point in which an ordinate passing through the
planet's true place in its orbit, meets the circumference
of a circle, described on the line of apses as a diameter.
Mean anomaly, is a sector of the elliptical orbit over
which the radius vector has passed, from the aphelion to
the place of the planet in its orbit ; and is proportional to
the time of description.
Antarctic circle. See Arctic circle.
Antipodes, those who inhabit parts of the earth diametrically
opposite to each other.
Anticipation of the equinoxes or seasons, the excess of the
civil Julian year of 365d. 6h. above the solar tropical
year of 365 days 5 hours 48 minutes 48 seconds. This
constitutes the difference between the Julian and Grego-
rian calendars, or old and new styles.
Aphelion, is that point of a planet's orbit which is at the
greatest distance from the sun.
The places of the aphelia of the several planets are all
different, and have each a small progressive motion, oc-
casioned by the mutual attractions of the planets on each
Apogee,\s that point of the moon's orbit which is at the great-
est distance from the earth. This term is also frequently
applied to the sun, to signify that point in which he is at
the greatest distance from the earth.
Apses or apsides, are the extremities of the greater axis of
the planets' elliptical orbits : the axis itself being called
the line oj" the apses.
Arctic circle, is a small circle parallel to the equator, and at
the same distance from the north pole that the tropics are
from the equator. A circle similarly situate round the
south pole, is called the antarctic circle. These are also
frequently termed the north-polar, and south-polar circles^
Ascension of a celestial body, is an arch of the equator,
reckoned from west to east, and intercepted between the
equinoctial point Aries, and that point which rises with
the body. This is distinguished into right, and oblique
ascension, according to the angle in which the equator
cuts the horizon.
"Aspect, is a term applied to signify the situation or apparent
distance, in longitude, of any two celestial bodies in the
zodiac, from one another, and is particularly denominated,
and designated by appropriate characters, according to
this distance as conjunction & , sextile >K, quartile n?
trine A, opposition , and some others, -which s,ce.
Asteroids, star-like bodies, a term of recent invention, and
applied to three small bodies lately discovered in the so-
lar system, between the orbits of Mars and Jupiter. Their
orbits are considerably more excentric than that of any of
the other planets ; though their elements are still but im-
perfectly ascertained. See note subjoined to the Table
of the solar system, page 73.
Astronomy, is that science which explains and demonstrates
the phenomena of the heavens.
Atmosphere, usually termed the air, is that transparent elas-
tic fluid which surrounds the earth. It is indispensably
necessary to animal and vegetable life, combustion, and
many other functions in nature. The atmosphere being a
perfectly elastic, compressible, and ponderous fluid, its
density must decrease upwards, in a geometrical ratio, of
the heights taken in arithmetical ratio. The whole weight
of any column of the atmosphere, on the surface of the
earth, is found, by experiment, to equal, in a mean state,
that of a column of mercury of an equal base and about
30 inches high ; that is, about 15 pounds avoir, on every
superficial inch. The planets, if not the sun and fixed
stars, are all probably furnished with similar atmospheres.
Attraction, is that power, either continually exerted by the
Deity, according to a fixed law, or by him communicated
to matter ; by which all bodies, or particles of bodies,
whether in contact, or at a distance, adhere, or tend to-
wards each other. Attraction, according to the manner
or circumstances of its operation, is commonly distin-
guished into that of gravity, that of cohesion, that of elec-
Axis of a planet, is that imaginary line passing through its
centre, round which it performs its diurnal rotation.
Azimuth of a celestial body, is an arch of the horizon inter-
cepted between the meridian of the place and the azimuth-
circle passing through the body. The true azimuth of a
body may readily be calculated by the resolution of a sphe-
ric triangle ; and then the difference between this, and
that observed by a compass furnished with a magnetic
needle, will be the -variation of the compass.
Azimuth-circles, are those great circles of the sphere which
pass through the zenith and nadir, and consequently cross
the horizon at right angles,
Barometer, is an instrument for measuring the weight of a
superincumbent column of the atmosphere, at any given
time and place. It is commonly made of a long glass
tube, of a moderate bore, open at one end ; which being
iilled with well-purified mercury is inverted, with the
o'pen end downwards, into a bason, of the same fluid. The
mercury in the tube will then subside, leaving a vacuum,
in the upper part of the tube ; and the height of the co-
lumn of mercury in the tube, thus sustained by the pres-
sure of the atmosphere on the surface of the mercury in
the bason, will be a just measure of its weight.
It is found by experiment that the height of the column
of mercury is not always the same in the same place, but
varies generally between 28 and 31 inches, on the surface
of the earth. The barometer has been applied with suc-
cess to the measuring of accessible altitudes. For this
purpose let the height of the mercury in a barometer,
both at the bottom and top of the eminence or depth to
be measured, be observed as nearly as may be at the same
time. Also observe the temperature of the air by ther-
mometers both attached to the barometers, and at a dis-
tance from them, in the shade. Then let the column of
mercury in the colder barometer be increased byits9600th
part for every degree of difference in the two attached ther-
mometers (Fahr. scale). Subtract the common logarithm
of the less column of mercury from that of the greater, and
the difference multiplied by 10000 will be the alt. nearly,
in fathoms. For a correction apply, by addition or sub-
traction, one 435th part of the above alt. for every degree
of the mean temperature of the two detached thermo-
meters above or below 3 1 degrees, and the result will be
the true alt.
Bissextile, a year consisting of 366 days, by adding a day
to the month of February every 4th year. This day was
by Julius Csesar appointed to be the 24th of March
(called by the Romans the 6th of the calends) which being
reckoned twice, the year was on this account termed bis-
sextile. This year is, on another account, called leap-
Calendar, is a table, almanac, or distribution of time, suited
to the several uses of society.
Various calendars have been adopted by different na-
tions in different ages of the world. The Roman calen-
dar, as corrected and established by Julius Caesar, and
thence called the Julian calendar, made the year to con-
sist of 365^ days ; viz. three years each containing 365, and
the 4th 366. But as the solar year actually falls short ot
the Julian by about 11 minutes, Pope Gregory XIII, in
1582, reformed this calendar, by striking out the surplus
days that thefseasons had then got a-head of the calendar ;
(viz. 10 days) and ordering that, in future, 3 days should
be stricken out of every 400 years of the Julian account,
by calling every centurial year not devisible by 4 (as 1700 ?
( 12 )
1 800, 1900, 2100, &c.) a common year, instead of a leap-
year. The year is divided into 12 calendar months, viz.
7 of 31 days, 4 of 30, and 1 of 28 or 29.
Central forces, are those by the influence of which the plan-
ets and comets perform revolutions round their centres of
motion, and are retained in their orbits. Those forces
are of two kinds, viz. the centrifugal, and the centripetal.
Centrifugal or projectile force, may be considered as a sin-
gle impulse, given by the Creator, and which, agreeably
to the laws of motion, would carry the body with a uni-
form velocity, in a rectilineal direction.
Centripetal force, or force of gravity, may be considered as
a continually-operating influence, urging the body down
towards the centre of motion : and according to the pro-
portion between these two forces the body will describe
a circular, or an elliptical orbit.
Chronology, is that science which treats of time, compre-
hending its remarkable aeras or epochs, divisions, subdi-
visions, and measures.
Circle, is a plane figure bounded by a uniformly-curved line
called the circumference, every part of which is equally
distant from a certain point within the same, called the
centre. Diameter is a right line passing through the cen-
tre, and terminated on each side by the circumference.
Radius, or semidiameter, is the distance from the centre
to the circumference.
Circles of the sphere are of two kinds great, and small.
Great circles, are those which divide the sphere into two
equal parts; the chief of which are, the equator, the eclip-
tic, meridians, horizon, azimuth-circles, and circles of
celestial longitude. Small circles, are those which divide
the sphere into two unequal parts ; the chief of which are,
parallels of altitude and of depression, parallels of terres-
trial, and parallels of celestial latitude.
Circles of celestial longitude, are those great circles of the
sphere which cross the ecliptic at right angles.
Circum-polar stars, are those which appear to perform daily
circuits round' the pole, without rising or setting; and such
are all those whose polar distance does not exceed the la-
titude of the place.
Colures, are those two meridians which pass through the
equinoctial and solstitial points of the ecliptic, and are
hence distinguished into the equinoctial and solstitial co-
Comets, are certain bodies in the solar system, moving in
very excentric orbits, in various planes and directions},
and visible but for a short time when near their perihe-
lia ; and then generally appearing with a lucid tail or train
( 13 )
of light, on the side of the comet opposite to the suib
Frequently, however, comets are seen without this lucid
train ; the body or nucleus being surrounded with a beard-
ed or hairy-like atmosphere. The whole list of comets
that have been hitherto observed amounts to upwards of
500 ; of which about 170 have been observed with accu-
racy, and the elements of their orbits computed.
Conjunction, is that aspect in which two celestial bodies, in
the zodiac, have the same longitude.
Constellation-, this term is applied to any assemblage or
number of neighbouring stars in the heavens, which as-
tronomers have classed together under one general name.
They are generally designated by the names and figures
of some living creatures, and thus delineated on the ce-
lestial globe or atlas. The number of constellations, ac-
cording to the ancients, was 48, viz. 12 near the ecliptic,
called the 12 signs of the zodiac, 21 on the north side of
the zodiac, and 15 on the south side. Modern astrono-
mers, by forming new constellations out of such stars as.
were not included in the above, have increased the num-
ber to about 70 The several stars in each constellation
are distinguished either by letters of the alphabet, or by-
numbers : and some few by proper names ; as, Aldebaran,
Castor, Pollux, Sec.
Crepusculum or twilight-circle, is a circle of depression, 1 8
degrees below the horizon ; for, it is found by observation
that when the sun crosses this circle, before rising, or af-
ter setting, twilight begins or ends. This is occasioned
by the rays of light from the sun being refracted and re-
flected by the earth's atmosphere.
Culmination .of a star, is the point of its greatest elevation
above the horizon, or where it crosses the meridian.
Cusfis, the horns of the moon, or any other planet, when less
than half its illuminated part is visible.
Cycle-, is any certain period of time in which the same cir-
cumstances, to which the cycle has a reference, regularly
return. The most noted chronological cycles are
1. The cycle of the suti, a period of 28 years, after which
the same day of the month will happen on the same day
of the week, as in the same year of a former cycle.
2. The Metonic or lunar cycle, a period of 19 years,
after which the change, full, and other phases of the moon,
will happen on the same days of the month, as in the