(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "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 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"

I 



I 



I 






> I 



















i 



LIBRARY 

OF THE 

UNIVERSITY OF CALIFORNIA, 






GIFT OF 



Ctos 



Presented by 








fattftt tljeo%ttal ientinatu, 



CON 1 COMPANV, PRINTERS. 






^t 
f 




A VALUABLE BOOK, 

For Academics and Colleges. 

FOR SALE AT 

MATHEW CAREY'S STORE, 

NO. 122, MARKET STREET, 
(PRICE 3 DOLLARS.) 

ROMAN A:\TIQUITIES; 

OR, 

AN ACCOUNT OF THE MANNERS 

AND 

CUSTOMS OF THE ROMANS, 

Respecting their 



Government, ' 

Magistracy, 

Laws, 

jfrtdicial proceedings, 



Religion, 

Games, 

Military and Naval affairs, 

Dress, 

Exercises, 

Baths, 

Marriages, 

BY ALEXANDER ADAMS, L. L. D. 



Divorces, 

Funerals, 

Weights and Measures, 

Coins, 

Method of Writing, 

Houses, 

Gardens, 

Agriculture, 



Carriages, 



Buildings, &c. 



(PRICE 6 DOLLARS,) 

FERGUSON'S LSCTURES 

ON 

SELECT SUBJECTS, 



IN 



Optics, 

Geography, 
Astronomy, 
Dialling. 



Mechanics, 
Hydrostatics, 
Hydraulics, 
Pneumatics, 

A NEW EDITION, 

CORRECTED AND ENLARGED, 

With Notes and ah Appendix, 

ADAPTED TO THE PRESENT STATE OF THE ARTS 
AND SCIENCES. 

BY DAVID BREWSTOR, A. M. 

IN TWO VOLUMES, WITH A 4to VOLUME OF PLATES. 

This American Edition carefully revised and corrected by ROBERT 
PATTERSON, Professor of Mathematics, University of Pennsylvania. 

A 



FOR SALE BY M. CAREY, 

(PRICE 5 DOLLARS,) 

SYST-EM OF 

THEORETICAL AND PRACTICAL 

CHEMISTRY, 

IN TWO VOLUMES WITH PLATES. 

BY FREDERICK ACCUM. 

(PRICE 8 DOLLARS,) 

FEMALE BIOGRAPHY; 

t>r Memoirs of Illustrious and Celebrated Women of all Ages and Countries, Alphabeti- 
cally arranged, in 3 vols. 



The History of the early part of the reign of James the II. with an introductory chap- 
ter, by the Right Hon. Charles James Fo.\.~ Price 3 dots. 



THE 

FAMILY EXPOSITOR; 

Or a Paraphrase and Version of the New Testament, with critical notes, and a practical 
improvement of each section. In 6 volumes. Volume first containing the former part 
of the history of our Lord Jesus Christ, as recorded by the four Evangelists. Disposed 
in the order of an harmony, by P. Doddridge, D. D. To which is prefixed, a Life of 
the author, by Andrew Kippis, D. D. F. H. S. and S. A. Price 16 dols. and 50 cts. 



THE 

WONDERFUL MAGAZINE, 

EXTRAORDINARY MUSEUM: 



,r; a complete repository of the wonders, curiosities and rarities of Nature and Art. 
(Price 2 dollars.) 



The Works of Saint Pierre, 

"With the additions of numerous Original notes and Illustration^. 

BY BENJ. S. BARTON, M. D. 

IN 3 VOLUMES. 

(Price 9 dollars.) 



ASTRONOMY 

EXPLAINED UPON 

SIR ISAAC NEWTON'S PRINCIPLES, 

AND 

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, 

BY THE 

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: 

~j 

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. 



PHILADELPHIA: 

PRINTED FOR AND PUBLISHED BY MATHEW CAREY, 

1 7 OR SALE BY C. &. A. CONRAD &. CO. BRADFORD &. INSKEEP, HOPKINS 
CARLE, JOHNSON & WARNER, AN.D KIMEER, CONUAB & CO. 

/* 



UNIVERSITY 



District of Pennsylvania, to wit : 

Be it remembered. That on the thirteenth day of February, in the thirtieth 
year of the Independence of the United Srates of America, A, D- 1806, Ma- 
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, 
" An Act fir the Encouragement of Learning, by securing the Copies of 
Maps, Charts, and Books, to the Authors, and Proprietors of such Copies, 
during the Times therein mentioned," And also to the Act, entitled " An Act 
supplementary to an Act, entitled, ' An Act for the Encouragement of Learn- 
ing, by securing the Copies of Maps, Charts, and Books, to the Authors 
and Proprietors of such Copies, during the Times therein mentioned,' and 
extending the Benefits thereof to the Art of designing, engraving, and etch- 
ing, historical and other Prints." 

(L. S.) D. CALDWELL, 

Clerk of the District of Pennsylvania 



F1 
/609 



PREFACE 

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 
patronage. 

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 
subjoined. 

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 

1 ! 



IV 

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 
times. 

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 
Sir, ,de. 

.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 
time. 

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- 
tance. 



( 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- 
pass. 

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 
other. 

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^ 
respectively. 

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. 

B 



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- 
tricity, &c. 

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 



11 ) 

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- 
year. 

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- 
lures. 

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 
same year of a former cycle. 

3. The cycle of Indiction, a period of 15 years, instituted 
by Constantine A. D. 312, probably as a stated period of 



( 14 ) 

levying a certain tax, and afterwards used as a civil epoch 
among the Romans. 

Note, the 1st year of the Christian aerawas the 1st af- 
ter leap-year, the 9th of the solar cycle, the 1st of the 
lunar cycle, and the 312th of the Christian aera, was the 
1st of the Roman Indiction. Hence rules may be easily 
deduced for computing what year of any of these cycles, 
corresponds to any given year of the Christian sera. 
Day, a portion of time measured by the apparent revolution 
of the sun, moon, or stars, round the earth. The day is 
variously distinguished and denominated, according to 
circumstances, as follows : 

1 . An artificial day, is the interval of time between sun- 
rising and sun-setting ; and thus contradistinguished from 
night which is the interval between sun-setting and sun- 
rising. 

2. A natural day, includes both the artificial day and 
the night. 

3. An afifiarent solar day, is the time in which the sun 
appears to make one complete revolution round the earth. 
These days, owing to sundry causes, (see equation of time} 
are not all of the same length, but continually varying. 

4. A mean solar day, is an exact mean of all the appa- 
rent solar days in the year Or it is that measured by a 
well-regulated time-piece. 

5. A Lunar day, is the time in which the moon appears 
to make one complete revolution round the earth ; and 
exceeds a solar day about f of an hour. 

6. A sidereal day, is the time in which any fixed star 
appears to make a complete revolution? and is 3m. 5 5". 9 
less than a raean solar day. 

The day, in civil reckoning, begins among different na- 
tions at different times. 

1. Among most of the ancient eastern nations, and 
some of the modern, it begins at sun-rising. 

2. Among the ancient Athenians and Jews, the eastern 
parts of Europe, and the modern Italians and Chinese, ft 
begins at sun-setting. 

3. With the ancient Arabians, and still with astrono- 
mers, it begins at noon. 

4. Among the ancient Egyptians and Romans, the 
Americans, and the greater part of Europeans, it begins 
at midnight. 

Declination of a celestial body, is an arch of the meridian 
passing through the body, and intercepted between it and 
the equator ; and is north or south according as the body 
is north or south of the equator. 



( 15 ) 

Degree, the 360th part of the circumference of any circle. Or 

the 90th part of a right angle. 

Dial, or sun-dial, is a delineation of the meridians of the 
sphere, on a plane, in such a manner that the shadow of 
a gnomon or stile, placed with its edge parallel to the 
Earth's axis, may point out the hour of the day. Dials 
are particularly denominated from the planes on which 
they are drawn ; as horizontal, equatorial, &c. 
Digit, the 1 2th part of the apparent diameter of the sun or 
moon. The quantity of an eclipse is generally estimated 
by the digits of the luminary's diameter eclipsed. 
Dip., the depression of the visible, below the true horizon, 
which will be more or less according to the height of the 
eye. The dip corresponding to any given height of the 
eye may be very readily, and very accurately, found by 
the following theorem. 

d = tfh Q yh + l"; in which h = height of eye 
in feet, and d the dip in minutes and parts, of a degree: 
thus for 16 feet the dip, per rulerr=4' .2' -f 1"= 3' 49". 
Direct motion of a planet, in its orbit, is that by which it 
appears to the observer to move according to the order 
of the signs. To a spectator in theu sun, the planetary 
motions would always appear direct'. To a spectator in 
the earth, the motions of Mercury and Venus will appeal- 
direct when they are in the superior or opposite parts of 
their orbits ; and the motions of the other planets will 
appear direct when the earth is in the opposite part of its 
orbit with respect to them. 

Disc, the body or face of the sun or moon as it appears to 
a spectator on the earth ; or of the earth, as it would ap- 
pear to a spectator in the moon, 

Dominical letter. In the Roman calendar, it was customary 
to prefix the first 7 letters of the alphabet to the several 
days of the week throughout the year, always beginning 
the year with the letter A. The letter, then, that was 
prefixed to the Sundays (Dominici dies) throughout the 
year, was called the Dominical letter. This may be found 
for any year of the Christian sera, by the following rule. 
Divide the centuries by 4, subtract twice the re- 
mainder from 6, and to what remains add the odd years 
and their 4th part, rejecting fractions ; divide the sum 
by 7, and then the remainder taken from 7 will leave 
the number of the Dominical letter in the alphabet, 
Thus for the year 1806 the Dominical letter will come 
out 5zrE. 



( 16 ) 

In a leap-year, the letter thus found will be the Domi- 
nical letter till the 28th of Feb. and the preceding one will 
be the Dom. let. from that time till the end of the year. 

Earth, the third planet in order from the sun ; at the dis- 
tance of about 95 millions of miles ; furnished with one 
moon. 

Eclipse. When any secondary planet passes through the 
shadow of its primary, it is said to be eclipsed ; as the 
moon by the shadow of the earth, or any of Jupiter's sa- 
tellites by his shadow. But when the shadow of a secon- 
dary planet falls on its primary, then, with respect to that 
part of the primary on which the shadow falls, the sun is 
said to be eclipsed. 

Ecliptic limit, is a certain distance from the node of the 
secondary's orbit, beyond which no eclipse can happen. 
This limit with respect to a solar eclipse is about 17. 
and with respect to a lunar eclipse, about 12. 

Ecliptic, a great circle of the sphere in the plane of which 
the earth performs its annual revolution round the sun. 

Ellipse or ellipsis, a plane curvilineal figure, which may be 
described round two centres thus. Take a thread of any 
determinate length, tie its two ends "together, and throw 
the loop round two pins stuck into a plane board then 
moving round a pencil, or the like, within the loop, so as 
to keep it always tight, the curve described will be an 
ellipsis. .The two central points are called the foci of 
the ellipsis ; a right line passing through the two foci, 
and terminated by the curve on each side, is called the 
trans-verse axis or diameter, and one bisecting this at right 
angles is called the conjugate. 

Elongation of a planet, (generally applied to Mercury and 
Venus) their angular distance from the sun as seen from 
the earth. 

Embolismic, or 'intercalary, a term applied to a lunar month 
occasionally thrown in to bring up the lunar to the solar 
years. It is also applied to the 29th of February, thrown 
in every 4th year to make the civil years correspond with 
the solar. 

Emersion, the end of an eclipse or of an occultation. 

Epact, the excess of solar time, above lunar. In the Gre- 
gorian calendar it is the moon's age at the beginning of 
the year, which may be found by the following rule, till 
the year 1900. 

Subtract 1 from the Golden number, multiply the re- 
mainder by 11, and the product, rejecting the 30's, will 
be the epact. 



( 17 ) 

See jEra, 

Equation of time, the difference between apparent, and mean- 
solar time. This arises from two causes, viz. the ellipti- 
cal figure of the earth's orbit in which the diurnal arches 
will of consequence be unequal; and the inclination of the 
the ecliptic to the equator, whence equal arches of the 
former, in which the earth moves, will not correspond to 
equal arches of the latter, on which time is measured. 

Equator, that great circle which cuts the axis of rotation at 
right angles. 

Equinoctial points, the beginning of the signs Aries and Li- 
bra, those two points of the ecliptic in which it crosses 
the equator; the former being called the vernal, and the 
latter the autumnal, equinoctial point. 

Equinoxes, the times when the sun appears to enter the 
equinoctial points; viz. the 2 1st of March, and 22d of 
September. 

Excentricity, or eccentricity, of a planet's orbit, is equal to 
half the distance between the two foci of the elliptical 
orbit. 

Focus, foci. See Ellipsis. 

Frigid zones, those round the poles, bounded by their re* 
spective polar circles. 

Geocentric jilace of a planet, is its place> (generally express- 
ed in latitude and longitude, or right ascension^ and decli- 
nation) as it appears from the earth* 

Globes (artificial) small spheres of paste-board, or the like, 
on one of Which (called the terrestrial globe) are drawn 
the principal circles of the sphere, together with the se- 
veral continents, islands, &c. of the earth, in their rela- 
tive situations and magnitudes. On the other, (called 
the celestial globe) besides the circles of the sphere, are 
inserted all the visible fixed stars, distributed into their 
respective constellations. The use of the Globes, explains 
the manner of solving geographical and astronomical pro- 
blems, by means of artificial globes. 

Golden number, is the year of the lunar cycle, increasing 
annually by unity from 1 to 19. 

Gravity, that species of attraction which takes place be- 
tween bodies at a distance from each other, and by which, 
if not otherwise prevented, they would mutually approach 
each other, with a continually-accelerated velocity. Gra- 
vity is directly proportional to the quantity of matter, and 
inversely, to the square of the distance. 

Heliocentric place of a planet, is its place in the heavens, as 
if viewed from the sun. 

*( C )* 



( 18 j 

Hcrschel, or Georgium Sidus the 7th primary planet in or- 
der from the sun, at the distance of about 1800 millions 
of miles. It is furnished with 6 satellites. 

Horizon, that great circle of the sphere which, extended to 
the heavens, is the boundary of our vision. It is usually 
distinguished into sensible or visible, and rational or 
true. 

TtJour, the 24th part of a natural day. 

Horary angle of a celestial body, an angle at the pole of the 
equator, included between the meridian of the place and 
that passing through the body. 

Immersion^ the beginning of an eclipse, or of an occultation. 

Inclination of the axis of a planet, the angle which it makes 
with the axis of the plane of its orbit. 

Inclination of the orbit of a planet, the angle in which it 
crosses the ecliptic. 

Jndiction, (Roman). See Cycle. 

Jufiitcr, the fifth primary planet from the sun, at the dis- 
tance of about 490 millions of miles. It is the largest in 
the system, and is furnished with four satellites. 

Latitude of a filace on the earth, its distance from the equa- 
tor, measured on the meridian of the place. 

Latitude of a celestial body, its distance from the ecliptic, 
measured on a circle of celestial longitude passing through 
the body. 

Leap-yew, one of 366 days, occurring every 4th year, and 
so called, because in that year the Dominical letter falls 
back two letters, or leaps over one. See Bissextile. 

Libration of the moon, a small apparent libratory motion, 
arising chiefly from her equable rotation round her axis, 
combined with her unequal motion in her orbit. 

Longitude of a place on the earth, an arch of the equator in- 
tercepted between the prime meridian, and that passing 
through the place, and is denominated east or west, ac- 
cording to its situation with respect to the prime meridian. 

Longitude of a celestial body, an arch of the ecliptic, reckon- 
ed according to the order of the signs, from the equinoc- 
tial point Aries to the circle of celestial longitude passing 
through the body. 

Lunar cycle. See Cycle. 

Mars, the fourth primary planet from the sun, at the dis- 
tance of about 144 millions of miles. 

Meridians, great circles crossing the equator at right angles. 

Meridian of the place, that passing through the north am! 
south points of the horizon. 



( 19 ) 

Midheaven, that point of the ecliptic, or of the equator, 

which is in the meridian. 

Minute, the 60th part of an hour, or of a degree. 
Month, the 12th part of a year. It is variously distinguish- 
ed according to circumstances, viz. 

Lunar illuminative month, the time between the first ap- 
pearance of one new moon, and of the next. The an- 
cient Jews, with the 'Turks and Arabs, reckon by this 
month. 

Lunar periodical month, the time in which the moon ap- 
pears to make a revolution through the zodiac = 27 d, 
7 h. 43 m. 8 s. 

Lunar si/nodical month, or lunation, the time between one 
new moon, or conjunction of the sun and-moon, and the 
next: at a mean == 29d. 12h. 44m. 3s. lit. 
Solar month, the 12th part of a solar tropical year = 30d. 

lOh. 29m. 5s. 

Calendar months, those made use of in the common reck- 
oning of time, as in Almanacs or Calendars. 
The judicial month, consists of 4 weeks or 28 days. 
Moon, the satellite or secondary of the Earth, at the dis- 
tance of about 240 thousand miles. 
J\1idir, the lower pole of the horizon. 

JVodes of a planet's orbit, {those two points in which it cros- 
ses the ecliptic. That in which the planet passes from 
the south side of the ecliptic to the north, is called its as- 
cending node or dragon's head SI , and the opposite point, 
its descending node, or dragon's tail ^ . The nodes of all 
the planets' orbits have a slow retrograde motion, occasion- 
ed by their moving in different planes, and their mutual 
attraction on each other. 
.Vonagesimal, that point in the ecliptic which is 90 from the 

horizon. 

Nutation of a star, a small apparent motion, occasioned by 
the variable attraction of the sun and moon on the sphe- 
roidal figure of the earth; by which the axis is made to 
revolve with a conical motion, the extremities or poles 
describing in i8y. 7m. the lunar period, or revolution of 
the moon's nodes, a small ellipse whose transverse diame- 
ter = 19".l and conjugate = 14 // .2. The correction of 
the right ascension and declination of a star arising from 
this cause may be readily found by the following theo- 
rems: in which A the right ascension of the star (per 
table), I) = its declination, and N = the longitude of the 
moon's ascending node. 

Th. 1. 8".3 cos. (N A) tan. D l".25 cos. (N -f 
A) tan. D 16". 2 5 sin. N. = the nutation in Rt. as. in 
seconds of time. 



Th. 2. 4- 9".55 cos. N. sin. A +*7".05 cos. A sin. N = 
the nutation in cleclin. in seconds of a degree. The up* 
per signs are to be used when the star has north dec. 
and the under signs when it has south dec. See Aberra- 
tion. 

Oblique ascension of a celestial body, that point of the equa/< 
tor which rises at the same time with the body in an ob- 
lique sphere. 

Obliquity of the ecliptic, the angle in which the ecliptic cros- 
ses the equator. 

Occultatio?i of a star, the moon's passing between the star 
and the observer, and thereby, for a time, hiding it from 
his sight. 

Olympiads. Games celebrated by the Greeks every 4 years. 
See jEra. 

Opposition, that aspect in which the difference of longitude 
of the two bodies is 180. 

Orbit of a planet, the path in which it revolves round its 
centre of motion. The orbits of all the planets, whether 
primary or secondary, are elliptical, though of but small 
excentricity; and all (with the exception of lierschel's 
satellites) nearly in the plane of the ecliptic, or earth's 
orbit. 

Parallax of a celestial body, is equal to the angle at the body, 
subtended by a semidiameter of the earth terminating in 
the place of the observer. Hence the horizontal parallax 
of a body will be the greatest, and in the zenith it will 
entirely vanish. The fixed stars, from their immense dis- 
tance, have no sensible parallax. 

Parallax of the earth's annual orbit, at a planet, is the angle 
at that planet subtended by the distance between the earth 
and sun. 

Penumbra, a faint or imperfect shade, observed in eclipses, 
and occasioned by a partial interception of the sun's light. 

Perigee, that point of the moon's orbit which is nearest to 
the earth. The term is sometimes applied to signify 
that point in which the sun is nearest to the earth. 

Perihelion, that point of a planet's orbit which is nearest to 
the sun. 

Periodical time of a planet, that in which it performs a com- 
plete revolution round its centre of motion. 

Perioeci, such as live in opposite points of the same parallel 
of latitude. 

Periscii, those whose shadows turn quite round during the 
day, the sun not setting and such, at certain times of 
the year, are the inhabitants of the frigid zones. 



( 21 ) 

Phases of a planet, the various appearances of the visible 
illuminated part, as horned, half illuminated, gibbous, 
full. 

Planets, bodies in the solar system, which revolve in orbits 
nearly circular, and all nearly in the same plane. They 
are distinguished into primary, and secondary. 

The primary jilanets, revolve round the sun as their 
centre, and the secondaries, round their respective prima- 
ries as their centres. 

The table at the end of this Glossary contains a correct 
synopsis of the distances, magnitudes, periods, and all 
the other important elements of the several planets, both 
primary and secondary, in the solar system, according to 
the latest observations. The sun's horizontal parallax, 
as determined from the transit of Venus in 1769, being 
8"|. 

Poles of any great circle of the sphere, two opposite points 
in the surface of the sphere, each 90 degrees distant from 
the circumference of the given circle. 

Precession, recession, or retrocession of the equinoxes, a 
slow motion of 50"^ per year, by which the equinoctial 
points of the ecliptic are carried backwards from east to 
"west, and consequently the epliptical stars carried forwards 
from west to east. 

This motion is occasioned by the attraction of the sun 
and moon, on the matter of the earth accumulated at the 
equator by its diurnal rotation. 

Primary planets-, those bodies in the solar system which re- 
volve round the sun as their centre of motion, in orbits 
nearly circular. 

Prime -vertical, that azimuth-circle which passes through 
the east and west points of the horizon. 

Quadrature, or quartile, that aspect in which the bodies have 
90. difference of longitude. 

Radius -vector of a planet, the distance from the planet, in 
any give'n part of its orbits, to the centre of motion. 

Refraction of a celestial body, the angle in which the rays 
of light coming from the body, are bent downwards from 
their right course in falling obliquely upon, and passing; 
through, the earth's atmosphere. This is greatest in the 
horizon, and entirely vanishes in the zenith. 

Retrograde motion of a planet, that by which it appears to 
the observer to move contrary to the order of the signs. 
To a spectator on the earth, Mercury and Venus will ap- 
pear retrograde when they are in the inferior or nearer 
part of their orbits, and all the other planets will appear 



retrograde when the earth is in the nearer part of its or- 
bit with respect to them. 

Satellites, or secondary planets, or moons, those smaller 
bodies in the solar system which regard the primaries as 
their centres of motion. 

'Saturn, a primary planet, the 6th in order from the sun, at 
the distance of about 900 millions of miles. It is furnish- 
ed with a stupendous double ring and 7 satellites. 

Second, the 60th part of a minute, whether of time or of a 
degree. 

Sex tile, that aspect where the difference of longitude of th'e 
two bodies = 60. 

Sign of the ecliptic, an arch of 30. or the 12th part of the 
whole circle. 

Signs of the zodiac, twelve constellations, distributed through 
the zodiac, and nearly at equal distances. The vernal equi- 
noctial point was formerly in the constellation Aries, but 
owing to the precession of the equinoxes it is now in the 
constellation Pisces; yet the artificial signs continue to be 
called by their former names. The equinoctial points be- 
ing still denominated Aries and Libra, and the solstitial 
points, Cancer and Capricorn. 

Solar system, comprehends the sun, the centre of the sys- 
tem, the primary planets, the secondary planets, and the. 
comets. 

Solar cycle. See Cycle. 

Solstices, the times when the sun enters the two solstitial 
points of the ecliptic, viz. the 21st of June, the time of 
the northern solstice, and the' 22d of December, that of 
the southern solstice. These with relation to the north- 
ern hemisphere, are frequently denominated the summer, 
and winter, solstices, respectively. 

Solstitial points of the ecliptic, those opposite points in which 
the sun has the greatest declination, viz. the beginning of 
the sign Cancer in the northern hemisphere, and the be- 
ginning of the sign Capricorn, in the southern. 

Sphere, in a geometrical sense, is a solid contained under a 
uniformly-curved surface, every point of which is equally 
distant from a certain point within the same, called the 
centre. This term is applied to the several celestial bo- 
dies, as they are probably all nearly of this figure. It is 
also applied to the apparent concave surface of the hea- 
vens, and is then called the celestial sphere. 

The sphere, in geography and astronomy, is frequently 
distinguished by the epithets right, oblique, or parallel? 
according to the position of the equator and horizon: 
bright sphere, is that in which the equator cuts tUe he- 



( 23 } 

rizon at right angles, and such is the case to an inhabitant 
at the equator. In this sphere the lengths of the days 
and nights are always equal. 

dn oblique sphere, is that in which the equator cuts the 
horizon at oblique angles; and such is the case to any 
inhabitant north or south of the equator. In this sphere 
the lengths of the days and nights are always varying 
the variation being greater, the greater the latitude. 

A parallel sphere, is that in which the equator is parallel, 
or rather coincident, with the horizon; and such is the 
case to an inhabitant at either pole. In this sphere, the 
sun Will be six months successively visible, and six in- 
visible. . 

Spheroid, a solid which may be conceived as generated by 
the rotation of an ellipsis round its tranverse or conju- 
gate diameter. In the former case, the spheroid is said 
to be prolate, and in the latter, oblate. The figure of the 
earth, and perhaps that of most of the other planets, is near- 
ly that of an oblate spheroid. This arises from their rotato- 
ry motion round their axes, by which, the attraction at the 
surface is continually diminished from the poles to the 
equator, by the Continued increase of the centrifugal force; 
and thus, the equatorial diameter becomes greater than 
the polar. It follows from this figure, that the length of 
the degrees of latitude gradually increase from the equa- 
tor to the poles. To this figure of the earth we are to 
ascribe many of the apparent irregularities in the motions 
of the celestial bodies: as, the precession of the equinoxes, 
the nutation of th6 stars, Sec. 

' Stars, or fixed stars, luminous bodies, at an immense dis- 
tance, appearing in all parts of the heavens. They all 
probably resemble the sun in matter and in magnitude, 
and are each the centre of a system, similar to the solar 
system. They are said to be fixed because they con- 
stantly preserve, very nearly, the same relative position 
to each other. Besides the small apparent motion of the, 
stars arising from aberration, and nutation, and the pre- 
cession of the equinoxes; in some of them there has been 
discovered a very slow (indeed) proper motion. Whence 
it is conjectured that not only the bodies belonging to the 
innumerable systems of stars are in motion round theu' 
respective centres, but that all the systems of bodies in 
the universe are themselves in motion round some com- 
mon centre and that thus they are prevented from ap- 
preaching each other, which, from their mutual attrac- 
tions, they must otherwise do. 



( 24 ) 

Stationary. This term is applied to a planet, when, for some 
time, it appears to a spectator to occupy the same place 
in the zodiac. To a spectator in the sun, the planets' 
motions would always appear direct; and that they ever 
appear otherwise to a spectator on the earth, is owing to 
its own motion, and being placed out of the centre of the 
system. To such a spectator, Mercury and Venus will 
appear stationary when at their greatest elongation; and 
all the other planets will appear stationary when the earth 
is at its greatest elongation with respect to them. 

Style, the particular manner of counting time. It is dis- 
tinguished into old and new. 

Old style, is that which follows the Julian calendar. 
New style, is that which follows the Gregorian calendar. 
See Calendar. In the year 1800 the latter was 12 days 
ahead of the former, and in every centurial year not divi- 
sible by 4, the difference will be increased 1 day. 

Systems of the Universe. Of these there are 3 noted ones 
in the history of astronomy, viz. the Ptolemean system, 
advocated by many of the ancient philosophers. Accord- 
ing to this, the earth occupies the centre of the universe* 
and is at rest; while all the celestial bodies revolve round 
it from east to west, every 24 hours. The Tychonean nys- 
tcm, invented by Tycho Brahe, a noted Danish Astrono- 
nomer, bom A. D. 1546. According to this system, the 
earth, as in the Ptolemean system, is placed in the centre 
of the universe, the moon revolving round the earth as 
her proper centre, while the sun, with all the other pla- 
nets moving round him as satellites, revolve also round 
the earth. 

Cofiernican system, maintained by many of the ancients, 
particularly by Pythagoras, revived by Copernicus a na- 
tive of Thorn in Prussia (born 1473), and demonstrated 
by Sir Isaac Newton. According to this it is demon- 
strated that the sun is the centre of the planetary sys- 
tem; the primary planets revolving round him in their 
annual orbits, and the secondaries round their respective 
primaries. That the orbits both of the primary and se- 
condary planets are all nearly circular, though in fact ellip- 
tical; the sun, or primary, being placed in one of the 
foci of the respective orbits. That they all lie nearly in 
the same plane. That all the planets revolve nearly in 
the same direction, the square of their periodical times 
being directly proportional to the cubes of their mean 
distances from the centre of motion. That the earth, 
and perhaps most, if not all the other primary planets. 



( 25 ) 

perform a diurnal rotation round their axes ; and that the 
moon, or satellite of the earth, as well as perhaps all 
the other satellites, constantly present the same face to- 
wards their primaries. That the inclination of the axis 
of rotation to the plane of the ctbit is different in differ- 
ent planets ; and that thus they experience a differenc6 
in their diversity of seasons. 

Syzigy. This general term is applied both to signify the con. 
junction and opposition of a planet with the Sun. It is 
however chiefly used in relation to the moon. 
Tides, a periodical alternate motion or flux and reflux of 
the waters of the sea. 

These are caused chiefly by the attraction of the moon, 
though in part by that of the Sun also ; and accordingly 
there are two tides of flood (and consequently two of 
ebb) in the course of every lunar day. The apex of one 
of the tides of high water is immediately under, or ra- 
ther about 45 eastward of, the moon; and the other, dia- 
metrically opposite. These are produced by the unequal 
attractions of the moon on the part of the eatth nearest 
to her, on the centre of the eartii, and on the part farthest 
from her (attraction decreasing inversely with the square 
of the distance.) One tide therefore is produced by a re- 
dundancy of attraction, drawing the waters up towards 
the moon, and the opposite tide, .by a deficiency of attrac- 
tion, leaving, as it were, the waters behind. When the 
sun and moon are in conjunction or opposition, the tides, 
being then produced by their joint influence, are higher 
than usual, and hence called spring -tides ; but when these 
bodies are in quadrature, the tides, being produced by the 
difference of their influence, are lower than usual, and 
hence called neap-tides L 

Time is measured by the apparent motion of the celestial 
bodies ; and is variously distinguished : thus 

Apparent solar time, is that measured by the apparent 
motion of the sun ; and hence the apparent solar time 
from noon, is equal to the sun's horary angle reduced to 
time, at the rate of 15 to the hour. 

Mean solar time, is that shewn by a true time-piece, 
going with an equable motion throughout the year. 

Sidereal time, is that measured by the apparent equa- 
ble motion of the stars. 

Lunar time, that measured by the apparent motion of 
the moon. See Day. 

Transit of an inferior planet (Mercury or Venus) over 
the sun's disc, is when the planet, at the time of an in- 
ferior conjunction, passes between the sun and the ob- 

C 



( 26 J. 

server. This will only happen when the planet, at the time? 

of this conjunction, is in or near its node. 

Trine, an aspect where the bodies are at the distance of 

i. of the ecliptic or 120 a 

Twilight. See Crepusculum. 

Venus, the second primary planet from the sun, at the 
distance of about 68 millions of miles. 

Fear, a period of time generally considered as compre- 
hending a complete revolution of the seasons. The year 
is variously distinguished, viz. 

1 . Tropical Solar year, the time in which the sun appears 
to perform a complete revolution through all the signs of 
the zodiac = 365d. 5h. 48m. 48s. 

2. Sidereal year, the time in which the sun appears to 
revolve from any fixed star to the same again = 365d. 6h. 
9m. 17s. The difference between the tropical and sidereal 
year (20m. 29s.) is the time of the sun's apparent motion 
through 50"1, the arch of annual precession. 

3. Lunar astronomical year, consists of 12 lunar synodi- 
cal months = 354d. 8h. 48m. 38s. and therefore 10d.21h.0m. 
1.0s. less than the solar year a difference which is the 
foundation of the epacU 

4. The common lunar civil year, consists of 12 lunar civil 
months, = 324 days 

5. The embolismic or intercalary lunar year,, consists of 
13 lunar civil months = 384 days. 

6. The common civil year, contains 365 days, divided into 
12 calendar months. 

7. Bissextile or leap-year, containing 366 days. See cal- 
endar. 

Zenith, the upper pole of the horizon. 

Zenith-distance of a celestial bod), its distance from the ze- 
nith, measured on the azimuth-circle passing through the 
body, and is equal to the complement of the altitude to 90, 
Zodiac, a zone or broad circle in the heavens including alt 
the planets, and extending about 10. on each side of the 
ecliptic. 

Zodiacal light, a pyramidal lucid appearance, sometimes ob- 
served in the zodi.ic, resembling the galaxy, or milky 
way. It is most plainly observable after the evening twi- 
light about the latter end of February ; and before the 
rooming twilight about the beginning of October. For at 
these times it appears near.y perpendicular to the horizon. 
This appearance is generally supposed to be occasioned 
by the sun's atmosphere. 



( 27 ) 

in astronomical geography? is applied to a division ot 
the earth's surface by certain parallels of latitude. 
The Zones are 5 in number, viz. 

1. The torrid zone, lying between the two tropics. It 
comprehends the West India Islands, the greater parts 
of South America and of Africa, the southern parts of 
Asia, and the East India Islands. 

2. The north frigid zone, lying round the north pole, 
and bounded by the north polar circle. It comprehends 
part of Greenland, of the northern regions of North 
America, and a little of the northern parts of Europe 
and Asia. 

3. The south frigid zone, lying round the south pole, 
and bounded by the south polar circle. It contains no 
dry land, so far as yet discovered. 

4. The north temfierate zone, lying between the torrid 
and north frigid. It comprehends almost the whole of 
North America, Europe, and Asia, with the northern 
part of Africa. 

5. The south temfierate zone, lying between the torrid 
and south frigid. It comprehends the southern part of 
South America, of Africa, and of the great island of New- 
Holland. 

In the torrid zone, the sun is vertical twice a year to 
every part of it, and there is very little diversity in the 
length of the clay throughout the year, the longest clay 
varying only from 12 to about 13J hours. In the tempe- 
rate zones the sun is never vertical, and the length of the 
longest day varies from about 13| to 24 hours. In the 
frigid zones, the length of the longest day (or time be- 
tween the sun's rising and setting) varies from 24 hours 
to 6 months. 



s 






















*s 


s^ 






















5 


s -g 


& 








CO 


CO 


ci 








? 


t ^ 


oo 




c^ 




(-1 


p " 


to 










J ir* 


to 




CO 




co 


tO 


ro 


00 






^ 


s S3 


O 

CO 




b- 
b- 




Q 


o* 


00 


00 

tc 


s 


o 


s 


s 








o 




CN 


_ 


2 


T+l 

c 


2 


b- 

c ! 






CO 




















s 


s 


o* 




















/ 


S j 


b- 


















^ 


S 3 


b- 

q 









a. 

co 


Ch 


c 








s 


s jjj 


M 


b! 


00 




Q * 


s 


b- 

c 


pi 

(N 


m 


^ 


- ^ 


s 


b- 







e* 






Oi" 
. b. 

00 


* 

V) 

O". 


to 

3 


cc 
a 


o 
b- 


I ^ 


Jj 


oc 
C 




















s 


s <s 


c^> 








-,c 


' 










s 


sf 


O 

CO 
CO 


o 

CO 

OJ 


b- 

co 

o * 


c 


o-. 
o' 

CTi 



CO 
' o' 





0* 


00 

c 

00 


OC 


S 


s 

1 s' 


c 




en 




2j 


b- 




'; 




X 







s 























? 


s 


b- 










in 










? 


s * 
s s 


b- 


in 




b- 

<o 


CO 





co 


8 




2 


s 

to S 


s ^ 





to 


00 


o ' 


Of' 


?_ 


(N 


CO 


o> 


cc 


T. ^ 


s s 


CO 

to 


^ 


o' 




b- 


CO 


,J 


q 


'^ 


CN 
CO 


>n S 


?, 


5 




















s 


S f 


oc 










_< 










s 


s s 

S td 


CO 
<> 

in 
to 

CO 


co 
" 

CO 


X 
X 


b- 

VO 

o* 

CO 


X 


. 

o * 

CO 

b- 




co 




IQ 


1 5 

C7< J* 
CM S 

r 


<J - 


b- 






















t 


Jl 










co 










c 


S c 


00 

8 


to 


~ 






CO 

b- 


CO 


CO 










b- 


to 


o^ 




^ 


' 


CO 


3Q 


CO 


b- 


J 


S 


C7 

C-1 


co 

CO 


co 



CO 


o" 
b- 


o' 
b- 


b- 


E 


O 


o> 

a. 


co 
b- 


< 


s 
























v 


in 


















to 


S 


? '""' 


U") 








CN 


r 1 


_, 


-~' 


c$ 


O) 




S ti 


1 








in 

CO 


5g 


b- 

co 

CO 


in 
m 



i 


2 


S 


s" 


b- 

cc 




b- 




" 


0* 
CO 
b- 




O' 




-J 


S 


1 


^ 


ex 








w 


^ 




1 


- S 

L 


s 


O 


3 

O 


1 jS 




CJD 


c 
.2 


s 

73 


'o 


Cfl 

EH 


!r 


~ s 


Elements. 


al revolution 
^ T S and parts. 


round axis in 

s. 


o ^ 

e ? 

c t v. 


o 




^-* 

S 

"o 

(0 


"w 

1 

o 

G 


G 
a; 

C 




1 - 

tfl 


on of cliamete 


'^ 

c 


5 5 

i e J 

ill 


JJ 


U -T* 


o tl 


'? -c' 


' 


3 


2 


| 


'r g 


" 


1.g 


T-' VTJ ^ 


^ 


.2 e 


'-g p. 


c ,_ 


.S 


"& y 


"So 


Cv p 


. S 


Q 

P- 


8L!i 


2_^ S 


^" 


1 


o "^ 


II 


"u 
p 


c "S 





c 2 


3 


C 


Is 


rT 5 Jj 




'S c ^3 2.2-2 S g'S'-r^^S 

. 3 25-5^^^3^430^600 




CONTENTS. 



PAGE. 

Explanation of the principal Terms relating to As- 

f tronomy, Chronology, and the astronomical 

Parts of Geography, with occasional Illustra- 

trations and Remarks, . . . 5 

*> Table of the Motions and Distances of the 

Planets, 28 

Table of the Satellites 29 

CHAP. I. Of Astronomy in general, 

II. A brief Description of the SOLAR SYSTEM, 40 

III. The COPERNICAN SYSTEM demonstrated to be 

true, 77 

IV. The Phenomena of the Heavens as seen from dif- 

ferent Parts of the Earth, .... 89 

V. The Phenomena of the Heavens as seen from differ- 

ent Parts of the Solar Sytem, . . . 97 

VI. The Ptolemean System refuted. The Motions and 

Phases of Mercury and Venus explained, . 102 
VII. The physical Causes of the Motions of the Planets. 
The Excentricities of their Orbits. The Times 
i in which the Action of Gravity would bring 
them to the Sun. ARCHIMEDES' ideal Problem 
for moving the Earth. The World not eternal, 109 
VIII. Of Light. Its proportional Quantities on the dif- 
ferent Planets. Its Refractions in Water and 
Air. The Atmosphere ; its Weight and Proper- 
ties. The horizontal Moon, . . .118 
IX. The Method of finding the Distances of the Sun, 

Moon, and Planets, 134 

X. The Circles of the Globe described. The different 
Lengths of Days and Nights, and the Vicissi- 
tudes of Seasons, explained. The Explanation of 
the Phenomena of Saturn's Ring, concluded, 142 
XI. The Method of finding the Longitude by the 
Eclipses of Jupiter's Satellites The amazing 
Velocity of Light demonstrated by these Eclip- 
ses, 154 

XII. Of Solar and Sidereal Time, . . . .162 

XIII. Of the Equation of Time, . . . .167 

XIV. Of the Precession of the Equinoxes, . . 183 
XV. The Moon's Surface mountainous : Her Phases 

described : Her Path, and the Paths of Jupi- 
ter's Moons delineated : The Proportions of the 
Diameters of their Orbits, and those of Saturn's 
Moons to each other, and to the Diameter of 
the Sun, 219 

XVI. The Phenomena of the Harvest-Moon explained by 

a common Globe: The Years in which the 
Harvest-Moons are least and most beneficial, 
from 1751 to 1861 The long Duration of Moon- 
light at the Poles in Winter, . , . 235 

XVII. Of the Ebbing and Flowing of the Sea, . 251 



CONTENTS. 

PAGE. 

CHAP. XVIII. Of Eclipses: Their Number and Periods. A large 

Catalogue of Ancient and Modern Eclipses, 263 
XIZ. Shewing the Principles on which the following 
Astronomical Tables are constructed, and the 
Method of calculating the Times of New and 
Full Moons and Eclipses, by them, . . 320 

XX. Of the fixed Stars, 370 

XXI. Of the Division of Time. A perpetual Table of 
New Moons . The Times of the Birth and Death 
of CHRIST. A Table of remarkable ./Eras or 

Events, 391 

XXII. A Description of the astronomical Machinery, 
serving to explain and illustrate the foregoing 

Part of this Treatise, 432 

XXIII. The Method of finding the Distances of the Planets 

from the Sun, 465 

ART. I. Concerning Parallaxes, and their Use in general, 467 
AIIT. II. Shewing how to find the horizontal Parallax of 
Venus by Observation, and from thence, by 
Analogy, the Parallax and Distance of the Sun, 
and of all the Planets from him, . . 472 

ART. III. Containing Doctor HALLEY'S Dissertation on 
the Method of finding the Sun's Parallax and 
Distance from the Earth, by the Transit of 
Venus over the Sun's Disc, June the 6th, 1761. 
Translated from the Latin in Matte's Abridg- 
ment of the Philosophical Transactions, Vol. I. 
page 243 ; with additional Notes, . . 482 

ART. IV. Shewing that the whole Method proposed by the 

Doctor cannot be put in Practice, and why, 498 
ART. V. Shewing how to project the Transit of Venus on 
the Sun's Disc, as seen from different Places of 
the Earth ; so as to find what its visible Dura- 
tion must be at any given Place, according to 
any assumed Parallax of the Sun ; and from the 
observed Intervals between the Times of Ve- 
nus's Egress from the Sun at particular Places, 
to find the Sun's true horizontal Parallax, . 500 
ART. VI. Concerning the Map of the Transit, . . 520 

ART. VII. Containing an Account of Mr. HORROX'S Observa- 
tion of the Transit of Venus over the Sun, in 
the Year 1639 ; as it is published in the Annual 
Register for the Year 1761, . . . . 521 
ART. VIII. Containing a short Account of some Observations 
of the Transit of Venus, A. D. 1761, June 6th ; 
and the Distance of the Planets from the Sun, 
9$ deduced from those Observations* - 52& 




CH ^V 



ASTRONOMY EXPLAINED. 

CHAP. L 

Of Astronomy in general* 

, /~\F all the sciences cultivated by mankind, ^ 

\^J astronomy is acknowledged to be, and a strono 
undoubtedly is, the most sublime, the most inter- m y 
esting, and the most useful. For, by knowledge 
derived from this sr.ieucc, not only the magnitude 
of the earth is discovered, the situation and extent 
of the countries and kingdoms upon it ascertained, 
trade and commerce carried on to the remotest 
parts of the world, and the various products of se- 
veral countries distributed for the health, comfort,, 
and conveniency of its inhabitants ; but our very fa- 
culties are enlarged with the grandeur of the ideas 
it conveys, our minds exalted above the low con- 
tracted prejudices of the vulgar, and our under- 
standings clearly convinced, and affected with the 
conviction, of the existence, wisdom, power, good- 
ness, immutability, and superintendency of the 
SUPREME BEING. So that, without an hy- 
perbole, 

" An unde-vout astronomer is mad.*" 

2. From this branch of knowledge we also learn 
by what means or laws the Almighty carries on, 
and continues, the wonderful harmony, order, and 
connexion, observable throughout the planetary 
system ; and are led, by very powerful arguments^ 
to form this pleasing deduction that minds capabk 

* Dr. Young's Night Thoughts* 

E 



32 Of Astronomy in general. 

of such deep researches, not only derive their ori- 
gin from that adorable Being, but are also incited 
to aspire after a more perfect knowledge of his na- 
ture, and a stricter conformity to his will. 
The Earth 3. By astronomy, we discover that the Earth is 
as Ut see P n mt at so reat a distance from the Sun, that it seen from 
from the thence it would appear no larger than a point ; al- 
Surt ' though its circumference is known to be 25,020 
miles. Yet even this distance is so small, compared 
with that of the fixed stars, that if the orbit in which 
the Earth moves round the Sun were solid, and seen 
from the nearest star, it would likewise appear no 
larger than a point ; although it is about 162 mil- 
lions of miles in diameter. For the Earth, in go- 
ing round the Sun, is 162 millions of miles nearer 
to some of the stars at one time of the year, than 
at another ; and yet their apparent magnitudes, si- 
tuations and distances from one another, still re- 
main the same; and a telescope which magnifies 
above 200 times, does not sensibly magnify them. 
This proves them to be at least 400 thousand times 
farther from us than we are from the Sun. 

4. It is not to be imagined that all the stars are 
placed in one concave surface, so as to be equally 
distant from us ; but that they are placed at im- 
mense distances from one another, through unli- 
mited space. So that there may be as great a dis- 
tance between any two neighbouring stars, as be- 
tween the Sun and those which are nearest to him. 
An observer, therefore, who is nearest any fixed 

The stars star, will look upon it alone as a real Sun ; and con- 
are aims, s jcj er t } ie rest as so man y shining points, placed at 

equal distances from him in the firmament. 

5. By the help of telescopes we discover thousands 
of stars which are invisible to the bare eye; and 
the better our glasses are, still the more stars become 

and innu- visible : so that we can set no limits either to their 
number or tne j r distances. The celebrated HUY- 
GENS carried his thoughts so far, as to believe it 
not impossible that there may be stars at such 



Of Astronomy In general. 33 

inconceivable distances, that their light has not yet 
reached the Earth since its creation; although the 
velocity of light be a million of times greater than 
the velocity of a cannon-ball, as shall be demon- 
strated aiu I \-.ard, \ 197.216. And, as Mr. AD- 
DISON very justly observes, this thought is far from 
being extravagant, when we consider that the uni- 
verse is the work of infinite power, prompted by in- 
finite goodness ; having an infinite space to exert it- 
self in ; so that our imaginations can set no bounds 
to it. 

6t The Sun appears very bright and large in Why the 
comparison with the fixed stars, because we keep j^ar s ap far- 
constantly near the Sun, in comparison with our ger than 
immense distance from the stars. For, a spectator the sUr -?* 
placed as near to any star as we are to the Sun, 
would see that star a body as large and bright as 
the Sun appears to us : and a spectator as far distant 
from the sun as we are from the stars, would see 
the Sun as small as we see a star, divested of all its 
circumvolving planets ; and would reckon it one of 
the stars in numbering them. ^ 

7. The stars, being at such immense distances Tbe stAs 
from the Sun, cannot possibly receive from him sof. re " ote ? 

% , . , lightened 

strong a light as they seem to have ; nor any bright* by the 
ness sufficient to make them visible to us. For the Sun - 
Sun's rays must be so scattered and dissipated 
before they reach such remote objects, that they 
can never be transmitted back to our eyes, so as to 
render these objects visible by reflection. The stars 
therefore shine with their own native and unbor- 
rowed lustre, as the Sun does. And since each par- 
ticular star, as well as the Sun, is confined to a par- 
ticular portion of space, it is plain that the stars are 
of the same nature with the Sun. 

8. It is no ways probable that the Almighty, 
who always acts with infinite wisdom, and does no- 
thing in vain, should create so many glorious suns, 
fit for so many important purposes, and place them 
.at such distances from one another, without pro- 



34 Of Astronomy in general. 

per objects near enough to be benefited by their 
They are influence. Whoever imagines that they were created 
summnd- only to give a faint glimmering light to the inha- 
e<] by pia- bitants of this globe, must have a very superficial 
knowledge of astronomy, and a mean opinion of the 
Divine Wisdom : since, by an infinitely less exer- 
tion of creating power, the Deity could have given 
our Earth much more li^ht by one single additional 
moon. 

9. Instead then of one Sun and one world only 
in the universe, as the unskilful in astronomy ima- 
gine, that science discovers to us such an incon- 
ceivable number of suns, systems, and worlds, dis- 
persed through boundless space, that if our Sun, 
with all the planets, moons, and comets, belonging 
to it, were annihilated, they would be no more 
missed, by an eye that could take in the whole 
creation, than a grain of sand from the sea-shore 
the space they possess being comparatively so small, 
that it would scarce be a sensible blank in the uni- 
verse. Saturn, indeed, the outermost of our plan- 
cts, revolves about the Sun in an orbit of 4884 mil- 
lions of miles in circumference ;* and some of our 
comets make excursions upwards of ten thousand 
millions of miles beyond Saturn's orbit ; and yet, 
at that amazing distance, they are incomparably 
nearer to the Sun than to any of the stars. This is 
evident from their keeping clear of the attractive 
power of all the stars, and returning periodically by 
virtue of the Sun's attraction. 

The stei- ]_(). From what we know of our own system, it 
may beha- mav be reasonably concluded that all the rest are 
4ntable, with equal wisdom contrived, situate, and pro- 
vided with accommodations for rational inhabit- 
ants. Let us therefore take a survey of the 
system to which we belong, the only one accessi- 
ble to us, and from thence we shall be the better 

* The Georgian planet, discovered since Mr. Ferguson's time, re- 
volves round the Sun in an orbit 5673 millions of miles in circumfer- 
ence, 



Of Astronomy in general. 35 

enabled to judge of the nature and end of the other 
systems of the universe. For, although there is an 
almost infinite variety in the parts of the creation, 
whicli we have opportunities of examining, yet there 
is a general analogy running through and connecting 
all the parts into one scheme, one design, one whole. 

11. And then, to an attentive considerer, it will 
appear highly probable, that the planets of our sys- 
tem, together with their attendants called satellites 
or moons, are much of the same nature with, our 
Earth, and destined for the like purposes. They 
are all solid opaque globes, capable of supporting are. 
animals and vegetables. Some of them are larger, 
some less, and some nearly of the same size of our 
Earth. They all circulate round the Sun, as the 
Earth does, in shorter or longer times, according to 
their respective distances from him ; and have, where 

it would not be inconvenient, regular returns of sum- 
mer and winter, spring and autumn. They have 
warmer and colder climates, as the various produc- 
tions ot our Earth require : and in such as afford a 
possibility of discovering it, we observe a regular 
motion round their axes like that of our Earth, caus- 
ing an alternate return of day and night ; which is 
necessary for labour, rest, and vegetation ; and that 
all parts of their surfaces may be alternately exposed 
to the rays of the Sun. 

12. Such of the planets as are farthest from theThefar- 
Sun, and therefore enjoy least of his light, have that t j )e sun 
deficiency made up by several moons, which con- have most 
stantly accompany, and revolve about them ; as our^j?^^ 
Moon revolves about the Earth. The remotest their 
planet* has, over and above, a broad ring encom- ni hts - 
passing it ; which, like a lucid zone in the heavens, 
reflects the Sun's light very copiously on that planet: 

so that if the remoter planets have the Sun's light 
fainter by day than our earth, they have an addition 
rrjiade to it morning and evening by one or more of 

is now known to.havc two of these lucid zones or ring)?. 



36 Of Astronomy in general. 

Our Moon their moons, and a greater quantity of light in the 



the Earth. 13. On the surface of the Moon, because it is 
nearer to us than any other of the celestial bodies 
are, we discover a nearer resemblance of our Earth. 
For, by the assistance of telescopes, we observe the 
Moon to be full of high mountains, large vallies, 
and deep cavities. These similarities leave us no 
room to doubt, that all the planets and moons in the 
system, are designed as commodious habitations for 
creatures endowed with capacities of knowing and 
adoring their beneficent Creator. 

14. Since the fixed stars are prodigious spheres 
of fire like our Sun,* and at inconceivable distances 
from one another, as well as from us, it is reasona- 
ble to conclude, they are made for the same pur- 
poses that the Sun is ; each to bestow light, heat, and 
vegetation on a certain number of inhabited planets ; 
kept by gravitation within the sphere of its activity. 

Number- ]^ What an august, whan an amazing concep- 

less suns . . P , . 5 . . . . * 

and tion, if human imagination can conceive it, does 
worlds, this give of the works of the Creator ! Thousands 
of thousands of suns, multiplied without end, and 
ranged all around us, at immense distances from each 
other ; attended by ten thousand times ten thousand 
worlds, all in rapid motion, yet calm, regular, and 
harmonious, invariably keeping the paths prescribed 
them ; and these worlds peopled with myriads of in- 
telligent beings, formed for endless progression in 
perfection and felicity ! 

16. If so much power, wisdom, goodness, and 
magnificence be displayed in the material creation, 
which is the least considerable part of the universe, 
how great, how wise, how good, must HE BE, 
who made and governs the whole ! 

* Though the Sun may not, strictly speaking, be a great sphere of 
fire, yet it is undoubtedly the principal source of light and heat to the 
other bodies in the system. 



Of the Solar System 



CHAP. II. 



A brief Description of the SOLAR SYSTEM. 



Sun, with the planets and comets [*'*/' 
which move round him as their centre, 
constitute the solar system. Those planets which 
are near the Sun not only finish their circuits sooner, 
but likewise move faster in their respective orbits, 
than those which are more remote from him. Their 
motions are all performed from west to east, in orbits 
nearly circular. Their names, distances, magni- 
tudes, and periodical revolutions, are as follows : 

18. The Sun , an immense globe of fire, i s ThcSun 
placed near 'the common centre, or rather in the 
lower* focus of the orbits of all the planets and co- 
metsf ; and turns round his axis in 25 days 6 hours, 
as is evident by the motion of spots seen on his sur- 
face. His diameter is computed to be 76 3 ,000 ^ff- 1 ? 
miles ; and by the various attractions of the circum- 
volving planets, he is agitated by a small motion 

* If the two ends of a thread be tied together, and die thread be 
then thrown loosely round two pins stuck in a table, and moderately 
stretched by the point of a black-lead pencil carried round by an 
even motion, and light pressure of the hand, and oval or ellipsis will 
be described ; and the points where the pins are fixed are called the 
foci or focuses of the ellipsis. The orbifs of all the planets are ellip- 
tical, and the Sun is placed in or near one of the foci of each of them : 
and that in which he is placed, is called the lower focus* 

t Astronomers are not far from the truth when they reckon the 
Sun's centre to be in the lower focus of all the planetary orbits. 
Though, strictly speaking, if we consider the focus of Mercury's 
orbit to be in the Sun's centre, the focus of Venus's orbit will be in 
the common centre of gravity of the Sun and Mercury ; the focus 
of the Earth's orbit in the common centre of gravity of the Sun, 
Mercury, and Venus ; the focus of the orbit of Mars in the com- 
mon centre of gravity of the Sun, Mercury, Venus, and the Earth; 
and so of the rest. Yet the focuses of the orbits of all the planets, 
except Saturn, will not be sensioly removed from the centre of the 
Sun ; nor will the focus of Saturn's orbit recede sensibly from the 
common centre of gravity of the Sun and Jupiter, 



38 Of the Solar System*. 

Plate I. round the centre of gravity of the system. All the 
planets, as seen from him, move the same way, and 
according to the order of the signs in the graduated 
circle T tf n s, fcfr. which represents the great 
ecliptic in the heavens : but, as seen from any one 
planet, the rest appear sometimes to go back ward ? 
sometimes forward, and sometimes to stand still. 
These apparent motions are not in circles nor in el- 
lipses, but* in looped curves, which never return 
into themselves. The comets come from all parts 
of the heavens, and move in all directions. 

19. Having mentioned the Sun's turning round 

his axis, and as there will be frequent occasion to 

speak of the like motion of the Earth and other 

planets, it is proper here to inform the young Tyro 

in astronomy, that neither the Sun nor planets have 

material axes to turn upon, and support them, as 

The axes i n the little imperfect machines contrived to repre- 

netsT pla " sent them. For the axis of a planet is an imginary 

what. line, conceived to be drawn through its centre, 

about which it revolves as if on a real axis. The 

extremities of this axis, terminating in opposite 

points of the planet's surface, are called its poles. 

That which points toward the northern part of the 

heavens, is called the north pole ; and the other, 

pointing toward the southern part, is called the south 

pole. A bowl whirled from one's hand into the open 

air, turns round such a line within itself, while it 

moves forward ; and such are the lines we mean, 

when we speak of the axes of the heavenly bodies. 

Their or- 20. Let us suppose the Earth's orbit to be a thin, 

notbtthe even > solid P lane > cut ting the Slln through the cen- 

same tre, and extended out as far as the starry heavens, 

P^j: lth where it will mark the great circle called the ecliptic. 

tic. This circle we suppose to be divided into 12 

equal parts, called signs ; each sign into 30 equal 

parts, called degrees; each degree into 60 equal 

parts, called minutes; and each minute into 60 

* As represented in Plate III. Fig. I. and described $ 138, 



Of the Solar System. 39 

into 60 equal parts, called seconds : so that a second Platt f. 
is the 60th part of a minute ; a minute the 60th 
part of a degree ; and a degree the 360th part of 
a circle, or ijOth part of a sign. The planes of 
the orbits of all the other planets likewise cut the 
Sun in halves ; but, extended to the heavens, form 
circles different from one another, and from the 
ecliptic ; one half of each being on the north side, 
and the other on the south side of it. Consequent- Their 
ly the orbit of each planet crosses the ecliptic in two node8 ' 
opposite points, which are called the planets' nodes. 
These nodes are all in different parts of the ecliptic ; 
and therefore, if the planetary tracks remained vi- 
sible in the heavens, they would in some measure 
resemble the different ruts of waggon wheels, cross- 
Ing one another in different parts, but never going 
far asunder* That node, or intersection of the or- 
bit of any planet with the Earth's orbit, from which 
the planet ascends northward above the ecliptic, is 
called the ascending node of the planet : and the other, 
which is directly opposite thereto, is called its de- 
scending node. Saturn's ascending node* is in 21 Where si- 
deg. 32 min. of Cancer 25 ; Jupiter's in 8 deg. 49 tuate - 
min. of the same sign; Mars's in 18 deg. 22 min. 
of Taurus tf ; Venus's in 14 deg. 44 min. of Ge- 
mini n ; and Mercury's in 16 deg. 2 min. of Taurus. 
Here we consider the Earth's orbit as the stand- 
ard, and the orbits of all the other planets as ob- 
lique to it. 

21. When we speak of the planets' orbits, all that T h e plan- 
is meant is, their paths through the open and unre- ets orbits, 
sisting space in which they move, and are retained what ' 
by the attractive power of the Sun, and the pro- 
jectile force impressed upon them at first. Between 
this power and force there is so exact an adjustment, 
that they continue in the same tracks without any- 
solid orbits to confine them. 

* In the year 1790. 

F 




40 Of the Solar System. 

Plate i. 22. MERCURY, the nearest planet to the Sun, 
Mercury ^^^ round him, in the circle marked 8, in 87 days, 
ri - I- 23 hours of our time, nearly; which is the length of 
his year. But being seldom seen, and no spots 
appearing on his surface or disc, the time of his ro- 
tation on his axis, or the length of his days and 
nights is as yet unknown. His distance from the 
Sun is computed to be 32 millions of miles, and his 
diameter 2600. In his course round the Sun, he 
moves at the rate of 95 thousand miles every hour. 
His light and heat from the Sun are almost seven 
times as great as ours ; and the Sun appears to him 
May be in- almost seven times as large as to us. The great 
habited. j^ Qn t j^ g pj anet j s no argument against its being 

inhabited ; since the Almighty could as easily suit 
the bodies and constitutions of its inhabitants to the 
heat of their dwelling, as he has done ours to the 
temperature of our Earth. And it is very probable 
that the people there have just such an opinion of us, 
as we have of the inhabitants of Jupiter and Saturn ; 
namely, that we must be intolerably cold, and have 
very little light, at so great a distance from the Sun. 
Has like 23. This planet appears to us with all the vari- 
withThe ous phases of the Moon, when viewed at different 
Moon. times by a good telescope : save only, that he never 
appears quite full, because his enlightened side is 
never turned directly toward us, but when he is so 
near the Sun as to be lost to our sight in its beams. 
And, as his enlightened side is always toward the 
Sun, it is plain that he shines not by any light of 
his own ; for if he did, he would constantly appear 
round. That he moves about the Sun in an orbit 
within the Earth's orbit, is also plain (as will be 
more largely shewn by and by, 141, & seq.J be- 
cause he is never seen opposite to the Sun, nor in- 
deed above 56 times the Sun's breadth from his 
centre. 



Of the Solar System. 41 



24. His orbit is inclined seven degrees to 
ecliptic. That node, 20, from which he ascends 
northward above the ecliptic, is in the 16th degree 
of Taurus ; and the opposite node, in the 16th de- 
gree of Scorpio. The Earth is in these points on 
the 7th of November and 5th of May\ and when 
Mercury comes to either of his nodes at his* infe- 
rior conjunction about these times, he will appear to 
pass over the disc or face of the Sun, like a dark 
round spot. But in all other parts of his orbit his 
conjunctions are invisible; because he either passes 
above or below the Sun. 

25. Mr. WHISTON has given us an account of when 
several periods at which Mercury might be seen on ^L e o n n JjJ 
the Sun's disc, viz. In the year 17fc2, Nov. 12th, sun. 

at 3 h. 44 m. in the afternoon, 1786, May 4th, at 
6 h. 57 m. in the forenoon ; 1789, Nov. 5th, at 3 
h. 55 m. in the afternoon ; and 1799, May 7th, at 
2 h. 34m. in the afternoon. There were several 
intermediate transits, but none of them visible at 
London. 

26. VENUS, the next planet in order, is com- Venus. 
puted to be 59 millions of miles from the Sun; 

and by moving at the rate of 69 thousand miles 
every hour, in her orbit in the circle marked 9 , she Fig. i: 
goes round the Sun in 224 days, 17 hours of our 
time, nearly ; in which, though it be the full 
length of her year, she has only 91 days, accord- 
ing toBiANCHiNi's observations'!* ; so that, to her, 

* When he is between the Earth and the Sun in the nearest part 
of his orbit. 

t The elder Cassini had concluded from observations made by 
himself in 1667, thnt Venus revolved on her axis in a little more 
than 23 h. because in 24 h. he found that a spot on her surface was 
about 15 more advanced than it was at the day before ; and it ap- 
peared to him that the spot was very sensibly advanced in a quar- 
ter of an hour. In 1728, Bianchini published a splendid work, in 
folio, at Rome, entitled Hesfieri et Phosfihori nova fihanomena; 
in which are the observations here referred to. Bianchini agrees 



42 Of the Solar System. 

Plate I. every clay and night together is as long as 24-| days 
and nights with us. This odd quarter of a c'av in 
every year makes every fourth a leap-year to Vtuiis ; 
as the like does to our Earth. Her dmmt-ter is 7906 
miles; and by her diurnal motion the inhabitants 
about her equator are carried 43 miles every hour, 
beside the 69,000 above-mentioned. 

Her orbit 27. Her orbit includes that ot Mercury within 
tween the ^ 5 f r at ^ er greatest elongation, or apparent dis- 
Earth andtance from the Sun, she is 96 times the breadth of 
Mercury. ^^ i ummar y f rorn his centre ; which is almost 
double of Mercury's greatest elongation. Her or- 
bit is included by the Earth's ; for ii it were not, 
she might be seen as often in opposition to the Sun, 
as she is in conjunction with him ; but she has ne- 
ver been seen 90 degrees, or a fourth part of a circle 
from the Sun. 

She is our 28. When Venus appears west of the Sun, she 
ImTeven- r * ses before him in the morning, and is called the 
ing slur by morning star: when she appears east of the Sun, 
turns. she shines in the evening after he sets, and is then 
called the evening star: being each in its turn 
for 290 days. It may perhaps be surprising at 
first view, that Venus should keep longer on the east 
or west of the Sun, than the whole time of her pe- 
riod round him. But the difficulty vanishes when 
we consider that the Earth is all the while going 
round the Sun the same way, though not so quick 
as Venus : and therefore her relative motion to the 

perfectly with Cassini that the spots, which are seen on the surface 
of Venus, advance about 15 in 24 h. but he asserts that he could 
not perceive they had made any advance in 3 h. and therefore con- 
dudes that instead of making one complete revolution and 15 of an- 
other, as Cassini conjectured, in 24 h. those spots advance but the odd 
15 in that time, and that the time of a revolution is somewhat more 
than 24 days. The arguments in favour of the two hypothv ses are 
very equal ; but almost every astronomer, except Mr. Ferguson* 
has adopted Cassini's. 



Of the Solar System. 43 

Earth must in every period be as much slower than 
her absolute motion in her orbit, as the Earth du- 
ring that time advances forward in the ecliptic ; 
which is 220 degrees. To us she appears, through 
a telescope, in all the various shapes of the moon. 

29. The axis of Venus is inclined 75 degrees to 
the axis of her orbit; which is 51* degrees more 
than our Earth's axis is inclined to the axis of the 
ecliptic : and therefore her seasons vary much more 
than ours do. The north pole of her axis inclines 
toward the 20th degree of Aquarius ; our Earth's 
to the beginning of Cancer ; consequently the 
northern parts of Venus have summer in the signs 
where those of our Earth have winter, and vice 
-versa. 

30. The* artificial day at each pole of Venus is Remark- 
as long as ll^lf natural days on our Earth. pelran P ces. 

31. The Sun's greatest declination on each side Her tro- ' 
of her equator amounts to 75 decrees ; therefore P i( r s an . d 

, t polar cir- 

herj tropics are only 15 degrees from her poles ; cks how 
and her ]| polar circles are as far from her equator, situate. 
Consequently the tropics of Venus are between her 
polar circles and her poles ; contrary to what those 
of our Earth are. 

32. As her annual revolution contains only 9.* The Sun's 
of her days, the Sun will always appear to go dail y 
through a whole sign, or twelfth part of rier c 
orbit, in a little more than three quarters of her 

* The time between the Sun's rising and setting. 

t One entire revolution, or 24 hours. 

\ These are lesser circles parallel to the equator, and as many 
degrees from it, toward the poles, as the axis of the planet is inclined 
to the axis of its orbit. When the Sun is advanced so far north or 
south of the equator, as to be directly over either tropic, he goes no 
farther ; but returns toward the other. 

|| These are lesser circles round the poles, and as far from them 
as the tropics are from the equator. The poles are the very north 
and south points of the planet. 



44 



Of the Solar System. 



natural day, or nearly in 18| of our days and 
nights. 

33 ' Because her da >" is so g reat a P^* of her year, 
. the Sun changes his declination in one day so mi: hu 
that if he passes vertically, or directly over fctaci of 
any given place on the tropic, the next day he will 
be 26 degrees from it ; and whatever place he passes 
vertically over when in the Equator, one day's re- 
volution will remove him 36| degrees from it. So 
that the Sun changes his declination e % very day in 
Venus about 14 degrees more, at a mean rate, than 
he does in a quarter of a year on our Earth. This 
appears to be providentially ordered, for preventing 
the too great effects of the Sun's heat, (which is 
twice as great on Venus as on the Earth,) so that 
he cannot shine perpendicularly on the same places 
for two days together; and on that account, the 
heated places have time to cool 

To deter- 34. if t h e inhabitants about the north pole of 

po'mts of ^ enus lix their south, or meridian line, through that 

the com- part of the heavens where the Sun comes to his 

her 5 poles. g reatest height, or north declination, and call those 

the east and west points of their horizon, which are 

90 degrees on each side from that point where the 

horizon is cut by the meridian line, these inhabitants 

will have the following remarkable appearances 

The Sun will rise 22| degrees north of the 
cast, and going on 112| degrees, as measured on 
the plane of the* horizon, he will cross the me- 
ridian at an altitude of 12|- degrees ; then making 
an entire revolution without setting, he will cross 
it again at an altitude of 48| degrees. At the 
next revolution he will cross the meridian as he 
comes to his greatest height and declination, at the 

* The limit of any inhabitant's view, where the sky seems tr, 
touch the planet all raund him. 



Of the Solar System. 45 

altitude of 75 degrees ; being then only 15 degrees 
from the zenith* or that point of the heavens which 
is directly over head : and thence he will descend in 
the like spiral manner, crossing the meridian first at 
the altitude of 48*. degrees, next at the altitude of 
12| degrees ; and going on thence lli^ degrees, he 
will set 22| degrees north of the west. So that, af- 
ter having made 4| revolutions above the horizon, 
he descends below it to exhibit the like appearances 
at the south pole. 

35. At each pole, the Sun continues half a year Surpris- 
without setting in summer, and as long without 
rising in winter ; consequently the polar inhabitants at her 
of Venus have only one day and one night in the poles " 
year ; as it is at the poles of our earth. But the 
difference between the heat of summer and cold of 
winter, or of mid-day and mid-night, on Venus, 

is much greater than on the Earth : because on Ve- 
nus, as the Sun is for half a year together above the 
horizon of each pole in its turn, so he is for a con- 
siderable part of that time near the zenith ; and du- 
ring tne other half of the year always below 7 the ho- 
rizon, and for a great part of that time at least 70 
degrees from it. Whereas, at the poles of our 
Earth, although the Sun is for half a year together 
above the horizon ; yet he never ascends above, nor 
descends below it, more than 23? degrees. When 
the Sun is in the equinoctial, he is seen with one half 
of his disc above the horizon of the north pole, and 
the other half above the horizon of the south pole ; 
so that his centre is in the horizon of both poles : 
and then descending below the horizon of one, he 
ascends gradually above that of the other. Hence, 
in a year, each pole has one spring, one autumn, a 
summer as long as them both, and a winter equal in 
length to the other three seasons. 

36. At the polar circles of Venus, the seasons At Lfirpo- 

J*r circles. 



46 Of the Solar System. 

are much the same as at the equator, because there 
are only 15 degrees between them, $ 31; only the 
winters are not quite so long, nor the summers so 
short : but the four seasons come twice round every 
year. 

At her 27. At Venus's tropics, the Sun continues for 
about fifteen of our weeks together without setting 
in summer ; and as long without rising in winter. 
While he is more than 15 degree from the equator, 
he neither rises to the inhabitants of the one tropic, 
nor sets to those of the other ; whereas, at our ter- 
restrial tropics, he rises and sets every day of the 
year. 

38. At Venus's tropics, the seasons are much 
the same as at her poles ; only the summers are a 
little longer, and the winters a little shorter* 

At her 39. At her equator, the days and nights are al- 
ways of the same length ; and yet the diurnal and 
nocturnal arches are very different, especially when 
the Sun's declination is about the greatest : for then, 
his meridian altitude may sometimes be twice as 
great as his midnight depression, and at other times 
the reverse. When the Sun is at his greatest cle- 
clination, either north or south, his rays are as ob- 
lique at Venus's equator, as they are at London on 
the shortest day of winter. Therefore, at her equa- 
tor there are two winters, two summers, two springs, 
and two autumns every year. But because the -Sun 
stays for some time near the tropics, and passes so 
quickly over the equator, every winter there will be 
almost twice as long as summer : the four seasons 
returning twice in that time, which consist only of 
9 days. 

40. Those parts of Venus which lie between 
the poles and tropics, between the tropics and polar 
circles, and also between the polar circles and equa- 
tor, partake more or less of the phenomena of those 
circles, as they are more or less distant from them. 



Of the Solar System. 4,7 

41. From the quick change of the Sun's declina- Great dif- 
tion it happens, that if he rises due east on any clay, [^Sun's* 
he will not set due west on that day, as with us. amplitude 

For if the place where he rises due east be on the at ? isin 
. and set- 

equator, he will set on that day almost west-north- ting. 

west, or about 18| degrees north of' the west. But 
if the place be in 45 degrees north latitude, then 
on the day that the Sun rises due east he will set 
north- west- by- west, or 33 degrees north of the west. 
And in 62 degrees north latitude, when he rises in 
the east, he sets not in that revolution, but just 
touches the horizon 10 degrees to the west of the 
north point ; and ascends again, continuing for 3-J 
revolutions above the horizon without setting. 
Therefore no place has the forenoon and afternoon 
of the same day equally long, unless it be on the 
equator, or at the poles. 

42. The Sun's altitude at noon, or any other The long- 
time of the day, and his amplitude at rising and t V de of 

J ... .. places ea- 

setting, being very different at places on the same S n y found 
parallel of latitude, according to the different longi- in Venus - 
tudes of those places, the longitude will be almost 
as easily found on Venus, as the latitude is found 
on the Earth. This is an advantage we can never 
have, because the daily change of the Sun's decli- 
nation, is by much too small for that important 
purpose. 

43. On this planet, where the Sun crosses theHerequi- 
equator in any year, he will have 9 degrees of de- ^quane? 
clination from that place on the same day and hour of a day 
next year, and will cross the equator 90 degrees far- 

ther to the west ; which makes the time of the equi- 
nox a quarter of a day (or about six of our days) 
later every year. Hence, although the spiral in 
which the Sun's motion is performed be of the same 
sort every year, yet it will not be the very same ; 
because the Sun will not pass vertically over the 
same places till four annual revolutions are finished, 

G 



48 Of the Solar System. 

Every 44. We may suppose that the inhabitants of Ve- 
Sa?*teap nus w ^ ke carem i to a dd a day to some particular 
3-&arta part of every fourth year ; which will keep the same 
to Venus. seasons to the same days. For, as the great annual 
change of the equinoxes and solstices shifts the sea- 
sons a quarter of a day every year, they would be 
shifted through all the days of the year in 36 years. 
But by means of this intercalary day, every fourth 
year will be a leap-year ; which will bring her time to 
an even reckoning r and keep her calendar always right, 
when she 45. Venus's orbit i> inclined 3 degrees 24 mi- 
pear^m nutes to the Earth's; and crosses it in the 15th de- 
the Sun. grees of Gemini and of Sagittarius ; and therefore, 
when the Earth is about these points of the ecliptic 
at the time that Venus is in her inferior conjunction, 
she will appear like a spot on the Sun, and afford a 
more certain method of finding the distances of all 
the planets from the Suo, than any other yet known. 
But these appearances happening very seldom, will 
be only twice visible at London for one hundred and 
ten years to come. The first time will be in 1761, 
June the 6th, in the morning; and the second in 1769,. 
on the 3d of Ju?te, in the evening. Excepting such 
transits as these, she exhibits the same appearances 
to us regularly every eight years ; her conjunctions, 
elongations, and times of rising and setting, being, 
very nearly the same, on the same days as before, 
she may 46. Venus may have a satellite or moon, al- 
mo V on%i- though it be undiscovered by us. This will not 
though appear very surprising,, if we consider how incon- 
veniently we are placed for seeing it. For its en- 
lightened side can never be fully turned toward 
us, except when Venus is beyond the Sun ; and 
then, as Venus appears but little larger than an or- 
dinary star, her moon may be too small to be per- 
ceived at such a distance. * When she is between us 
and the Sun, her full moon has its dark side toward 
us ; and then we cannot see it any more than we 
can our own moon at the time of change. When 



Of the Solar System. 49 

Venus is at her greatest elongation, we have but Plate I, 
one half of the enlightened side of her full moon 
toward us ; and even then it may be too far distant 
to be seen by us. But if she have a moon, it may 
certainly be seen with her upon the Sun, in the year 
1761; unless its orbit be considerably inclined to 
the ecliptic : for if it should be in conjunction or op- 
position at that time, we can hardly imagine that it 
moves so slow as to be hid by Venus all the six 
-hours that she will appear on the Sun's disc*. 

47. The EARTH is the next planet above Venus The Earth 
in the system. It is 82 millions of miles from the Pip. i. 
Sun, and goes round him, in the circle , in 365 

days 5 hours 49 minutes, from any equinox or sol- 
stice to the same again ; but from any fixed star to 
the same again, as seen from the Sun, in 365 days 
6 hours and 9 minutes.: the former being the length its diurnal 
of the tropical year, and the latter lfoe length of theJ^jJJJ"* 
sidereal. It travels at the rate of 58 thousand miles 
every hour; which motion, though 120 times swift- 
er than that of a cannon-ball, is little more than half 
as swift as Mercury's motion in his orbit. The 
Earth's diameter is 7970 miles; and by turning 
round its axis every 24 hours, from west to east, it 
causes an apparent diurnal motion of all the heaven- 
ly bodies, from east to west. By this rapid motion 
of the Earth on its axis, the inhabitants about the 
equator are carried 1042 miles every hour, while 
those on the parallel of London are carried only 
about 580; besides the 58 thousand miles, by the 
annual motion above-mentioned, which is common 
to all places whatever. 

48. The Earth's axis makes an angle of 23*. de- inclination 
grees with the axis of its orbit; and keeps always ? it8 "^ 
the same oblique direction ; inclining toward the 

... * Both her transits are over since this was written, and no satel- 
lite was seen with Venus on the bun's disc. 



50 Of the Solar System. 

same fixed star* throughout its annual course, 
which causes the returns of spring, summer, au- 
tumn, and winter ; as will be explained at large in 
the tenth chapter. 

A proof of 49. The Earth is round like a globe ; as appears, 
L B 7 its shadow in eclipses of the Moon ; which 
shadow is always bounded by a circular line ; 314. 
2. By our seeing the masts of a ship while the hull 
is hid by the convexity of the water. 3. By its hav- 
ing been sailed round by many navigators. The 
hills take oft' no more from the roundness of the 
Earth in comparison, than grains of dust do from 
the roundness of a common globe, 
its num. 50. The seas and unknown parts of the Earth (by 
a measurement OI * ^ ie best maps) contain 160 mil- 
lions 522 thousand and 26 square miles ; the inhab- 
ited parts 38 millions 990 thousand 569 : Europe 4 
millions 456 thousand and 65 ; Asia 10 millions 768 
thousand 823; Africa 9 millions 654 thousand 807; 
America 14 millions 1 10 thousand 874. In all, 199 
millions 512 thousand 595; which is the number of 
square miles on the whole surface of our globe. 
The pro- 51. Dr. LONG, in the first volume of his Astro- 
portion of nom y p. 168, mentions an ingenious and easy me- 

landand , / r r* v ,111 

S ea. thod of finding nearly what proportion the land 
bears to the sea ; which is, to take the papers of a 
large terrestrial globe, and after separating the land 
from the sea, with a pair of scissars, to weigh them 
carefully in scales. This supposes the globe to be 
exactly delineated, and the papers all of equal thick- 
ness. The doctor made the experiment on the pa- 
pers of Mr. SEN EX'S seventeen inch globe; and 
found that the sea-papers weighed 349 grains, and 
the land only 124 : by which it appears that almost 

* This is not strictly true, as will appear when we come to treat 
of the recession of the equinoctial points in the heavens, 246 ; which 
recession is equal to the deviation of the Earth's axis from its pa- 
rallelism ; but this is rather too small to be sensible in an age, ex- 
cept to those who make very nice observations. 



Of the Solar System. 51 

three fourth parts of the surface our Earth between 
the polar circles are covered with water, and that lit- 
tle more than one fourth is dry land. The doctor 
omitted weighing all within the polar circles ; be- 
cause there is no certain measurement of the land 
within them, so as to know what proportion it bears 
to the sea. 

52. The MOON is not a planet, but only a satel- The 
lite or attendant of the Earth ; going round the Earth M 
from change to change in 29 days 12 hours and 44 
minutes ; and round the Sun with it every year. The 
Moon's diameter is 2180 miles; and her distance 
from the Earth's centre 240 thousand. She goes 
round her orbit in 27 days 7 hours 43 minutes, 
moving about 2290 miles every hour; and turns 
round her axis exactly in the time that she goes round 
the Earth, which is the reason of her keeping always 
the same side toward us, and that her day and night, 
taken together, is as long as our lunar month. 

53. The Moon is an opaque globe, like the Earth, Her 
and shines only by reflecting the light of the Sun : P hase 
therefore, while that half of her which is toward the 
Sun is enlightened, the other half must be dark and 
invisible. Hence, she disappears when she comes 
between us and the Sun ; because her dark side is 
then toward us. When she is gone a little way 
forward, we see a little of her enlightened side ; 
which still increases to our view, as she advances 
forward, until she comes to be opposite to the Sun ; 

and then her whole enlightened side is toward the 
Earth, and she appears with a round illumined orb, 
which we call the^// moon : her dark side being 
then turned away from the Earth. From the full 
she seems to decrease gradually as she goes through 
the other half of her course ; shewing us less and 
less of her enlightened side every day, till her next 
change or conjunction with the Sun, and then she 
disappears as before. 



52 Of the Solar System. 

A -proof 54. This continual change of the Moon's phases 
'^ e s ^ wt demonstrates that she shines not by any light of her 
by her own ; for if she did, being globular, we should ai- 
ovm light. W ays see her with a round full orb like the Sun. 

Her orbit is represented in the scheme by the little 
* J - L circles, upon the Earth's orbit . It is indeed 

drawn fifty times too large in proportion to the 

Earth's; and yet is almost to small too be seen in the 

diagram. 
One hair 55^ The Moon has scarce any difference of sea- 

of her al- , . . J ,. 

ways en- sons; her axis being almost perpendicular to the 
lightened, ecliptic. What is very singular, one half of her 
has no darkness at all ; the Earth constantly afford- 
ing it a strong light in the Sun's absence ; while 
the other half has a fortnight's darkness, and a fort- 
night's light by turns. 

Our Earth 56. Our Earth is a moon to the Moon; waxing 
Tnooo, ar *d waneing regularly, but appearing thirteen times 
as big, and affording her thirteen times as much 
light, as she does to us. When she changes to us, 
the Earth appears full to her ; and when she is in 
her first quarter to us, the Earth is in its third quar- 
ter to her ; and vice versa. 

57. But from one half of the Moon, the Earth 
is never seen at all. From the middle of the other 
half, it is always seen over head ; turning round al- 
most thirty times as quick as the Moon does. From 
die circle which limits our view of the Moon, only 
one half of the Earth's side next her is seen ; the 
other half being hid below the horizon of all places 
on that circle. To her, the Earth seems to be the 
largest body in the universe : appearing thirteen 
times as large as she does to us. 

58. The Moon has no atmosphere of any visi- 
ble density surrounding her, as we have : for if she 
had, we could never see her edge so well defined 

A proof as it appears ; but there would be a sort of mist 
Moon's or h az * ness around her, which would make the 
having no stars look fainter, when they are seen through it. 



atmos- B u t observation proves, that the stars which disap- 



Of the Solar System. 

pear behind the Moon, retain their full lustre until 
they seem to touch her very edge, and then they 
vanish in a moment. This has been often observed 
by astronomers, but particularly byCAssiNi of the 
star p in the breast of Virgo, which appears single 
and round to the bare eye j but through a refracting 
telescope of 16 feet, appears to be two stars so near 
together, that the distance between them seems to 
be but equal to one of their apparent diameters. 
The moon was observed to pass over them on the 
21st of April 1720,. A*. S. and as her dark edge 
drew near to them, it caused no change whatever 
in their colour or situation. At 25 min. 14 sec. 
past 12 at night, the most westerly of these stars was. 
hid by the dark edge of the Moon ; and in 30 se- 
conds afterward, the most easterly star was hid : each 
of them disappearing behind the Moon in an instant, 
without any preceding diminution of magnitude or 
brightness ; \vhich by no means could have been the 
case if there were an atmosphere round the Moon : 
for then one of the stars falling obliquely into it be- 
fore the other, ought, by refraction, to have suffered 
some change in its colour, or in its distance from the 
other star, which was not yet entered into the atmos- 
phere. But no such alteration could be perceived ; 
though the observation was made with the utmost 
attention to that particular ; and was very proper to 
have made such a discovery. The faint light which 
has been seen all round the Moon, in total eclipses 
of the Sun, has been observed, during the time of 
darkness, to have its centre coincident with the cen- 
tre of the Sun ; and was therefore much more likely 
to arise from the atmosphere of the Sun, than from 
that of the Moon ; for if it had been owing to the 
latter, its centre would have gone along with the 
Moon's.* 

* It has been lately ascertained by Mr. Schroeter, that the Moon 
is indeed furnished with an atmosphere, similar to that cf the Earth, 
and of proportional density ; the former being about one 29th par? 
the density of the latter. 



54 Of the Solar System 

Nor seas, 5 9< jf tnere were seas j n the Moon, she could have 
no clouds, rains, or storms, as we have ; because 
she has no such atmosphere to support the vapours 
which occasion them. And every one knows, that 
when the Moon is above our horizon in the night 
time, she is visible, unless the clouds of our atmos- 
phere hide her from our view; and all parts of her 
appear constantly with the same clear, serene, and 

of c^erns CallT1 aS P CCt - But th SC dark P artS of the Moon, 

and deep which were formerly thought to be seas, are now 
pits. found to be only vast deep cavities, and places which 
reflect not the Sun's light so strongly as others ; hav- 
ing many caverns and pits, whose shadows fall with- 
in them, and are always dark on the side next the 
Sun. This demonstrates their being hollow : and 
most of these pits have little knobs like hillocks 
standing within them, and casting shadows also ; 
which cause these places to appear darker than others 
which have fewer, or less remarkable caverns. All 
these appearances shew that there are no seas in the 
Moon ; for if there were any, their surfaces \vould 
appear smooth and even like those on the Earth. 
The stars 60. There being no atmosphere about the Moon, 
s!bie y to VI " tne heavens in the day time have the appearance of 
the Moon, night to a Lunarian who turns his back toward the 
Sun ; the stars then appearing as bright to him as 
they do in the night to us. For it is entirely owing 
to our atmosphere that the heavens are bright about 
us in the day. 

61. As the Earth turns round its axis, the several 
continents, seas, and islands, appear to the Moon's 
inhabitants like so many spots of different forms and 
brightness, moving over its surface ; but much faint- 
er at some times than others, as our clouds cover 
The Earth them or leave them. By these spots the Lunarians 
the Moon. can determine the time of the Earth's diurnal motion, 
just as we do the motion of the Sun ; and perhaps 
they measure their time by the motion of the Earth's 
spots; for they cannot have a truer dial, 



Of the Solar System. 55 

62. The Moon's axis is so nearly perpendicular Plate /. 
to the ecliptic, that the Sun never removes sensibly 
from her equator : and the * obliquity of her orbit, 
which is next to nothing as seen from the Sun, can- 
not cause the Sun to decline sensibly from her equa- 
tor. Yet her inhabitants are not destitute of means HOW the 
for ascertaining the length of their year, though their 



method and ours must differ. We can know the the length 
length of our year by the return of our equinoxes ; } 
but the Lunarians, having always equal day and 
night, must have recourse to another method ; and 
we may suppose, they measure their year by observ- 
ing when either of the poles of our Earth begins to 
be enlightened, and the other to disappear, which is 
always at our equinoxes; they being conveniently 
situate for observing great tracts of land about our 
Earth's poles, which are entirely unknown to us. 
Hence we may conclude, that the year is of the 
same absolute length both to the Earth and Moon, 
though very different as to the number of days : we 
having 365-J natural days, and the Lunarians only 
12 ; every day and night in die Moon being as 
as long as 29j on the Earth* 

63. The Moon's inhabitants, on the side next the and the 
Earth, may a easily find the longitude of their pla-^fheh- 
ces as we can find the latitude of ours. For the places. 
Earth keeping constantly, or very nearly so, over 

one meridian of the Moon, the east or west distan- 
ces of places from that meridian are as easily found, 
as we can find our distance from the equator by the 
altitude of our celestial poles. 

64. The planet MARS is next in order, being the Mars, 
first above the Earth's orbit. His distance from the 
Sun is computed to be 125 millions of miles ; and 

* The Moon's orbit crosses the ecliptic in two opposite points, 
called the moon's nodes; so that one half of her orbit is above the 
ecliptic, and the other half below it. The angle of its obliquity is 
5 1-3 degrees. 

H 



56 Of the Solar System. 

by travelling at the rate of 47 thousand miles every 
$S> * hour, in the circle <p , he goes round the Sun in 686 
of our days and 23 hours, which is the length of his 
year, and contains 66 7~ of his days ; every day and 
night together being 40 minutes longer than with us. 
His diameter is 4444 miles ; and by his diurnal ro- 
tation, the inhabitants about his equator are carried 
556 miles every hour. His quantity of light and 
heat is equal but to one half of ours ; and the Sun 
appears but half as large to his inhabitants as to us. 
His at- 65. This planet being but a fifth part of the mag- 
mosphere nitude of the Earth, if any moon attends him, it 
and phas- must j^ e verv sm ^ an( j ] ias no t y e t been discover. 

ed by our best telescopes. He is of a fiery red co- 
lour, and by his appulses to some of the fixed stars, 
seems to be encompassed by a very gross atmos- 
phere. He appears sometimes gibbous, but never 
horned; which shews both that his orbit includes the 
Earth's within it, and that he shines not by his own 
light. 

66. To Mars, our Earth and Moon appear like 
two moons, a larger and a less : changing places 
with one another, and appearing sometimes horned, 
sometimes half or three quarters illuminated, but 
never full ; nor at most above one quarter of a de- 
gree from each other ; although they are 240 thou- 
sand miles asunder. 

HOW the 67. Our Earth appears almost as large to Mars aa 
other pia- Venus does to us ; and at Mars it is never seen above 
pear to" 4 ^ degrees from the Sun. Sometimes it appears to 
Mars, pass over the disc of the Sun, and so do Mercury 
and Venus. But Mercury can never be seen from 
Mars by such eyes as ours, unassisted by proper in- 
struments; and Venus will be as seldom seen as we 
see Mercury. Jupiter and Saturn are as visible to. 
the inhabitants of Mars as to us. His axis is per, 
' pendicular to the ecliptic, and his orbit is inclined to 

it in an angle of 1 degree 50 minutes. 
Jupiter. 68 ' J UPITE R> tne largest of all the planets, ia 
still higher in the system, being about 426 millions. 



Of the Solar System. 57 

of miles from the Sun : and going at the rate of ^f. ate L 
25 thousand miles every hour, in his orbit, which 
is represented by the circle % . He finishes his an- 
nual period in eleven of our years 314 days and 12 
hours. He is above 1000 times as large as the 
Earth; his diameter being 81,000 miles; which 
is more than ten times the diameter of the Earth. 

69. Jupiter turns round his axis in 9 hours 56 the num. 
minutes; so that his year contains 10 thousand ^Pj^f 

1 1 i* r* t HAS C<** 

470 days ; the diurnal velocity of his equatorial 
parts being greater than that with which he moves 
in his annual orbit a singular circumstance, as 
far as we know. By this prodigious quick rota- 
tion, his equatorial inhabitants are carried 25 thou- 
sand 920 miles every hour (which is 920 miles an 
hour more than an inhabitant of our Earth's equa- 
tor moves in 24 hours) beside the 25 thousand 
above mentioned, which is common to all parts of 
his surface, by his annual motion. 

70. Jupiter is surrounded by faint substances, His belts 
called belts; in which so many changes appear, an 
that they are generally thought to be clouds; for 
some of them have been first interrupted and bro- 
ken, and then have vanished entirely. They have 
sometimes been observed of different breadths, and 
afterward have all become nearly of the same 
breadth. Large spots have been seen in these belts ; 

and when a belt vanishes, the contiguous spots dis- 
appear with it. The broken ends of some belts 
have been generally observed to revolve in the same 
time with the spots : only those nearer the equator 
in somewhat less time than those near the poles ; 
perhaps on account of the Sun's greater heat near 
the equator, which is parallel to the belts and course 
of the spots. Several large spots, which appear 
round at one time, grow oblong by degrees, and 
then divide into two or three round spots. The 
periodical time of the spots near the equator is 9 
hours 50 minutes, v but of these near the poles 9 
hours 56 minutes. See Dr. SMITH'S Optics, 
5 1004, & sej. 



58 Of the Solar System. 



of ^** ^e ax * s ^ J u pi ter ' ls so nearly perpendicu- 
; lar to his orbit, that he has no sensible change of 
seasons; which is a great advantage, and wisely 
ordered by the Author of Nature. For, if the 
axis of this planet were inclined any considerable 
number of degrees, just so many degrees round 
each pole would in their turn be almost six of our 
years together in darkness. And, as each degree 
of a great circle on Jupiter contains 706 of our 
miles, at a mean rate, it is easy to judge what vast 
tracts of land would be rendered uninhabitable by 
any considerable inclination of his axis. 
but has 72. The Sun appears but ~ part as large to Ju- 

Soons P* ter as to us ; anc * kis light and heat are in the 
same small proportion, but compensated by the 
quick returns thereof, and by four moons (some 
larger and some less than our Earth) which revolve 
about him : so that there is scarce any part of this 
huge planet, but what is, during the whole night, 
enlightened by one or more of these moons ; except 
his poles, where only the farthest moons can be 
seen, and where light is not wanted ; because the 
Sun constantly circulates in or near the horizon, 
and is very probably kept in view of both poles by 
the refraction of Jupiter's atmosphere, which, if it 
be like ours, has certainly refractive power enough 
for that purpose. 

Their pe- 73. The orbits of these moons are represented in 
nods t k e scnerne O f the solar system by four small circles 

round Ju- *',-*.. T i 

piter. * marked 1,2, 3, 4, on Jupiter's orbit 2/ ; drawn, in- 
deed, fifty times too large in proportion to it. 
The first moon, or that nearest to Jupiter, goes 
round him in 1 day 18 hours and 36 minutes of our 
time ; and is 229 thousand miles distant from his 
centre: the second performs its revolution in 3 days 
13 hours and 15 minutes, at 364 thousand miles dis- 
tance: the third in 7 days 3 hours and 59 minutes, 
at the distance of 580 thousand miles : and the fourth, 
or outermost, in 16 days 18 hours and 30 minutes, 
at the distance of one million of miles from his centre., 



Of the Solar Sys' 



cm. 



74. The angles under which the orbits of Jupi- 

,, i T- i of their or- 

ter's moons are seen from the iLarth, at its mean bits, and 
distance from Jupiter, are as follows : The first, distances 
3' 55"; the second, 6' 14"; the third, 9' 58"; and { m Jui 
the fourth, 17' 30". And their distances from Ju- 
piter, measured by his semi-diameters, are thus : 
The first, 5f; the second 9, the third, 14|J; and 
the fourth, 25~*. This planet, seen from its HOW he 
nearest moon, appears 1000 times as laree as our a PP ears t& 

,. , . - 11 i his nearest 

Moon does to us; waxing and waneing in all her moon. 
monthly shapes, every 42- hours. 

75. Jupiter's three nearest moons fall into his Two 
shadow, and are eclipsed in every revolution : butteries' 55 " 
the orbit of the fourth moon is so much inclined, made by 
that it passes by its opposition to Jupiter, without e^of jupi- 
falling into his shadow, two years in every six. Byter's 
these eclipses, astronomers have not only discov- moons - 
cred that the Sun's light takes up eight minutes of 

time in coming to us ; but they have also determin- 
ed the longitudes of places on this Earth, with 
greater certainty and facility, than by any other me- 
thod yet known ; as shall be explained in the ele- 
venth chapter. 

76. The difference between the equatorial and J. 1 ^ reat 
polar diameters of Jupiter is 6230 miles ; for his better 
equatorial diameter is to his polar, as 13 to 12. So the . e( i ua - 
that his poles are 3115 miles nearer his centre than anTpoiar 
his equator is. This results from his quick motion diameters 
round his axis; for the fluids, together with the ot Juplter ' 
light particles, which they can carry or wash away 

with them, recede from the poles, which are at 
rest, toward the equator, where the motion is 
quickest; until there be a sufficient number accu- 
mulated to make up the deficiency of gravity lost 
by ^ the centrifugal force which always arises from a 
quick motion round an axis : and when the defi- 
ciency of wdght or gravity of the particles is made 
up by a sufficient accumulation, there is an equili- 

* CASSINI JSlemens d'SlstronQinie, Liv. ix. Chafi, 3, 



60 Of the Solar System. 

Plate I. brium, and the equatorial parts rise no higher. Our 
The dif- Earth being but a very small planet, compared with 
[ut!"^n ^piter, and its motion round its axis being much 
those of slower, it is less flattened of course. The propor- 
our Earth, tion between its equatorial and polar diameters be- 
ing only as 230 to 229 ; and their difference 36 
miles.* 

Place of 77. Jupiter's orbit is inclined to the ecliptic in an 
his nodes. an g le of ! degree 20 minutes. His ascending node 
is in the 8th degree of Cancer, and his descending 
node in the 8th degree of Capricorn. 

Saturn. 78. SATURN, the remotest of all the planets,f 
is about 780 millions of miles from the Sun ; and 
travelling at the rate of 18 thousand miles every 
Fig. I. hour, in the circle marked ^ > performs its annual 
circuit in 29 years 167 days, and 5 hours of our 
time ; which makes only one year to that planet. 
Its diameter is 67,000 miles; and therefore it is 
near 600 times as large as the Earth. 
His ring-. 79. This planet is surrounded by a thin broad 
Fi r- v - ring, as an artificial globe is by an horizon. The 
ring appears double when seen through a good tele- 
scope, and is represented, by the figure, in such an 
oblique view as that in which it generally appears. 
It is inclined 30 degrees to the ecliptic, and is 
about 21 thousand miles in breadth; which is equal 
to its distance from Saturn on all sides. There is 
reason to believe that the ring turns round its axis ; 

* According to the French measures, a degree of the meridian at 
the equator contains 340606.63 French feet ; and a degree of the 
meridian in Lapland contains 344627. 40 : so that a degree in Lap- 
land is 4020.72 French feet (or 4280.02 English feet) longer than a 
degree at the equator. The difference is J^ parts of an English 
mile. Hence, the Earth's equatorial diameter contains 39386196 
French feet, or 41926356 English ; and the polar diameter 3y202920 
French feet, or 41731272 English. The equatorial diameter there- 
fore is 195084 English feet, or 36.948 English miles, longer than the 
axis, 
t The Georgian planet was not discovered when this was written* 



Of the Solar System. 61 

because, when it is almost edge- wise to us, it ap- Platc L 
pears somewhat thicker on one side of the planet 
than on the other ; and the thickest edge has been 
seen on different sides at different times*. Saturn 
having no visible spots on his body, whereby to de- 
termine the time of his turning round his axis, 
the length of his days and nights, and the position 
of his axis, are unknown to usf. 

80. To Saturn, the Sun appears only ~th part as His five 
large as to us ; and the light and heat he receives moons. 
from the Sun are in the same proportion to ours. 
But to compensate for the small quantity of sun- 
light, he has five moons, all going round him on the 
out- side of his ring, and nearly in the same plane 
with it. The first, or nearest moon to Saturn, goes 
round him in 1 day 21 hours 19 minutes; and is 
140 thousand miles from his centre : the second, in 
2 days 17 hours 40 minutes; at the distance of 187 
thousand miles . the third, in 4 days 12 hours 25 
minutes ; at 263 thousand miles distance : the fourth, 
in 15 days 22 hours 41 minutes; at the distance of 
600 thousand miles : and the fifth, or outermost, at 
one million 800 thousand miles from Saturn's cen- 
tre, goes round him in 79 days 7 hours 48 min- 
utes J. Their orbits, in the scheme of the solar sys- Fig. i. 



* Dr. Herschel, from some srxrts he has seen on the exterior ring, 
has determined that it revolves in about 10 1-2 hours. 

t Dr. Herschel having discovered that there are some belt-like 
appearances on this planet, similar to those which are seen on Jupi- 
ter, concluded that it must revolve on its axis, and that with a pretty 
quick motion. He also thinks he has determined, from some parts of 
those belts which are less black than others, that this revolution is 
performed in 10 hours 16 minutes. 

\ Dr. Herschel has discovered two other moons belonging to Sa- 
turn, which revolves between the nearest of the old ones and the pla- 
net ; so that Saturn is now known to have seven moons. The exteri- 
or of the new satellites, called the sixth, revolves at the distance ot 
near 120 thousand miles, in one day 8 hours 53 minutes; and that 
which is nearest the primary, termed the seventh, is distant from it 
about 91 thousand miles, and performs its revolution in 22 hours 37 
minutes: but the Doctor esteems this last article rather uncertain. 
Jie has moreover discovered that the fifth satellite revolves on its 



Of the Solar System. 

tern, are represented by the five small circles, mark. 
ed 1, 2, 3, 4, 5, on Saturn's orbit; but these, like 
the orbits of the other satellites, are drawn fifty times 
too large in proportion to the orbits of their primary 
planets. 

81. The Sun shines almost fifteen of our years 
together on one side of Saturn's ring without set- 
ting, and as long on the other, in its turn. So that 
the ring is visible to the inhabitants of that planet 
for almost fifteen of our years, and as long invisible, 
by turns, if its axis have no inclination to its ring : 
but if the axis of the planet be inclined to the ring, 
suppose about 30 degrees, the ring will appear and 

his ring, disappear once every natural day, to all the inhabi- 
tants within 30 degrees of the equator on both 
sides, frequently eclipsing the Sun in a Saturnian 
day. Moreover, if Saturn's axis be thus inclined 
to his ring, it is perpendicular to his orbit; and 
thereby the inconvenience of different seasons to 
that planet is avoided. For considering the length 
of Saturn's year, which is almost equal to 30 of 
ours, what a dreadful condition must the inhabitants 
of his polar regions be in, if they be half that time de- 
prived of the light and heat of the Sun! which is not 
their case alone, if the axis of the planet be perpendi- 
cular to the ring, for then the ring must hide the Sun 
from vast tracts of land on each side of the equator 
for 13 or 14 of our years together, on the south side 
and north side, by turns, as the axis inclines to or 
from the Sun. This furnishes another good pre- 
sumptive proof of the inclination of Saturn's axis 
to its ring, and also of his axis being perpendicular 
to its orbit. 

HOW the 82. This ring, seen from Saturn, appears like 
a vast luminous arch in the heavens, as if it did 



Saturn 

and to us. 

axis, as our Moon does, in the same time it revolves in its orbit : a 
very remarkable as well as curious coincidence in the motions of the 
secondaries to two different, and very distant primaries. And it is 
probably a general law of nature, that all secondary planets con- 
stantly present the same face towards \heirfirimaries. 



Of the Solar System. 63 

not belong to the planet. When we see the ring 
most open, its shadow upon the planet is broadest; 
and from that time the shadow grows narrower, as 
the ring appears to do to us ; until by Saturn's an- 
nual motion the Sun comes to the plane of the ring, 
or even with its edge ; which being then directed to- 
ward us, becomes invisible on account of its thin- 
ness ; as shall be explained more largely in the tenth 
chapter, and illustrated by a figure. The ring dis- in wha t 
appears twice in every annual revolution of Saturn ; ^iTap** 
namely, when he is in the -20th degrees of Pisces and pears to 
of Virgo. And when Saturn is in the middle be-^f^ 
tween these points, or in the 20th degree either of in what 
Gemini or of Sagittarius, hi&ring appears most open * ign ^ s 
to us; and then its longest diameter is to its shortest, S> s t open 
as 9 to 4. tous - 

83. To such eyes as ours, unassisted by instru- _ 

T . . J , J . No planet 

ments, Jupiter is the only planet that can be seen but Sa- ' 
from Saturn ; and Saturn the only planet that can be turn can be 
seen from Jupiter. So that the inhabitants of these jupherT 
two planets must either see much farther than we do, nor any ' 
or have equally good instruments to carry their sight [ b ^" 
to remote objects, if they know that there is such a sides ju- 
body as our Earth in the universe; for the Earth isP iter - 
no larger, seen from Jupiter, than his moons are, seen 
from the Earth; and if his large body had not first 
attracted our sight, and prompted our curiosity to 
view him with a telescope, we should never have 
known any thing of his moons; unless indeed by I 

chance, we had directed the telescope toward that 
small part of the heavens where they were, at the time 
of observation. And the like is true of the moons of 
Saturn. 

84. The orbit of Saturn is 2i degrees inclined to puce qf 
the ecliptic or orbit of our Earth, and intersects it 

in the 22d degrees of Cancer and of Capricorn ; so 
that Saturn's nodes are only 14 degrees from those 
of Jupiter, 77*. 

* Since Mr. Ferguson's death, a seventh primary planet, belong- G 
ing to the solar system, has been discovered by Dr, Herschel, and Si 



64 Of the Solar System. 



35. The quantlty o f light afforded by the Sun to 
much Jupiter, being but Ath part, and to Saturn only -sVh 
stronger^ part of what we enjoy ; may at first thought induce us 
and Sa- ** to believe that these two planets are entirely unfit for 
turn than rational beings to dwell upon. But, that their light 
ly behey 1 . " * s not so we ^k as we imagine, is evident from their 
ed. brightness in the night-time ; and also from this re- 
markable phenomenon, that when the Sun is so 

called by him, the Georgium Sidus, out of respect to his pre- 
sent Majesty King George the III. This planet is still higher in the 
system than Saturn, being about 1565 millions of miles from the 
Sun ; and performs its annual circuit in 83 years, 140 days and 8 
hours of our time: consequently its motion in its orbit, is at the rate 
of about 7 thousand miles in an hour. To a good eye unassisted 
by a telescope, this planet appears like a faint star of the 5th mag- 
nitude ; and cannot be readily distinguished from a fixed star with 
a less magnifying power than 200 times. Its apparent diameter 
subtends an angle of no more than 4" to an observer on the Earth ; 
but its real diameter is about 34,000 miles, and consequently, it is 
about 80 times as large as the Earth. Hence we may infer that as 
the Earth cannot be seen under an angle of quite 1" to the inhabi- 
tants of the Georgian planet, it has never yet been seen by them, 
unless their eyes and instruments are considerably better than ours. 
The orbit of this planet is inclined to the ecliptic in an angle of 
46' 26". Its ascending node is in the 13th degree of Gemini, and 
its descending node in the 13th degree of Sagittarius. As no spots 
have yet been discovered on its surface, the position of its axis, and 
the length of its day and night are not known. 

On account of the immense distance of the Georgian planet from 
the source of light and heat to all the bodies in our system, it was 
highly probable that several satellites, or moons revolved round it : 
accordingly, the high powers of Dr. Herschel's telescopes have en- 
abled him to discover six ; and there may be others which he has 
not yet seen. The first, and nearest to the planet, revolves at the 
distance of 12 of the planet's semi-diameters from it, and performs 
its revolution in 5 days, 21 hours 25 minutes : the second i evolves 
at 16 1-2 semi-diameters of the primary from it, and completes its 
revolution in 8 days 17 hours 1 minute : the third at 19 semi-diam- 
eters, in 10 clays 23 hours 4 minutes : the fourth at 22 semi-dia- 
meters, in 13 days 11 hours 5 minutes: the 5th at 44 semi-diame- 
ters, in 38 days 1 hour 49 minutes: and the sixth at 88 semi-dia- 
meters, in 107 days 16 hours 40 minutes. It is remarkable that the 
orbits of these Satellites are almost at right angles to the plane of 
the ecliptic: and that the motion of all of them, in their orbits is 
retrograde. 



Of the Solar System. 65 

much eclipsed to us, as to have only the 40th part 
of his disc left uncovered by the Moon, the de- 
crease of light is not very sensible ; and just at the 
end of darkness in total eclipses, when his western 
limb begins to be visible, and seems no bigger than 
a bit of fine silver wire, every one is surprised at 
the brightness wherewith that small part of him 
shines. The Moon, when full, affords travellers 
light enough to keep them from mistaking their 
way; and yet, according to Dr. SMITH*, it is 
equal to no more than a 90 thousandth part of the 
light of the Sun : that is, the Sun's light is 90 thou- 
sand times as strong as the light of the Moon when 
full. Consequently, the Sun gives a thousand times 
as much light to Saturn as the full Moon does to us , 
and above three thousand times as much to Jupiter. 
So that these two planets, even without any moons, 
would be much more enlightened than we at first 
imagine ; and by having so many, they may be ve- 
ry comfortable places of residence. Their heat, so 
far as it depends on the force of the Sun's rays, is 
certainly much less than ours ; to which no doubt the 
bodies of their inhabitants are as well adapted as ours 
are to the seasons we enjoy. And if we consider 
that Jupiter never has any winter, even at his poles, 
which probably is also the case with Saturn, the 
cold cannot be so intense on these two planets as is 
generally imagined. Besides, there may be some- 
thing in the nature of their soil, that renders it warm- 
er than that of our Earth ; and we find that all our All our 
heat depends not on the rays of the Sun : for if itp^d^ 
did, we should always have the same months equal- on the 
ly hot or cold at their annual returns. But it is 
otherwise, for February is sometimes warmer than 
May ; which must be owing to vapours and exha- 
lations from the Earth. 

86. Every person who looks upon, and compares 
the systems of moons together, which belong to 

* Optics, Ajct 95. 



ravs. 



66 Of the Solar System. 

Jupiter and Saturn must be amazed at the vast mag- 
nitude of these two planets, and the noble attend- 
ance they have in comparison with our little Earth ; 
and can never bring himself to think, that an infi- 
nitely wise Creator should dispose of all his animals 
and vegetables here, leaving the other planets bare 
it is high- and destitute of rational creatures. To suppose 
WeUiaTail ^ iat ^ e k a( * anv v * cw to our benefit, in creating these 
the plan- moons, and giving them their motions round Jupi- 
ter and Saturn; to imagine that he intended these 
vast bodies for any advantage to us, when he well 
knew they could never be seen but by a few astrono- 
mers peeping through telescopes ; and that he gave 
to the planets regular returns of days and nights, 
and different seasons to all where they would be 
convenient; but of no manner of service to us; ex- 
cept only what immediately regards our own planet 
the Earth. To imagine, I say, that he did all this 
on our account, would be charging him, impiouslyx 
with having done much in vain ; and as absurd as 
to imagine that he has created a little sun and a pla- 
netary system within the shell of our Earth, and in- 
tended them for our use. These considerations 
amount to little less than a positive proof, that all the 
planets are inhabited ; for if they be not, why all this 
care in furnishing them with so many moons, to 
supply those with light which are at the greater dis- 
tances from the Sun? Do we not see that the farther 
a planet is from the Sun, the greater apparatus it 
has for that purpose ? save only Mars, which being 
but a small planet, may have moons too small to be 
seen by us. We know that the Earth goes round 
the Sun, and turns round its own axis, to produce 
the vicissitudes of summer and winter by the former, 
and of day and night by the latter motion, for the 
benefit of its inhabitants. May we not then fairly 
conclude, by parity of reason, that the end or de- 
sign of all the other planets is the same ? and is not 
this agreeable to the beautiful harmony which exists 
throughout the universe ? Surely it is : and this con- 



Of the Solar System. 67 

sideration must raise in us the most magnificent ideas plate r: 
of the SUPREME BEING; who is every where, 
and at all times present ; displaying his power, wis- 
dom and goodness, among all his creatures ; and dis- 
tributing happiness to innumerable ranks of various 
beings ! 

87. In Fig. II. we have a view of the proportion- Fig. n. , 
al breadth of the Sun's face or disc, as seen from j?^ a e 
the different planets. The Sun is represented No. pears to 
1, as seen from Mercury ; No. 2, as seen from Ve-^ differ-. 
nus; No. 3, as seen from the Earth; No. 4, aSet s . P 
seen from Mars ; No. 5, as seen from Jupiter ; and 

No. 6, as seen from Saturn. 

Let the circle B be the Sun, as seen from any pla- Fig. in. 
net at a given distance : to another planet, at double 
that distance, the Sun will appear just of half that 
breadth, as A ; which contains only one fourth part 
of the area or surface of B. For all circles, as \vell 
as square surfaces, are to one another as the squares 
of their diameters or sides. Thus the square A is Fl ' lv * 
just half as broad as the squared; and yet it is plain 
to sight, that B contains four times as much sur- 
face as A. Hence, by comparing the diameters of 
the above circles (Fig. II.) together, it will be found 
that in round numbers, the Sun appears 7 times 
larger to Mercury than to us, 90 times larger to us 
than to Saturn, and 630 times as large to Mercury 
as to Saturn. 

88. In Fig. V. we have a view of the magnitudes Fig. v. 
of the planets, in proportion to each other, and to a 
supposed globe of two feet diameter for the Sun. 

The Earth is 27 times as large as Mercury, very Propor- 
little larger than Venus, 5 times as large as Mars; J^fand 
but Jupiter is 1049 times as large as the Earth, Sa- distances 
turn 586 times as large, exclusive of his ring; 
and the Sun is 877 thousand 650 times as large as 
the Earth. If the planets in this figure were set at 
.heir due distances from a Sun of two feet diame- 
ter, according to their proportionable magnitudes, 
as in our system, Mercury would be 28 yards from 
the Sun's centre ; Venus 51 yards 1 foot ; the Earth 



<>8 Of the Solar Systenu ' 

Plate L 70 yards 2 feet; Mars 107 yards 2 feet ; Jupiter 
370 yards 2 feet ; and Saturn 760 yards 2 feet. The 
comet of the year 1680, at its greatest distance, 
10 thousand 760 yards. Jn this proportion, the 
Moon's distance from the centre of the Earth would 
be only 7 inches. 

AnideaoF 89. To assist the imagination in forming an idea 
their dis- of the vast distances of the Sun, planets and stars, 
:es * let us suppose that a body projected from the Sun 
should continue to fly with the swiftness of a cannon 
ball, /. e. 480 miles every hour ; this body would 
reach the orbit of Mercury, in 7 years 221 days; 
of Venus, in 14 years 8 days; of the Earth, in 19 
years 91 days; of Mars, in 29 years 85 days; of 
Jupiter, in 100 years 280 days; of Saturn, in 184 
years 240 days; to the comet of 1680, at its great- 
est distance from the Sun, -in 2660 years; and to 
the nearest fixed stars, in about 7 million 600 thou- 
sand years. 

Why the 90. As the Earth is not in the centre of the orbits 
planets j n which the planets move, they come nearer to it 
greater andgofartherfrom.it, at different times; on which 
and less at account they appear greater and less by turns. 
times 611 Hence, the apparent magnitudes of the planets arc 
not always a certain rule to know them by. 

91. Under fig. III. are the names and characters 
of the twelve signs of the zodiac, which the reader 
should be perfectly well acquainted with; so as to know 
Fi L the characters without seeing the names. Each sign 
contains 30 degrees, as in the circle bounding the 
solar system; to which the characters of the signs 
are set in their proper places. 

The com- 92. The COMETS are solid opaque bodies, with 
ns - long transparent trains or tails, issuing from that 
side which is turned away from the Sun. They 
move about the Sun in very eccentric ellipses ; and 
are of a much greater density than the Earth ; for 
some of them are heated in every period to such a 
degree, as would vitrify or dissipate any substance 
known to us. Sir ISAAC NEWTON computed the 



Of the Solar System. 69 



heat of the comet which appeared in the year 1680, 
when nearest the Sun, to be 2000 times hotter than 
red-hot iron ; and that being thus heated, it must re- 
tain its heat until it comes round again ; although its 
period should be more than twenty thousand years ; 
though it is computed to be only 575. The method 
of computing the heat of bodies, keeping at any 
known distance from the Sun, so far as their heat 
depends on the force of the Sun's rays, is very easy ; 
and shall be explained in the eighth chapter. 

93. Part of the paths of three comets is delineat- F1 - I- 
ed in the scheme of the solar system, and the years 
marked in which they made their appearance. - 
There are, at least, 21 comets belonging to our sys- They 
tern, moving in all sorts of directions ; and all Ao^SJ^wS? 
which have been observed, have moved through theofthepia- 
ethereal regions and the orbits of the planets, with- pets a f 

rr i MI , ,1 not SOlld. 

out suffering the least sensible resistance in their mo- 
tions ; which plainly proves that the planets do not 
move in solid orbits. Of all the comets, the periods The peri. 
of the above mentioned three only are known with tinware 
any degree of certainty. The first of these comets known. 
appeared in the years 1531, 1607, and 1682; and 
is expected to appear again in the year 1758, and 
every 75th year afterward. The second of them 
appeared in 1532, and 1661, and may be expected 
to return in 1789, and every 129th year afterward. 
The third, having last appeared in 1680, and its 
period being no less than 575 years, cannot return 
until the year 2225. This comet, at its greatest 
distance, is about eleven thousand two hundred mil- 
lions, of miles from the Sun ; and at its least dis- 
tance n\>mthe Sun's centre, which is 49,000 miles, 
is within less than a third part of the Sun's 'semi- di- 
ameter from his surface. In that part of its orbit 
which is nearest the Sun, it flies with the amazing 
swiftness of 880,000 miles in an hour ; and the Sun, 
as seen from it, appears a hundred degrees in breadth ; 
consequently 40 thousand times as large as he ap- 



70 Of the Solar System. 

They pears to us. The astonishing length that this comet 
starTto be runs out mto empty space, suggests to our minds 
at im- an idea of the vast distance between the Sun and 
t ^ e neare st fixed stars; of whose attractions all the 
comets must keep clear, to return periodically, and go 
round the Sun ; and it shews us also, that the near- 
est stars, which are probably those that seem the 
largest, are as big as our Sun, and of the same na- 
ture with him; otherwise, they could not appear so 
large and bright to us as they do at such an im- 
mense distance, 

inferenc- 94 * ^ ie extreme neat > the dense atmosphere, the 
es drawn gross vapours, the chaotic state of the comets, seem 
? t *i rsts ig nt to m ^icate them altogether unfit for the 
" purposes of animal life, and a most miserable habi- 
tation for rational beings ; and therefore some* are 
of opinion that they are so many hells for torment- 
ing the damned with perpetual vicissitudes of heat 
and cold. But when we consider, on the other hand, 
the infinite power and goodness of the Deity ; the 
latter inclining, the former enabling him to make 
creatures suited to all states and circumstances ; that 
matter exits only for the sake of intelligent beings; 
and that wherever we find it, we always find it preg- 
nant with life, or necessarily subservient thereto ; 
the numberless species, the astonishing diversity of 
animals in earth, air, water, and even on other ani- 
mals ; every blade of grass, every tender leaf, eve- 
ry natural fluid, swarming with life; and every one 
of these enjoying such gratifications as the nature and 
state of each requires : when we reflect, moreover, 
that some centuries ago, till experience undeceived 
us, a great part of the Earth was adjudged uninhabi- 
table; the torrid zone, by reason of excessive heat, and 
the two frigid zones because of their intolerable cold ; 
it seems highly probable, that such numerous and 

* Mr. WHISTON, in his Astronomical Principles of Religion. 



Of the Solar System. 71 

large masses of durable matter as the comets are, 
however unlike they be to our Earth, are not des- 
titute of beings capable of contemplating with 
wonder, and acknowledging with gratitude, the 
wisdom, symmetry, and beauty of the creation ; 
which is more plainly to be observed in their ex- 
tensive tour through the heavens, than in our more 
confined circuit. If farther conjecture be per- 
mitted, may we not suppose them instrumental in 
recruiting the expended fuel of the Sun ; and sup- 
plying the exhausted moisture of the planets? 
However difficult it may be, circumstanced as we 
are, to find out their particular destination, this is 
an undoubted truth, that wherever the Deity ex- 
erts his power, there he also manifests his wisdom 
and goodness. 

95. THE SOLAR SYSTEM, here described,^- 
is not a late invention ; for it was known and taught ancient y 
by the wise Samiari philosopher PYTHAGORAS, and de- 
and others among the ancients : but in latter times nstra * 
was lost, till the 15th century, when it was again 
restored by the famous Polish philosopher, NICHO- 
LAUS COPERNICUS, born at Thorn in the year 
1473. In this he was followed by the greatest ma- 
thematicians and philosophers that have since lived ; 

as KEPLER,GALILEO,DESCARTES,GASSENDUS, 
and Sir ISAAC NEWTON ; the last of whom has es- 
tablished this system on such an everlasting founda- 
tion of mathematical and physical demonstration, 
as can never be shaken ; and none who understand 
him can hesitate about it. 

96. In the Ptolemean system, the Earth was sup- ThePtole- 
posed to be fixed in the centre of the universe ; 

and the Moon, Mercury, Venus, the Sun, Mars, 
Jupiter, and Saturn, to move round the Earth. 
Above the planets, this hypothesis placed the fir- 
mament of stars, and then the two crystalline 
spheres : all which were included in and received 
motion from the primum mobile, which constantly 

K 



72 Of the Solar System. 

revolved about the Earth in 24 hours from east to 
west. But as this rude scheme was found inca- 
pable of standing the test of art and observation, it 
was soon rejected by all true philosophers; not- 
withstanding the opposition and violence of blind 
and zealous bigots. 

The Ty. 97. The Tychonic system succeeded the Ptolo- 
system mean, but was never so generally received. In this 
partly the Earth was supposed to stand still in the centre 
*Trd and f ^ ie un i yerse or firmament of stars, and the Sun 
false. to revolve about it every 24 hours ; the planets, 
Mercury, Venus, Mars, Jupiter, and Saturn, go- 
ing round the Sun in the times already mentioned. 
But some of TYCHO'S disciples supposed the Earth 
to have a diurnal motion round its axis, and the 
Sun with all the above planets to go round the 
Earth in a year; the planets moving round the 
Sun in the aforesaid times. This hypothesis being 
partly true and partly false, was embraced by few ; 
and soon gave way to the only true and rational sys- 
tem, restored by COPERNICUS, and demonstrated 
by Sir ISAAC NEWTON. 

98. To bring the foregoing particulars into one 
point of view, with several others which follow, 
concerning the periods, distances, magnitudes, sfc. 
of the planets, the following table is inserted. 



rdi 



aas, 

. . QCj* 



re$ 


?gS-2:er. 

***g 

{^g H?. rt 

i'sf? 

^ c-rt^ 

ifs-g 
f"s 

3 55 o 
5-1 S P 

Sf ?a 

S2.|-S S 
"4 S3 

22 2!g- 

?53 

*I|? 

as ft & n> 

3 co p 3 

^o 3 p- 

P ?M' 

2J| 
Zfl 

^ 2 i 

>0^ 
w p-^x 

^ffi* 

S ?3 
^5 g t 

^'S'rt S, 

w. - JS n 

w Js-^ 
2 ^ 

^s^-r 

es-p* & 

p ^ 3 n> 

03 t~* r+ , 

UN 

13 ^ r* O 

S^I 
4"^ 

HM 

i*.| 

?g^s 

.8-nfg 1 
8L^ ? 

I S.2,5' 
-gSS: 

?lll 

rM 

&Sni 

3- 

i*$* 

:o-s, 
f|38 

2,1-1. 
g?5| 

Mil 

e po'rt 
&5?? 



c 

o -2 



03 M t- o> u, 

+ 




^IrtO o'bo'oooa'to 



zr. p. >ri 
p*orcj o -J 



S 3-0 

s-?Ss 
5s, 1-1 



to 
-v| 



tO tO X- 



O3 tO Or? CO O 
Ort Cft OC tO 4*- 



ooocootoo-o 
oo*>-oosooo 

OOOOOOOOO 




, 



3 ~^ o> u, ^ 03 to - 



f 






: 

D ps 



f 3" 



iO M 03 *- 

> ' K- H- 
00 O3 O3 00 

tr H* CD 
O <O tri 



O OO >- M 

^ i to o oo o. 



o <o u ^ >-* 



5-9 n rf ^ 

n> . oc 

^^3 erg 

- **.'-< O -f 

= 5* s- c: 

' 



z . 



iods ro 
Saturn. 



n 







o' 



s 



O> 00 

-v7H- 

oo 

OO 

O O ^ O O J7-. 



-. CO *- JO 03 to 



O^OCtOtOOOOOUtOD 
- 



O O O O O O O 

<C O O O O O O 

o o o o o o o 



<D O O O O 

o o o o o 
o o o o o 



Ntia 03 ^ M 

O OJ Ut C/J K-* M >- tO 



o o o o o o o o 
oooooooo 



ooooo- o 



o to t-i K* o> 

O O O 



* OO to Ort H* 

q o o to oo 



o 4^ 



H- tO tO 
O3 "^ -v| O 

O O O 



>-* tO >-* "J 

to i "-j -vj - 

0000^ 

* ;r 
. 



^ M to H* 
^ oo <o ^ 






S^ S' 3. 
- 3 



3 . 



ace of i 
phelion 



, 

I PI 
' 



the Period 
distan 



Revolutions, Magnitudes, &.c. of t 
from the SUN, as determined from 



Planets, on the Sup 
servations of the tran 



f! 

"I." 

5' CA! 



llax being 10" 
761, see 194. 



74 The Cop ernican System demonstrated to be true. 



CHAP. III. 

The COPERNICAN SYSTEM demonstrated to 
be true. 

ndmo 99 ' "\yfATTER is of itself inactive, and indif- 
tion. xVA ferent to motion or rest. A body at rest 

can never put itself in motion ; a body in motion 
can never stop or move slower of itself. Hence, 
when we see a body in motion, we conclude that some 
other substance must have given it that motion ; 
when we see a body fall from motion to rest we con- 
clude that has some other body or cause stopt it. 

100. All motion is naturally rectilineal. A bullet 
thrown by the hand, or discharged from a cannon, 
would continue to move in the same direction it re- 
ceived at first, if no other power diverted its course. 
Therefore, when we see a body moving in a curve of 
whatever kind, we conclude it must be acted upon 
by two powers at least : one to put it in motion, and 
another drawing it off from the rectilineal course 
which it would otherwise have continued to move 
in. 

Gravity 101. The power by which bodies fall toward the 
IrtraWe" ^ art ^' * s ca ^ e( l gravity or attraction. By this 
power in the Earth it is, that all bodies on what- 
ever side, fall in lines perpendicular to its surface. 
On opposite parts of the Earth, bodies fall in op- 
posite directions ; all toward the centre, where the 
whole force of gravity is, as it were, accumulated. 
By this power constantly acting on bodies near the 
Earth, they are kept from leaving it altogether; 
and those on its surface are kept there on all sides, 
so that they cannot fall from it. Bodies thrown 
with any obliquity are drawn, by this power, from 
a straight line into a curve, until they fall to the 
ground : the greater the force by which they are 
thrown, the greater is the distance they are carried 
before they fall. If we suppose a body carried se- 



The Copernican System demonstrated to be true. 75 

veral miles above the Earth, and there projected in 
a horizontal direction, with so great a velocity, that 
it would move more than a semidiameter of the 
Earth in the time it would take to fall to the Earth 
by gravity ; in that case, if there were no resisting 
medium in the way, the body would not fall to the 
Earth at all, but continue to circulate round the 
Earth, keeping always the same path, and returning 
to the point from whence it was projected, with the 
same velocity as at first. 

102. We find that the Moon moves round the Earth Projectile 
in an orbit nearly circular. The Moon therefore 



must be acted on by two powers or forces ; one, bie. 
which would cause her to move in a right line; 
another, bending her motion from that line into a 
curve. This attractive power must be seated in 
the Earth ; for there is no other body within the 
Moon's orbit to draw her. The, attractive power 
of the Earth therefore extends to the Moon ; and, 
in combination with her projectile force, causes her 
to move round the Earth, in the same manner as the 
circulating body above supposed. 

103. The moons of Jupiter and Saturn are ob- The Sun 
served to move round their primary planets : there- 

fore there is an attractive power in these planets, each 
All the planets move round the Sun, and respect it other> 
for their centre of motion : therefore the Sun must 
be endowed with an attracting power, as well as the 
Earth and planets. The like may be proved of the 
comets. So that all the bodies or matter of the solar 
system, are possessed of this power; and so per- 
haps is all matter universally. 

104. As the Sun attracts the planets with their 
satellites, and the Earth the Moon ; so the planets 
and satellites re-attract the Sun, and the Moon the 
Earth; action and re-action being always equal. 
This is also confirmed by observation ; for the 
Moon raises tides in the ocean, and the satellites 
and planets disturb one another's motions. 



76 The Copernican System demonstrated to be true. 

105. Every particle of matter being possessed of 
an attracting power, the effect of the whole must 
be in proportion to the number of attracting parti- 
cles : that is, to the quantity of matter in the body. 
This is demonstrated from experiments on pendu- 
lums : for, when they are of equal lengths, whatever 
their weights be, they always vibrate in equal 
times. Now, if one be double the weight of an- 
other, the force of gravity or attraction must be 
double to make it oscillate with the same celerity ; 
if one have thrice the weight or quantity of matter 
of another, it requires thrice the force of gravity to 
make it move with the same celerity. Hence it is 
certain, that the power of gravity is always propor- 
tional to the quantity of matter in bodies, whatever 
may be their magnitudes or figures. 

106. Gravity also, like all other virtues or ema- 
nations, either drawing or impelling a body toward 
the centre, decreases as the square of the distance 
increases: that is, a body at twice the distance attracts 
another with only a fourth part of the force ; at four 
times the distance, with a sixteenth part of the force, 
&c. This too is confirmed from observation, by 
comparing the distance which the MOOR falls in a 
minute from a right line touching her orbit, with the 
space which bodies near the Earth fall in the same 
time : and also by comparing the forces which retain 
Jupiter's moons in their orbits: as will be more fully 
explained in the seventh chapter. 

on V and~ 107 ' Tlie mutual Attraction of bodies may be 

projection exemplified by a boat and a ship on the water, 

exempli- tied together by a rope. Let a man either in the 

ship or boat pull the rope (it is the same in effect at 

which end he pulls, for the rope will be equally 

stretched throughout) the ship and boat will be 

drawn toward one another ; but with this difference, 

that the boat will move as much faster than the ship, 

as the ship is heavier than the boat. Suppose the 

boat as heavy as the ship, and they will draw one 



The Copernican System demonstrated to be true. 77 

another equally, (setting aside the greater resistance 
of the water on the larger body) and meet in the 
middle of the first distance between them. If the 
ship be a thousand or ten thousand times heavier 
than the boat, the boat will be drawn a thousand or 
ten thousand times faster than the ship ; and meet 
proportionably nearer the place from which the ship 
set out. Now, while one man pulls the rope, en- 
deavouring to bring the ship and boat together, let 
another man in the boat, endeavour to row it off side- 
ways, or at right angles to the rope ; and the former, 
instead of being able to draw the boat to the ship, 
will find it enough for him to keep the boat from 
going further off; while the latter endeavouring to row 
off the boat in a straight line, will, by means of the 
other's pulling it toward the ship, row the boat round 
the ship at the rope's length from her. Here the 
power employed to draw the ship and boat to one 
another represents the mutual attraction of the Sun 
and planets by which the planets would fall freely to- 
ward the Sun with a quick motion ; and would also 
in falling attract the Sun toward them. And the 
power employed to row off the boat, represents the 
projectile force impressed on*the planets, at right 
angles, or nearly so, to the Sun's attraction; by 
which means the planets move round the Sun, and 
are kept from falling to it. On the other hand, if it 
be attempted to make a heavy ship go round a light 
boat, they will meet sooner than the ship can get 
round ; or the ship will drag the boat after it. 

108. Let the above principles be applied to the 
Sun and Earth ; and they will evince, beyond a pos- 
sibility of doubt, that the Sun, not the Earth, is the 
centre of the system ; and that the Earth moves 
round the Sun as the other planets do. 

For, if the Sun move about the Earth, the 
Earth's attractive power must draw the Sun toward 
it, from the line of projection, so as to bend its 
motion into a curve. But the Sun being at least 



78 The Copernican System demonstrated to be true. 

227 thousand times as heavy as the Earth, being so 
much heavier as its quantity of matter is greater, it 
must move 227 thousand times as slowly toward the 
Earth, as the Earth does toward the Sun ; and con- 
sequently the Earth would fall to the Sun in a short 
time, if it had not a very strong projectile motion to 
carry it off. The Earth therefore, as well as e very- 
other planet in the system, must have a rectilineal im- 
srurdity "ofP u ^ se to prevent its falling to the Sun. To say, 
supposing that gravitation retains all the other planets in their 
earth or bits, without affecting the Earth, which is placed 
between the orbits of Mars and Venus, is as absurd 
as to suppose that six cannon bullets might be pro- 
jected upward to different heights in the air ; and 
that five of them should fall down to the ground, 
but the sixth, which is neither the highest nor the 
lowest should remain suspended in the air without 
falling, and the Earth move round about it. 

109. There is no such thing in nature as a heavy 
body moving round a light one, as its centre of mo- 
tion. A pebble fastened to a mill-stone, by a string, 
may, by an easy impulse, be made to circulate 
round the mill-stone ; but no impulse whatever can 
make a mill- stone circulate round a loose pebble ; 
for the mill- stone would go off, and carry the pebble 
along with it. 

1 10. The Sun is so immensely greater and hea- 
vier than the Earth,* that if he were moved out of 
his place, not only the Earth, but all the other pla- 
nets, if they were united into one mass, would be 
carried along with the Sun, as the pebble would be, 
with the mill-stone. 

111. By considering the law of gravitation which 
takes place throughout the solar system, in another 
light, it will be evident, that the Earth moves 
round the Sun in a year ; and not the Sun round 
the Earth. It has been shewn ( 106) that the 

* As will be demonstrated in the ninth chapter. 



The Copermcan System demonstrated to be true. 79 

power of gravity decreases as the square of the dis- Th e har- 
tance increases ; and from this it follows, with mathe- J^cdeg. 
matjcal certainty, that when two or more bodies tial mo. 
move round another as their centre of motion, the tlons * 
squares of their periodic times Will be to one another 
in the same proportion as the cubes of their distances 
from the central body. This holds precisely with 
regard to the planets round the Sun, and the satel- 
lites round the planets ; the relative distances of all 
which are well known. But, if we suppose the Sun 
to move round the Earth, and compare its period 
with the Moon's by the above rule, it will be found 
that the Sun would take no less than 173,510 days 
to move round the Earth ; in which case our year 
would be 475 times as long as it now is. To this 
we may add, that the aspects of increase and de- 
crease of the planets, the times of their seeming to 
stand still, and to move direct and retrograde, an- 
swer precisely to the Earth's motion ; but not at .all 
to the Sun's, without introducing the most absurd 
and monstrous suppositions, which would destroy all 
harmony, order, and simplicity in the system. More- 
over, if the Earth be supposed to stand still, and the 
stars to revolve in free space about the Earth in 24 
hours, it is certain that the forces by which the stars 
revolve in their orbits are not directed to the Earth, 
but to the centres of the several orbits ; that is, of the 
several parallel circles which the stars on different The ab- 
sides of the equator describe every day ; and the like JU" 1 ^ f 
inferences may be drawn from the supposed diurnal the stars S 
motion of the planets, since they are never in the* n ^P |a - 
cquinoctial but twice in their courses with regard to mov e 
the starry heavens. But, that forces should^be di- round the 
rected to no central body, on which they physically Earth ' 
depend, but to innumerable imaginary points in the 
axis of the Earth produced to the poles of the hea- 
vens, is a hypothesis too absurd to be allowed of 
by any rational creature. And it is still more ab* 

L 



80 The Copernican System demonstrated to be true. 

surd to imagine that these forces should increase ex- 
actly in proportion to the distances from this axis ; 
for that is an indication of an increase to infinity ; 
whereas the force of attraction is found to decrease 
in receding from the fountain from whence it flows. 
But the farther any star is from the quiescent pole, 
the greater must be the orbit which it describes ; and 
yet it appears to go round in the same time as the 
nearest star to the pole does. And if we take into 
consideration the two-fold motion observed in the 
stars, one diurnal round the axis of the Earth in 24 
hours, and the other round the axis of the ecliptic in 
25920 years, 251, it would require an explication 
of such a perplexed composition of forces, as could 
by no means be reconciled with any physical theory. 

objec- 112. There is but one objection of any weight 
against tnat can ^ e ma de against the Earth's motion round 
the the Sun, which is, that in opposite points of the 
motionan- F' artn ' s or bit, its axis, which always keeps a paral- 
swered. lei direction, would point to different fixed stars ; 
which is not found to be fact. But this objection 
is easily removed, by considering the immense dis- 
tance of the stars in respect to the diameter of the 
Earth's orbit ; the latter being no more than a point 
when compared to the former. If we lay a ruler on 
the side of a table, and along the edge of the ruler 
view the top of a spire at ten miles distance, and 
then lay the ruler on the opposite side of the table 
in a parallel situation to what it had before, the spire 
will still appear along the edge of the ruler, because 
our eyes, even when assisted by the best instru- 
ments, are incapable of distinguishing so small a 
change at so great a distance. 

113. Dr. BRADLEY found, by a long series of the 
most accurate observations, that there is a small ap- 
parent motion of the fixed stars, occasioned by the 
aberration of their light, and so exactly answering to 



The Coper mean System demonstrated to be true. 81 

an annual motion of the Earth, as evinces the same, 
even to a mathematical demonstration. Those who 
are qualified to read the Doctor's modest account of 
this great discovery, may consult the Philosophical 
Transactions, No. 406. Or they may find it treated 
of at large by Drs. SMITH*, LoNcf, DESAGU- 
LiERsf, RUTHERFURTH||, Mr. MACLAURIN, Mr. 
SIMPSON^, and M. DE LA CAILLE**. 

114. It is true that the Sun seems to change his wh y the 

11-1 i 11 Sun ap- 

place daily, so as to make a tour round the starry p ear sto 
heavens in a year. But whether the Sun or Earth change 
moves, this appearance will be the same; for, when hls place ' 
the Earth is in any part of the heavens, the Sun will 
appear in the opposite. And therefore this appear- 
ance can be no objection against the motion of the 
Earth. 

115. It is well known to every person who has 
sailed on smooth water, or been carried by a stream 
in a calm, that, howevel* fast the vessel goes, he 
does not feel its progressive motion. The motion 
of the Earth is incomparably more smooth and uni- 
form than that of a ship, or any machine made and 
moved by human art : and therefore it is not to be 
imagined that we can feel its motion. 

116. We find that the Sun, and those planets Th 

on which there are visible spots, turn round their motion 3 on 
axes : for the spots move regularly over their discs, its axis 
From hence we may reasonably conclude, that^' 
the other planets on which we see no spots, and 
the Earth, which is likewise a planet, have such 
rotations. But being incapable of leaving fhe Earth, 
and viewing it at a distance, and its rotation being 
smooth and uniform, we can neither see it move 

* Optics, B. I. 1178. t Astronomy, B. II. 838. 

| Philosophy, vol. 1. p. 401, |j Account of Sir Isaac New- 

ton's PhUosoftiical Discoveries, B. III. c. 2. 3. 
Mathemat. Essays, p. 1. ** Elements d' Astronomic* 381. 



82 The Copcrnican System demonstrated to be true. 

on its axis as we do the planets, nor feel ourselves 
affected by its motion. Yet there is one effect of 
such a motion, which will enable us to judge with 
certainty whether the Earth revolvVs on its axis or 
not. All globes which do not turn round their axes 
will be perfect spheres, on account of the equality 
of the weight of bodies on their surfaces ; especi- 
ally of the fluid parts. But all globes which turn on 
their axes will be oblate spheroids ; that is, their 
surfaces will be higher or farther from the centre in 
the equatorial than in the polar regions ; for, as the 
equatorial parts move quickest, they will recede far- 
thest from the axis of motion, and enlarge the equa- 
torial diameter. That our Earth is really of this 
figure, is demonstrable from the unequal vibrations 
of a pendulum, and the unequal lengths of degrees 
in different latitudes. Since then the Earth is higher 
at the equator than at the poles, the sea, which na- 
turally runs downward, or toward the places which 
are nearest the centre, would run toward the polar 
regions, and leave the equatorial parts dry, if the 
centrifugal force of these parts by which the waters 
were carried thither did not keep them from return- 
ing. The Earth's equatorial diameter is 36 miles 
longer than its axis. 

All bodies \yj . Bodies near the poles are heavier than those 
the^oie* toward the equator, because they are nearer the 
than they Earth's centre, where the whole force of the Earth's 
atthe e attraction is accumulated. They are also heavier, 
equator, because their centrifugal force is less, on account 
of their diurnal motion being slower. For both 
these reasons, bodies carried from the poles toward 
the equator gradually lose of their weight. Ex- 
periments prove that a pendulum which vibrates 
seconds near the poles, vibrates slower near the 
equator ; which shews, that it is lighter or less 
attractive there. To make it oscillate in the same 
time, it is fdund necessary to diminish its length. 
By comparing the different lengths of pendulums 



The Copernican System demonstrated to be true. 83 

swinging seconds at the equator and at London, it is 
found that a pendulum must be 2 T is 6 A lines, or 12th 
part of an inch shorter at the equator than at the poles. 

118. If the Earth turned round its axis in 84 mi- 
nutes 43 seconds, the centrifugal force would be S 
equal to the power of gravity at the equator ; and all weight, 
bodies there would entirely lose their weight. If 

the Earth revolved quicker, they would all fly off, 
and leave it. 

119. A person on the Earth can no more be sen-3" he , , 

.,,/.. -.. ,1 . . . i &artn $ 

sible oi its^undisturbed motion on its axis, than one motion 
in the cabin of a ship, on smooth water, can be sen- cannotbe 
sible of the ship's motion when it turns gently and e 
uniformly round. It is therefore no argument 
against the Earth's diurnal motion, that we do not 
feel it : nor is the apparent revolutions of the celes- 
tial bodies every day a proof of the reality of these 
motions ; for whether we or they revolve, the ap- 
pearance is the very same. A person looking 
through the cabin- windows of a ship, as strongly 
fancies the objects on land to go round when the 
ship turns, as if they were actually in motion. 

120. If we could translate ourselves from planet 
to planet, we should still find that the stars would 
-appear of the same magnitudes, and at the same 
distances from each other, as they do to us on the 
Earth, because the diameter of the remotest planet's 
orbit bears no sensible proportion to the distance of 

the stars. But then, the heavens would seem tojF othedif 
revolve about very different axes; and con sequent- ne^the* 
ly, those quiescent points, which are our poles in heavens 
the heavens, would seem to revolve about other Aroun 
points, which, though apparently in motion as seen on differ- 
from the Earth, would be at rest as seen from any ent axes * 
other planet. Thus the axis of Venus which lies 
almost at right angles to the axis of. the Earth, 
would have its motionless poles in two opposite 
points of the heavens, lying almost in our equi- 



The Copernican System demonstrated to be true. 

noctial, where the motion appears quickest; be^ 
cause it is seemingly performed in the greatest circle. 
And the very poles which are at rest to us, have the 
quickest motion of all as seen from Venus. To 
Mars and Jupiter, the heavens appear to turn round 
with very different velocities on the same axis, whose 
poles are about 23^ degrees from ours. Were we 
on Jupiter, we should be at first amazed at the rapid 
motion of the heavens ; the Sun and stars going 
round in 9 hours 56 minutes. Could we go from 
thence to Venus, we should be as much surprised 
at the slowness of the heavenly motions ; the Sun 
going but once round in 584 hours, and the stars in 
540. And could we go from Venus to the Moon, 
we should see the heavens turn round with a yet 
slower motion ; the Sun in 708 hours, the stars in 
655. As it is impossible these various circumvo- 
lutions in such different times, and on such different 
axes, can be real, so it is unreasonable to suppose 
the heavens to revolve about our Earth, more than 
it does abbut any other planet. When we reflect 
on the vast distance of the fixed stars, to which 
162,000,000 of miles, the diameter of the Earth's 
orbit, is but a point, we are filled with amazement at 
the immensity of their distance. But if we try to 
frame an idea of the extreme rapidity with which the 
stars must move, if they move round the Earth in 
24 hours, the thought becomes so much too big for 
our imagination, that we can no more conceive it than 
we do infinity or eternity. If the Sun were to go round 
the Earth in 24 hours, he must travel upward of 
300,000 miles in a minute : but the stars being at least 
400,000 times as far from the Sun as the Sun is from 
us, those about the equator must move 400,000 times 
as quick. And all this to serve no other purpose 
than what can be as fully and much more simply ob- 
tained by the Earth's turning round eastward, as on 
an axis, every 24 hours; causing thereby an apparent 



Objections answered. 35 

diurnal motion of the Sun westward, and bringing 
about the alternate returns of day and night. 

121. As to the common objections against the 
Earth's motion on its axis, they are all easily an- 
swered, and set aside. That it may turn without be- Earth's di- 

,, , , , , urnal mo- 

ing seen or felt by us to do so, has been already t i on an- 
shewn, 119. But some are apt to imagine that ii swered. 
the Earth turns eastward (as it certainly does, if it 
turns at all) a ball fired perpendicularly upward in the 
air must fall considerably westward of the place it 
was projected from. This objection, which at first 
seems to have some weight, will be found to have 
none at all, when we consider that the gun and ball 
partake of the Earth's motion ; and therefore the ball 
being carried forward with the air as quick as the 
Earth and air turn, must fall down on the same place. 
A stone let fall from the top of a main- mast, if it 
meet with no obstacle, falls on the deck as near the 
foot of the mast when the ship sails as when it does 
not. If an inverted bottle full of liquor, be hung up 
to the ceiling of the cabin, and a small hole be made 
in the cork to let the liquor drop through on the 
floor, the drops will fall just as far forward on the 
floor when the ship sails as when it is at rest. And 
gnats or flies can as easily dance among one another 
in a moving cabin, as in a fixed chamber. As for 
those scripture-expressions which seem to contradict 
the Earth's motion, the following reply may be made 
to them all : It is plain, from many instances, that 
the Scriptures were never intended to instruct us in 
philosophy or astronomy; and therefore, on those 
subjects, expressions are not always to be taken in 
the literal sense ; but for the most part as accom- 
modated to the common apprehensions of mankind. 
Men of sense in all ages, when not treating of the 
sciences purposely, have followed this method: 
and it would be in vain to follow any other in ad- 
dressing ourselves to the vulgar, or bulk of any 



86 The Phenomena of the Heavens as seen 

community. Moses calls the Moon a GREAT 
LUMINARY (as it is in the Hebrew) as well as 
the Sun : but the Moon is known to be an opaque 
body, and the smallest that astronomers have observ- 
ed in the heavens ; and that it shines upon us, not 
by any inherent light of its own, but by reflecting 
the light of the Sun. Moses might know this ; but 
had he told the Israelites so, they would have stared at 
him ; and considered him rather as a madman, than 
as a person commissioned by the Almighty to be 
their leader. 

CHAP. IV. 

The Phenomena of the Heavens as seen from different 
Parts of the Earth. 

We are "ITITTE are kept to the Earth's surface, on 

E e a?Aby e ' W al1 si des, by the power of its central 

gravity, attraction ; which laying hold of all bodies accord- 
ing to their densities or quantities of matter, with- 
out regard to their bulks, constitutes what we call 
their weight. And having the sky over our heads, 
go where we will, and our feet toward the centre 
of the Earth ; we call it up over our heads, and 
down under our feet : although the same right line 
which is dozvn to us, if continued through and be- 
yond the opposite side of the Earth, would be up to 
Plate //. the inhabitants on the opposite side. For, the in- 
Flg * L habitants n, z, e, m, s, 0, g, /, stand with their feet 
toward the Earth's centre C; and have the same 
figure of sky JV, /, E, M, S, 0, Q, Z, over their 
heads. Therefore, the point S is as directly upward 
to the inhabitant s on the south pole, as N is to the 
inhabitant n on the north pole : so is E to the 
inhabitant e supposed to be on the north end of 
Peru ; and Q to the opposite inhabitant q on the mid- 
A "*j- die of the island Sumatra. Each of these observers 
is surprised that his opposite or antipode can stand 
with his head hanging downward- But let eittejr 



from different Parts of the Earth. 87 

go to the other, and he will tell him that he stood as pi ate //. 
upright and firm on the place where he was, as he 
now stands where he is. To all these observers, the 
Sun, Moon, and, stars, seem to turn round the 
points A" and S, as the poles of the fixed axis jVCS; Axis of 
because the Earth does really turn round the mathe- th world. 

maticai line n C s as round an axis of which n is the T , , 

i rm -II- r T * ts poles- 

north pole, and s the south pole. 1 he inhabitant u 

(Fig. II.) affirms that he is on the uppermost side of Fig. n. 
the Earth, and wonders how another at L can stand at 
the undermost side, with his head hanging down- 
wards. But Lf'm the mean time forgets, that in twelve 
hours time he will be carried half round with the 
Earth, and then be in the very sit nation tliat L now 
is; although as far from him as before^ a'ffd yet, when 
//comes there, he will find no difference as to his 
manner of standing ; only he will see the opposite 
half of the heavens, and imagine the heavens to have 
gone half round the Earth. 

123. When we see a globe hung up in a room, H ow our 
we cannot help imagining it to have an upper and an Earth 
under side, and immediately form a like idea of the J^Je L 
Earth ; from whence we conclude, that it is as im- upper 
possible for people to stand on the under side of the ^"f le ^ n 
Earth, as for pebbles to lie on the under side of a side. 
common globe, which instantly fall down from it to 
the ground; and well they may, because the attraction 
of the Earth being greater than the attraction of the 
globe, pulls them away. Just so would it be with 
our Earth, if it were fixed near a globe much big- 
ger than itself, such as Jupiter: for then, it would 
really have an upper and an under side with respect 
to that large globe; which, by its attraction, would 
pull away every thing from the side of the Earth next 
to it ; and only those bodies on its surface, at the op- 
posite side, could remain upon it. But there is no 
larger globe near enough our Earth to overcome its 

M 



88 The Phenomena of the Heavens as seen 

Plate II. central attraction ; and therefore it has no such thing 
as an upper and an under side ; for all bodies on or 
near its surface, even to the Moon, gravitate toward 
its centre. 

124. Let any man imagine the Earth, and every 
thing but himself, to be taken away, and he left alone 
in the midst of indefinite space ; he could then have 
no idea of up or clorun; and were his pockets full of 
gold, he might tdke the pieces one by one, and throw 
them away on all sides of him, without any danger 
of losing them ; for the attraction of his body would 
bring them all back by the ways they went, and he 
would be down to every one of them. But then, if 
a sun, or any other large body, were created and 
placed in any part of space, several millions of miles 
from him, he would be attracted toward it, and could 
not save himself from falling down to it. 

*% I- 125. The Earth's bulk is but a point, as that at 

C, compared to the heavens ; and therefore every 
inhabitant upon it, let him be where he will, as at 
?z, , 7?z, s, ckc. sees half of the heavens. The inha- 
bitant >7, on the north pole of the Earth, constantly 
sees the hemisphere E N Q; and having the north 
pole A* of the heavens just over his head, his hori. 
zon coincides with the celestial equator E C Q. 
Half of Therefore all the stars in the northern hemisphere 
the hea- j? jy> Q between the equator and north pole, appear 

vensvisi- , , ,. f^ 

bietoan f6 turn round the line JV C, moving parallel to the 
inhabitant horizon. The equatorial stars keep in the horizon, 
partof the anc ^ a ^ those in the southern hemisphere E S Q are 
Earth. invisible. The like phenomena are seen by the ob- 
server s on the south pole, with respect to the hemi- 
sphere E S Q; and to him the opposite hemisphere 
is always invisible. Hence, under either pole, only 



from different Parts of the Earth. 89 

one half of the heavens is seen; for those parts which 
are once visible never set, and those which are once 
invisible never rise. But the ecliptic 1' C X, or or- 
bit which the Sun appears to describe once a year 
by the Earth's annual motion, has the half Y C con- 
stantly above the horizon E C Q of the north pole 
n; and the other half C X always below it. There- Pheno- 
fore while the Sun describes the northern half Y C!? ena f 

.. . . . the poles. 

of the ecliptic, he neither sets to tne north pole, nor 
rises to the south ; and while he describes the sou- 
thern half C X, he neither sets to the south pole, 
nor rises to the north. The same things are true 
with respect to the Moon; only with this difference, 
that as the Sun describes the ecliptic but once a year, 
he is for half that time visible to each pole in its turn, 
and as long invisible; but as the Moon goes round 
the ecliptic in 27 days 8 hours, she is only visible for 
13 days 16 hours, and as long invisible to each pole 
by turns. All the planets likewise rise and set to the 
poles, because their orbits are cut obliquely in halves 
by the horizon of the poles. When the Sun (in his 
apparent way from X) arrives at C, which is on the 
20th of March, he is just rising to an observer at n, 
on the north pole, and setting to another at ,y, on the 
south pole. From C he rises higher and higher in 
every apparent diurnal revolution, till he comes to 
the highest point of the ecliptic y, on the 21st of 
June; when he is at his greatest altitude, which is 
23 degrees, or the arc E y, equal to his greatest 
north declination ; and from thence he seems to de- 
scend gradually in every apparent circumvolution, 
till he sets at C on the 23d of September; and then 
he goes to exhibit the like appearances at the south 
pole for the other half of the year. Hence the Sun's 
apparent motion round the Earth is not in parallel 
circles, but in spirals ; such as might be represented 
by a thread wound round a globe from tropic to tro- 
pic ; the spirals being at some distance from one an- 



90 The Phenomena of the Heavens as seen 

Plate ii. other about the equator, and gradually nearer to each 

other as they approach toward the tropics, 
pheno- 1^* ^ tne observer be an y where on the terres- 
mena at trial equator e C q, as suppose at ?, he is in the plane 
tor CqUa " ^ tne ce ^ est ^ al equator; or under the equinoctial 
E C Q; and the axis of the Earth n C s is coinci- 
_. . dent with the plane of his horizon, extended out to 
JVand 6*, the north and south poles of the heavens. 
As the Earth turns round the line A* C S> the whole 
heavens MOLL seem to turn round the same line, 
but the contrary way. It is plain that this observer 
has the celestial poles constantly in his horizon, and 
that his horizon cuts the diurnal paths of all the ce- 
lestial bodies perpendicularly, and in halves. There- 
fore the Sun, planets, and stars, rise every day, as- 
cend perpendicularly above the horizon for six hours, 
and, passing over the meridian, descend in the same 
manner for the six following hours ; then set in the 
horizon, and continue twelve hours below it. Con- 
sequently at the equator the days and nights arc 
equally long throughout the year. When the obser- 
ver is in the situation e> he sees the hemisphere 
S E A"; but in twelve hours after, he is carried half 
round the Earth's axis to q, and then the hemisphere 
S Q A' becomes visible to him, and SE N disap- 
pears. Thus we find, that to an observer at either of 
the poles, one half of the sky is always visible, and 
the other half never seen ; but to an observer on the 
equator the whole sky is seen every 24 hours. 

The figure here referred to, represents a celes- 
tial globe of glass, having a terrestrial globe within 
it : after the manner of the glass sphere invented by 
my generous friend Dr. LONG, JLtiWrides's Profes- 
sor of Astronomy in Cambridge. 

Remark. 127. If a globe be held side wise to the eye, at 
some distance, and so that neither of its poles can 
be seen, the equator E C Q, and all circles parallel 
to it, as D L, y z x, a b X, MO, &c. will appear to be 



from different Parts of the Earth. 91 

straight lines, as projected in this figure ; which is 
requisite to be mentioned here, because we shall 
have occasion to call them circles in the following 
articles of this chapter*. 

128. Let us now suppose that the observer has^^ 
gone from the equator toward the north pole 7?, tween the 
and that he stops at i, from which place he then e q uator 
sees the hemisphere MEWL; his horizon 7IfCX andpo1 
having shifted as many degrees from the celestial 
poles A* and S, as he has travelled from under the 
equinoctial . And as the heavens seem constantly 
to turn round the line NCS as an axis, all those stars 
which are not as many degrees from the north pole 
A" as the observer is from the equinoctial, namely, 
the stars north of the dotted parallel DL, never set 
below the horizon ; and those which are south of the 
dotted parallel MO never rise above it. Hence the 
former of these two parallel circles is called the cir- The cir- 
cle of perpetual apparition, and the latter the circle ^^^ 
of perpetual occultation : but all the stars between apparition 
these two circles rise and set every clay. Let us im- andoccul - 

* tation. 

agine many circles to be drawn between these two, 
and parallel to them ; those which are on the north 
side of the equinoctial will be unequally cut by the 
horizon MCL, having larger portions above the ho- 
rizon than below it : and the more so, as they are 
nearer to the circle of perpetual apparition ; but the 
reverse happens to those on the south side of the 
equinoctial while the equinoctial is divid< d in two 
equal parts by the horizon. Hence, by the apparent 
turning of the heavens, the northern stars describe 
greater arcs or portions of circles above the horizon 
than below it ; and the greater, as they are farther 
from the equinoctial toward the circle of perpetual 
apparition ; while the contrary happens to all stars 

* The plane of a circle, or a thin circular plate, being turned 
edge-wise to the eye, appears to be a straight line. 



1 

\f 
92 The Phenomena of the Heavens as seen 

south of the equinoctial ; but those upon it describe 
equal arcs both above and below the horizon, and 
therefore they are just as long above it as below it. 

129. An observer on the equator has no circle of 
perpetual apparition or occultation, because all the 
stars, together with the Sun and Moon, rise and set 
to him every day. But, as a bare view of the fi- 
gure is sufficient to shew that these two circles DL 
and MO are just as far from the poles A* and as the 
observer at i (or one opposite him at o,) is from the 
equator ECQ; it is plain, that if an observer begins 
to travel from the equator to ward either pole, his cir- 
cle of perpetual apparition rises from that pole as 
from a point, and his circle of perpetual occultation 
from the other. As the observer advances toward 
the nearer pole, these two circles enlarge their diame- 
ters, and come nearer to one another, until he comes 
to the pole ; and then they meet and coincide in the 
equinoctial. On different sides of the equator, to 
observers at equal distances from it, the circle of per- 
petual apparition to one is the circle of perpetual oc- 
cultation to the other. 

130, Because the stars never vary their distances 
^ rom ^ e e( l u i noc ^ a lj so. as to be sensible in an age, 

scribe the the lengths of their diurnal and nocturnal arcs are al- 
same par- ways the same to the same places on the Earth. But 
motion, as ^ e E- artn goes round the Sun every year in the 
and the ecliptic, one half of which is on the north side of 
tne equinoctial, and the other half on its south side, 
the Sun appears to change his place every day ; so 
as to go once round the circle YCX every year, 
114. Therefore while the Sun appears to advance 
northward, from having described the parallel a b X 
touching the ecliptic in Jf, the days continually 
lengthen and the nights shorten, until he comes to y, 
and describes the parallel yzx; when the days are 
at the Ipngest and the nights at the shortest: for then 



JVEf ; 



from different Parts of the Earth. 



us the Sun goes no farther northward, the greatest Plate IL 
portion that is possible of the diurnal arc y z is above 
the horizon of the inhabitant i; and the smallest por- 
tion z x below it. As the Sun declines southward 
from z/, he describes smaller diurnal and greater noc- 
turnal arcs or portions of circles every day ; which 
causes the days to shorten and the nights to length- 
en, until he arrives again at the parallel a b X; which 
having only the small part a b above the horizon 
MCL, and the great part b A" below it, the days 
are at the shortest and the nights at the longest : be- 
cause the Sun recedes no farther south, but returns 
northward as before. It is easy to see that the Sun 
must be in the equinoctial E C Q twice every year, 
and then the days and nights are equally long ; that 
is, 12 hours each. These hints serve at present to 
give an idea of some of the appearances resulting 
from the motions of the Earth : which will be more 
particularly described in the tenth chapter. 

131. To an observer at either pole, the horizon pig-, i. 
and equinoctial are coincident ; and the Sun and stars Parallel, 
seem to move parallel to the horizon : therefore such and^lg 
an observer is said to have a parallel position of the spheres, 
sphere. To an observer any where between either what * 
pole and equator, the parallels described by the Sun 
and stars are cut obliquely by the horizon, and there- 
fore he is said to have an oblique position of the 
sphere. To an observer any where on the equator 
the parallels of motion, described by the Sun and 
stars, are cut perpendicularly, or at right angles, by 
the horizon ; and therefore he is said to have a right 
position of the sphere. And these three are all the 
different ways that the sphere can be posited to the 
inhabitants of the Earth. 



94 The Phenomena of t/ie Heavens as seen 



CHAP. V. 

The Phenomena of the Heavens as seen from diffe- 
rent Parts oj the Solar System. 

132 C^ vastly great is the distance of the starry 
" I^J heavens, that if viewed from any part of 
the solar system, or even many millions of miles 
beyond it, the appearance would be the very same 
as it is to us. The Sun and stars would all seem to 
be fixed on one concave suriace, oi which the spec- 
tator's eye would be the centre. But the planets, 
being much nearer than the stars, their appearances 
will vary considerably with the place from which 
they are viewed. 

133. If the spectator be at rest without the orbits 
of the planets, they will seem to be at the same dis- 
tance as the stars; but continually changing their 
places with respect to the stars, and to one another ; 
assuming various phases of increase and decrease 
like the Moon ; and, notwithstanding their regular 
motions about the Sun, will sometimes appear to 
move quicker, sometimes slower, be as often to the 
west as to the east of the Sun, and at their greatest 
distances seem quite stationary. The duration, ex- 
tent, and distance, of those points in the heavens 
where these digressions begin and end, would be 
more or less, according to the respective distances 
of the several planets from the Sun : but in the same 
planet, they would continue invariably the same at 
all times ; like pendulums of unequal lengths oscil- 
lating together, the shorter would move quick, and go 
over a small space ; the longer would move slow, and 
go over a large space. If the observer be at rest with- 
in the orbits of the planets, but not near the common 
centre,their apparent motions will be irregular; but less 
so than in the former case. Each of the several planets 
will appear larger and less by turns, as they approach 



from different Parts of the Solar System. 95 

nearer to, or recede farther from, the observer; the 
nearest varying most in their size. They will also 
move quicker or slower with regard to the fixed stars, 
but will never be either retrograde or stationary. 

134. If an observer in motion view the heavens, 
the same apparent irregularities will be observed, 
but with some variation resulting from his own mo- 
tion. If he be on a planet which has a rotation on 
its axis, not being sensible of his own motion, he 
will imagine the whole heavens, Sun, planets, and 
stars, to revolve about him in the same time that his 
planet turns round, but the contrary way ; and will 
not be easily convinced of the deception. If his pla- 
net move round the Sun, the same irregularities 
and aspects as above mentioned will appear in the 
motions of the other planets ; and the Sun will seem 
to move among the fixed stars or signs, in an oppo- 
site direction to that in which his planet moves, 
changing its place every day as he does. In a word, 
whether our observer be in motion or at rest, whe- 
ther within or without the orbits of the planets, their 
motions will seem irregular, intricate, and perplex- 
ed, unless he be placed in the centre of the system; 
and from thence, the most beautiful order and har- 
mony will be seen by him. 

135. The Sun being the centre of all the planets' The Sun's 
motions, the only place from which their motions 



could be truly seen, is the Sun's centre ; where the from 
observer being supposed not to turn round with the whlcl 



true mo- 



Sllll (which, in this case, we must imagine to be ations and 
transparent body) would see all the stars at rest, gj* 06 ^ 
and seemingly equidistant from him. To such an n et s P couid 
observer, the planets would appear to move among be seen, 
the fixed stars ; in a simple, regular, and uniform 
manner : only, that as in equal times they describe 
equal areas, they would describe spaces somewhat 
unequal, because they move in elliptic orbits, 155. 
Their motions would also appear to be what they 
are in fact, the same way round the heavens ; in 

N 



96 The Phenomena of the Heavens as seen 

paths which cross at small angles in different parts 
of the heavens, and then separate a little from one 
another, $ 20. So that, if the solar astronomer 
should make the path or orbit of any planet a stand- 
ard, and consider it as having no obliquity, 201, 
he would judge the paths of ail the rest to be inclined 
to it ; each planet having one half of its path on one 
side, and the other half on the opposite side of the 
standard-path or orbit. And if he should ever see 
all the planets start from a eonj unction with each 
other *, Mercury would move so much faster than 
Venus, as to overtake her again (though not in the 
same point of the heavens) in a space of time about 
equal to 145 of our days and nights, or, as we com- 
monly call them, natural days? which include both 
the days and nights : Venus would move so much 
faster than the Earth, as to overtake it again in 585 
natural days : the Earth so much faster than Mars, 
as to overtake him again in 778 such days : Mars so 
much faster than Jupiter, as to overtake him again 
in 817 such days : and Jupiter so much faster than 
Saturn, as to overtake him again in 7236 days, all 
of our time. 
Theju%- 13 g r B ut as our so i ar astronomer could have no 

ment that . , P . ., , , 

a solar as- idea of measuring the courses of the planets by our 
tronomer days, he would probably take the period of Mer- 
probably curv > which is the quickest-moving planet, for a 
make con- measure to compare the periods of the others with. 
the^E ^ s a ^ ^ e stars wou ld appear quiescent to him, he 
tances and would never think that they had any dependance 
ma & ni - upon the Sun; but would naturally imagine that 

tildes of J * . i 

the pia- the planets have, because they move round the 
net*. Sun. And it is by no means improbable, that he 

* Here we dp Rot mean such a conjunction, as that the nearest 
planet should hide all the rest from the observer's sight ; (for that 
would be impossible, unless the intersections of all their orbits were 
coincident, which they are not. See 21.) but when they were all 
in a line crossing the standard-orbit at right angles. 



from different Parts of the Solar System. 97 

would conclude those planets, whose periods are 
quickest, to move in orbits proportionably less than 
those do which make slower circuits. But being 
destitute of a method for finding their parallaxes, or, 
more properly speaking, as they would have no pa- 
rallax to him, he could never know any thing of 
their real distances or magnitudes. Their relative 
distances he might perhaps guess at by their periods, 
and from thence infer something of truth concerning 
their relative magnitudes, by comparing their appa- 
rent magnitudes with one another. For example, 
Jupiter appearing larger to him than Mars, he would 
conclude it to be so in fact ; and that it must be far- 
ther from him, on account of its longer period* 
Mercury and the Earth would appear to be .nearly 
of the same magnitude ; but .by comparing the pe- 
riod of Mercury with that of the Earth, he would 
conclude that the Earth is much farther from him 
than Mercury,, and consequently that it must be 
really larger though apparently of the same magni- 
tude ; and so of the rest. And as each planet would 
appear somewhat larger in one part of its orbit than 
in the opposite, and to move quickest when it seems 
largest, the observer would be at no loss to con- 
clude that all the planets move in orbits, of which 
the Sun is not precisely the centre. 

137. The apparent magnitudes of the planets The pia- 
continually change as seen from the Earth, which ^n^very" 
demonstrates that they approach nearer to it, and irregular 
recede farther from it by turns. From these phe- ^^ 
nomena, and their apparent motions among the Earth, 
stars, they seem to describe loeped curves, which 
never return into themselves,-*- Venus's path ex- 
cepted. And if we were to trace out all their ap- 
parent paths, and put the figures of them together 
in one diagram, they would appear so anomalous 
and confused, that no man in his senses could be- 
lieve them to be representations of their real paths ; 
but would immediately conclude, diat such appa- 



98 The apparent Paths of Mercury and Venus. 

Plate ill. rent irregularities must be owing to some optic illu- 
sions. And after a good deal of enquiry, he might 
perhaps be at a loss to find out the true causes of 
these irregularities; especially if he were one of 
those who would rather, with the greatest justice, 
charge frail man with ignorance, than the Almighty 
with being the author of such confusion. 
Mem f ^ ^' ^ r * ^ N G ' * n ki s fi rst volume of Astronomy , 
and Venus nas gi yen us figures of the apparent paths of all the 
represent- planets, separately from CASSINI; and on seeing 
ed * them I first thought of attempting to trace some of 
them by a machine* that shews the motions of the 
Sun, Mercury, and Venus, the Earth, and Moon, 
according to the Copernican System. Having taken 
off* the Sun, Mercury, and Venus, I put black-lead 
pencils in their places, with the points turned up- 
ward ; and fixed a circular sheet of paste- board so, 
that the Earth kept constantly under its centre in 
going round the Sun ; and the paste-board kept its 
parallelism. Then, pressing gently with one hand 
upon the paste- board, to make it touch the three 
pencils; with the other hand I turned the winch that 
moves the whole machinery : and as the Earth, 
together with the pencils in the places of Mercury 
Fte-L and Venus, had their proper motions round the 
Sun's pencil, which kept at rest in the centre of 
the machine, all the three pencils described a dia- 
gram, from which the first figure of the third plate 
is truly copied in a smaller size. As the Earth 
moved round the Sun, the Sun's pencil described 
the dotted circle of months, whilst Mercury's pen- 
cil drew the curve with the greatest number of 
loops, and Venus's that with the fewest. In their 
inferior conjunctions they come as much nearer to 
the Earth, or within the circle of the Sun's appa- 
rent motion round the heavens, as they go beyond 
it in their superior conjunctions. On each side of 
the loops they appear stationary : in that part of 

* The ORRERY fronting the Title-Page. 



The apparent Paths of Mercury and Venus. 

each loop next the Earth, retrograde ; and in all the & ate 
rest of their paths, direct. 

If Cassini's figures of the paths of the Sun, Mer- 
cury, and Venus, were put together, the figure, as 
above traced out, would be exactly like them. It 
represents the Sun's apparent motion round the eclip- 
tic, which is the same every year ; Mercury's rr.o- 
tion for seven years; and Venus's for eight; in which 
time Mercury's path makes 23 loops, crossing itself 
so many times, and Venus's only five. In eight 
years Venus falls so nearly into the same apparent 
path again, as to deviate very little from it in some 
ages ; but in what number of years Mercury and the 
rest of the planets would describe the same visible 
paths over again, I cannot at present determine. 
Having finished the above figure of the paths of 
Mercury and Venus, I put the ecliptic round them 
as in the doctor's book ; and added the dotted lines 
from the Earth to the ecliptic, for shewing Mercu- 
ry's apparent or geocentric motion therein for one 
year ; in which time his path makes three loops, and 
goes on a little farther. This shews that he has three 
inferior, and as many superior conjunctions with the 
Sun in that time ; and also that he is six times sta- 
tionary, and thrice retrograde. Let us now trace 
his motion for one year in the figure. 

Suppose Mercury to be setting out from A to- 
ward B (between the Earth and left-hand corner 
of the plate) and as seen from the Earth, his mo- Fig. i. 
tion will then be direct, or according to the order of 
the signs. But when he comes to B, he appears 
to stand still in the 23d degree of nj, at F, as shewn 
by the line B F. While he goes from B to C, the 
line B F, supposed to move with him, goes back- 
ward from F. to J2, or contrary to the order of 
signs : and when he is at C, he appears stationary 
at E; having gone back 111 degrees. Now, sup- 
pose him stationary on the first of January at C, on 
the tenth of that month he will appear in the heavens 



100 The apparent Paths of Mercury and Venus. 

as at 20, near F ; on the 20th he will be seen as at 
G; on the 31st at//; on the iOth of February at F; 
on the 20th at K; and on the 28th at L ; as the 
dotted lines shew, which are drawn through every 
tenth days' motion in his looped path, and con- 
tinued to the ecliptic. On the 10th of March he 
appears at M; on the 20th at A"; and on the 31st 
at O. On the tenth of April he appears stationary 
at P ; on the 20th he seems to have gone back 
again to O; and on the 30th he appears stationary at 
Q, having gone back llf degrees. Thus Mercury 
seems to go forward 4 signs 11 degrees, or 31 de- 
grees ; and to go back only 1 1 or 12 degrees, at a 
mean rate. From the 30th of April to the 10th of 
May, he seems to move from Q to R ; and on the 
20th he is seen at S, going forward in the same 
manner again, according to the order of letters ; and 
backward when they go back ; which it is needless 
to explain any farther, as the reader can trace him 
out so easily, through the rest of the year. The 
same appearances happen in Venus 's motion ; but 
as she moves slower than Mercury, there are longer 
intervals of time between them. 

Having already, $ 120, given some account of 
the apparent diurnal motions of the heavens as seen 
Irom the different planets, we shall not trouble the 
reader any more with that subject. 

CHAP. VI. 

TJie Ptolemean System refuted. The Motions Mnd 
Phases of Mercury and Venus explained. 

HE Tychonic System, 97, being suffi- 
ciently refuted in the 109th article, we 
shall say nothing more about it. 

140. The Ptolemean System, 96, which asserts 
the Earth to be at rest in the centre of the uni- 
verse, and all the planets with the Sun and stars 
to move round it, is evidently false and absurd. 



The Phenomena of the inferior Planets. 101 

For if this hypothesis were true, Mercury and Ve- 
nus could never be hid behind the Sun, as their or- 
bits are included within the Sun's ; and again, these 
two planets would always move direct, and be as 
often in opposition to the Sun as in conjunction with 
him. But the contrary of all this is true : for they 
are just as often behind the Sun as before him, ap- 
pear as often to move backward as forward, and are 
so far from being seen at any time in the side of the 
heavens opposite to the Sun, that they are never seen 
a quarter of a circle in the heavens distant from him. 

141. These two plaftets, when viewed at different Appear - 
times with a good telescope, appear in all the various Mercury- 
shapes of the Moon j which is a plain proof that they and Ve~ 
are enlightened by the Sun, and shine not by any nus * 
light of their own ; for if they did, they would con- 
stantly appear round as the Sun does ; and could 
never be seen like dark spots upon the Sun when 
they pass directly between him and us. Their re- 
gular phases demonstrate them to be spherical bo- 
dies; as may be shewn by the following experiment : 

Hang an ivory ball by a thread, and let any per- Ex peri- 
son move it round the flame of a candle, at two or ^e [hey 
three yards distance from your eye ; when the ball are round., 
is beyond the candle, so as to be almost hid by the 
flame, its enlightened side will be toward you, and 
appear round like the full Moon : When the ball 
is between you and the candle, its enlightened side 
will disappear as the Moon does at the change : 
When it is half-way between these two positions, it 
will appear half illuminated, like the Moon in her 
quarters : but in every other place between these 
positions, it will appear more or less horned or gib- 
bous. If this experiment be made with a flat cir- 
cular plate, you may make it appear fully enlight- 
ened, or not enlightened at all ; but can never mak/ 
it appear either horned or gibbous. 



102 The Phenomena of the inferior Planets. 

Plate n. 142. If you remove about six or seven yards from 
Experi- the candle, and place yourself so that its flame may 
represent ^ e J ust a t>out the height of your eye, and then de- 
the mo- sire the other person to move the ball slowly round 
MercuL ^ ie canc ^ le as before, keeping it as nearly of an equal 
and Ve- height with the flame as he possibly can, the ball 
nus - will appear to you not to move in a circle, but to vi- 
brate backward and forward like a pendulum ; mov- 
ing quickest when it is directly between you and the 
candle, and when directly beyond it ; and gradually 
slower as it goes farther to the right or left side of 
the flame, until it appears at the greatest distance 
from the flame ; and then, though it continues to 
move with the same velocity, it will seem for a mo- 
ment to stand still. In every revolution it will shew 
all the above phases, 141 ; and if two balls, a 
smaller and a greater, be moved in this manner round 
the candle, the smaller ball beng kept nearest the 
flame, and carried round almost three times as often 
as the greater, you will have a tolerable good repre- 
sentation of the apparent motions of Mercury and 
Venus ; especially if the greater ball describe a cir- 
cle almost twice as large in diameter as that describ- 
ed by the lesser. 

Fi S- "I- 143. Let A B C D E be a part or segment of the 
visible heavens, in which the Sun, Moon, planets, 
and stars, appear to move at the same distance from 
the Earth E. For there are certain limits, beyond 
which the eye cannot judge of different distances; 
as is plain from the Moon's appearing to be as far 
from us as the Sun and stars are. Let the cir- 
cle fg h ik Im n o be the orbit in which Mercury m 
moves round the Sun S, according to the order 
of the letters. When Mercury is at/^ he disap- 
pears to the Earth at E, because his enlightened 
The elon- s id e i s turned from it ; unless he be then in one of 
dtgrTs 8 . r his nodes, $ 20, 25; in which case he will appear 
sions of like a dark spot upon the Sun. When he is at g 
froTthl m hi s or bit, he appears at B in the heavens, west- 

Sun. 



The Phenomena of the inferior Planets. 103 

ward of the Sun S, which is seen at C: when at A, Plate n. 
he appears at A, at his greatest western elongation 
or distance from the Sun ; and then seems to stand 
still. But, as he moves from h to i, he appears to 
go from A to B ; and seems to be in the same place 
when at i, as when he was at g, but not near so 
large : at k he is hid from the Earth E, by the Sun 
6'; being then in his superior conjunction. In go- 
ing from k to /, he appears to move from C to D ; 
and when he is at ;z, he appears stationary at E ; 
being seen as far east from the Sun then, as he was 
west from it at A. In going from n to 0, in his 
orbit, he seems to go back again in the heavens, 
from E to D ; and is seen in the same place (with 
respect to the Sun) at 0, as when he was at /; but 
of a larger diameter at 0, because he is then nearer 
the Earth E : and when he comes to f, he again 
passes by the Sun, and disappears as before. In go- 
ing from n to A, in his orbit, he seems to go back- 
ward in the heavens from E to A; and in going 
from h to 72, he seems to go forward from A to E : 
as he goes on from f, a little of his enlightened side 
at g is seen from E ; at h he appears half full, be- 
cause half of his enlightened side is seen ; at i y 
gibbous, or more than half full ; and at k he would 
appear quite full, were he not hid from the Earth 
E by the Sun S. At / he appears gibbous again, at 
n half decreased, at o horned, and at f new, like the 
Moon at her change. He goes sooner from his 
eastern station at n to his western station at A, than 
again from h to n ; because he goes through less 
than half his orbit in the former case, and through 
more in the latter. 

144. In the same figure, let FGHIKLMN be Fig. in. 
the orbit in which Venus v goes round the Sun S, 
according to the order of the letters : and let E be 
the Earth, as before. When Venus is at F, she is The eion- 
in her inferior conjunction ; and disappears like ^ e f^ ion h s a 
new Moon, because her dark side is toward theses of * 
Earth. At (r, she appears half enlightened to the v nu s- 

O 



104 The Phenomena of the inferior Planets. 

Earth, like the moon in her first quarter : at H 9 she 

appears gibbous ; at /, almost full ; her enlightened 

side being then nearly towards the Earth ; at K, she 

would appear quite full to the Earth E ; but is hid 

from it by the Sun S ; at Z/, she appears upon the 

decrease, or gibbous ; at M, more so ; at N, only half 

The great- enlightened ; and at F, she again disappears. In mov- 

est eion- i ns , f rom jy to Q s j le seems t o o backward in the 

gallons 01, ir-/^f -\i 11 11 

Mercury heavens ; and from Cr to N 9 forward ; but as she de- 

and Ve- scribes a much greater portion of her orbit in going 

from G to A", than from JVto 6r, she appears much 

longer direct than retrograde in her motion. At A* 

and G she appears stationary ; as Mercury does at 

n and /z. Mercury, when stationary, seems to be 

only 28 degrees from the Sun ; and Venus, when 

so, 47 ; wh'ch is a demonstration that Mercury's 

orbit is included within Venus's, and Venus's within 

the Earth's. 

145. Venus, from her superior conjunction at K> 
to her inferior conjunction at F, is seen on the east 
side of the Sun S, from the Earth E; and therefore 
she shines in the evening after the Sun sets, and is 

Morning called the evening star ; for, the Sun being then to 
and even- the westward of Venus, must set first. From her 
v?hat tar * * n f er * r conjunction to her superior, she appears on 
the west side of the Sun ; and therefore rises before 
him ; for which reason she is called the nwrmng star. 
When she is about A" or Gr, she shines so bright, 
that bodies by her light cast shadows in the night- 
time. 

146. If the Earth kept always at E, it is evident 
that the stationary places of Mercury and Venus 
would always be in the same points of the heavens 
where they were before* For example : whilst 
Mercury m goes from h to 77, according to the order 

f he sta- of the letters, he appears to describe the arc ABCDE 
tionary j n the heavens, direct : and while he goes from n to 
fhe C pia? h> ^ ie seems to describe the same arc back again, 
netsvari- from E to A y retrograde j always at n and n he 

able. 



The Phenomena of the inferior Planets* 105 

appears stationary at the same points E and A as 
before. But Mercury goes round his orbit, from/* 
to f again, in 88 days; and yet there are 116 days 
from any one of his conjunctions, or apparent sta- 
tions, to the same again : and the places of these con- 
junctions and stations are found to be about 114 de- 
grees eastward from the points of the heavens where 
they were last before ; which proves that the Earth 
has not kept all that time at E., but has bad a pro- 
gressive motion in its orbit from E to /. Venus also 
differs every time in the places of her conjunctions 
and stations ; but much more than Mercury ; be- 
cause, as Venus describes a much larger orbit than 
Mercury does, the Earth advances so much the far- 
ther in its annual path, before Venus comes round 
again. 

147. As Mercury and Venus, seen from theTheelon- 
Earth, have their respective elongations from the f^g of 
Sun, and stationary places ; so has the Earth, seen turn's in. 
from Mars; and Mars, seen from Jupiter; and ferior P la ' 
Jupiter, seen from Saturn : that is, to every supe- seen from 
rior planet, all the inferior ones have their stations him - 
and elongations; as Venus and Mercury have to 

the Earth. As seen from Saturn, Mercury never 
goes more than 2^ degrees from the Sun ; Venus 
4*; the Earth 6; Mars 9|; and Jupiter 33i ; so that 
Mercury, as seen from the Earth, has almost as 

freat a digression or elongation from the Sun, as 
upiter, seen from Saturn. 

148. Because the Earth's orbit is included with- A proof of 
in the orbits of Mars, Jupiter, and Saturn, they are ^ e n ^[ th ' s 
seen on all sides of the heavens : and are as often in motion. 
opposition to the Sun as in conjunction with him. 

If the Earth stood still, they would always appear 
direct in their motions ; never retrograde nor station- 
ary. But they seem to go just as often backward 
as forward ; which, if gravity be allowed to exist, 
affords a sufficient proof of the Earth's annual mo- 
tion : and without its existence, the planets could 
never fall from the tangents of their orbits towards 



106 The Phenomena of the inferior Planets. 

Plate II. the Sun, nor could a stone, which is once thrown 
up from the Earth, ever fall to the earth again. 

149. As Venus and the Earth are superior pla- 
nets to Mercury, they exhibit much the same ap- 
pearances to him, that Mars and Jupiter do to us. 
Let Mercury m be at/; Venus v at F, and the Earth 
p. In at E; in which situation Venus hides the Earth 
General* from Mercury ; but being in opposition to the Sun, 
phenome- sne shines on Mercury with a full illumined orb ; 
periorVia- though, with respect to the Earth, she is in con- 
net to an junction with the Sun, and invisible. When Mer- 
mfenor. cur y j g at y- an( j y enus at , her enlightened side 

not being directly toward him, she appears a little 
gibbous ; as Mars does in a like situation to us : but, 
when Venus is at /, her enlightened side is so much 
toward Mercury at/J that she appears to him almost 
of a round figure. At K, Venus disappears to Mer- 
cury at/J being then hid by the Sun , as all our su- 
perior planets are to us, when in conjunction with 
the Sun. When Venus has, as it were, emerged 
out of the Sun-beams, as at L, she appears almost 
full to Mercury at/; at M and A", a little gibbous; 
quite full at F, and largest of all ; being then in op- 
position to the Sun, and consequently nearest to 
Mercury at F; shining strongly on him in the night, 
because her distance from him then is somewhat less 
than a fifth part of her distance from the Earth, when 
she appears roundest to it between / and K, or be- 
tween JSf and Z,, as seen from the Earth E. Con- 
sequently, when Venus is opposite to the Sun as 
seen from Mercury, she appears more than 25 times 
as large to him as she does to us when at the fullest. 
Our case is almost similar with respect to Mars, 
when he is opposite to the Sun ; because he is then 
so near the Earth, and has his whole enlightened 
side toward it. But, because the orbits of Jupiter 
and S-iturn are very large in proportion to the Earth's 
orbit, these two planets appear much less magnified 



The Physical Causes of the Planets" Motions. 107 



at their oppositions, or diminished at their 
junctions, than Mars does, in proportion to their 
mean apparent diameters. 

CHAP. VII. 

The Physical Causes of the Motions of the Planets. 
The Eccentricities of their Orbits. The Times in 
which the Action of Gravity 'would bring them to 
the Sun. ARCHIMEDES'S ideal Problem for 
moving the Earth. Tlie World not eternal. 



ROM the uniform projectile motion 
bodies in straight lines, and the universal 
power of attraction which draws them off from these tion. 
lines, the curvilineal motions of all the planets arise, pig. iv. 
If the body A be projected along the right line ABX y 
in open space, where it meets with no resistance, 
and is not drawn aside by any other power, it would 
for ever go on with the same velocity, and in the 
same direction. For, the force which moves it 
from A to B in any given time, will carry it from B circular 
to Jf in as much more time, and so on, there being orbits - 
nothing to obstruct or alter its motion. But if, when 
this projectile force has carried it, suppose to Y?, the 
body S begin to attract it, with a power duly adjust- 
ed, and perpendicular to its motion atY?, it will then 
be drawn from the straight line ABX, and forced to 
revolve about S in the circle BYTU. When the Fi^. iv. 
body A comes to U, or any other part of its orbit, if 
the small body z/, within the sphere of IPs attraction, 
be projected, as in the right line Z, with a force per- 
pendicular to the attraction of Z7, then u will go 
round 7 in the orbit W, and accompany it in its 
whole course round the body S. Here S may re- 
present the Sun, 7 the Earth, and u the Moon. 

151. If a planet at B gravitate, or be attracted, 
toward the Sun, so as to fall from B to y in the 



108 The Physical Causes of 

time that the projectile force would have carried it 
from B to X, it will describe the curve B Y by the 
combined action of these two forces, in the same 
time that the projectile force singly would have car- 
ried it from B to X, or the gravitating power singly 
have caused it to descend from B to y ; and these 
two forces being duly proportioned, and perpendi- 
cular to each other, the planet, obeying them both, 
will move in the circle BYTU*. 

152. But if, while the projectile force would carry 
the planet from B to A, the Sun's attraction (which 
constitutes the planet's gravitation) should bring it 
down from B to 1, the gravitating power would then 
be too strong for the projectile force ; and would 
cause the planet to describe the curve B C. When 
Elliptical the planet comes to C, the gravitating power (which 
rbits. a l w ays increases as the square of the distance from 
the Sun S diminishes) will be yet stronger on ac- 
count of the projectile force ; and by conspiring in 
some degree therewith, will accelerate the planet's 
motion all the way from C to K ; causing it to de- 
scribe the arcs BC, CD, DE, EF, &c. all in equal 
times. Having its motion thus accelerated, it there- 
by gains so much centrifugal force or tendency to 
fly off at Km the line JO*, as overcomes the Sun's 
attraction : and the centrifugal force being too great 
to allow the planet to be brought nearer the Sun, or 
even to move round him in the circle Klmn, &c. it 
goes off, and ascends in the curve KLMN, &c. its 
motion decreasing as gradually from K to B, as it 
increases from B to K; because the Sun's attraction 
now acts against the planet's projectile motion just 
as much as it acted with it before. When the pla- 
net has got round to J5, its projectile force is as 
much diminished from its mean state about G or A*, 

* To make the projectile force talance the gravitating power sc 
exactly as that the body may move in a circle, '.he projectile velocity 
of the "body must be such as it would have acquired by gravity alone, 
in falling through half the radius of the circle. 



the Planets' Motion. 

as it was augmented at K ' ; and so, the Sun's attrac- Plate IL 
tion being more than sufficient to keep the planet 
from going off at B, it describes the same orbit over 
again, by virtue of the same forces or powers. 

153. A double projectile force will always balance 
a quadruple power of gravity. Let the planet at B 
have twice as great an impulse from thence toward 
Jf, as it had before ; that is, in the same length of 
time that it was projected from B to 6, as in the last 
example, let it now be projected from B to c ; and it 
will require four times as much gravity to retain it in 
its orbit : that is, it must fall as far as from B to 4 in 
the time that the projectile force would carry it from 
to c; otherwise it could not describe the curve 
BD ; as is evident by the figure. But, in as much 

time as the planet moves from B to C in the higher Fig. iy. 
part of its orbit, it moves from /to K, or from Jfto e P**- 
L, in the lower part thereof; because, from the joint scriVe^ 
action of these two forces, it must always describe equal are- 
equal areas in equal times, throughout its annual Jfmes. q 
course. These areas are represented by the triangles 
BSC, CSD y DSE, ESF, &c. whose contents' are 
equal to one another quite round the figure. 

154. As the planets approach nearer the Sun, and A difficui- 
recede farther from him, in every revolution ; there *y remov - 
may be some difficulty in conceiving the reason why 

the power of gravity, when it once gets the better of 
the projectile force, does not bring the planets nearer 
and nearer the Sun in every revolution, till they fall 
upon, and unite with him ; or why the projectile force, 
when it once gets the better of gravity, does not 
carry the planets farther and farther from the Sun, 
till it removes them quite out of the sphere of his 
attraction, and causes them to go on in straight lines 
for ever afterward.' But by considering the effects 
of these powers as described in the two last articles, 
this difficulty will be removed. Suppose a planet 



1 10 The Physical Causes of 

at B, to be carried by the projectile force as far a$ 
from B to , in the time that gravity would have 
brought it down from B to 1 : by these two forces 
it will describe the curve B C. When the planet 
comes down to K, it will be but half as far from the 
Sun A$*as it was at B ; and therefore by gravitating 
four times as strongly towards him, it would fall 
from K to V in the same length of time that it would 
have fallen from B to 1 in the higher part of its or- 
bit; that is through four rimes as much space ; but 
its projectile force is then so much increased at Jf, 
as would carry it from JTto k in the same time; 
being double of what it was at B ; and is therefore 
too strong for the gravitating power, either to draw 
the planet to the Sun, or cause it to go round him in 
the circle Klmn, &c. which would require its falling 
from K to w, through a greater space than that 
through which gravity can draw it, while the pro- 
jectile force is such as would carry it from A" to k : 
and therefore the planet ascends in its orbit KLMN; 
decreasing in its velocity, for the causes already as- 
signed in 152. 

The pia- 155. The orbits of all the planets are ellipses, very 

netary or- little different from circles : but the orbits of the 

tical? lp comets are very long ellipses ; and the lower focus 

of them all is in the Sun. If we suppose the mean 

distance (or middle between the greatest and least) 

of every planet and comet from the Sun to be divid- 

Their ec- ed into 1000 equal parts, the eccentricities of their 

centricU orbits, both in such parts and in English miles, will 

be as follow: Mercury's, 210 parts, or 6,720,000 

miles; Venus's, 7 parts, or 413,000 pniles; the 

Earth's, 17 parts, or 1,377,000 miles; Mars's, 93 

pans, or 11,439,000 miles; Jupiter's, 48 parts, or 

20,352,000 miles ; Saturn's, 55 parts, or 42,755, 

000 miles. Of the nearest of the tree foremen- 

tioned comets, 1,458,000 miles; of the middlemost, 

2,025 000,000 miles; and of the outermost, 6,600, 

000,000. 



the Planets' 1 Motions. 1 1 1 

156. By the above-mentioned law, J 150 & seq. The above 
bodies will move in all kinds of ellipses, whether Ions; ] * ws !. uffi ' 

. P , A i . , . , . cient for 

or short, if the spaces they move in be void of resist- motions 
ance. Only those which move in the longer ellipses b ? th in 
have so much the less projectile force impressed upon ami einV 
them in the higher parts of their orbits ; and their ve- tic orbits. 
locities, in coming down towards the Sun, are so pro- 
digiously increased by his attraction, that their centri- 
fugal forces in the lower parts of their orbits are so 
great, as to overcome the Sun's attraction there, and 
cause them to ascend again towards the higher parts 
qf their orbit ; 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 in what 
comets were destroyed at their mean distances from times thc 
the Sun, their gravities would bring them down so, wouid*faH 
as that Mercury would fall to the Sun in 15 days 13 totheSun 
hours; Venus, in 39 days 17 hours; the Earth or b o4 h rof 
Moon, in 64 days 10 hours; Mars, in 121 days ; Ju- gravity, 
piter, 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, and his fifth in 336 hours. A stone 
would fall to the Earth's centre, if there were a hollow 
passage, in 21 minutes 9 seconds. Mr. WHISTON 
gives the following rule for such computations. " *It 
is demonstrable, 'that half the period of any planet, 
when it is diminished in the sesquialteral proportion 

* Astronomical Principles of Religion, p. 66. 



112 The Physical Causes of 

of the number 1 to the number 2, or nearly in the 
proportion of 1000 to 2828, is the time in which it 
would fall to the centre of its orbit. 

The pro- 158. The quick motions of the moons of Jupiter 
dlgl us n a *fand Saturn round their primaries, demonstrate that 
ibe C Sun these two planets have stronger attractive powers 
and Pia- than the Earth has. For the stronger that one body 
nets * attracts another, the greater must be the projectile 
force, and consequently the quicker must be the mo- 
tion of that other body to keep it from falling to its 
primary or central planet. Jupiter's second moon is 
124 thousand miles farther from Jupiter than our 
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 mo- 
tions at first ! Amazing indeed to us, because impos- 
sible to be effected by the strength of all the living 
creatures in an unlimited number of worlds ; but no 
ways hard for the ^taighty, whose planetarium takes 
in the whole universe. 

ARCH i- 159. The celebrated ARCHIMEDES affirmed he 

ME biem COU ^ move tne Earth, if he had a place at a dis- 

Frlts?ng tance from it to stand upon to manage his machine- 

the Earth. r y,#. This assertion is true h\ 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 

* AOJ err* JA), x.a.i rov xo<r/xov X^^TT, z. e. Give me a place to stand 
en, and I shall move the Earth. 



the Planet? Motions. 1 13 

the former ; and the length of the long arm of the 
lever must be in the same proportion to the length 
of the short one. Now, suppose a man to pull, or 
press the end of the long arm with the force of 
200 pounds weight, and that the Earth contains in 
round numbers, 4,000, 000,000, 000,000,000,000, 
or 4000 trillions of cubit feet, each at a mean rate 
weighing 100 pound ; and that the prop or centre of 
motion of the lever is 6000 miles from the Earth's 
centre : in this case, the length of the lever from the 
fulcrum or centre 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 it is easy to compute, that if ARCHI- 
MEDES, 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. 

If any other machine, such as a combination of 
wheels and screws, were 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 Hard to 
other : the power by which they do so we call determine 
gravity. ' But whether this power be mechanical or^ t h y a | 9 f r *' 
not, is very much disputed. Observation proves that 
by it the planets disturb one another's motions, and 
that it decreases, according to the squares of the dis- 
tances of the Sun and planets inversely ; as light, 
which is known to be material, likewise does. Hence, 
gravity should seem to arise from the agency of some 
subtle matter pressing toward the Sun and planets, 
and acting, like all mechanical causes, by contact. 



1 14 The Physical Causes of 

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 bulk 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 la\v 
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, or some subordinate in- 
telligence, must therefore be constantly impelling the 
planets towards 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, it 
seems to me no more an absurdity, to suppose the 
Deity capable of infusing a law, or what law he 
pleases, into 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 within the powder of Omnipotence. 

161. That the projectile force was at first given by 
the Deity is evident. For matter can never put it- 
self in motion, and all bodies may be moved in any 
direction whatever ; and yet the planets, both primary 
and secondary, move from west to east, in planes 
nearly coincident ; while the comets move in all di- 
rections, and in planes very different from one an- 
other ; these motions can therefore be owing to no 
mechanical cause or necessity, but to the free will and 
power of an intelligent Being. 

162. Whatever gravity be, it is plain that it acts 
every moment of time : for if its action should cease, 
the projectile force w^ould instantly carry off the 



the Planets' Motions. 1 15 

planets in straight lines from those parts of their or- 
bits 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 re- 
sistance 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 pia- 
the planets in their motions, arising from their mutual net * &*- 

i , . , c A i turb one 

attractions, when they are in the same quarter or the another's 
heavens ; and the best modern observers find that our motions, 
years are not always precisely of the same length*. 
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, T j ie con . 
which in the present age shew the times of solar and sequences 
lunar eclipses to great precision, do not answer so th 
well for very ancient eclipses. Hence it appears, that 
the Moon does not move in a medium void of all re- 
sistance, ^ 174 : and therefore her projectile force be- 
ing a little weakened, while there is nothing to dimi- 
nish 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 re- 
gard 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 sufficent pro- 

* If the planets did not mutually attract one another, the areas 
described by them would be exactly proportionate to the times of de- 
scription, 153. But observations prove that these areas are not in 
such exact proportion, and are most varied when the greatest num- 
ber of planets are in any particular quarter of the heavens. When 
any two planets are in conjunction, their mutual attractions, which 
tend to bring them nearer to one another, draw the inferior one a 
little farther from the Sun, and the superior one a little nearer t<. 
him ; by which means, the figure of their orbits is somewhat altered; 
but this alteration is too small to be discovered in several ages. 



116 Concerning the Nature and 

jectile force at the beginning, adds a little more to it 
in due time. And, as all the planets move in spaces 
full of ether and light, which are material substances, 
they too must meet with some resistance. And, 
therefore, if their gravities be not diminished, nor 
their projectile forces increased, they must necessa- 
rily approach nearer and nearer the Sun, and at length 
fall upon and unite with him. 

The world 164. Here we have a strong philosophical argu- 
not eter- ment against the eternity of the' YVorld. For, had it 
existed from eternity, and been left by the Deity to 
be 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 its Author, who 
ought no more to be found fault with for framing so 
perishable a work, than for making man mortal*. 

CHAP. VIII. 

Of Light. Its proportional Quantities on the different 
Planets. Its Refractions in Water and Air. The 
Atmosphere ; its Weight and Properties. The 
Horizontal moon. 



I A 



I G H T consists of exceeding small par- 
tides of matter issuing from a luminous 
body ; as, from a lighted candle such particles of 
matter constantly flow in all directions. Dr. NIEW- 
Theamaz- ENTYxf computes, that in one second of time there 
ing small- fl ow 418,660,000,000,000,000,000,000,000,000, 
parUdes 000,000,000,000,000, particles of light out of a 
ofiight. burning candle; which number contains at least 

* M. de la Grange has demonstrated, on the soundest principles of 
philosophy* that the solar system is not necessarily perishable; but 
that the seeming irregularities in the planetary motions oscillate, as 
it were, within narrow lin.its ; and that the world, according to the 
present constitution of nature, may be permanent* 

t Religious Philosopher, Vol. HI. p. 65. 



Properties of Light. 117 

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 consequent- 
ly, every cubit inch of the Earth to contain one mil- 
lion of such grains. 

166. These amazingly small particles, by striking The 
upon our eyes, excite in our minds the idea of light ; ^ffccis" 1 
and if they were as large as the smallest particles of that would 
matter discernible by our best microscopes, instead * i ? s I ^ e their 
of being serviceable to us, they would soon deprive being 
us of sight, by the force arising from their immense lar s el '- 
velocity ; which is above 164 thousand miles every 
second*, 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 sand, we 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 HOW ob- 
Sun or from a candle, fall upon bodies, and are there- jects be- 
by reflected to our eyes, they excite in us the idea of Sto us!" 
that body, by forming its picture on the retina f. 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 The rays 
particles, flowing from any visible body in a straight of h & ht 
line. That the rays move in straight, and not in movTi/ 
crooked lines, unless they be refracted, is evident s . trai ^ rM 
from bodies not being visible if we endeavour to look lmes< 

at them through the bore of a bended pipe ; and from 
their ceasing to be seen on 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. A proof 
And that these rays do not interfere, or jostle 



hinder not 
one ano- 



This will be demonstrated in the eleventh chapter. ther's 

t A fine net-work membrane in the bottom of the eye. motions. 



118 Concerning the Nature and 

Plate IL another out of their ways, in flowing from different 
bodies all around, is plain from the following experi- 
ment. Make a little hole in a thin plate of metal, and 
set the plate upright on a table, facing a row of light- 
ed candles standing by one another; then place a 
sheet of paper or pasteboard at a little dibtance from 
the other side of the plate, and the rays of all the 
candles, flowing through the hole, will lorm as many 
specks of light on the paper as there are candles be- 
fore 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 hindrance 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, toward the end,) decreases 
in the inverse proportion of the squares of the distances 
of the planets from the Sun. This is easily demon- 
strated by a figure; which, together with its de- 
Fig. XL scription, I have taken from Dr. SMITH'S Optics*. 
Let the light which flows from a point A, and passes 
through a square hole B, be received upon a plane C, 
in what parallel to the plane of the hole ; or, if you please, let 
%h P tTnd n the % ure C be the shadow of the plane B; and when 
Leat de- the distance C is double of B, the length and breadth 
crease at o f t ^ e snac iow C will be each double of the length 
dwtan'ce" and breadth of the plane B ; and treble when AD is 
from the 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 7?, being suffered to pass to double that 
distance, will be uniformly spread over four times 
the space, and consequently will be four times 

* Book I. Art. 57. 



Properties of Light. 119 

thinner in every part of that space ; at a treble dis- Plate n 
tance, it will be nine times thinner ; and at a quad- 
ruple distance, sixteen times thinner, than it was at 
first ; and so on, according to the increase of the 
square surfaces B, C, Z), E, described upon the 
distances AB, AC, AD, AE. Consequently, the 
quantities of this rarefied light received upon a sur- 
face of any given size and shape whatever, removed 
successively to these several distances, will be but 
one-fourth, one-ninth) one-sixteenth, respectively, of 
the whole quantity received by it at the first distance 
AB. Or, in general words, the densities and quan- 
tities of light, received upon any given plane, are 
diminished in the same proper ion, 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 discs of why the 

the Moon and planets, so much the dimmer they P lanets 

* appeal- 
appear than to the bare eye ; because the telescope dimmer 

cannot magnify the quantity of light as it does the ^hen 
surface ; and, by spreading the same quantity of light through 
over a surface so much larger than the naked eye telescopes 
beheld, just so much dimmer must it appear when 
viewed by a telescope, than by the bare eye. eye. 

171. When a ray of light passes out of one me- 
dium* into another, it is refracted, or turned put of 
its 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 ex- 
periments ; of which we shall onlv give three for ex- 
ample's sake. 1. In a bason, FGH, put a piece of Fig. vm. 
money, as DB, and then retire from it to A ; that 

is, till the edge of the bason at E just hides the 
money from your sight ; then keeping your head 

* A medium, in this sense, is any transparent body, or that through 
which the rays of light c; n '*ass; as water, glass, diamond, air; aiu' 
even a vacuum is sometimes called a medium. 

Q 



120 Concerning the Atmosphere. 

steady, let another person fill the bason gently witk 

water. As he fills it, you will see more and more 

Refrao of the piece DB ; which will be all in view when the 

i-l 'so f f the bason is full > and a PP ear as if lifted U P to C - For 
light. the ray AEB, which was straight while the bason 

was empty, is now bent at the surface of the water 
in J, and turned out of its rectilineal course into 
the direction ED. Or, in other words, the ray 
DEK, that proceeded in a straight line from the 
edge D while the bason was empty, and w r ent above 
the eye at A, is now bent at E ; and instead of going 
on in the rectilineal direction DEK> goes in the an- 
gled direction DEA, and by entering the eye at A 
renders the object DIJ 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 downward into it. 

172. The less obliquely the rays of light fall upon 
the surface of any medium, the less they are refract- 
ed ; and if they fall perpendicularly on it, 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 in the 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 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. 

the at- 174. The Earth is surrounded by a thin fluid 

rnosphere. mass of matter, called the air or atmosphere ', which 

gravitates to the Earth, revolves with it in its diurnal 

motion, and goes round the Sun with it every year. 



Concerning the Atmosphere. 12i 

This fluid is of an elastic or springy nature, and its 
lowest part, being pressed by the weight of ajl the 
air above it, is pressed the closest together; and 
therefore the atmosphere is densest of all at the 
Earth's surface, and higher up becomes gradually 
rarer. " It is well known* that the air near the sur- 
face of our Earth possesses a space about 1200 times 
greater than water of the same weight. And there- 
fore, a cylindric column of air 1200 feet 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 feet highf ; 
and therefore, if from the whole cylinder of air, the 
lower part of 1200 feet high be taken away, the re- 
maining upper part will be of equal weight with a 
cylinder of water 32 feet, high ; wherefore, at the 
height of 1200 feet or two -furlongs, the weight of 
the incumbent air is less, and consequently the rarity 
f the compressed air is greater, than near the Earth's 
surface, in the ratio of 33 to 32. And the air, at all 
heights whatever, supposing the expansion thereof 
to be reciprocally proportional to its compression 
(and this proportion has been proved by the experi- 
ments of Dr. Hooke and others) will be set down in 
the following 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 its rarity or expansion, supposing gravity 
to decrease in the duplicate ratio of the distances 
from the Earth's centre : The small numeral figures 
being here used to shew what number of ciphers 



* NEWTON'S system of the World, p. 120, 
t This is evident from common pumps. 



122 



Concerning the Atmosphere. 

must be joined to the numbers expressed by the 
larger figures, as 0. 17 1224 for 0.000000000000000 
00*1224, and 26956 15 for 26956000000000000000. 



The air's 
compres- 
sion and 
rarity at 
different 
heights. 





AIR '.i 




U :j?ht. 


Comprc ^sion. 


| Expansion. 


(j ' 


33 


. . 1 


5 

10 
20 


17.8515 . . 
9.6717 . . 
2.852 . . . 


. . 1.8486 
. . 3.4151 
.11 571 


.40 
400 
4000 
40000 
400000 
4000000 
infinite. 


0.2525 . 
0. 17 1224. 
0. 10 H4C5 
0. 192 1628 
0. 201 7895 
0. 212 9878 
0. 212 994l 


. 136.83 
26956 15 
73907 102 
26263 189 
41798 207 
33414 209 
54622 269 



From the above table it appears that the air in 
proceeding upward is ratified in such manner, that 
a sphere of that air which is nearest the Earth but 
of one inch diameter, if dilated to an equal rarefac- 
tion with that of the air at the height of ten semi- dia- 
meters of the Earth, would fill up more space than 
is contained in the whole heavens on this side the 
fixed stars. And it likewise appears that the Moon 
does not move in a perfectly free and unresisting 
medium; although the air, ;:t a height equal to her 
distances, is at least 340G 19[) times thinner than at 
the Earth's surface ; and therefore cannot resist her 
motion, so as to be sensible, in many ages, 
its weight 175. The weight of the air, at the Earth's sur- 
face, is found by experiments made with the air-pump; 
and also by the quantity of mercury that the atmos- 
phere balances in the barometer ; in which, at a mean 
state, the mercury stands 29-J inches high. And if 
the tube were a square inch wide, it would at that 
-height contain 29 cubic inches of mercury, which 



how 
found. 



Concerning the Atmosphere. 123 

is just 15 pounds weight; and so much weight of 
air every square inch of the Earth's surface sustains ; 
and consequently every square foot 144 times as 
much. Now, as the Earth's surface contains, in 
round numbers, 200,000,000 square miles, it must 
contain no less than 5,575,680,000,000,000 square 
feet; which being multiplied by 2160, the number 
of pounds on each square foot, amounts to 12,043, 
468,800,000,000,000 pounds, for the weight of the 
whole atmosphere. At this rate, a middle-sized man, 
whose surface is about 15 square feet, is pressed by 
32,400 pounds weight of air ail around ; 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 air diffused 
through all parts of our bodies, it is not in the least 
degree felt by us. 

176. Oftentimes the state of the air is such, that A common 
we feel ourselves languid and dull ; which is com- I^f^e 
monly thought to be occasioned by the air's being weight of 
foggy and heavy about us. But that the air is then the air - 
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, and the air is more 
elastic and weighty above us, by which means it 
balances the internal spring of the air within us, 
braces up our blotftl- vessels and nerves, and makes 
us brisk and lively. 

177. According to * Dr. KEILL, and other astro- without 
nomical writers, it is entirely owing to the atmos- ^^^e 
phere that the heavens appear bright in the day- heavens 
time. For, without an atmosphere, only that part 

of the heavens would shine in which the Sun was 
placed : and if we could live without air, and should and 
turn our backs toward the Sun, the whole heavens 

twilight. 
* See his Astronomy, p. 232. 



124 Concerning the Atmosphere 

Plate a. 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 sun-shine to the black- 
est 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, for some time before he rises, 
and after he sets. For, when the Earth by its rota- 
tion has withdrawn our sight from the Sun, the at- 
mosphere being still higher than we, has the Sun's 
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 the height 
of two miles to bear up the clouds. 

5t brings 178. The atmosphere refracts the .Sun's rays so, 
the Sun in as f- o bring h' im j n sight every clear day, before he 
fore he rises in the horizon ; and to keep him in view for 
and some minutes after he is really set below it. For, at 
some times of the year, we see the Sun ten minutes 
after he longer above the horizon than he would be if there 
were no refraction ; and above six minutes every day 
at a mean rate. 

.. ix. 179. To illustrate this, let IEK be a part of 
the Karth's surface, covered with the atmosphere 
HGFC; and let HEO be the 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 

* As far as one can see round him on the Earth, 



Concerning the Atmosphere* 125 

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 above the horizon, ai\d 
being extended out to the heavens, shtws the Sun 
at B, J 171. 

IbO. 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 Ej'L 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 32| min. of a deg. inThequa- 
breadth, when at his mean distance from the Earth ; tity of re- 
and the horizontal refraction of his rays is 33| min. fracUOIW 
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. ; and at the zenith, it 
is nothing : the quantity throughout, is shew n by the 
following table, calculated by Sir ISAAC NEWTON, 



126 



Concerning the Atmosphere. 



182. A TABLE shewing the Refractions of the 
Sun, Moon, and Stars; adapted to their 
aji/iarcnt Altitudes. 


Appar. 


Retrac- 


A! 


i \ e frac- 


A P 


Refrac- 


Alt. 


tion. 


All 


tion. 


Alt. 


tion. 


0. M. 


M. S. 


D. 


vi. s. 


D. 


M. S. 





33 45 


21 


2 18 


56 


3 


15 


30 24 


22 


2 11 


57 


35 


30 


27 35 


23 


2 5 


58 


34 


45 


25 11 


24 


1 59 


59 


32 


1 


23 7 


25 


1 54 


60 


31 


1 15 


21 20 


26 


1 49 


61 


30 


1 30 


19 46 


27 


1 44 


62 


28 


1 45 


18 22 


28 


1 40 


63 


27 


2 


17 8 


29 


1 36 


64 


26 


2 30 


15 2 


30 


1 32 


65 


25 


3 


13 20 


3 1 


i 28 


66 


24 


3 30 


11 57 


32 


1 25 


67 


23 


4 


10 48 


3 


1 22 


68 


22 


4 30 


9 50 


34 


1 19 


69 


21 


5 


9 2 


35 


1 16 


70 


20 


5 30 


8 21 


36 


1 13 


71 


19 


6 


7 45 


37 


1 11 


72 


18 


6 30 


7 14 


38 


1 8 


73 


17 


7 


6 47 


39 


1 6 


74 


16 


7 30 


6 22 


40 


1 4 


75 


15 


8 


6 


4! 


1 2 


76 


14 


8 30 


5 40 


42 


1 


77 


13 


9 


5 22 


43 


58 


78 


12 


9 30 


5 6 


44 


56 


79 


11 


10 


4 52 


45 


54 


80 


10 


11 


4 27 


46 


52 


81 


9 


12 


4 5 


47 


50 


82 


8 


13 


3 47 


48 


48 


83 


7 


14 


3 31 


49 


47 


84 


6 


15 


3 17 


50 


45 


85 


5 


16 


3 4 


51 


44 


8n 


4 


17 


2 53 


52 


42 


87 


3 


18 


2 43 


53 


40 


88 


2 


19 


2 34 


54 


39 


89 


1 


20 


2 26 


55 


o r^\ ;;. 


, 



Concerning the Atmosphere. 127 

183. In all observations, to obtain the true alti- Plate n * 
tude 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 of refrac- 
at the same altitude; because heat diminishes the tu 
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 cli- 
mates ; it having been observed that the horizontal 
refractions are near a third part less at the equator 
than at Paris. This is mentioned by Dr. SMITH 
in the 37()th remark on his Optics, where the follow- 
ing account is given of an extraordinary refraction 
of the Sun-beams by cold. u There is a famous A very re- 
observation of this kind made by some Hollanders markabie 
that wintered mNova-Zembia in the year 1596, who^^J^f" 
were surprised to find, that after a continual night rcfrac- 
of three months, the Sun began to rise seventeen tl( 
days sooner than according to computation, dedu- 
ced from the altitude of the pole, observed to be 76 ; 
which cannot otherwise be accounted for, than by 
an extraordinary refraction of the Sun's rays passing 
through the cold dense air in that climate. Kepler* 
computes that the Sun was almost five degrees be- 
low the horizon when he first appeared ; and conse- 
quently 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 Fig. x. 
setting : the reason of which is, the refraction be- 
ing greater in the horizon than at any distance above 
it, the lower limb G is more elevated by it than the 
upper. But although the refraction shortens the 
vertical diameter FG, it has, no sensible effect on the 
horizontal diameter CZ),. which is all equally elevat- 
ed. When the refraction is so small as to be im- 



128 Concerning the Atmosphere. 

perceptible, the Sun and Moon appear perfectly- 
round, as A E B F. 

ination " *^ 5 ' When we h ave nothing but our imagination to 
fannot n assist us in estimating distances, we are liable to be 
judge deceived ; for bright objects seem nearer to us than 
- ^ lose which are less bright, or than the same objects 
do when they appear less bright and worse denned, 
even though their distance be the same. And if in 
jects ; both cases they are seen under the same angle*, 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 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 w r e may be deceived : for we may 
make a wrong conclusion even when we view them 



nor at- * ^ ne nearer an object is to the eye ? the bigger it appears, and 

ways of ** is seen H nder the greater angle. To illustrate this a little, suppose 
those an arrow in thc position IK, perpendicular to the right line HA, 
which are drawn n ' om tne eve at H through the middle of the arrow at O. It 
accessi- ls V} am t V at tne arrow is seen under the angle IHK, and that HO, 
kk -which is its distance from the eye, divides mto halves both the ar- 

row and the angle under which it is seen, v/z. the arrow into 1O, 
OK; and the angle into I HO and KHO: and this will be the 
case at whatever distance the arrow is placed; Let now three ar- 
rows, all of the same length with IK, be placed at the distances 
HA, HCK, H, still perpendicular to, and bisected by the right 
line HA; then will AB, CD, EF, be each equal to, and represent 
O I; and A B (the same as OI) will be seen Irom H under the angle 
AHB ; but CD (the same as OI) will be seen under the angle CHD, 
or A.HL; and RF(\\\z same as OI) will be seen under the angle 
jL'l-1^ or C7/A, or AHM. Also EF. or OI, at the distance HE, 
will appear as long as ON wruld at the distance HC, or as AM 
would at the distance HA; and CD, or 7O,at the distance HC, will 
appear as long as AL would at the distance HA. So that as an ob- 
ject approaches the eye, both its nsagnitude and the angle under 
which it is seen increase ; and the contrary as the object recedes. 



The Phenomena of the Horizontal Mow, cc. 

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 The 
river by a person standing on a low ground, who 
sees nothing of the river, nor knows of it before- 
hand ; 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 dis- 
tance 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 per- 
ceives the house to be at a greater distance than he 
bad imagined ; and therefore fancies it to be bigger 
than he did at first ; although in both cases it ap- 
pears under the same angle, and consequently makes 
no bigger picture on the retina of his eye in the lat- 
ter 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.* Pia# 

Secondly, In foggy weather, at first sight, we 
generally imagine a small house which is just at 



* The fields which are beyond the gate rise gradually till they are 
just seen over it ; and the arms being red, are often mistaken for a 
house at a considerable distance in those fields. 

I once met with a curious deception in a gentleman's garden at 
Hackney^ occasioned by a large pane of glass in the garden wall at 
some distance from his house. The glass (through which the sky 
was seen from low ground) reflected a very faint image of the house ; 
but the image seemed to be in the clouds near the horizon, and at 
that distance looked as if k were a huge castle in the air.-^Yet the 
angle, under which the image appeared, was equal to that under 
which the house was seen : but the image being mentally referred 
to a much greater distance than the house, appeared much bigger 
to the imagination. 



130 The Phenomena of the 

Plate 1L hand, to be a great castle at a distance ; because ft 
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 
Fig- xu an &k'> we judge it to be much bigger. For, the 
near object FE, seen by the eye A B D, appears 
under the same angie GC77that the remote obiect 
G///does; and the rays GFCN and HECM, 
crossing one another at C in the pupil oi 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 ob- 
ject ///, only worse defined ; because GHI being 
farther off, appears duller and fainter than FE did. 
But when a fog, as KL^ comes between the eye 
and the object FE, the object appears dull and ill- 
defined like GHI; which causes otir imagination to 
refer FE to the greater distance C//, instead of the 
small distance CJ5, which it really is at. And con* 
sequently, as misjudging 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 GHL 

Fig. ix. 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 HG Ffe C, a little way beyond 

Whyfhe tne clouds; of which those about F y directly over 

Sun and our heads at , are nearer us than those about 77 or 

ar n bi a g." e in the horizon HEe. Therefore, when the Sun 

g-est in the or Mopn appears in the horizon at e, they are not 

honzon, on jy seen ^ n a p art o f t k e s k V) w hich is really farther 

from us than if they were at any considerable alti- 
tude, as about/; 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 de- 
ceive our imagination, and cause us to refer the Sun 



Horizontal Moon explained. 131 

and Moon to a greater distance at their rising or setting 
about e , than when they are considerably high as atyV 
first, their seeming to be on a part of the atmosphere 
at (?, which is really farther than^'from a spectator at 
Ef and secondly, their being seen through a grosser 
medium, when at e y than when aty/ which, by ren- 
dering them dimmer, causes us to imagine them to 
be at a yet greater distance. And as, in both cases, 
they are seen* much under the same angle, we na- 
turally judge them to be biggest when they seem 
farthest from us ; like the abovementioned house, 
186, seen from a higher ground, which shewed it 
to be farther off than it 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 Their ap- 
appears under no greater angle in the horizon than parent di- 
on the meridian, by taking a large sheet of paper, are^ot* 
and rolling it up in the form of a tube, of such a less on the 
width, that observing the Moon through it when she 

rises, she may, as it were, just fill the tube ; then tie horizon, 
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 perigee, 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 

* The Sun and Moon subtend a greater angle on the meridian 
than in the horizon, being nearer the observer's place in the forme*- 
case than in the latter, 



The Method of finding the Distances 

vapours than usual, she appears so much the dim- 
mer ; and therefore we fancy her to be still the big- 
ger, 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. 



CHAP. IX. 



Hie Method of finding the Distances of the Sun, 
Moon, and Planets, 

, Q Q Y | ^HOSE who have not learnt how to take 
J[_ the # altitude of any celestial phenome- 
non by a common quadrant, nor know any thing of 
plane 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 plane right 



* The altitude of any celestial object, is an arc of the sky intercep- 
ted between the horizon and the object. In Fig. VI. of Plate //. let 
HOX be a horizontal line, supposed to be extended from the eye at 
A to X) where the sky and Earth seem to meet at the end of a long 
and level plane; and let 5 be the Sun. The arc AY will be the 
Sun's height above the horizon at X y and is found by the instrument 
JSCD, which is a quadrantal board, or plate of metal, divided into 
90 equal parts or dcgives on its limb DPC, and has a couple of lit- 
tle brass plates, as a and , with a small hole in each of them, call- 
ed sight-holes, tor looking through, parallel to the edge of the quad- 
rant which they stand on. To the centre JS, is fixed one end of a 
thread 1>\ called the plumb-line, which has a small weight or plum- 
met P fixed to its other end. Now, if an observer hold the quad- 
rant upright, without inclining it to either side, and so that the hori- 
zon at X is seen through the sight-holes a and 6, the plumb-iine will 
cut or hang over the beginning of the degrees at 0, in the edge JiC ; 
but if he elevate the quadrant so as to look through the sight-holes 
at any part of the heavens, suppose the Sun at S^just so many de- 
grees as he elevates the sight-hole b above the horizontal line HOX, 



vf the Sun, Moon, and Planets. 13o 

ingled triangle, the following method of finding the Plate tv. 
distances of the Sun and Moon will be easily under- 
stood. 

Let BAG be one half of the Earth, AC its semi- Fr L 
diameter, $' the Sun, m the Moon, and EKOL a 
quarter of the circle described by tlie Moon in re- 
volving from the meridian to the meridian again. 
Let CjRiS be the rational horizon of an observer at 
A, extended to the Sun in the heavens ; and HAG 
his sensible horizon, extended to die Moon's orbit. 
ALC is the angle under which the Earth's semidi- 
ameter^C* is seen from the Moon at L y which is equal 
to the angle OAL, because the right lines AO and 
CLj which include both these angles, are parallel. 
ASCis the angle under which the Earth's semidiame- 
ter AC is seen from the Sun at -S 9 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, asASC is much less than ALC, it 
proves that the Earth's semidiameter AC appears 
much greater as seen from the Moon at Z/, than 
from the Sun at S ; and therefore the Earth is much 
farther from the Sun than from the Moon.* The 



so many degrees -will the plumb-line cut in the limb CP ot the quad- 
rant. For, let the observer's eye at A be in the centre of the celes- 
tial arc XY7, (and he may be said to be in the centre of the Sun's 
apparent diurnal orbit, tet him be on what part of the Earth he will) 
in which arc the Sun is at that time, suppose 25 degrees high, and let 
the observer hold the quadrant so that he may see the Sun through 
the sight-holes; the plumb-line freely playing on the quadrant will 
cut the 25th degree in the limb C 1 /*, equal to the number of degrees 
of the Sun's altitude at the time of observation* 

.'V*. /?. Whoever looks at the Sun must have a smoked glass be- 
fore his eyes to save them from hurt. The better way is not to look 
at the Sun through the sight-holes, but to hold the quadrant facing 
the eye at a little di&tance, and so that the Sun shining through one 
hole, the ray may be seen to fall on the other. 

* See the Note on $ 185-. 



134 The Method of finding the Distances 

quantities of these angles may be determined by ob- 
servation in the following manner ; 

Let a graduated instrument, as DAE, (the larg- 
er the better^) having a moveable Index with sight- 
holes, be fixed in such a manner, that its plane sur- 
face may be parallel to the plane of the equator, and its 
edge AD in the plane of the meridian : so that when the 
Moon is in the equinoctial, and on the meridian 
ADE, she may be seen through the sight-holes 
when the edge of the moveable index cuts the be- 
ginning of the divisions at 0, on the graduated limb 
DE; and when she is so seen, let the precise time 
be noted. Now, as the Moon revolves about the 
Earth from the meridian to the meridian again in 
about 24 hours 48 minutes, she will go a fourth 
part round it in' a fourth part of that time, viz. in 
six hours twelve minutes, as seen from C, that is, 
from the Earth's centre 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 0; 
for the index through the sights of which she is then 
viewed, will be at </, 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 care- 
fully noted*, that it may be known in what time she 
has gone from E to O ; which time subtracted from 
6 hours 12 minutes (the times of her going from E 
The to L) leaves the time of her going from to _, 
Moon's anc j affords an easy method for finding the angle 
parHiiu OAL, (called the Moon's horizontal parallax, which 
what. is equal to the angle ALCJ by the following analo- 



* Here proper allowance must be made for the refraction, which 
being about 34 minutes of a degree in the horizon, will cause the 
moon's centre to appear 34 minutes above the horizon when her cen- 
tre is really in iU 



of the Sun, Moon, and Planets. 135 

gy : 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 Dele, which measures the an- 
gle 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 together equal to 180 degrees, 
or to two right angles, and the sides of a triangle are al- 
ways proportional to the sines of the opposite an- The 
gles, say by the Rule of Three, as the sine of the Moon's 
ande ALC, at the Moon L, is to its opposite side distance 

^Pt i -r i , T i i i determm* 

AL, the Earth's semi-diameter, which is known to e( j. 
be 3985 miles, so is radius, viz. the sine of 90 de- 
grees, or of the right angkylLC, to its opposite side 
AD, 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 cen- 
tre, 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 ^ghtj^ance'* 
be found in the same way, though with more diffi- cannot C be 
culty, if his horizontal parallax, or the angle OAS, yet so ex- 
equal to the angle ASC, were not so small, as tobe^ermined 
hardly perceptible; being scarce 10 seconds of a as the 
minute, or the 360th part of a degree. But Moon '* 4 
the Moon's horizontal parallax, or angle OAL, 
equal to the angle ALC, is very discernible, 
being 57' 18", or 3438" at its 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 parallax- 
es, the Sun's distance from the Earth is at least 340 
times as great as the Moon's : and is rather under- 
rated at 81 millions of miles, when the Moon's dis- 
tance is certainly known to be 240 thousand. But 

S 



136 The Method of finding the Distances 

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 ob- 
servations, 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. But Dr. HAL LEY 
has shewn us how the Sun's distance from the Earth, 
and consequently the distances of all the planets 
How near from the Sun, may be known to within a 500th 
the truth p ar t o f the whole, by a transit of Venus over the 
soorTbe Sn's disc, which will happen on the 6th of June, 
determine in the year 1761 ; till which time we must content 
ourselves with allowing the Sun's distance to be a- 
bout 81 millions of miles, as commonly stated by 
astronomers. 

Sun "^' ^k e ^ un anc *Moon appear much about the 
provetUo same bulk ; and every one who understands geom- 
b^ much etry, knows how their true bulks may be deduced 
thaifthe fr m ^ ie apparent, when their real distances are 
Moon. 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 thou- 
sand 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 



of the Sun, Moon, and Planets. 13~ 

equal every day v that the refractions are almost con- 
stantly 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 par- 
allel of latitude, as a or b. 

194. The Earth's distance from the Sun being The rek- 
determined, the distances of all the other planets Jances S of 
from him are easily found by the following analogy, the pian- 
their periods round him beiner ascertained by obser- e , ts *5 om 

A i p i r i 1 i ** le -5U11 

vation. As the square ot the karth 's period round are known 
the Sun, is to the cube of its distance from the Sun ; to S 1 ' 6 ^ 
so is the square of the period of any other planet, to though. "' 
the cube of its distance in such parts or measurestheirreal 
as the Earth's distance was taken; see 111. This *f * n c t es 
proportion gives the relative mean distances of the well 
planets from the Sun to the greatest degree of e x- knowa 
actness. They are as follows, having been dedu- 
ced from their periodical times ; according to the law 
just mentioned, which was discovered by KEPLER, 
and demonstrated by Sir ISAAC NEWTON,* 



* All the following calculations except those in the two last lines 
before 195, were printed informer editions of this work, before the 
year 1761. Since that time the said two lines (as found by the tran- 
sit A. D. 17611 were added ; and also 195. 



138 The Periods and Distances of the Planets. 

Periodical Revolutions to the same fixed Star, in 
Days and Decimal Parts of a day. 

Mercury I Venus I The Earth I Mars I Jupiter I Saturn I Georgian 
87,9692 I 2246.176 | 365.2564 | 686.9785 | 4332.514 | 1079.275 | 30456.07 

Relative mean distances from the Sun. 

38710 | 72333 | 100000 | 152369 | 520096 | 954006 \ 1908580 

From these numbers we deduce, that if the Sun's horizontal 
fiarallax be 10", t he real mean distances of the planets 
from the Sun in English miles, are 

[31,742,200 | 59,313,060 | 82,000,000 | 124,942,680 | 426,478,720 | 782,284,920 | 1,565,035,600 

But if the Sun'.? parallax be 1 1"" their distances are no more than 

29,032,500 I 54,238,570 '| 75,000,000 | 114,276,750 1 390,034,500 | 715,504,500 | 1,431,435,000 

Errors in distance arising from the mistake of \" in the Sun's 
parallax. 

2,709,700 | 5,074,490 \ 7,000,000 | 10,665,830 | 35,444,220 | 66,780,420 | 133,600,600 

But, from the late transit of Venus, A. D. 1761, the Sun's 

fiarallax appears to be only % f -$-5 i and according to that, 

their real distances in miles are 

36,841,468 I 68,891,486 | 95,173,127 | 145,014,148 | 494,990,976 | 907,956,130 | 1,816,455,526 

And their diameters in wiles, are, 

3100 1 9360 | 7970 | 5150 | 94,1000 | 77,990 | 35,226 

195. These numbers shew, that although we 
have the relative distances of the planets from the 
Sun, to the greatest nicety, yet the best observers 
could not ascertain their true distances until the late 
long-wished-for transit appeared, in 1761, which we 
must confess was embarrassed with several difficul- 
ties. But another transit of Venus over the Sun, 
has now been observed, on the third of June. 1769, 
much better suited to the resolution of this great 
problem than that in 1761 was; and the result of 
the observations does not differ materially from the 
result of those in 1761. No other transit will hap- 
pen till the year 1874. 

196. The Earth's axis produced to the stars, be- 
ing carried parallel* to itself during the Earth's an- 
nual revolution, describes a circle in the sphere of 

why the the fixed stars equal to the orbit of the Earth. But 
oies tial ^* s or k" lt ' though very large, would seem no big- 
seem to ger than a point, if it were viewed from the stars ; 

keep still 

in * By this is meant, that if a line be supposed to be drawn paral- 

lel to the Earth's axis in any part of its orbit, the axis keeps parallel 
to that line in every other part of its orbit : as in fig. I. of plate V. 
where abed efgh represents the Earth's orbit in an oblique view, 
and N$ the Earth's axis keeping always parallel to the line M A, 



The amazing velocity of Light. 139 



and consequently the circle described in the sphere th< r sarn 

i r-1 T? .1 i -rPOintsof 

of the stars by the axis ot the Earth, produced, ifthehea- 
viewed from the earth, must appear but as a point ; vens, not- 
that is, its diameter appears too little to be measur- ^the" 
ed by observation: for Dr. BRADLEY has assured Earth's 
us, that if it had amounted to a single second, or two ^J n the 
at most, he should have perceived it in the number sun. 
of observations he has made, especially upon T Dra- 
conis; 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 means disproves the Earth's annual 
motion, but plainly proves the distance of the stars 
to be exceeding great, 

197. The small apparent motion of the stars, J 113, 
discovered by that great astronomer, he found to be 
no ways owing to their annual parallax, (for it came 
out contrary thereto,) but to the aberration of their 
light, which can result from no known cause, be- 
sides that of the Earth's annual motion ; and as it 
agrees so exactly therewith, it proves beyond dispute, 
that the Earth has such a motion ; for this aberration 
completes all its various phenomena every year ; and The ama- 
proves that the velocity of star-light is such as car- z j n Do- 
ries it through a space equal to the Sun's distance 
from us in 8 minutes 13 seconds of time. Hence 
the velocity of light is *10 thousand 2 10 times as great 
as the Earth's vetocity in its orbit ; which velocity, 
f from what we know already of the Earth's distance 
from the Sun) may be asserted to be at least between 
57 and 58 thousand miles every hour : and suppos- 
ing it to be 58000, this number multiplied by 
10210, gives 592 million 180 thousand miles for 
the hourly motion of light : which last number divi- 
ded by 5600, the number of seconds in an hour, 

* SMITH'S Optic's 1197. 



140 Of the different Seasons. 

Plate ir. shews that light flies at the rate of more than 164 
thousand miles every second of time, or swing of a 
common clock pendulum. 

CHAP. X. 

The Circles of the Globe described. The different 
Lengths of Days and Nights, and the Vicissitudes 
of the Seasons y explained. The explanation oj* 
the Phenomena of Saturn* s Ring concluded. (See 
81 and 82. 

circi of 198 T^ ? t ^ ie reac ^ er be hitherto unacquainted with 
the e ' JL tne principal circles of the globe, he should 

sphere, now learn to know them ; which he may do suffi- 
ciently for his present purpose in a quarter of an 
hour, if he sets the ball of a terrestrial globe before 
Fi - H. him, or looks at the figure of it, wherein these cir- 

E uator C ^ es are ^ rawn an ^ name ^' The equator is that 
tropics*' great circle which divides the northern half of the 
polar cir- Earth from the southern. The tropics are lesser 
poles and c i rc l es parallel to the equator ; each of them being 
231 degrees from it; a degree in this sense being 
the 360th part of any great circle ; or that which di- 
vides the Earth into two equal parts. The tropic of 
Cancer lies on the north side of the equator, and the 
tropic of Capricorn on the south. The Arctic cir- 
Flg ' IL cle has the North pole for its centre, and is just as 
far from it as the tropics are from the equator ; and 
the Ant arctic cir cle, (hid by the supposed convexity 
of the figure) is just as far from the southpole every 
way round it. These poles are the very north 
and south points of the globe : and all other places 
are denominated northward or southward^ according 
to the side of the equator they lie on, and the pole to 
Earth's which they are nearest. The Earth* s axis is a straight 
a** 5 - line passing through the centre of the Earth, perpen- 
dicular to the equator, and terminating in the poles 
at its surface. This, in the real Earth and planets, 
is only an imaginary line \ but in artificial globes or 
planets it is a wire by which they are supported, and 



Of the different Seasons. 141 

turned round in Orreries, or such like machines, by plate lv - 
wheel- work. The circles 12. 1. 2. 3. 4. &c. arc 
meridians to all places they pass through; and weMeridi- 
must suppose thousands more to be drawn, because ans * 
every place, that is ever so little to the east or west 
of any other place, has a different meridian from that 
other place. All the meridians meet in the poles ; 
and whenever the Sun's centre is passing over any- 
meridian in his apparent motion round the Earth, it 
is mid-day or noon to all places on that meridian. 

199. The broad space lying between the tropics, 
like a girdle surrounding the globe, is called the tor- 
rid zone, of which the equator is in the middle all 201 
round. The space between the tropic of Cancer 
and Arctic circle, is called the north temperate zone ; 
that between the tropic of Capricorn and the An- 
tarctic circle, the south temperate zone; and the 
two circular spaces bounded by the polar circles, are 
the two frigid zones; denominated north or south, 
from that pole which is in the centre of the one or 
the other of them. 

200. Having acquired this easy branch of know- 
ledge, the learner may proceed to make the follow- 
ing experiment \vith his terrestrial ball ; which will 
give him a plain idea of the diurnal and annual mo- 
tions of the Earth, together with the different lengths 
of days, nights, and all the beautiful variety of sea- 
sons, depending on those motions. 

Take about seven feet of strong wire, and bend Fig. in. 
it into a circular form, as abed, which being viewed ^gxp'e- 
obliquely, appears elliptical, as in the figure. Place riment 
a lighted candle on a table, and having fixed one en d*^^| r 
of a silk thread K, to the north pole of a small terres- e nt 
trial plobe H, about three inches diameter, cause lengths o 

i , , , . , , . days and 

another person to hold the wire-circle, so that it may ni^ts, 
be parallel to the table, and as high as the flame of and the 
the candle /, which should be in or near 



142 Of the different Seasons, 

centre. Then, having twisted the thread as to 
ward the left hand, that by untwisting it may 
turn the globe round eastward, or contrary to 
the way that the hands of a watch move, hang 
the globe by the thread within this circle, al- 
most contiguous to it ; and as the thread untwists, 
the globe (which is enlightened half round by the 
candle, as the Earth is by the Sun) will turn round 
its axis, and the different places upon it will be car- 
ried through the light and dark hemispheres, and 
have the appearance of a regular succession of days 
and nights, as our Earth has in reality by such a 
motion. As the globe turns, move your hand slow- 
ly, so as to carry the globe round the candle accor- 
ding to the order of the letters abed, keeping its 
centre even with the wire-circle ; and you will per- 
ceive, that the candle, being still perpendicular to 
the equator, will enlighten the globe from pole to 
pole in its whole motion round the circle; and that 
every place on the globe goes equally through the 
light and the dark, as it turns round by the untwist- 
ing of the thread, and therefore has a perpetual 
equinox. The globe thus turning round represents 
the Earth turning round its axis ; and the motion of 
the globe round the candle represents the Earth's 
annual motion round the Sun, and shews, that if 
the Earth's orbit had no inclination to its axis, all 
the days and nights of the year would be equally 
long, and there would be no different seasons. But 
now, desire the person who holds the wire to hold 
it obliquely in the position ABCD, raising the side 
93 just as much as he depresses the side >5 , that 
the flame may be still in the plane of the circle ; 
and twisting the thread as before, that the globe 
may turn round its axis the same way as you 
carry it round the candle, that is, from west to 
east, let the globe down into the lowermost part 
of the wire circle at VJ , and if the circle be pro- 
perly inclined, the candle will shine perpendicular 



OftJte different Seasons. 143 

cularly on the tropic of Cancer, and tlieffigid zone, Summer 
lying within the Arctic or north polar circle, will be solstice - 
all in the light, as in the figure ; and will keep in the 
light, let the globe turn round its axis ever so often. 
From the equator to the north polar circle all the 
places have longer days and shorter nights ; but 
from the equator to the south polar circle just the 
reverse. The Sun does not set to any part of the 
north frigid zone, as shewn by the candle's shining 
on it, so that the motion of the globe can carry no 
place of that zone into the dark : and at the same 
time the south frigid zone is involved in darkness, 
and the turning of the globe brings none of its places 
into the light. If the Karth were to continue in the 
like part of its orbit, the Sun would never set to the 
inhabitants of the north frigid zone, nor rise to those 
of the south. At the equator it would be alvyays 
equal day and night; and as places are gradually 
more and more distant from the equator, toward the 
Arctic circle, they would have longer days and 
shorter nights ; while those on the south side of the 
equator would have their nights longer than their 
days. In this case there w r ould be continual sum- 
mer on the north side of the equator, and continual 
winter on the south side of it. 

But as the globe turns round its axis, move your 
hand slowly forward, so as to carry the globe from 
//toward E, and the boundary of light and dark- 
ness will approach toward the north pole, and recede 
from the south pole; the northern places will go 
through less and less of the light, and the southern 
places through more and more of it ; shewing how 
the northern days decrease in length, and the 
southern days increase, while the globe proceeds 
from H to E. When the globe is at E, it is at a 
mean state between the lowest and highest parts of Autumnal 
its orbit ; the candle is directly over the equator, the equinox. 
boundary of light and darkness just reaches to both 

T 



144 Of the different Seasons. 

the poles, and all places on the globe go equally 
through the light and dark hemispheres, shewing 
that the days and nights are then equal at ail places 
of the Earth, the poles only excepted ; for the Sun 
is then setting to the north pole, and rising to the 
south pole. 

Continue moving the globe forward, and as it 
goes through the quarter A, the north pole recedes 
still farther into the dark hemisphere, and the south 
pole advances more into the light, as the globe 
comes nearer to 25 : and when it comes there at F t 
winter the candle is directly over the tropic of Capricorn, 
solstice. the days are at tne shortest, and nights at the longest, 
in the northern hemisphere, all the way from the 
. equator to the Arctic circle ; and the reverse in the 
southern hemisphere from the equator to the Antarc- 
tic circle ; within which circles it is dark to the north 
frigid zone, and light to the south. 

Continue both motions, and as the globe moves 
through the quarter J3, the north pole advances to- 
ward the light, and the south pole toward the dark ; 
the days lengthen in the northern hemisphere, and 
shorten in the southern ; and when the globe comes 
to G, the candle will be again over the equator, (as 
Vernal when the globe was at E,) and the days and nights 
w -j| a g a j n b e e q ua i as formerly ; and the north pole 
will be just coming into the light, the south pole go- 
ing out of it. 

Thus we see the reason why the days lengthen 
and shorten from the equator to the polar circles 
every year ; why there is sometimes no day or night 
for many turnings of the Earth, within the polar cir- 
cles ; why there is but one day and one night in the 
whole year at the poles ; and why the days and nights 
are equally long all the year round at the equator, 
which is always equally cut by the circle bounding 
light and darkness. 



Of the different Seasons. 145 

201. The inclination of an axis or orbit is merely Remark, 
relative, because we compare it with some other 
axis or orbit which we consider as not inclined at all. 
Thus, our horizon being level to us, whatever place 
of the Earth we are upon, we consider it as having P j atc jj^ 
no inclination ; and yet, if we travel 90 degrees from Fig. in. 
that place, we shall then have a horizon perpendicu- 
lar to the former, but it will still be level to us. 
And if this book be held so that the * circle ABCD 
be parallel to the horizon, both the circle abed, and 
the thread or axis K, will be inclined to it. But if 
the book or plate be held so that the thread be per- 
pendicular to the horizon, then the Q?\y\lABCD will 
be inclined to the thread, and the orbit abed perpen- 
dicular to it, and parallel to the horizon. We gene- 
rally consider the Earth's annual orbit as having no 
inclination, and the orbits of all the other planets as 
inclined to it, $ 20. 

202: Let us now take a view of the Earth in its 
annual course round the Sun, considering its orbit 
as having no inclination, and its axis as inclining 23 J 
degrees from a line perpendicular to the plane of its 
orbit, and keeping the same oblique direction in all 
parts of its annual course ; or, as commonly termed, 
keeping always parallel to itself, 196. 

Let #, b, c, d, e,,f,g, h, be the Earth in eight dif- Plate r. 
ferent parts of its orbit, equidistant from one another: Fi ff- L 
JV s its axis, JVits north pole, s its south pole, and 
S the Sun nearly in the centre of the Earth's orbit, 
18. As the Earth goes round the Sun according 

* All circles appear elliptical in an oblique view, as is evident by 
looking obliquely at the rim of a bason. For the true figure of a cir- 
cle can only be seen when the eye is directly over its centre. The 
more obliquely it is viewed, the more elliptical it appears, until the 
eye be in the same plane with it, and then it appears life a straight 
linr. 



146 Of the different Seasons. 

Plate v. to the order, of the letters abed, &c. its axis A"^ keeps 
the same obliquity, and is still parallel to the line 
A concise M N s. When the Earth is at a, its north pole in- 
Ieasons the c ^ nes towar d the Sun S, and brings all the northern 
places more into the light than at any other time of 
the year. But when the Earth is at e in the opposite 
time of the year, the north pole declines from the 
Sun, which occasions the northern places to be more 
in the dark than in the light ; and the reverse at the 
southern places, as is evident by the figure, which 
I have taken from Dr. LONG'S Astronomy. When 
the Earth is either at c or g, its axis inclines not 
cither to or from the Sun, but lies side wise to him ; 
and then the poles are in the boundary of light and 
darkness; and the Sun, being directly over the equa- 
tor, makes equal day and night at all places. When 
the Earth is at b, it is half-way between the Summer 
solstice and harvest equinox ; when it is at d, it is 
half way from the harvest equinox to the winter sol- 
stice ; at s, half way from the winter solstice to the 
spring equinox ; and at /z, half way from the spring 
equinox to the summer solstice. 

Fig. II. 203. From this oblique view of the Earth's orbit, 

let us suppose ourselves to be raised far above it, 

and placed just over its centre S, looking down upon 

it from its north pole ; and as the Earth's orbit differs 

but very little from a circle, we shall have its figure in 

such a view represented by the circle ABCDEFGH. 

Let us suppose this circle to be divided into 12 equal 

parts, called sigm, having their names affixed to them: 

and each sign into 30 equal parts, called degrees, 

The sea- numbered 10, 20, 30, as in the outermost circle of 

sons the figure, which represents the great ecliptic in the 

another 11 heavens. The Earth is shewn in eight different 

view of positions in this circle : and in each position M is the 

Indfts^ 1 e( l uator > ^ the tropic of Cancer, the dotted circle 

orbit. 



Of the different Seasons. 147 

the parallel of London, U the Arctic or north polar 
circle, and Pthe north pole, where all the meridians 
or hour-circles meet, 198. As the Earth goes 
round the Sun, the north pole keeps constantly to- 
ward one part of the heavens, as it does in the figure 
toward the right-hand side of the plate. 

When the Earth is at the beginning of Libra, 
namely, on the 20th of March in tiiis figure (as at g 
in Fig. I.) the Sun S, as seen from the Earth, ap- 
pears at the beginning of Aries, in the opposite part 
of the heavens*, the north pole is just coming into 
the light, and the Sun is vertical to the equator; vernal 
which, together with the tropic of Cancer, parallel equinox, 
of London, and Arctic circle, are all equally cut by 
the circle bounding light and darkness, coinciding 
with the six o'clock hour-circle, and therefore the 
days and nights are equally long at all places : for 
every part of the meridians JETjLd comes into the 
light at six in the morning, and revolving with the 
Earth according to the order of the hour-letters goes 
into the dark at six in the evening. There are 24 
meridians, or hour-circles drawn on the Earth in this 
figure, to shew the time of sun-rising and setting at 
different seasons of the year. 

As the Earth moves in the ecliptic according to 
the order of the letters ABCD, &c. through the 
signs, Libra, Scorpio, and Sagittarius,- the north 
pole P comes more and more into the light ; the 
days increase as the nights decrease in length at all 
places north of the equator./; which is plain by 
viewing the Earth at b on the 5th of May, when it 
is in the 15th degree of Scorpio f, and the Sun, as 

* Here \ve nmst suppose the Sun to be no bigger than an ordinary 
point ( s.) because he only covers a circle half a degree in diameter 
in the heavens; whereas in the figure he hides a -whole sign at once 
from the Earth. 

t Here we must suppose the Earth to be a much smaller point than 
that in the preceding note marked for the Sun. 



148 Of the different Seasons. 

Plate r. seen from the Earth, appears in the 15th degree of 
Taurus. For then, the tropic of Cancer T is in the 
Fig. ii. light from a little after five in the morning till almost 
_ seven in the evening; the parallel of London from 
half an hour past four till half an hour past seven ; 
the polar circle U from three till nine ; and a large 
track round the north pole P has day all the 24 
hours, for many rotations of the Earth on its axis. 

When the Earth comes to c, at the beginning of 
Capricorn, and the Sun, as seen from the Earth ap- 
pears at the beginning of Cancer, on the 21st of 
June, as in this figure, it is in the position a in Fig. 
I; and its north pole inclines toward the Sun, so as 
to bring all the north frigid zone into the light, and 
the northern parallels of latitude more into the light 
than the dark from the equator to the polar circle ; 
and the more so as they are farther from the equator. 
The tropic of Cancer is in the light from five in die 
morning till seven at night ; the parallel of London 
from a quarter before four till a quarter after eight ; 
and the polar circle just touches the dark, so that the 
Summer Sun has only the lower half of his disc hid from the 
solstice, inhabitants* on that circle for a few minutes about 
midnight, supposing no inequalities in the horizon, 
and no refraction. 

A bare view of the figure is enough to shew, that 
as the Earth advances from Capricorn toward Aries, 
and the Sun appears to move from Cancer toward 
Libra, the north pole advances toward the dark, 
which causes the days to decrease, and the nights to 
Autumnal increase in length, till the Earth comes to the begin- 
Equinox. n ing of A rics, and then they are equal as before ; for 
the boundary of light and darkness cuts the equator 
and all its parallels equally, or in halves. The north 
pole then goes into the dark, and continues in it until 
the Earth goes half way round its orbit ; or, from 
the 23d of * September till the 20th of March. In the 



Of the different Seasons. 149 

middle, between these times, viz. on the 22d ,of Winter 
December, the north pole is as far as it can be in the solstlce * 
dark, which is 23 degrees, equal to the inclination 
of the Earth's axis from a perpendicular to its orbit: 
and then the northern parallels are as much in the 
dark as they were in the light on the 21st of June; 
the winter nights being as long as the summer days, 
and the winter days as short as the summer nights. 
It is needless to enlarge farther on this subject, as 
we shall have occasion to mention the seasons again 
in describing the Orrery > & 397. Only this must be 
noted, that whatever has been said of the northern 
hemisphere, the contrary must be understood of the 
southern ; for on different sides' of the equator the 
seasons are contrary ; because, when the northern 
hemisphere inclines toward the Sun, the southern 
declines from him. 

204. As Saturn goes round the Sun, his oblique- The phe- 
ly-posited ring, like our Earth's axis, keeps parallel s 
to itself, and is therefore turned edgewise to the Sun ring7 
twice in a Saturnian year; which is almost as long 
as 30 of our years, 81. But the ring, though con- 
siderably broad, is too thin to be seen by us when it 
is turned edgewise to the Sun, at which time it is 
also edgewise to the Earth ; and therefore it disap- 
pears once in every fifteen years to us. As the 
Sun shines half a year together on the north 
pole of our Earth, then disappears to it, and shines 
as long on the south pole; so, during one half 
of Saturn's year, the Sun shines on the north side 
of his ring, then disappears to it, and shines as long 
on the south side. When the Earth's axis inclines 
neither to nor from the Sun, but is side wise to him, 
he then ceases to shine on one pole, and begins to 
enlighten the other; and when Saturn's ring inclines 
neither to nor from the Sun, but is edgewise to him, 



150 Of the different Seasons. 

Plate v. he ceases to shine on the one side of it, and begins 
to shine upon the other. 

Fi ff . in. Let S be the Sun, ABCDEFGII Saturn's orbit, 
and IKLMNO the Earth's orbit. Bqth Saturn and 
the Earth move according to the order of the letters : 
v. hen Saturn is at A his ring is turned edgewise to 
the Sun S, and he is then seen from the Earth as if 
he had lost his ring, let the Earth be in any part of 
its orbit whatever, except between N and O; for 
while it describes that space, Saturn is apparently so 
near the Sun as to be hid in his beams. As Saturn 
goes from A to C, his ring appears more and more 
open to the Earth : at Cthe ring appears most open of 
all; and seems to gro\v narrower and narrower, as Sa- 
turn goes from CtoE, and when he comes to E, the 
ring is agnin turned edgewise both to the Sun and 
Earth ; and as neither of its sides are illuminated, it 
is invisible to us, because its edge is too thin to be 
perceptible ; and Saturn appears again as if he had 
lost his ring. But as he goes from E to G, his ring 
opens more and more to our view on the under side ; 
and seems just as open at G as it was at C; and may 
be seen in the night time from the Eartli in any part 
of its orbit, except about J/, when the Sun hides 
the planet from our view. As Saturn goes from G 
to A, his ring turns more and more edgewise to us, 
and therefore it seems to grow narrower and nar- 
rower; and at A, it disappears as before. Hence, while 
Saturn goes from A to E, the Sun shines on the upper 
side of his ring, and the under side is dark ; and 
while he goes from E to A, the Sun shines on the 
under side of his ring, and the upper side is dark. 

It may perhaps be imagined that this article 
might have been placed more properly after $ 81, 
than here; but when the candid reader considers 

Fi.i. and that all the various phenomena of Saturn's ring 

In - depend upon a cause similar to that of our Earth's 



Of the different Seasons. 151 

seasons, he will readily allow that they are best ex- Piate VL 
plained together ; and that the two figures serve to 
illustrate each other. 

205. The Earth's orbit being elliptical, and the The Earth 
Sun keeping constantly in its lower focus, which is stmin ^ 
1,377,000 miles from the middle point of the longer winter 
axis, the Earth comes twice so much, 0^2,754,000^^ 
miles, nearer the Sun at one time of the year than 

at another : for the Sun appearing to us under a 
larger angle in winter than in summer, proves that 
the Earth is nearest the Sun in winter (see the 
Note on Article 185^. But here this natural ques- why th 
tion will arise : Why have we not the hottest weather ^Jit* IS 
when the Earth is nearest the Sun ? In answer it when the 
must be observed, that the eccentricity of the Earth?s ^*^ 
orbit, or 1,377,000 miles, bears no greater proper- the Sun. 
tion to the Earth's mean distance from the Sun, 
than 17 does to 1000; and therefore this small differ- 
ence of distance cannot occasion any sensible differ- 
ence of heat or cold. But the principal cause of this 
difference is, that in winter the Sun's rays fall so ob- 
liquely upon us, that any given number of them is 
spread over a much greater portion of the Earth's 
surface where we live, and therefore each point must 
then have fewer rays than in summer. Moreover, 
there comes a greater degree of cold in the long 
winter nights, than there can return of heat in so short 
days ; and on both these accounts the cold must in- 
crease. But in summer the Sun's rays fall more 
perpendicularly upon us, and therefore come with 
greater force, and in greater numbers on the same 
place ; and by their long continuance, a much great- 
er degree of heat is imparted by day than can fly off 
by night. 

206. That a greater number of 'rays fall on the 
same place, when they come perpendicularly, than 
when they come obliquely on it, will appear by the 
figure. For, let AB be a certain number of the Fig. it 
Sun's 'rays falling on CD (which let us suppose to 



152 The Method of finding the Longitude. 

be London ) on the 21st of June: but, on the 22d 
of December, the line CD, or London, has the ob- 
lique position CD to the same rays ; and therefore 
scarce a third part of them falls upon it, or only those 
between *4ande>; all the rest, cB, being expended 
on the space d P, which is more than double 
the length of CD or Cd. Besides, those parts 
which are once heated, retain the heat for some 
time ; which, with the additional heat daily impart- 
ed, makes it continue to increase, though the Sun 
declines toward the south ; and this is the reason 
why July is hotter than June, although the Sun has 
withdrawn from the summer tropic ; as we find it is 
generally hotter at three in the afternoon, when the 
Sun has gone toward the west, than at noon when 
he is on the meridian. Likewise, those places which 
are well cooled require time to be heated again ; for 
the Sun's rays do not heat even the surface of any 
body till they have been some time upon it. And 
therefore we find January, for the most part, colder 
than December, although the Sun has withdrawn 
from the winter tropic, and begins to dart his beams 
more perpendicularly upon us, when we have the 
position CF. An iron bar is not heated immediate- 
ly upon being put into the fire, nor grows cold till 
some time after it has been taken out. 

CHAP. XL 

The Method of finding the Longitude by the Eclips- 
es of Jupiter' 1 s Satellites : the amazing Velocity of 
Light demonstrated by these Eclipses. 

OA - /^ EOGRAPHERS arbitrarily choose to 

Virstihe- 207. I -w n a -j- r 111 

ridian, \J call the meridian of some remarkable 

and ion- place the first meridian. There they begin their 

places, reckoning ; and just so many degrees and minutes 

what. as any other place is to the eastward or westward of 

that meridian, so much east or west longitude they 

say it has. A degree is the 360th part of a circle, 



p 

The Method of finding the Longitude. 153 

be it great or small, and a minute the 60th part of a pla * ' v - 
degree. The English geographers reckon the longi- 
tude from the meridian of the Royal Observatory at 
Greenwich, and the French from the meridian of 
Paris. 

208. If we imagine two great circles, one of FJ ff- IL 
which is the meridian of any given place, to inter- Hour cir- 
sect each other in the two poles of the Earth, and to cles - 
cut the equator M at every 15th degree, they will 

be divided by the poles into 24 semi-circles, which 
divide the equator into 24 equal parts ; and as the 
Earth turns on its axis, the planes of these semicir- 
cles come successively one after another every hour 
to the Sun. As in an hour of time there is a revo- An hour 
lution of fifteen degrees of the equator, in a minute 
of time there will be a revolution of 15 minutes 
the equator, and in a second of time a revolution of grees of 
15 seconds. There are two tables annexed to this 1 " 
chapter, for reducing mean solar time into degrees 
and minutes of the terrestrial equator ; and also for 
converting degrees and parts of the equator into 
mean solar time. 

209. Because the Sun enlightens only one half of 
the Earth at once, as it turns round its axis, he rises 
to some places at the same moment of absolute time 
that he sets at to others ; and when it is mid-day to 
some places, it is mid-night to others. The XII on 
the middle of the Earth's enlightened side, next the 
Sun, stands for mid-day; and the opposite XII, on 
the middle of the dark side for midnight. If we 
suppose this circle of hours to be fixed in the plane 
of the equinoctial, and the Earth to turn round with- 
in it, any particular meridian will come to the differ- 
ent hours so as to shew the true time of the day or 
night at all places on that meridian. Therefore, 

210. To every place 15 degrees eastward from 
any given meridian, it is noon an hour sooner than 
on that meridian; because their meridian 



154 The Method of finding the Longitude. 

to the Sun an hour sooner; and to all places 15 de- 
grees westward, it is noon an hour later, 208, be- 
cause their meridian comes an hour later to the Sun ; 
and so on ; every 15 degrees of motion causing an 
And con- hour's difference of time. Therefore they who have 
sequently noon an hour later than we, have their meridian, 
grees of tnat is their longitude, 15 degrees westward from us ; 
longitude, and they who have noon an hour sooner than we, 
have their meridian 15 degrees eastward from ours ; 
and so for every hour's difference of time, 15 de- 
Lunar e- grees difference of longitude. Consequently, if the 
usefuHn Beginning or ending of' a lunar eclipse be observed, 
finding the suppose at London, to be exactly at midnight, and 
longitude. j n some other place at 11 at night, that place is 15 
degrees westward from the meridian of London ; if 
the same eclipse be observed at one in the morning 
at another place, that place is 15 degrees eastward 
from the said meridian. 

Eclipses 211. But as it is not easy to determine the exact 
terStel rnoment either of the beginning or ending of a lunar 
lites mucii eclipse, because the Earth's shadow through which 
61 " f r ^ e ^ oon P asses * s f amt an ^ ill-defined about the 
J " edges, we have recourse to the eclipses of Jupiter's 
satellites, which disappear much more quickly as 
they enter into Jupiter's shadow, and emerge more 
suddenly out of it. The first or nearest satellite to Ju- 
piter is the most advantageous for this purpose, be- 
cause its motion is quicker than the motion of any of 
the rest, and therefore its immersions and emersions 
are more frequent and more sudden than those of 
the others are. 

212 The English astronomers have calculated ta- 
bles for shewing the times of the eclipses of Jupi- 
ter's satellites to great precision, for the meridian of 
Greenwich. Now, let an observer, who has these 
tables, with a good telescope and a well-regulated 
clock, at any other place of the Earth, observe the 



The Method of finding the Longitude. 155 



beginning or ending of an eclipse of one of Jupiter's ** to r> 
satellites, and note the precise moment of time that solve this 
he saw the satellite either immerge into, or emerge important 
out of the shadow, and compare that time with the pr 
time shewn by the tables for Greenwich; then, 15 
degrees difference of longitude being allowed for 
every hour's difference of time, will give the longi- 
tude of that place from Greenwich, as above, 210: 
and if there be any odd minutes of time, for every 
minute a quarter of a degree, east or west, must be 
allowed, as the time of observation is later or earlier 
than the time shewn by the tables. Such eclipses 
are very convenient for this purpose on land, be- 
cause they happen almost every day ; but are of no 
use at sea, because the rolling of the ship hinders all 
nice telescopical observations. 

213. To explain this by a figure, let / be Jupiter, Fi - H. 
K, L, M, N, his four satellites in their respective lUustra- 
orbits, 1, 2, 3, 4; and let the Earth be at/ sup.^y 
pose in November, although that month is no other- 

wise material than to find the Earth readily in this 
scheme, where it is shewn in eight different parts of 
its orbit. Let Q be a place on the meridian of 
Greenwich, and R a place on some other meridian 
eastward from Greenwich. Let a person at R ob- 
serve the instantaneous vanishing of the first satellite 
If into Jupiter's shadow, suppose at three in the 
morning ; but by the tables he finds the immersion 
of that satellite to be at midnight at Greenwich; he 
can then immediately determine, that, as there are 
three hours difference of time between Q and R, and 
that R is three hours forwarder in reckoning than Q, 
it must be in 45 degrees of east longitude from the 
meridian of Q. Were this method as practicable at 
sea as on land, any sailor might almost as easily, and 
.with almost equal certainty, find the longitude as the 
latitude. 

214. While the Earth is going from C to F in Fig. IL 
its orbit, only the immersion of Jupiter's satellites 



155 The Method of finding the Longitude. 

dom S S ee mto n * s shadow are generally seen; and their emer- 
the beg-in- sions out of it while the Earth goes from G to B. 
Tnd^oTtbe Indeed > both tnese appearances may be seen of the 
same e- second, third and fourth satellite when eclipsed, 

an P o G f T f u Wmle ^ ie ^ art h * s between D and E, or between 
Piter's 6 and A; but never of the first satellite, on account 
moons, of the smallness of its orbit and the bulk of Jupiter, 
except only when Jupiter is directly opposite to the 
Sun, that is, when the Eartfi is at g: and even then, 
strictly speaking, we cannot see either the immer- 
sions or emersions of any of his satellites, because 
his body being directly between us and his conical 
shadow his satellites are hid by his body a few mo- 
ments before they touch his shadow ; and are quite 
emerged from thence before we can see them, as it 
were, just dropping from behind him. And when 
the Earth is at c, the Sun, being between it and Ju- 
piter, hides both him and his moons from us. 

In this diagram, the orbits of Jupiter's moons 
are drawn in true proportion to his diameter ; but in 
Jupiter's proportion to the Earth's orbit, they are drawn 81 
conjunc- times too large. 

tii*8iBBb* 215 * In whatever month of the year Jupiter is in 
or opposi- conjunction with the Sun, or in opposition to him, 

him 8 are m t ^ 1C nCXt ^ Caf ^ W ^ ^ e ^ montn ^ ater at ^ east ' For 

every year while the earth goes once round the Sun, Jupiter de- 

in differ- scr ibes a twelfth part of his orbit. And, therefore, 

of SSL- when the Earth has finished its annual period from 

vens. being in a line with the Sun and Jupiter, it must go 

as much forwarder as Jupiter has moved in that time, 

to overtake him again : just like the minute-hand of 

a waxh, which must, from any conjunction with 

the hour-hand, go once round the dial-plate and 

somewhat above a twelfth part more, to overtake the 

hour-hand again. 

216. It is found by observation, that when the 
Earth is between the Sun and Jupiter, as at g, his 



The Motion of Light demonstrated. 157 

satellites are eclipsed about 8 minutes sooner than f^teiv. 
they should be according to the tables; and when 
the Earth is at B or C, these eclipses happen about 
8 minutes later than the tables predict them.* Hence 
it is undeniably certain, that the motion of light is 
not instantaneous, since it takes about 16- \ minutes 
of time to go through a space equal to the diameter 
of the Earth's orbit which is 190 millions of miles 
in length ; and consequently the particles of light fly 
about 193 thousand 939 miles every second of time, 
which is above a million of times swifter than the mo- 
tion of a cannon ball. And as light is 16^ minutes The sur- 
iii travelling across the Earth's orbit, it must be 
minutes coming from the Sun to us ; therefore, 
the Sun were annihilated, we should see him for 
minutes after ; and if he were again created, he would 
be 8^ minutes old before we could see him. 

217. To explain the progressive motion of light, Fig- v - 
let A and B be the Earth, in two different parts of 'niustwt- 
its orbit, whose distance from each other is 95 mil- *** a fi ~ 
lions of miles, equal to the Earth's distance from 
the Sun S. It is plain that if the motion of light 
were instantaneous, the satellite 1 would appear to 
enter into Jupiter's shadow FF & the same moment 
of time to a spectator in A as to another in B. But 
by many years observations it has been found, that 
the immersion of the satellite into the shadow is seen 
8 minutes sooner when the Earth is at B, than 
when it is at A. And so, as Mr. ROE ME a first 
discovered, the motion of Light is thereby proved 
to be progressive, and not instantaneous, as was 
formerly believed. It is easy to compute in what 
time the Earth moves from A to B ; for the chord 
of 60 degrees of any circle is .equal to the semi- di- 
ameter of that circle; and as the Earth goes through 

* In the tables which have been published in the nautical alma- 
nacs, &c. a proper allowance for the progress ef light is made. 



158 The Motion of Light demonstrated. 

all the 360 degrees of its orbit in a year, it goes 
through 60 of those degrees in about 61 days, 
Therefore, if on any given day, suppose the first of 
June, the Earth be at A, on the first of August it 
will be at B : the chord, or straight line AB, being 
equal to DS, the radius of the Earth's orbit, the 
same with AS, its distance from the Sun. 

218. As the Earth moves from D to C, through 
the side AB of its orbit, it is constantly meeting the 
light of Jupiter's satellites sooner, which occasions 
an apparent acceleration of their eclipses : and as it 
moves through the other half H of its orbit from C 
to Z), it is receding from their light, which occa- 
sions an apparent retardation of their eclipses ; be- 
cause their light is then longer before it overtakes 
the Earth. 

219. That these accelerations of the immersions 
of Jupiter's satellites into his shadow, as the Earth 
approaches toward Jupiter, and the retardations of 
their emersions out of his shadow, as the Earth is 
going from him, are not occasioned by any inequal- 
ity arising from the motions of the satellites in ec- 
centric orbits, is plain, because it affects them all 
alike, in whatever parts of their orbits they are eclips- 
ed. Besides, they go often round their orbits every 
year, and their motions are no way commensurate to 
the Earth's. Therefore, a phenomenon, not to be 
accounted for from the real motions of the satellites, 
but so easily deducible from the Earth's motion, and 
so answerable thereto, must be allowed to result 
from it. This affords one very good proof of the 
Earth's annual motion. 



7 convert Motion into Time, and the reverse. 



159 



'00. Tables for converting mean solar TIME into Degrees and 
Parts of the terrestrial EQJJATOR ; and also for converting De- 
grees.and Parts of the EOJJATOR into mean solar TIME. 



TABLE!. For converting 
Time into Degrees and 


TABLE 11. For converting ' 
Degrees and Parts of the 


3 arts of the Equator. 


Equator into Time. 








S? s 


i 


a % 


1 


2 S 


_ 


K _ 
2 S 










5 


^ 5' 


? 


jq 5' 


a 


S ? 


t 


S i 3 








a 




















*j 


a 




n> 


n 


^ w 


IT. 


S 


Z 


S 8? 


g 


^ CA 

O 


1 


H jri 


~ 
x 


P, 


~> 


3 P 





5' p 


a 




S 


5' P 


( 


g- 




W 


















n 








H 


H' i- 5 


^ 




H 




H 










- 


a* ^ 


g* 


c/) jr 


9- 


C/5 *r 




en er 










^ 


p a 


a 


a 


o 


^ *^ 
. Z- 




a 










' 








V. 




w. 






1 


15 


1 


15J31 


7 45 


] 


4 


1 


4 


70 


440 


. . 
-. 


30 


g 


30J32 


8 


2 


8 


2 


8 


80 


5 20 


2 


45 


i 


) 45,33 


8 15 


o 


12 


S 


12 


90 


6 


4 


60 


4 


1 034 


8 30 


4 


a 16 


4- 


16 


00 


6 40 




75 





15 


35 


8 45 


5 


20 


5 


20 


10 


7 2C 


6 


90 


(j 


I 30 


36 


9 


6 


24 


36 


24 


20 


8 


7 


105 


; 


1 45 


J7 


9 15 


7 


28 


>7 


88 


30 


840 


8 


120 


8 


2 


38 


9 30 


8 


32 


18 


32 


140 


920 


o 


135 


9 


2 15 


39 


9 45 


9 


36 


J9 


36 


150 





10 


150 





2 30 


40 





to 


40 


A. 


2 40 


160 


040 


11 


165 


1 


2 45 


41 


15 


11 


44 


11 


44 


170 


120 


1,2 


180 


2 


3 


1-2 


30 


12 


48 


1-2 


2 48 


180 


2 


K 


195 


3 


3 15 


45 


45 


15 


52 


13 


2 52 


190 


240 


14 


210 


4 


3 30 


44 


1 


14 


56 


M 


2 56 


200 


3 20 


15 


225 


5 


3 45 


15 


1 15 


15 


1 


15 


3 C 


210 


14 


16 


240 


C 


4 


,6 


11 30 


16 


1 4 


US 


3 4 


22f 


1440 


17 


255 


7 


4 15 


17 


U 45 


1? 


1 8 


17 


3 8 


230 


5 2' 


IS 


270 


8 


4 30 


18 


12 


18 


1 12 


1 


3 12 


24f 


16 


19 


285 


c. 


4 45 


49 


12 15 


19 


i 16 


11 


3 16 


250 


6 4 


2( 


300 


20 


5 


50 


12 30 


20 


1 20 


>( 


3 20 


260 


.7 20 


21 


315 


>] 


5 15 


51 


12 45 


21 


1 2< 


51 


3 24 


27 




22 


330 


>_ 


5 30 


5' 


13 




1 28 


":" 


3 28 


28 


1840 


23 


345 


25 


J 45 


5* 


13 15 


25 


1 32 


5, 


3 32 


29 


1920 


2' 


360 


X 


6 C 


5< 


13 30 


24 


1 36 


5' 


3 36 


30 


20 


25|37c 


2; 


6 15 


5. 


13 45 


25 


1 40 


5 


3 40 


31 


2040 


2<3 


390 


->> 


6 3C 


5( 


14 


2C 


1 44 


5 


3 4 


32 


2 20 


27 


40 


r 


6 45 


5! 


14 15 


27 


1 4 


5 


3 4 


33 


22 


2'- 


42 


: 


7 t 


5 


14 30 


>c 


1 5 


5 


3 5 


34 


2-2 40 


2 


43 


2i 


7 li 


5 


14 45 


2! 


I 5 


5 


3 5 


35 


23 20 


3( 


145 


3< 


7 3( 


(S 


15 Oi)3C 


2 


6 


4 


36 


24 



160 



Of Solar and Sidereal Time. 

These are the tables mentioned in the 208th Ar- 
ticle, and are so easy that they scarce require any 
farther explanation than to inform the reader, that if, 
in Table I. he reckon the columns marked with as- 
terisks to be minutes of time, the other columns give 
the equatorial parts or motion in degrees and mi- 
nutes; if he reckon the asterisk- columns to be se- 
conds, the others give the motion in minutes and se- 
conds of the equator; if thirds, in seconds and 
thirds : And if in Table II. he reckon the asterisk- 
columns to be degrees of motion, the others give 
the time answering thereto in hours and minutes ; if 
minutes of motion, the time is minutes and seconds; 
if seconds of motion, the corresponding time is 
given in seconds and thirds. An example in each 
case will make the whole very plain. 



EXAMPLE I. 

In 10 hours 15 mi- 
nutes 24 seconds 20 
thirds, Qu. How much 
of the equator revolves 
through the meridian ? 

Deg. M. S. 

Hours 10 150 
Min. 15 3 45 

Sec. 24 6 

Thirds 20 5 



EXAMPLE II. 

In what time will 153 
degrees 5 1 minutes 5 se- 
conds of the equator 
revolve through the me- 
ridian ? 

H. M.S.T. 
150 10 
3 12 
Min. 51 3 24 

Sec. 5 20 



Deg.{ 



Armver 153 51 5 Answer 10 15 24 20 
CHAP. XII. 

Of Solar and Sidereal Time. 

sidereal Q91 r I ^HE stars appear to go round the Earth 
daysshor.^1- in 33 hours 55 m i nutes 4 seconds, and 

t-or- tlan .. - 



ter than 



solar days, the Sun in 24 hours : so that the stars gain three 
and why. minutes 56 seconds upon the Sun every day, which 



Of Solar and Sidereal Time. 161 



amounts to one diurnal revolution in a year ; 
therefore, in 365 days, as measured by the returns 
of the Sun to the meridian, there are 366 days, as 
measured by the stars returning to it : the former 
are called solar days, and the latter sidereal days. 

The diameter of the Earth's orbit is but a phy- 
sical point in proportion to the distance of the stars ; 
for which reason, and the Earth's uniform motion 
on its axis, any given meridian will revolve from any 
star to the same star again in every absolute turn of 
the Earth on its axis, without the least perceptible 
difference of time shewn by a clock which goes ex- 
actly true. 

If the Earth had only a diurnal motion, without 
an annual, any given meridian would revolve from 
the Sun to the Sun again in the same quantity of time 
as from any star to the same star again ; because the 
Sun would never change his place with respect to 
the stars. But, as the Earth advances almost a de- 
gree eastward in its orbit in the time that it turns east- 
ward round its axis, whatever star passes over the 
meridian on any day with the Sun, will pass over the 
same meridian on the next day when the Sun is al- 
most a degree short of it ; that is, 3 minutes 56 se- 
conds sooner. If the year contained only 360 days, 
as the ecliptic doeb 360 degrees, the Sun's apparent 
place, so far as his motion is equable, would change 
a degree every day ; and then the sidereal days would 
be just 4 minutes shorter than the solar. 

Let ABCDEFGHIKLM be the Earth's orbit, F ; g . n. 
in which it goes round the Sun every year, accord- 
ing to the order of the letters, that is, from west to 
east; and turns round its axis the same way from 
the Sun to the Sun again in every 24 hour's. Let S 
be the Sun, and R a fixed star at such an immense 
distance, that the diameter of the Earth's orbit 
bears no sensible proportion to that distance. Let 
N m be any particular meridian of the Earth, and 
N a given point or place upon that meridian. 



162 Of Solar and Sidenal Time. 

When the Earth is at A the Sun S hides the sta 
which would be always hid if the Earth never remov- 
ed from A; and consequently, as the Earth turns 
round its axis, the point A r would always come round 
to the Sun and star at the same time. But when the 
Earth has advanced, suppose a twelfth part of its or- 
bit from A to B, its motion round its axis will bring 
the point JVa twelfth part of a natural day, or two 
hours, sooner to the star than to the Sun, for the an- 
gle N B n is equal to the angle A SB: and therefore 
any star which comes to the meridian at noon with 
the Sun when the Earth is at A, .will come to the 
meridian at 10 in the forenoon when the Earth is at 
B. When the Earth comes to C, the point N will 
have the star on its meridian at 8 in the morning, or 
four hours sooner than it comes round to the Sun ; 
for it must revolve from JVton before it has the Sun 
in its meridian. When the Earth comes to Z), the 
point A* will have the star on its meridian at 6 in the 
morning, but that point must revolve six hours more 
from A* to ;z, before it has mid-day by the Sun : for 
now the angle ASD is a right angle, and so is ND 
n ; that is, the Earth has advanced 90 degrees in its 
orbit, and must turn 90 degrees on its axis to cany 
the point A* from the star to the Sun : for the star al- 
ways comes to the meridian when A" m is parallel to 
R S A; because D Sis but a point in respect to 
R S. When the Earth is at E, the star comes to 
the meridian at 4 in the morning ; at F, at 2 in the 
morning; and at G, the Earth having gone half 
round its orbit, A* points to the star R at midnight, 
it being then directly opposite to the Sun. And 
therefore, by the Earth's diurnal motion, the star 
comes to the meridian 12 hours before the Sun. 
When the Earth is at H, the star comes to the me- 
ridian at 10 in the evening ; at / it comes to the me- 
ridian at 8, that is, 16 hours before the Sun; at K 
18 hours before him; atZ20 hours; atJ/22; and 
at A equally with the Sun again. 



Of Solar and Sidereal Time. 



163 



TABLE, shewing ho>v much of the Celestial Equator 
passes over the Meridian in any Part of a mean SOLAR 
DAY; and how much the FIXED STARS gum upon the 
mean SOLAR TIME every Day, ibr a Month, 



165 27 6111 2 45 2' 
180 29 34 12 3 




164 Of Solar and Sidereal Time. 

Plate in. 222. Thus it is plain, that an absolute turn of 
Anabso- tne Earth % on its axis (which is always completed 
lute turn when any particular meridian comes to be parallel to 
Earth on * ts s i tuat i n at any time of the day before) never 
its axis brings the same meridian round from the Sun to the 
"fsbes!" ^ un a S a * n kut that the Earth requires as much 
solar day. more than one turn on its axis to finish a natural day, 
as it has gone forward in that time ; which, at a mean 
state, is a 365th part of a circle. Hence, in 365 
days, the Earth turns 366 times round its axis ; and 
therefore, as a turn of the Earth on its axis com- 
pletes a sidereal day, there must be one sidereal day 
more in a year than the number of solar days, be the 
number what it will, on the Earth, or any other 
planet, one turn being lost with respect to the num. 
her of solar days in a year, by the planet's going 
round the Sun ; just as it would be lost to a travel- 
ler, who, in going round the Earth, would lose one 
day by following the apparent diurnal motion of the 
Sun ; and consequently would reckon one day less 
at his return (let him take what time he would to go 
round the Earth) than those who remained all the 
while at the place from which he set out. 

So, if there were two Earths revolving equally on 
Fig. II. their axes, and if one remained at A until the other 
had gone round the Sun from A to A again, that 
Earth which kept its place at A would have its solar 
and sidereal days always of the same length ; and so 
would have one solar day more than the other at its 
return. Hence, if the Earth turned but once round 
its axis in a year, and if that turn were made the same 
way as the Earth goes round the Sun, there would 
be continual day on one side of the Earth, and con- 
tinual night on the other. 

223. The first part of the preceding table shews 
how much of the celestial equator passes over the 
meridian in any given part of a mean solar day, 
and is to be understood the same way as the table 
in the 220th article. The latter part, intituled, 






Of the Equation of Time. 165 

Accelerations of the fixed Stars, affords us an easy To know 
method of knowing whether or not our clocks and by the 
watches go true : For if, through a small hole in a j^? he ~ 
window-shutter, or in a thin plate of metal fixed to clock goes 
a window, we observe at what time any star disap- * e or 
pears behind a chimney, or corner of a house, at a 
little distance ; and if the same star disappear the 
next night 3 minutes 56 seconds sooner by the clock 
or watch ; and on the second night, 7 minutes 52 se- 
conds sooner ; the third night 11 minutes 48 seconds 
sooner ; and so on, every night as in the table, which 
shews this difference for 30 natural days, it is an in- 
fallible proof that the machine goes true; otherwise 
it does not go true, and must be regulated accord- 
ingly ; and as the disappearing of a star is instanta- 
neous, we may depend on this information to half a 
second. 

CHAP. XIII. 

Of the Equation of Time. 



^24 V 1'^HE Earth's motion on its axis being per- 
_1_ fectly uniform, and equal at all times of 
the year, the sidereal days are always precisely of an 
equal length ; and so would the solar or natural days 
be, if the Earth's orbit were a perfect circle, and its 
axis perpendicular to its orbit. But the Earth's di- The Sun 

i *. v -. i . , and clocks 

urnal motion on an inclined axis, and its annual mo- eq uaioniy 
tion in an elliptic orbit, cause the Sun's apparent mo- on 
lion in the heavens to be unequal : for sometimes he 
revolves from the meridian to the meridian again in 
somewhat less than 24 hours, shewn by a well-regu- 
lated clock; and at other times in somewhat more; 
so that the time shewn by an equal- going clock and 
a true Sun-dial is never the same but on the 14th of 
April, the 15th of June, the 31st of August, and 
the 23d of December. The clock, if it go equa- 

blv and true all the vear round, will be before the 

* * 



166 Of the Equation of Time. 

Sun from the 23d of December till the 14th of April; 
from that time till the 16th of June the Sun will be 
before the clock ; from the 15th of June till the 31st 
of August the clock will be again before the Sun ; 
and from thence to the 23d of December the Sun 
will be faster than the clock. 

use of the -25. The tables of the equation of natural days, 
equation- at the end of the following chapter, shew the time 
that ought to be pointed out by a well regulated 
clock or watch, every day of the year, at the pre- 
cise moment of solar noon; that is, when the Sun's 
centre is on the meridian, or when a true sun-dial 
shews it to be precisely twelve. Thus, on the 5th 
of January in leap-year, when the Sun is on the me- 
ridian, it ought to be 5 minutes 52 seconds past 
twelve by the clock : and on the 15th of May, when 
the Sun is on the meridian, the time by the clock 
should be but 56 minutes 1 second past eleven : in 
the former case, the clock is 5 minutes 52 seconds 
before the Sun ; and in the latter case, the, Sun is 3 
minutes 59 seconds faster than the clock. But with- 
out a meridian-line, or a transit- instrument fixed in the 
plane of the meridian, we cannot set a sun-dial true. 

HOW to 226. The easiest and most expeditious way of 
meridian- drawing a meridian-line is this : Make four or five con- 
line, centric circles, about a quarter of an inch from one an- 
other, oh a fiat board about a foot in breadth ; and let 
the outmost circle be but little less than the board will 
contain. Fix a pin perpendicularly in the centre, and 
of such a length that its whole shadow may fall within 
the inner most circle for at least four hours in the mid- 
dle of the day. The pin ought to be about an 
eighth part of an inch thick, and to have a round 
blunt point. The board being set exactly level in a 
place where the Sun shines, suppose from eight in 
the morning till four in the afternoon, about which 
hours the end of the shadow should fall without 



Of the Equation oj Time. * 10* 

all the circles; watch the times in the forenoon, 
when the extremity of the shortening shadow just 
touches the several circles, and there make marks. 
Then, in the afternoon of the same day, watch 
the lengthening shadow, and where its end touches 
the several circles in going over them, make 
marks also. Lastly, with a pair of compasses, find 
exactly the middle point between the two marks on 
any circle, and draw a straight line from the centre 
to that point : this line will be covered at noon by 
the shadow of a small upright wire, which should 
be put in the place of the pin. The reason for draw- 
ing several circles is, that in case one part of the 
day should prove clear, arid the other part somewhat 
cloudy, if you miss the time when the point of the 
shadow should touch one circle, you may perhaps 
catch it in touching another. The best time for 
drawing a meridian line in this manner is about the 
summer solstice ; because the Sun changes his de- 
clination slowest and his altitude fastest on the long- 
est days. 

If the casement of a window on which the Sun 
shines at noon be quite upright, you may draw a 
line along the edge of its shadow on the floor, 
when the shadow of the pin is exactly on the 
meridian line of the board : and as the motion of the 
shadow of the casement will be much more sensible 
on the floor than that of the shadow of the pin on 
the board, vou may know to a few seconds when it 
touches the meridian line on the floor; and so regu- 
late your clock for the day of observation by that 
line and the equation-tables above mentioned, \ 225. 

227. As the equation of time, or difference Equation 
between the time shewn by a well regulated clock ^ n f^ al 
and that by a true sun-dial, depends upon two caus- pfained. 
es, namely, the obliquity of the ecliptic, and the 
unequal motion of the Earth in it; we shall first 

Y 



168 i Of the Equation of Time. 

explain the effects of these causes separately, and 
then the united effects resulting from their combi- 



a 
nation. 



228. The Earth's motion on its axis being 

perfectly equable, or always at the same rate, and 

the* plane of the equator being perpendicular to its 

axis, it is evident that m equal times equal portions 

of the equator pass over the meridian ; and so would 

equal portions of the ecliptic, if it were parallel to 

The first or coincident with the equator. But, as the ecliptic 

part of the j s oblique to the equator, the equable motion of the 

equation -,-, , * . L -, . *> i i 

of time. Earth carries unequal portions of the ecliptic over 
the meridian in equal times, the difference being 
proportionate to the obliquity ; and as some parts of 
the ecliptic are much more oblique than others, 
those differences are unequal among themselves. 
Therefore if two Suns should start either from 
the beginning of Aries or of Libra, and continue to 
move through equal arcs in equal times, one in the 
equator, and the oth^r in the ecliptic, the equatorial 
Sun would always return to the meridian in 24 hours 
time, as measured by a well-regulated clock ; but 
the Sun in the ecliptic would return to the meridian 
sometimes sooner, and sometimes later than the 
equatorial Sun ; and only *at the same moments with 
him on four days of the year ; namely, the 20th of 
March, when the Sun enters Aries; the 21st of 
June, when he enters Cancer ; the 23d of Septem- 
ber, when he enters Libra; and the 21st of Decem- 
ber, when he enters Capricorn. But, as there is 
only one Sun, and his apparent motion is always in 
the ecliptic, let us henceforth call him the real Sure, 
and the other, which is supposed to move in the 

* If the Earth were cut along the equator, quite through the cen- 
tre, the flat surface of this section would be the plane of the equa- 
tor ; as the paper contained within any circle may be justly termed 
the plane of that circle. 



Of the Equation of Time. 169 

equator, the fictitious : to which last, the motion of Plate vi. 
a well- regulated clock always answers. 

Let Z T z =2= be the Earth, ZFRz its axis., Fig. in, 
abcde,&c. the equator, ABCDE,&.c.\h(t northern half 
of the ecliptic from *v to =0= on the side of the globe 
next the eye, and MNOP, &c. the southern half on 
the opposite side from =& to r. Let the points at 
y/, .#, C, Z), E, F, &c. quite round from v to T 
again, bound equal portions of the ecliptic, gone 
through in equal times by the real Sun ; and those 
at #, &, r, of, ?,/; &c. equal portions of the equator 
described in equal times by the fictitious Sun ; and 
let Z > z be the meridian. 

As the real Sun moves obliquely in the ecliptic, 
and the fictitious Sun directly in the equator, with 
respect to the meridian, a degree, or any number of 
degrees, between p and F on the ecliptic, must be 
nearer the meridian Z y z, than a degree, or any 
corresponding number of degrees, on the equator 
from IT to/; and the more so, as they are the more 
oblique .: and therefore the true Sun comes sooner to 
the. meridian every day while he is in the quadrant 
T F) than the fictitious sun does in the quadrant ** 
f; for which reason, the solar noon precedes noon 
by the clock, until the real Sun comes to F, and the 
fictitious to/; which two points, being equidistant 
from the meridian, both suns will come to it pre- 
cisely at noon by the clock. 

While the real Sun describes the second qua- 
drant of the ecliptic FGHIKL from <& to =a, he 
comes later to the meridian every day than the fic- 
titious sun moving through the second quadrant of 
the equator from/" to =2=; for the points at G, H, /, 
K, and L, being farther from the meridian than their 
corresponding points at g, h, i, k, and /, they must 
be later in coming to it . and as both suns come at 
the same moment to the point ^, they come to the 
meridian at the moment of noon by the clock. 



170 Of the Equation of Time. 

In departing from Libra, through the third quad- 
rant, the real Sun going through MNOPQ toward 
X? at 7i, and the fictitious sun through mnopq toward 
r; the former comes to the meridian every day soon- 
er than the latter, until the real Sun comes to V5 , and 
the fictitious to r, and then they both come to the 
meridian at the same time. 

Lastly, as the real Sun moves equably through 
STUFIV, from v? toward r ; and the" fictitious 
sun through sfuvw, from r toward T, the former 
comes later every day to the meridian than the lat- 
ter, until they both arrive at the point V, and then 
they make it noon at the same time with the 
clock. 

229. The annexed table shews how much the 

Sun is faster or slower than the clock ought to be, 

so far as the difference depends upon the obliquity 

of the ecliptic ; of which the signs of the first and 

A table of third quadrants are at the head of the table, and their 

tion < oT a degrees at the left hand ; and in these the Sun is 

time de. faster than the clock : the signs of the second and 

pending fourth quadrants are at the foot of the table, and their 

Sun's 6 degrees at the right hand ; in all which the Sun is 

place in slower than the clock ; so that entering the table 

theechp- ^^ ^ gj ven s jg n o f tne Sun's place at the head 

of the table, and the degree of his place in that sign 
at the left hand; or with the given sign at the 
foot of the table, and degree at the right hand ; 
in the angle of meeting is the number of minutes 
and seconds that the Sun is faster or slower than 
the clock : or, in other words, the quantity of time 
in which the real Sun, when in that part of the 
ecliptic, comes sooner or later to the meridian 
than the fictitious sun in the equator. Thus, 
when the Sun's place is 8 Taurus 12 degrees, he 
is 9 minutes 47 seconds faster than the clock; 



Of the Equation of Time. 

and when his place is 25 Cancer 18 degrees, he Is 6 
minutes 2 seconds slower. 



171 



Sun faster than the Clock in 


C 


T 


| 


n 


1st Ci- 


1 


* 


"I 


/ 


3d Q. 


n 
gp 


f 


/ ;; 


" 


Deg. 





, < 


S i-3 


7*46 


30 


1 


) iji 


3 34 


3 35 


*9 


2 


J 41 


* 4:1 


8 24 


28 


3 


1 ( 


S 5.> 


8 13 


27 


4 


I V. 


) 1 


8 


26 


5 


i 3: 


) C 


7 48 


gjj 


6 


1 5 ( 


1 1? 


r 54 


24 


7 


2 U 


J 24 


r 2' 


23 


8 


1 37 


^ 30 


7 t 


22 


9 


J 5t 


) 36 


6 50 


21 


10 


J 15 


9 4(. 


6 35 


20 


11 


> 3-. 


."> 44 


5 Ib 


19 


12 


3 5v 


Q 47 


3 


18 


13 


4 '11 


J 5( 


5 4-" 


17 


14 


1 2*- 


') 5, 


5 27 


16 


15 


1 4(r 


J 53 


5 t 


15 


16 


5 - , 


) 54 


4 5*' 


14 


17 


2( 


3 54 


4 31 


13 


18 


3? 


'J 5 , 


t 1) 


12 


19 


5; 


J 5] 


J 5. 


11 


20 





y 4 


> 32 


10 


21 


25 


> 4e 


3 1- 


9 


22 


4( 


' 4. 


> 5' 


8 


23 


5 54 




o - 


- 30 


7 


24 


r c 


9 3? 


2 < 


6 


25 


7 22 


9 2f 


1 4^ 


5 


26 


7 36 


9 1' 


t !Ct 


4 


27 


;' 4fc 


9 1 


t 


3 


28 


s c 


9 4 


.t 4 


2 


29 


y 12 


8 55 


fi 2' 


1 


30 


S 23 


8 4t 


) ( 





2d Q. 


"nJT 


a 


25 




4th ( 


X 




VJ 


Deg: 


Sun silver tk'in thp Clock in j 



This table is formed by taking the difference be- 
tween the Sun's longitude and its right ascension, 
and turning it into time. 



172 Of the Equation of Time. 

Plate in. 230. This part of the equation of time may per- 
Fig in. haps be somewhat difficult to understand by a figure, 
because both halves of the ecliptic seem 'to be on 
the same side of the globe : but it may be made very 
easy to any person who has a real globe before him, 
by putting small patches on every tenth or fifteenth 
degree both of the equator and ecliptic, beginning 
at Aries T ; and then turning the ball slowly round 
westward, he will see all the patches from Aries to 
Cancer come to the brazen meridian sooner than the 
corresponding patches on the equator ; all those from 
Cancer to Libra will come later to the meridian than 
their corresponding patches on the equator ; those 
from Libra to Capricorn sooner, and those from 
Capricorn to Aries later ; and the patches at the be- 
ginnings of Aries, Cancer, Libra, and Capricorn, 
being either on or even with those on the equator, 
shew that the two suns either meet there, or are even 
with one another, and so come to the meridian at 
the same moment. 

A ma- 231. Let us suppose that there are two little balls 
shewin* movm g equably round a celestial globe by clock- 
theli'df- work, one always keeping in the ecliptic, and gilt 
real, the w ^h ffold, to represent the real Sun; and the other 

equal, and , . . A * , ., , 

the solar keeping in the equator, and silvered, to represent the 
time. fictitious sun : and that while these balls move once 
round the globe according to the order of signs, the 
clock turns the globe 366 times round its axis west- 
ward. The stars will make 366 diurnal revolutions 
from the brazen meridian to it again, and the two 
balls representing the real and fictitious suns always 
going farther eastward from any given star, will come 
later than it to the meridian every following day : 
and each ball will make 365 revolutions to the 
meridian ; coming equally to it at the beginnings 
of Aries, Cancer, Libra, and Capricorn ; but in 
every other point of the ecliptic, the gilt ball will 

come either sooner or later to the meridian than the 
I 



Of the Equation of Time, 173 

silvered ball, like the patches above-mentioned. This Plate VL 
would be a pretty way enough of shewing the rea- 
son why any given .star, which, on a certain day of 
the year, conies to the meridian with the Sun, pas- 
ses over it so much sooner every following day, as 
on that day twelvemonth to come to the meridian 
with the Sun again ; and also to shew the reason 
why the real Sun comes to the meridian sometimes 
sooner, and sometimes later, than the time when it 
is noon by the clock ; and on four days of the year, 
at the same time ; while the fictitious sun always 
conies to the meridian when it is twelve at noon by 
the clock. This would be no difficult task for an 
artist to perform ; for the gold ball might be carried 
round the ecliptic by a wire from its north pole, and 
the silver ball round the equator by a wire from its 
south pole, by means of a few wheels to each; 
which might be easily added to my improvement of 
the celestial globe, described in N 483 of the Phi- 
losophical Transactions ; and of which I shall give a 
description in the latter part of this book, from the 
third figure of the third plate. 

232. It is plain that if the ecliptic were more ob- Fig. iTl 
liquely posited to the equator, as the dotted circle T x 
d^, the equal divisions from Ttox would come still 
sooner to the meridian Z T than those marked 
A, B, C, Z), and E, do : for two divisions contain- 
ing 30 degrees, from v to the second dot, a little 
short of the figure 1 , come sooner to the meridian 
than one division containing only 15 degrees from T 
to A does, as the ecliptic now stands ; and those of 
the second quadrant from x to ^ would be so much 
later. The third quadrant would be as the first, and 
the fourth as the second. And it is likewise plain, 
that where the ecliptic is most oblique, namely, 
about Aries and Libra, the difference would be 
greatest; and least about Cancer and Capricorn, 
where the obliquity is least. 




174 Of the Equation of Time, 

Plate vi. 234. Having explained one cause of the differ. 
The se- ence of time shewn by a well-regulated clock and a 
S? l the >art ** ue sun 'dial, and considered the bun, not the Earth, 
equation as moving in the ecliptic, we now proceed to ex- 
oftime. plain the other cause of this difference, namely, the 
inequality of the Sun's apparent motion, \ 205, 
which is slowest in summer, when the Sun is far- 
thest from the Earth, and swiftest in winter when he 
is nearest to it. But the Earth's motion on its axis 
is equable all the year round, and is performed from 
west to east ; which is the way that the Sun appears 
to change his place in the ecliptic. 

235. If the Sun's motion were equable in the 
ecliptic, the whole difference between the equal time 
as shewn by the clock, and the unequal time as 
shewn by the Sun, would arise from the obliquity of 
the ecliptic. But the Sun's motion sometimes ex- 
ceeds a degree in 24 hours, though generally it is 
less ; and when his motion is slowest, any particular 
meridian will revolve sooner to him than when his 
motion is quickest ; for it will overtake him in less 
time when he advances a less space than when he 
moves through a larger. 

236. Now, if there were two suns moving in the 
plane of the ecliptic, so as to go round it in a year ; 
the one describing an equal arc every 24 hours, and 
the other describing sometimes a less arc in 24 
hours, and at other times a larger ; gaining at one 
time of the year what it lost at the opposite; it is 
evident that either of these suns would come sooner 
or later to the meridian than the other, as it happen- 
ed to be behind or before the other : and when they 
were both in conjunction, they would come to the 
meridian at the same moment. 

237. As the real Sun moves unequably in the 
ecliptic, let us suppose a fictitious sun to move 

Fig. iv. equably in a circle coincident with the plane of 
the ecliptic. Let A BCD be the ecliptic or orbit 



Of the Equation of Time. 175 

in which the real Sun moves, and the dotted circle 
a, b> c, d, the imaginary orbit of the fictitious sun ; 
each going round in a year according to the order 
of letters, or from west to east* Let HIKL be the 
Earth turning round its axis the same way every 24 
hours ; and suppose both suns to start from A and 
a, in a right line with the plane of the meridian 
EH, at the same moment : the real Sun at A, being 
then at his greatest distance from the Earth, at which 
time his motion is slowest ; and the fictitious sun at 
a, whose motion is always equable, because his dis- 
tance from the Earth is supposed to be always the 
same. In the time that the meridian revolves from 
If to H again, according to the order of the letters 
HIKL, the real Sun has moved from A to F; and 
the fictitious, with a quicker motion, from a to f, 
through a larger arc ; therefore, the meridian E H 
will revolve sooner from Hto h under the real Sun 
at F, than from //to Sunder the fictitious sun aty> 
and consequently it will then be noon by the sun* 
dial sooner than by the clock* 

As the real Sun moves from A toward C, the 
swiftness of his motion increases all the way to C, 
where it is at the quickest. But notwithstanding 
this, the fictitious sun gains so much upon the real, 
soon after his departing from A, that the increasing 
velocity of the real Sun does not bring him up with 
the equably-moving fictitious sun till the former 
comes to C, and the latter to r, when each has gone 
half round its respective orbit ; and then, being in 
conjunction, the meridian E H revolving to E K 
comes to both Suns at the same time, and therefore 
it is noon by them both at the same moment. 

But the increased velocity of the real Sun, now 
being at the quickest, carries him before the ficti- 
tious one ; and, therefore, the same meridian will 
come to the fictitious sun sooner than to the real : 
for while the fictitious sun moves from c to g, the 
real Sun moves through a greater arc from C to O: 
consequently the point .AT has its noon by the clock 

Z 



1 76 Of the Equation of Time. 



PLATE 
VI. 



when it comes to , but not its noon by the Sun 
till it comes to /. And although the velocity of the 
real Sun diminishes all the way from C to A, and 
the fictitious sun by an equable motion is still com- 
ing nearer to the real Sun, yet they are not in con- 
junction till the one comes to A, and the other to a; 
and then it is noon by them both at the same mo- 
ment. 

Thus it appears, that the solar noon is always 

later than noon by the clock while the Sun goes 

from C to A; sooner, while he goes from A to C, 

and at these two points, the Sun and clock being 

equal, it is noon by them both at the same moment. 

Apogee, 238. The point A is called the Sun's apogee^ be- 

and apt* cause when he is there, he is at his greatest distance 

sides, from the Earth ; the point C, his perigee, because 

what - when in it he is at his least distance from the Earth : 

Fi - 1V - and a right line, as AEC, drawn through the Earth's 

centre, from one of these points to the other, is 

called the line of the apsides. 

239. The distance that the Sun has gone in any 
time from his apogee (not the distance he has to go 

Meanano-to it, though ever so little) is called his mean ano- 
what'. maly, and is reckoned in signs and degrees, allow- 
ing 30 degrees to a sign. Thus, when the Sun has 
gone 174 degrees from his apogee at A, he is said 
to be 5 signs 24 degrees from it, which is his mean 
anomaly; and when he has gone 355 degrees from 
his apogee, he is said to be 11 signs 25 degrees 
from it, although he be but 5 degrees short of A, 
in coming round to it again. 

240. From what was said above, it appears, that 
when the Sun's anomaly is less than 6 signs, that 
is, when he is any where between A and C, in the 
half ABC of his orbit, the solar noon precedes the 
clock- noon ; but when his anomaly is more than 6 
signs, that is, when he is any where between C and 
A, in the half CDA of his orbit, the clock-noon pre- 
cedes the solar. When his anomaly is signs, 
degrees, that is, when he is in his apogee at A; 



Of the Equation of Time. 1 77 

or 6 signs, degrees, which is when he is in his pe- 
rigee at C; he comes to the meridian at the moment 
that the fictitious sun does, and then it is noon by 
them both at the same instant. 

241. The following table shews the variation, or 
equation of time depending on the Sun's anomaly, 
and arising from his unequal motion in the ecliptic ; 
as the former table, 229, shews the variation de- 
pending on the Sun's place, and resulting from the 
obliquity of the ecliptic : this is to be understood the 
same way as the other, namely, that when the signs 
are at the head of the table, the degrees are at the 
left hand ; but when the signs are at the foot of the 
table, the respective degrees are at the right hand ; 
and in both cases the equation is in the angle of meet- 
ing. When both the above-mentioned equations are 
either faster or slower, their sum is the absolute 
equation of time ; but when the one is faster, and 
the other slower, it is their difference. Thus sup- 
pose the equation depending on the Sun's place be 
6 minutes 41 seconds too slow, and the equation 
depending on the Sun's anomaly, 4 minutes 20 se- 
conds too slow, their sum is eleven minutes one se- 
cond too slow. But if the one had been 6 minutes 
41 seconds too fast, and the other 4 minutes 20 se- 
conds too slow, their difference would have been 2 
minutes 2 1 seconds too fast, because the greater 
quantity is too fast. 



178 



Of the Equation of Time. 



S Sun faster than the Clock if his anomaly be S 



A Table 
of the 
equation 
of time, 
depending 1 
on the 
Sun's ano^ 
maty. 



s 


a Siimb 1 


1 


2 


3 


4 


5 




s 















S 


D 


M. S 


M. S. 


M. S. 


M. S. 


M. S. 


M. S. 


!* 
















s 


'-'""-"- 


RW 


~- ~ ~ ^ - 


** 


-~~ *"" 






s 








3 47 


6 36 


7 43 


6 45 


3 56 


30 S 


t 


8 


3 54 


6 40 


/ 43 


6 41 


3 49 


29 5 


2 


16 


4 1 


6 44 


7 43 


6 37 


3 41 


28 S 


3 


24 


4 8 


6 48 


7 43 


6 32 


3 34 


27$ 


4 


32 


4 14 


6 52 


7 42 


6 28 


3 27 


26S 


S 5 


40 


4 21 


6 56 


7 42 


6 24 


3 19 


25? 


S 6 


47 


4 27 


6 59 


7 41 


6 19 


3 12 


24 S 


S ? 


55 


4 34 


7 2 


7 40 


6 14 


3 4 


23? 


S 8 


1 3 


4 40 


7 6 


7 39 


6 9 


2 57 


22 S 


S 9 


1 11 


4 47 


7 9 


7 38 


6 4 


2 49 


21 ? 


SlO 


19 


4 53 


7 12 


7 37 


5 59 


2 41 


20 S 


|u 


27 


4 59 


7 14 


r 36 


5 54 


2 34 


19? 


Sl2 


34 


5 5 


7 17 


7 35 


5 49 


2 26 


18 w 


5 13 


42 


5 11 


7 20 


7 33 


5 43 


2 18 


17$ 


S 14 


50 


5 17 


7 2.2 


7 31 


5 38 


2 10 


16> 




57 


5 22 


24 


7 29 


5 32 


2 2 


\$ 


*i 


2 5 


5 28 


27 


7 27 


5 26 


1 54 




S 17 


2 13 


5 34 


29 


7 25 


5 20 


1 46 


13 S 


S18 


2 20 


5 39 


31 


7 23 


5 14 


1 38 


12 s 


> 19 


2 28 


5 44 


32 


7 20 


5 8 


1 30 


US 


S20 


2 35 


5 50 


34 


7 18 


5 2 


1 22 


10 S 


?2l 


2 43 


5 55 


35 


7 15 


4 56 


1 14 


9 c 


*22 


2 50 


6 


37 


7 12 


4 50 


I 6 


8 V 


c 23 


2 57 


6 5 


38 


7 9 


4 43 


58 


7S 


S24 


3 5 


6 10 


7 39 


7 6 


4 37 


49 


6 ' 


S 25 


3 12 


6 14 


7 40 


7 3 


4 30 


41 


5 S 


S 26 


3 19 


6 19 


7 41 


7 


4 23 


33 


4 ' 


<27 


3 26 


6 24 


7 41 


6 56 


4 17 


25 


3S 


?28 


3 33 


6 28 


7 42 


6 53 


4 1C 


17 


2V 


S29 


3 40 


6 32 


7 42 


6 49 


4 3 


8 


1 S 


^ 30 


3 47 


6 36 


7 43 


6 45 


3 56 





OS 


S 


1 iSign 


10 


9 


8 


7 


6 


D -s 



This table is formed by turning the equation of 
the Sun's centre (see p. 344) into time. 

242. The obliquity of the ecliptic to the equator, 
which is the first mentioned cause of the equation 
of time, would make the Sun and clock agree on 



Of the Equation of Time. 179 

four days of the year ; namely, when the Sun enters 
Aries, Cancer, Libra, and Capricorn : but the other 
cause, now explained, would make the Sun and 
clock equal only twice in a year ; that is, when the 
Sun is in his apogee,and in his perigee. Consequently, 
when these two points fall in the beginnings of Can- 
cer and Capricorn, or of Aries and Libra, they con- 
cur in making the Sun and clock equal in these 
points. But the apogee at present is in the 9th de- 
gree of Cancer, and the perigee in the 9th degree 
of Capricorn ; and therefore the Sun and clock 
cannot be equal about the beginnings of these signs, 
nor at any time of the year, except when the swift- 
ness or slowness of the equation resulting from one 
cause just balances the slowness or swiftness arising 
from the other. 

243. The second table in the following chapter 
shews the Sun's place in the ecliptic at the noon of 
every day by the clock, for the second year after 
leap-year ; and also the Sun's anomaly to the near- 
est degree, neglecting the odd minutes of that de- 
gree. Its use is only to assist in the method of 
making a general equation- table from the two fore- 
mentioned tables of equation depending on the Sun's 
place and anomaly, 229, 241 ; concerning which 
method we shall give a few examples presently. The 
next tables which follow them are made from those 
two ; and shew the absolute equation of time result- 
ing from the combination of both its causes ; in which 
the minutes as well as degrees, both of the Sun's 
place and anomaly, are considered. The use of 
these tables is already explained, 225 : and they 
serve for every day in leap-year, and the first, se- 
cond, and third years after : For on most of the 
same days of all these years the equation differs, 
because of the odd six hours more than the 365 days 
of which the year consists. 

EXAMPLE I. On the 14th of April, the Sun is m|^S" 
the 25th degree of r Aries and his anomaly is 9 ing equa- 
signs 15 degrees; the equation resulting from the tion * tables * 



1 80 Of the Equation of Time. 

former is 7 minutes 22 seconds of time too fast, 
229; and from the latter, 7 minutes 24 seconds 
too slow, \ 241 ; the difference is 2 seconds that the 
Sun is too slow at the noon of that day, taking it in 
gross for the degrees of the Sun's place and ano- 
maly, without making proportionable allowance for 
the odd minutes. Hence at noon, the swiftness of 
the one equation balancing so nearly the slowness 
of the other, makes the Sun and clock equal on 
some part of that day. 

EXAMPLE II. On the 16th of June, the Sun is 
in the 25th degree of n Gemini, and his anomaly 
is 11 signs 16 degrees; the equation arising from 
the former is 1 minute 48 seconds too fast ; and 
from the latter 1 minute 50 seconds too slow ; which 
balancing one another at noon to 2 seconds, the Sun 
and clock are again equal on that day. 

EXAMPLE III. On the Slstofdugtist, the Sun's 
place is 8 degrees 11 minutes of i# Virgo (which 
we call the 8th degree, as it is so near), and his ano- 
maly is 1 sign 29 degrees ; the equation arising from 
the former is 6 minutes 40 seconds too slow ; and 
from the latter, 6 minutes 32 seconds too fast ; the 
difference being only 8 seconds too slow at noon, 
and decreasing toward an equality, will make the 
Sun and clock equal in the evening of that day. 

EXAMPLE IV. On the 23d of December, the 
Sun's .place is 1 degree 58 minutes (call it 2 degrees 
of V3 Capricorn), and his anomaly is 5 signs 23 de- 
grees ; the equation for the former is 43 seconds too 
slow, and for the latter 58 seconds too fast ; the dif- 
ference is 15 seconds too fast at noon ; which de- 
creasing will come to an equality, and so make the 
Sun and clock equal in the evening of that day. 

And thus we find, that on some part of each of 
the above-mentioned four davs, the Sun and clock 



Of the Precession of the Equinoxes* 18 r 

are equal ; but if we work examples for all other days 
of the year, we shall find them different. And, 

244. On those days which are equidistant from 
any equinox or solstice, we do not find that the 
equation is as much too fast or too slow on the one 
side, as it is too slow or too fast on the other. The 
reason is, that the line of the apsides, 238, does Remark, 
not, at present, fall either into the equinoctial or the 
solstitial points, 242. 

245. The four following equation- tables, for leap- T he rea- 
year, and the first, second, and third years after, son why 
would serve for ever, if the Sun's place and anomaly tablet a"ii 
were alwavs the same on every given day of the year, but tem- 
as on the same day four years before or after. But porarv 
since that is not the case, no general equation-tablets 

can be so constructed as to be perpetual. 



CHAP. XIV. 

Of the Precession of the Equinoxes. 

TT has been already observed, 116, that by 
' J[ the Earth's motion on its axis, there is more 
matter accumulated all around the equatorial parts, 
than any where else on the Earth. 

The Sun and Moon, by attracting this redundancy 
of matter, bring the equator sooner under them in 
every return towards it, than if there was no such 
accumulation. Therefore, if the Sun sets out from 
any star, or other fixed point in the heavens, the 
moment when he is departing from the equinoctial, 
or from either tropic ; he will come to the same 
equinox or tropic again 20 min. 17| sec. of time, 
or 50 seconds of a degree, before he completes his 
course, so as to arrive at the same fixed star or poini: 
from whence he set out. For the equinoctial point-, 
recede 50 seconds of a degree westward every year, 
contrary to the Sun's annual progressive motion. 



182 Of the Precession of the Equinoxes. 

PLATE When the Sun arrives at the same* equinoctial 
or solstitial point, he finishes what we call the tropi- 
cal year ; which, by observation, is found to con- 
tain 365 days 5 hours 48 minutes 57 seconds : and 
when he arrives at the same fixed star again, as seen 
from the Earth, he completes the sidereal year, 
which contains 365 days 6 hours 9 minutes 14| se- 
conds. The sidereal year is therefore 20 minutes 
17-J seconds longer than the solar or tropical year, 
and 9 minutes 14j seconds longer than the Julian 
or civil year, which we state at 365 days 6 hours: 
so that the civil year is almost a mean betwixt the 
sidereal and the tropical. 

247. As the Sun describes the whole ecliptic, or 
360 degrees, in a tropical year, he moves 59' 8" of 
a degree every day at a mean rate : and consequently 
50' of a degree in 20 minutes 17^ seconds of time: 
therefore he will arrive at the same equinox or sol- 
stice when he is 50" of a degree short of the same 
star or fixed point in the heavens from which he set 
out the year before. So that, with respect to the 
fixed stars, the Sun and equinoctial points fall back 
(as it were) 30 degrees in 2160 years, which will 
make the stars appear to have gone 30 deg. forward, 
with respect to the signs of the ecliptic in that time : 
for the same signs always keep in the same points 
of the ecliptic, without regard to the constellations. 
Fig. iv To explain this by a figure, let the Sun be in con- 
junction with a fixed star at S, suppose in the 30th 
degree of 8, on the 21st day of May 1756. Then 
making 2160 revolutions through the ecliptic VWX, 



* The two opposite points in which the ecliptic crosses 
the equinoctial, are called the equinoctial points : and the two 
points where the ecliptic touches the tropics (which are 
likewise opposite, and 90 degrees from the former) are 
called ike solstitial ficints. 



Of the Precession of the Equinoxes. 183 



0'; 



S - TABLE shewing the Precession of the Equinoctial Points in the\ 
Heavens^ both in Motion and Time ; and the Anticipation of the ^ 
Equinoxes on the Earth. 



1 

Julian 
years. 


Recession of the Equinoctial Points 
in the Heavens. 


Anticipation of the s 
Equinoxes on $ 
the Earth. s 

s; 


Motion. 


Time. 




s. ' " 


Days H. M. S. 


D. H. M. S. ! 


1 

2 

4 


50 
1 40 
2 30 
3 20 
4 10 


20 17 
40 35 
1 52-J 
1 21 10 
1 41 27-| 


Oil 3 s 
22 6 <J 
33 9 S 
44 12 
55 15 S 


6 

7 
8 
g 

10 
"20 
30 
40 
50 
60 


0050 
5 50 
6 40 
7 30 
8 20 


% \ 45 
2 22 2-J 
2 42 20 
032 37| 
3 22 55 


1 6 18 S 
1 17 21 Ij 
1 28 24 S 
1 39 27 
1 50 30 S 


O 16 40 
O 25 
33 20 
41 40 
50 


6 45 50 
10 8 45 
13 31 40 
16 54 35 
20 17 30 


3 41 OS 
5 31 30 S 
7 22 OS 
9 12 30 Jj 
Oil 8 OS 


70 
80 
90 
100 
200 


58 20 
1 6 40 
1 15 
1 23 20 
2 46 40 


23 40 25 
1 3 3 20 
1 6 20 15 
1 9 49 10 
2 19 38 20 


12 53 30 S* 

14 44 jj 
16 34 30 S 
18 25 0^ 
1 12 50 OS 


300 
400 
500 
600 
700 


4 10 
5 33 20 
6 56 40 
8 20 
9 43 20 


4 5 27 30 
5 15 16 40 
7 1 5 50 
8 10 55 
9 20 44 10 


2 7 15 0^ 
3 1 40 > 
3 20 5 OS 
4 14 3.0 J* 
5 8 55 Os 


800 
900 
1000 
2000 
3000 

4000 
5000 
6000 
. 7000 
8000 


11 6 40 
12 30 
13 53 20 
27 40 40 
1 11 40 


11 6 33 20 
12 16 22 30 
14 2 11 40 
28 4 23 20 
42 6 35 


6 3 20 
6 21 45 OS 
7 16 10 ,0! 

15 8 20 S 
23 ^30 <| 


1 25 33 20 
2 9 20 40 
2 23 20 
3 7 13 20 
3 21 6 40 


56 8 40 40 
70 10 58 20 
84 13 10 
98 15 21 40 
112 17 33 20 


30 10 -40 \ 
38 8 50 OS 
46 1 Ij 
53 17 10 OS 
61 9 20 0j( 


9000 
1000 
2000 
25920 


4500 
4 18 53 20 
9 7 46 40 
12 


126 19 45 
140 21 56 40 
281 19 53 20 
365 6 


69 1 30 ? 
76 17 40 S 
153 11 20 Jj 
198 21 36 OS 



184 Of the Precession of the Equinoxes. 

at the end of so many sidereal years, he will be found 
again at AS: but at the end of so many Julian years, 
he will be found at M y short of S, and at the end of 
so many tropical years, he will be found short of M, 
in the 30th degree of Taurus at J 1 , which has reced- 
ed back from S to T in that time, by the precession 
of the equinoctial points <f Aries and ^= Libra. 

The arc ST will be equal to the amount of the 
precession of the equinox in 2160 years at the rate 
of 50'' of a degree, or 20 min. 17-| sec. of time an- 
nually : this, in so many years, makes 30 days lOf 
hours : which is the difference between 2160 side- 
real and tropical years. And the arc MT will be equal 
to the space moved through by the Sun in 2160 
times 11 min. 3 sec. or 16 days 13 hours 48 mi- 
nutes, which is the difference between 2160 Julian 
and tropical years. 

248. From the shifting of the equinoctial points, 
and with them all the signs of the ecliptic, it follows 
that those stars which in the infancy of astronomy 
were in Aries are now got into Taurus: those of 
Taurus into Gemini, &tc. Hence likewise it is, that 
the stars which rose or set at any particular season 
of the year, in the times of HESIOD, EUDOXUS, 
VIRGIL, PLINY, &c. by no means answer at this 
time to their descriptions. The preceding table 
shews the quantity of this shifting both in the hea- 
vens and on the Earth, for any number of years to 
25,920; which completes the grand celestial peri- 
od : within which any number and its quantity is 
easily found, as in the following example, for 5763 
years; which at the autumnal equinox, A. D. 1756, 
is thought to be the age of the world. So that with 
regard to the fixed stars, the equinoctial points in 
the heavens have receded 2 s 20 2' 30" since the 
creation ; which is as much as the Sun moves in 
in 81 d 5f> O ra 52 s . And since that time, or in 5763 
years, the equinoxes with us have fallen back 44 d 
5 h 21 m 9 s ; hence, reckoning from the time of the 
Julian equinox, A. D. 1756, viz. Sept. llth, it 



Of the Precession of the Equinoxes. 

appears that the autumnal equinox at the creation 
was on the 25th of October. 



185 



j^vy-sX\/-w/\r\ 

S Julian 
^ years. 

is 


r*r*r^r*r<J*>r'*rjr*rJ**'**r*r'-J'^'>f **''*''*'*'<* 

Precesssion of the Equinoctial 
Points in the Heavens. 


^+r*rs*r*r*r. $fc 

Anticipation 
of the Equi- , 
noxes on the S 
Earth. ? 

\ 


Motion. 


TLne. 


s '2* 


D. H. M. S. 


D.H.M.S. 

t. 


J> 5000 
S 700 
^ 60 


2 9 26 40 
9 43 20 
O 50 O 
O 2 3O 


70 10 58 20 
9 20 44 10 
020 17 30 
1 O52 


38 850 0\ 
5 8 55 Jj 
Oil 3 OS 
O O 33 9 s 


5763 


2 20 2 30 


81 5 O52 


44 5 21 9 S 



249. The anticipation of the equinoxes, and con- J 
sequently of the seasons, is by no means owing to thequL- 
the precession of the equinoctial and solstitial points noxes an 
in the heavens (which can only affect the apparent se 
motions, places and declinations of the fixed stars) 

but to the difference between the civil and solar 
year, which is 11 minutes 3 seconds \ the civil year 
containing 365 days 6 hours, and the solar year 
365 days 5 hours 48 minutes 57 seconds. The next 
following table, page 189, shews the length, and 
consequently the difference of any number of side- 
real, civil and solar years, from 1 to 10,000. 

250. The above 11 minutes 3 seconds, by which The rea- 
the civil or Julian year, exceeds the solar, amounts teSn^t 
to 11 days in 1433 years: and so much our seasons style, 
have fallen back with respect to the days of the 
months, since the time of the Nicene council in 

A, D. 325 ; and therefore, in order to bring back all 
the fasts and festivals to the days then settled, it was 
requisite to suppres 1 1 nominal days. And that 
the same seasons might be kept to tfre same times 
of the^ year for the future, to leave out the Bissex- 



186 Of the Precession of the Equinoxes. 

PLATE tile-day in February at the end of every century of 
years where the significant figures are not divisible 
by 4 ; reckoning them only common years, as the 
17th, 18th, and 19th centuries, viz. the years 
1700, 1800, 1900, &c. because a day intercalated 
every fourth year was too much, and retaining the 
Bissextile-day at the end of those centuries of years 
which are divisible by 4, as the 16th, 20th and 24th 
centuries; viz. the years 1600, 2000, 2400, &c. 
Otherwise, in length of time, the seasons would be 
quite reversed with regard to the months of the 
year; though it would have required near 23,783 
years to have brought about such a total change. If 
the Earth had made exactly 365J diurnal rotations 
on its axis, while it revolved from any equinoctial 
or solstitial point to the same again, the civil and so- 
lar years would always have kept pace together, and 
the style would never have required any alteration. 
the pre- 251. Having already mentioned the cause of the 
cesssion of precession of the equinoctial points in the heavens, 
noctiai 11 * & ^6, which occasions a slow deviation of the 
points. Earth's axis from its parallelism, and thereby a 
change of the declination of the stars from the equa- 
tor, together with a slow apparent motion of the 
stars forward with respect to the signs of the eclip- 
tic, we shall now explain the phenomena by a dia- 
gram. 

Fig. vi. Let NZS7L be the Earth, SONA its axis pro- 
cluced to the starry heavens, and terminating in A, 
the present north pole of the heavens, which is ver- 
tical to JV, the north pole of the Earth. Let EOQ 
be the equator, T 95 Zt the tropic of Cancer, and 
VT x? the tropic of Capricorn : 70 Z the ecliptic, 
and BO its axis, both which are immoveable among 
the stars. But as * the equinoctial points recede in 

* The equinoctial circle intercepts the ecliptic in two opposite 
points ; namely, the ferst points of the signs Aries and Libra. They 
are called the equinoctial points, because when the bun is in either 



Of the Precession of the Equinoxes. 187 

the ecliptic, the Earth's axis SON is in motion 
upon the Earth's centre O, in such a manner as to 
describe the double cone JVOn and Sos, round the 
axisof the ecliptic, BO, in the time that the equinoctial 
points move quite round the ecliptic, which is 25, 920 
years; and in that length of time the north pole of the 
Earth's axis produced, describes the circled? CZ)^, 
in the starry heavens, round the pole of the ecliptic, 
which keeps immoveable in the centre of that circle, 
the Earth's axis being 23| degrees inclined to the 
axis of the ecliptic, the circle ABC D A, described 
by the north pole of the Earth's axis produced to 
A, is 47 degrees in diameter, or double the inclina- 
tion of the Earth's axis. In consequence of this mo- 
tion, the point A, which at present is the north pole 
of the heavens, and near to a star of the second mag- 
nitude in the tail of the constellation called the Lit- 
tle Bear, must be deserted by the Earth's axis; 
which moving backward a degree every 72 years, 
will be directed toward the star or point B in 6480 
years from this time ; and in twice that time, or 
12960 years, it will be directed toward the star or 
point C: which will then be the north pole of the 
heavens, although it is at present 8~ degrees south 
of the zenith of London L, The present position 
of the equator EOQ will then be changed into eOg, 
the tropic of Cancer T<s Z into Vt 25 and the tro- 
pic of Capricorn FT v? into / >5 Z; as is evident 
by the figure ; and the Sun, when in that part of the 
heavens, where he is now over the terrestrial tropic 
of Capricorn, and makes the shortest days and 
longest nights in the northern hemisphere, will then 
be over the terrestrial tropic of Cancer, and make 
the days longest and nights shortest. And it will 
require 12,960 years more, or 25,920 from the pre- 

of them, he is directly over the terrestrial equator : and then the day* 
and nights a r e equal. 



188 Of the Precession of the Equinoxes. 

sent time, to bring the north pole N quite round, so 
as to be directed toward that point of the heavens 
which is vertical to it at present. And then, and not 
till then, the same stars, which at present describe 
the equator, tropics, polar circles, &c. by the Earth's 
diurnal motion, will describe them over again. 






Of Sidereal, Julian, and Solar Time. 185 

TABLE shewing the Time contained in any Number of Sidereal, Julian, 
and Solar Years, from 1 to 10000. 



Sidereal Years. 


Julian Years, j] Solar Years. 


___ 
S. 


fears. | D ys | H. | M. 


S. 


Days. 


H. || Days. | H. M. 


1 


365 


6 


9 


141 


365 


6 


365 


5 


4b 


57 


C) 




730 


12 


18 


29 


730 


12 


73( 


11 


37 


54 


o 


1095 


18 


27 


43- 


1095 


18 


1095 


17 


26 


51 


4 


1461 





36 


58 


1461 





146C 


23 


15 


48 


c 


1826 


6 


4C 


121 


1826 


6 


1826 


5 


4 


45 





2191 


12 


55 


27 


2191 


12 


2191 


10 


53 


42 


7 


2556 


19 


5 


44 


2556 


18 


2556 


16 


42 


39 


8 


2,922 


1 


13 


56 


2922 





2921 


22 


31 


36 


9 


3287 


7 


23 


101 


3287 


el 


3287 


4 


20 


33 


10 


3652 


13 


32 


25 


3652 


12 


3652 


10 


9 


30 


20 


7305 


3 


4 


50 


7305 





7304 


20 


19 





30 


10957 


16 


37 


15 


10957 


12 


10957 


6 


28 


30 


40 


14610 


6 


9 


40 


I461C 





14609 


16 


38 





50 


18262 


19 


42 


5 


18262 


12 


18262 


2 


47 





60 


21915 


9 


14 


30 


21915 


6 


21914 


12 


57 





70 


25567 


22 


46 


55 


25567 


12 


25566 


2 


6 


30 


80 


29220 


12 


19 


20 


29220 





292J9 


9 


16 





90 


32873 


1 


51 


45 


32872 


12 


32871 


19 


25 


30 


100 


36525 


15 


24 


10 


36525 




36524 


5 


35 




200 


73051 


6 


48 


20 


73050 




73048 


n 


10 




300 


109576 


22 


12 


30 


109575 




109572 


16 


45 




400 


146102 


13 


36 


40 


146100 




146096 


22 


20 




500 


182628 


5 





50 


182625 




182621 


o 


55 




600 


219153 


20 


25 




219150 




219145 


9 


30 




700 


255679 


11 


49 


10 


255675 




255669 


15 


5 




800 


292205 


3 


13 


20 


292200 




292193 


20 


40 




900 


228730 


18 


37 


30 ' 


328725 




328718 


2 


15 




1000 


365256 


10 


1 


40 


365250 




365242 


7 


50 




2000 


730512 


20 


3 


20 


730500 




730484 


15 


40 




3000 


1095769 


6 


5 




1095750 




1095720 


23 


30 




4000 


1461025 


16 


6 


40 


1461000 




1460969 


'7 


90 




5000 


1826282 


2 


8 


20 


1826250 




1826211 


IS 


10 




6000 


2191538 


12 


10 




2191500 




2191453 


23 


o 




7000 


2556794 


22 


11 


40 


2556750 




2556696 


c 


50 




8000 


2952051 


8 


13 


20 


292200C 




2921938 


14 


40 




9000 
10000 

K*yy* 


3287037 
3652564 

fVVyw 


18 
4 
,r,r.r,, 


15 
16 

r^W 


40 

V*Wy\^ 


3287250 
3652500 

^vr,^,/-^^ 


<-^y*,r 


3287180 
365242S 

XV",r^V%^ 


22 
6 

f^-f*j 


30 
20 
"^^^ 





190 



Tables of the Surfs 



A TABLE shewing the Sun's true Place, and Distance from its S 
Apogee, for the second Year after Leap-Year. 



5 


January- | February. 


March. 


April. J 


s o 


Sun's 


Sun's 


Sun's 1 Sun's 


Sun's 


Sun's 


Sun's 


Sun's S 


5i 


Place. 


Anom. 


Place. 1 Anom. 


Place. 


Anom . 


Place. 


Anom. <J 


i f 


D. M. | D. M. 


D. vi. D ' . 


1). M. | D. M.|D. M 


D. M. \ 


^ i 


11X523 


6 2 


1256 


7 4 


11 X 10 


8 2 


Ilcy357 


9 3 S 


S 2 


12 24 


6 3 


13 57 


7 5 


12 10 


8 3 


12 56 


9 4 ^ 


S 3 


13 25 


6 4 


14 58 


7 6 


13 10 


8 4 


13 55 


9 5S 


S 4 


14 27 


6 5 


15 58 


7 7 


14 10 


8 5 


i4 54 


9 6 J; 


5 


15 28 


6 6 


16 59 


7 8 


15 10 


8 6 


15 53 


9 7 S 


?"" 

(5 


16 29 


6 7 


18 00 


7 9 


16 10 


8 7 


16 52 


9 8 S 


j 


17 30 


6 8 


19 0! 


7 10 


17 10 


8 8 


17 51 


9 8 !j 


S 8 


18 31 


6 9 


20 01 


7 11' 


18 10 


8 9 


18 49 


9 9 S 


9 


19 32 


6 10 


21 02 


7 12 


19 09 


8 10 


19 48 


9 10 


10 


20 34 


6 11 


22 03 


7 13 


20 09 


8 11 


20 47 


9 11 S 


11 


21 35 


6, 12 


23 03 


7 14 


21 09 


8 12 


21 46 


9 12 S 


12 


22 36 


6 13 


24 04 


7 15 


22 09 


8 13 


22 44 


9 13 5 


13 


23 37 


6 14 


25 04 


7 16 


23 09 


8 14 


23 43 


9 14 S 


14 


24 38 


6 15 


26 05 


7 17 


24 08 


8 15 


24 42 


9 15 < 


" 


25 39 


6 16 


27 06 


7 18 


25 08 


8 16 


25 40 


9 16 Jj 


flS 


26 40 


6 17 


28 06 


7 19 


26 08 


8 17 


26 39 


9 17 S 


S17 


27 42 


6 18 


29 07 


7 20 


27 07 


8 18 


27 38 


9 18 Ij 


?I8 


28 43 


6 19 


X 07 


7 21 


28 07 


8 19 


28 36 


9 19 S 


S 19 


29 44 


6 20 


1 07 


7 22 


29 06 


8 20 


29 35 


9 20!; 


^ 20 


y~ 45 


6 21 


2 08 


7 23 


cy 06 


8 21 


33 


9 21 S 


ill 


1 46 


6 22 


3 08 


7 24 


1 05 


8 22 


1 32 


9 22 S 


S22 


2 47 


6 23 


4 08 


7 25 


2 05 


8 23 


2 30 


9 23 ? 


** 23 


3 48 


6 24 


5 09 


7 26 


3 04 


8 2* 


3 28 


9 24 S 


S 24 


4 49 


6 25 


6 09 


7 27 


4 03 


8 25 


4 27 


9 25 ^ 


5 25 


5 50 


6 26 


7 09 


7 28 


5 03 


8 26 


5 25 


9 26 S 


c 
















2 


^ 

V At V 


6 51 


6 28 


8 09 


7 29 


6 02 


8 27 


6 23 


9 27 ? 


S27 


7 52 


6 29 


9 10 


8 


7 01 


8 28 


7 21 


9 28 s 


^28 


8 53 


7 


10 10 


8 1 


8 00 


8 29 


8 20 


9 29 *s 


S29 


9 53 


7 1 






9 00 


9 


9 18 


10 > 


5 30 


10 54 


7 2 






9 59 


9 1 


10 16 


10 1 S 


S 31 


11 55 


7 3 






10 58 


9 2 




S 
S 


*. . 'i^ 

W, " 



Place and Anomaly. 



191 



A TABLE shewing the Sim's true Place, and Distance from its 
Apogee, for the second Year after Leap- Year. 



t 


May. 


June. 


July. 


August. 


s e 


Sun's 


Sun's 


Sun's 


Sun's 


Sun's 


Sun's 


Sun's 


Sun's 


S W! 


Place. 


Anom. 


Place. 


Anom. 


Place. 


Anom. 


Place. 


Anom. 


S ' 


D. M. 


S. D. 


D. M. 


S. D. 


D. M. 


S. D. 


D. M. 


S. D. 


S i 


U 014 


10 2 


11 D04 


11 2 


99542 





D&1S 





S 2 


12 12 


10 3 


12 01 


11 3 


10 39 


1 


10 16 


1 


S S 


13 10 


10 4 


12 59 


11 A 


11 37 


2 


11 13 


2 


S 4 


14 08 


10 5 


13 56 


11 5 


12 34 


3 


!2 11 


3 




15 06 


10 6 


14 53 


11 e 


13 31 


4 


13 08 


4 


S 


16 04 


10 7 


15 51 


11 6 


14 28 


5 


14 06 


5 


7 


17 02 


10 8 


16 48 


11 7 


i 5 2 5 


6 


15 03 


6 


5 R 


18 00 


10 9 


17 46 


11 8 


16 23 


7 


1 6 i 


7 


s 

S 9 


18 58 


10 10 


18 43 


11 9 


17 20 


8 


16 58 


8 


jo 


19 56 


10 11 


19 40 


11 10 


18 17 


9 


17 56 


1 9 


s~ 


20 54 


10 12 


20 38 


11 11 


19 14 


10 


18 54 


1 10 


%)s 


21 52 


10 12 


21 35 


11 12 


20 12 


11 


19 51 


I 10 




22 49 


10 13 


22 32 


11 13 


21 09 


12 


20 49 


1 11 


S 14 


23 47 


10 14 


23 30 


11 14 


22 06 


13 


:i 47 


1 12 


S 15 


24 45 


10 15 


24 27 


11 15 


23 03 


14 


22 44 


1 13 


S lfi 


25 43 


10 16 


25 24 


11 16 


24 01 


15 


23 42 


1 14 


SIT 


26 41 


10 17 


26 21 


11 17 


24 58 


16 


24 40 


1 15 




27 38 


10 18 


27 19 


11 18 


25 55 


17 


25 38 


1 16 


S S19 


28 36 


10 19 


28 16 


11 19 


26 53 


18 


26 36 


1 17 


^ 20 


29 34 


10 20 


29 13 


1 I 20 


27 50 


18 


27 33 


1 18 


S 2 1 


a 31 


10 21 


55 10 


11 21 


28 47 


19 


28 31 


1 19 


<2? 


1 29 


10 22 


1 08 


11 22 


29 44 


20 


29 29 


1 20 


^23 


2 26 


10 23 


2 05 


11 23 


SI 42 


21 


fH|1 ^ 7 


1 21 




3 24 


10 24 


3 02 


11 24 


1 39 


22 


I 25 


1 22 


$23 

t 


4 22 


10 25 


3 59 


11 25 


2 36 


23 


2 23 


i 23 


26 


5 19 


10 26 


4 5611 26 


3 34 


24 


3 21 


1 24 


$27 


6 17 


10 27 


5 53 11 27 


4 31 


25 


4 19 


1 25 


J-28 


7 14 


10 28 


6 51 


11 27 


5 28 


26 


5 17 


1 26 


<J 29 


8 12 


10 29 


7 48 


11 28 


6 26 


27 


6 15 


1 27 


S 30 


9 09 


11 


8 45 


11 29 


7 23 


28 


7 13 


1 28 


S 


















S 31 


10 06 


: 1 1 






8 21 


29 


8 11 


1 29 






Bb 



192 



Tables of the Swfs Place, fcfc. 



" >* -^ <* >^^ ^ ^^^f^f^'^r^- jf^f^-^-^-^r^-^ *r ,w ^*r^ . i^ys 

t \ TABLE shewing the Sun's true Place, and Distance from its'S 
Apogee, for the second Year after Leap-Year. 



1 September. 


October. 


November. 


December. 


5 


Sun's 


Sun's 


SUD'S \ 


Sun's 


Sun's 


Sun's 


Sun's 


Sun's Jj 


* 


Place. 


Anom. 


Place. 


Anom. 


Place. 


Anom. 


Place. 


Anom. s 




D. M. 


S. D. 


D. :Vr. 


S. D. 


D. M. 


S. D. 


D. M. 


S. JLX t 


i 


9^09 


2 


8=^=28 


2 29 


9fi U 7 


4 


9 34 


5 c 


2 


10 07 


2 1 


9 27 


3 


10 17 


4 1 


10 35 


5 IS 


i-> 


11 05 


2 2 


10 2f 


1 


11 17 


4 2 


11 36 


5 2 c 


4 


12 04 


2 3 


11 25 


2 


12 IP 


4 r 


12 37 


5 3S 


5 


13 02 


2 4 


12 25 


3 


13 IS 


4 4 


13 38 


5 4 Jj 


I __ 

















6 


14 CO 


2 5 


13 24 


4 


14 18 


4 5 


14 39 


5 5 S 


7 


14 59 


2 6 


14 23 


5 


15 19 


4 6 


1 5 4( 


5 6 J[ 


8 


13 57 


2 7 


15 23 





16 19 


4 7 


16 4-1 


5 7 S 


9 


16 55 


2 - 8 


16 22 


7 


17 19 


4 8 


17 42 


5 S$ 


10 


17 54 


2 9 


17 21 


8 


18 20 


4 9 


18 43 


5 9S 


















S 


















s 


11 


18 52 


2 9 


18 21 


o 


19 20 


4 1C 


19 4 


5 10 S 


12 


19 51 


2 10 


19 20 


10 


20 21 


4 11 


20 45 


5 11 J; 


1 3 


20 49 


2 11 


20 20 


11 


21 22 


4 12 


21 46 


5 12 S 


14 


21 48 


2 12 


21 20 


12 


22 23 


4 13 


22 47 


5 13 Jj 


15 


22 46 


2 13 


22 19 


15 


23 22 


4 14 


23 49 


5 14 S 


16 


23 45 


2 14 


23 19 


14 


24 25 


4 15 


24 50 


5 15* 


17 


24 44 


2 15 


24 18 


15 


25 23 


4 16 


25 51 


5 16 > 


18)25 42 


2 16 


25 18 


16 


26 24 


4 17 


26 52 


5 17S 


19 


26 41 


2 17 


26 18 


17 


27 25 


4 18 


27 53 


5 19? 


20 


27 4C 


2 18 


27 18 


18 


28 25 


4 19 


28 54 


5 20 S 


21 


28 3<v 


2 19 


28 17 


3 19 


29 26 


4 20 


29 55 


5 21 S 


22 


29 37 


2 20 


29 17 


3 20 


/ 27 


4 21 


V? 56 


5 22 Ij 


23 


=2= 36 


2 2! 


T, 17 


3 21 


1 27 


4 22 


1 58 


5 23 


24 


1 35 


2 22 


1 17 


3 22 


2 28 


4 23 


2 59 


5 24 v 


25 


2 34 


2 25 


2 17 


3 23 


3 29 


4 24 


4 00 


5 25 S 


26 


3 33 


2 24 


3 17 


3 24 


4 30 


4 25 


5 01 


5 26 ? 


'27 


4 32 


2 25 


4 17 


3 25 


5 30 


4 26 


6 02 


5 27 > 


28 


5 31 


2 26 


5 17 


3 26 


6 31 


4 27 


7 03 


5 28 S 


2P 


6 30 


2 27 


6 17 


3 27 


7 52 


4 28 


8 05 


5 29 > 


30 


7 29 


2 28 


7 17 


3 28 


8 So 


4 29 


9 06 


6 OS 


S 1 






8 17 


*3 29 






10 07 


6 IS 



s _ 

V S 



TABLES 



OF THE. 



EQUATION OF TIME* 



FOR 



LEAP-YEARS AND COMMON YEARS ; 



Shewing what Time it ought to be by the Clock 
when the Sun's Centre is on the Meridian. 



194 



Equation-Tables. 



S A TABLE shewing what Time it ought to be by the Clock's 


S when the Sun's Centre is on the Meridian. v, 


S The Bissextile or Leap-Year. Jj 


S ? 


January. 


J* ebruary. 


March. April. Jj 


s s" 


H. M. S. 


H. M. S. 


H. M. S 


H. M. S. s 


s 








<J 




XII 4 20 


XII 14 S 


XII 12 30 


XII 3 42 S 


S 2 


4 30 


14 1C) 


12 17 


3 24 5 


S 

s s 


4 58 


14 17 


12 4 


3 6S 


S 4 


5 25 


14 22 


11 50 


2 48 S 


s 


5 52 


14 27 


11 35 


2 30 Jj 


p 


XII 6 19 


XII 14 31 


XII 11 21 


XII 2 13 


S 7 


6 45 


14 34 


11 6 


1 55 S 


S 8 


7 10 


14 37 


10 50 


1 38 > 


S 9 


7 35 


14 38 


10 34 


1 21 S 


s s io 


8 


14 39 


10 18 


1 4\ 


s n 


XII 8 24 


XII 14 39 


XII 10 2 


XII 48 S 


5 12 


8 47 


14 38 


9 45 


32 vj 


?13 


9 10 


14 37 


Q <"> <; 


17S 


$14 


9 32 


14 35 


9 11 


1 ^ 


S15 


9 53 


14 32 


8 54 


XI 59 47 S 


^ 16 


XII 10 14 


XII 14 28 


XII 8 36 


XI 59 32 S 


^ 17 


10 34 


14 24 


8 18 


59 18 ^ 


1-18 


10 53 


14 19 


8 C 


59 4 S 


S 19 


1 1 12 


14 13 


7 42 


58 51 s 


S20 


11 30 


14 7 


7 24 


58 38 S 


fc 


XII 1 1 47 


XII 14 


XII 7 C 


XI 58 26 S 


; 22 


12 3 


13 52 


6 47 


58 14 lj 


S 2 


12 19 


13 44 


6 29 


58 2 S 


s 24 


12 3t 


13 35 


6 10 


57 51 <J 


S25 


12 48 


13 26 


5 52 


57 41 S. 


S 26 


XII 13 


XII 13 16 


XII 5 33 


XI 57 3l| 


S 27 


13 13 


13 5 


5 15 


57 21 


S 28 


13 25 


12 54 


4 56 


57 12 S 


S 29 


13 36 


12 42 


4 37 


57 4> 


^30 


13 45 




4 19 


56 55 Ij 


Vj 


13 54 




4 


S 


i . . 



195 



J A 

s 



TABLE shewing what Time it ought to be by the 
Clock when the Sun's Centre is on the Meridian. 
The Bissextile, or Leap^-Ycar. 



II 

s ^ 


1 


May. 




June. 


July. 


August 


' S 


H. 


M. 


S.[H. 


M. 


S 


II. 


M. 


S. 


H. M. 




XI 


56 


48JXI 


57 


30 


XII 


3 


29 


XII 5 


51 S 


S 2 




56 


41 




57 


40 




3 


40 


5 


4^ 


ij 
S 3 




56 


34 




57 


49 




3 


51 


5 


42 S 


I 4 




56 


28 




57 


59 




4 


02 


5 


36 1* 







56 


23 




58 


10 




4 


12 


5 


30 S 


? 


XI 


56 


18 


XI 


58 


20 


XII 


4 


22 


XII 5 


23 ^ 


s r 




56 


14 




58 


31 




4 


31 


5 


16? 


S 8 




56 


10 




58 


42 




4 


40 


5 


2 S 


> 9 




56 


7 




58 


,54 




4 


49 


5 


os 


S sio 




56 


5 




59 


6 




4 


57 


4 


51 S 


V 






















J* 


~ 


XI 


56 


3 


XI 


59 


18 


XII 


5 


5 


XII 4 


41 S 


S 12 




56 


1 




59 


3( 




5 


13 


4 


31 ^ 


?3 




56 







59 


42 




5 


20 


4 




S 14 




56 







59 


55 




5 


26 


4 


>o* 


?15 




56 


01 


XII 





8 




5 


32 


3 


58 S 


s 






















5 


& 


XI 


56 


2 


XII 





20 


XII 


5 


38 


XII 3 


46 S 


5 17 




56 


4 







33 




5 


43 


3 


33 v 


S 1 




56 


6 







46 




5 


48 


3 


20 S 


19 




56 


9 







59 




5 


52 


3 


7 c 


S 20 




56 


12 




1 


13 




5 


56 


2 


52 


s 






















? 


&I 


XI 


56 


16 


XII 


1 


26 


XII 


5 


59 


XII 2 


38 


$22 




56 


20 




1 


39. 




6 


1 


2 


23S* 


S 23 




56 


25 




1 


52 




6 


3 


2 


7 


^24 




56 


31 




2 


4 




6 


4 


1 


52 s 


5 25 




56 


36 




2 


17 




6 


4 


1 


35 > 


S 






















*> 


? 


XI 


56 


43 


XII 


2 


30 


XII 


6 


4 


XII 1 


18 S 


^27 




56 


50 




2 


42 




6 


4 


1 


1-5 


S 28 




56 


57 




2 


54 




6 


2 





44 Jj 


S 29 




57 


5 




3 







6 








26 S 


^ 30 




57 


13 




3 


18 




5 


58 





8 {V 


s 






















c 


V 


















C 


S 31 




57 


21 




5 


55 


XI 59 


40 > 



195 



Equation- Tables. 



'#% , w * 

S A TABLE shewing what Time it ought to be by the S 

^ Clock when the Sun's Centre is on the Meridian. Ij 

The Bissextile, or Leap-Year. 



1 


September. 


October. 


November. 


December. Jj 


S ri 


H. M. S. 


a. M. s. 


H. M. S. 


H. M. S. S 


S 1 


XI 59 30 


XI 49 22 


XI 43 45 


XI 49 43 S 


S 2 


59 11 


49 


43 45 


50 7s 


S 3 


58 52 


48 45 


43 45 


50 31 S 


S A> 


58 32 


48 27 


43 47 


50 56 s 


\ 5 


58 12 


48 9 


43 49 


51 21 S 


si 


XI 57 52 


XI 47 52 


XI 43 53 


XI 51 47 


S 7 


57 32 


47 36 


43 57 


52 13 ? 


W o 


57 12 


47 19 


44 2 


52 40 > 


S 9 


56 51 


47 4 


44 8 


*i si 

OO o S 


S 10 


56 30 


46 48 


44 14 


53 35 jj 


\- 




















XI 56 10 


XI 46 33 


XI 44 22 


XI 54 3 S 


S 12 


55 49 


46 19 


44 30 


54 32 s 


S 13 


55 28 


46 6 


44 40 


55 01 J> 


^ 14 


55 7 


45 52 


44 50 


55 30 S 


s 15 


54 46 


45 40 


45 1 


56 jj 


s 

S 16 


XI 54 25 


XI 45 28 


XI 45 13 


XI 56 29 Jj 


s ]7 


54 5 


45 16 


45 25 


56 59 S 


S 18 


53 44 


45 6 


45 39 


57 29 Jj 


v 1^ 
j 

;>20 


53 23 
53 2 


44 55 

44 46 


45 53 

46 8 


57 59"' S 
53 29 S 


S21 


XI 52 41 


XI 44 37 


XI 46 24 


XI 58 59 S 


c 22 


52 21 


44 29 


46 41 


59 29 ^ 


$23 


52 


'44 21 


46 58 


59 59 s 


S 24 


51 40 


44 14 


47 16 


XII 29 S 


S 25 


51 19 


44 8 


47 35 


59 s 


J 








<* 


J26 


XI 50 59 


XI 44 2 


XI 47 55 


XII 1 29 ^ 


^27 


50 39 


43 57 


48 15 


1 58 S 


S28 


50 20 


43 53 


48 36 


2 27 ^ 


S 29 


50 


43 50 


48 58 


2 56 S 


S30 


49 41 


43 48 


49 20 


3 25 ? 


S 31 




43 46 




3 54 S; 



Equation- Tables. 



^v w . ,/ 

S A TABLE shewing what Time it ought to be by the S 


^ Clock w';cn the Sun's Centre is on the Meridian. Jj 


<J The tirst Year after Leap-Year. Jj 


S ^ 


January. 


February. 


March. 


April. Jj 


S ? 


H. M. S. 


II. M. S. 


II. M. S 


H. M. S. s 


H 








. s 


XII 4 23 


XII 14 9 


XII 12 33 


XII 3 47 s 


S 2 


4 51 


14 16 


12 20 


3 39 S 


S 3 


5 19 


14 21 


12 7 


3 10 s 


5 4 


5 46 


14 27 


11 54 


2 52 S 


\ 5 


6 13 


14 31 


11 40 


2 35 J 
c, 


S 


XII 6 59 


XII 14 34 


XII 11 25 


Xil 2 17s 


S ^ 


7 4 


14 37 


11 10 


2 0^ 


s 8 


7 30 


14 39 


10 55 


1 43V 


s ^ 


7 54 


14 40 


10 39 


1 25 ^ 


^ 10 


8 18 


14 40 


10 23 


1 9' ? 


s' 11 


XII 8 42 


XII 14 39 


XII 10 7 


XII 53 S 


S 12 


9 4 


14 38 


9 50 


0. 36^: 


S 13 


9 26 


14 36 


9 33 


20 ** 


S 14 


9 48 


14 33 


9 16 


5 V 


SH 


10 .9 


14 30 


8 58 


XI 59 50 S 


16 


XII 1 29 


XII 14 25 


'XII 8 ft 


XI 59 35 S 


S I? 


10 48 


14 20 


8 23 


59 t 21 . 




11 7 


14 15 


8 5 


59 7 V 


S 19 


11 25 


14 9 


7 47 


58 54 


|j 20 


11 42 


14 2 


7 29 


58 4J S 


S 21 


XII 11 59 


XII 13 54 


XII 7 10 


XI 58 28 S 


S 22 


12 15 


13 46 


6 52 


58 16 Sj 


S23 


12 50. 


13 37 


6 33 


58 4 S 


S24 


1 3 44 


13 28 


6 15 


57 53^. 


S25 


1:3 58 


13 18 


5 56 


57 43 s 


j f 






_ 


. _ S 


t 


XII IS 10 


XII 13" 8 


XII 5 38 


XI 57 32 v 




13 22 


12 57 


5 19 


57 23 


S 28 


13 33 


12 45 


5 1 


57 14 t 


29 


13 43 




4 42 


57 5S 


S 30 


13 53 




4 23 


56 ^ 


S 








W 


\3, 


14 1 




4 5 


\ 



<J8 



Equation- Table's, 



S A TABLE shewing what Time it ought to be by the 'S 
> Clock when the Sun's Centre is on the Meridian. Ij 


S 'I' 


he first Year alter Leap-Year. J 


S J? 

| 


May. 


June. July. 


August. ^ 


!!. M. 


S. 


H. M. S.iH. M. S. 


H. M. S. s 


Xi 56 

56 
56 
56 
56 


49 

35 

29 
24 


XI 57 27 

57 36 
57 46 
57 56 
58 6 


Xll 3 26 

3 37 
3 48 
3 58 

4 9 


XII 5 52 ^ 
5 48 > 
5 43 Jj 
5 38 S 


1 

s 10 


XI 56 
56 
56 
56 
56 


19 
14 
1) 
7 
5 


XI 58 17 

58 27 
58 38 
58 50 
59 2 


XII 4 19 

4 28 
4 37 
4 46 
4 55 


XII 5 25 ^ 
5 18 S 
5 10 

5 2S 
4 53 


\ u 

s. 

S 13 

$5 


XI 56 
56 
56 

. 56 
56 


2 
1 






XI 59 14 
59 26 
59 38 
59 50 
XII 3 


XII 5 3 

5 10 
5 17 
5 24 
5 30 


XII 4 44 S 
4 34 s 
4 24 S 

4 1 <J 


S 16 

S 18 
S-19 

S 20 


XI 56 

56 
56 
56 
56 


1 

2 
4 
7 
10 


XII 16 

29 
42 
55 
1 8 


XII 5 36 

5 41 
5 46 
5 50 

5 54 


XII 3 49 S 

3 37 s 
3 24 J> 
3 10? 
2 56 Jj 


5 2 ! 

S 25 


XI 56 

56 
56 
56 
56 


1 3 

17 

22 
28 
33 


XII 1 21 

1 34 
1 47 
2 
2 13 


XII 5 57 
6 
6 2 
6 3 
6 4 


XII 2 42 S 

2 27 s 
2 12 S 

1 56 s 
1 40 S 


^26 
J 27 
,S 28 
S 29 
S 30 


XI 56 
56 

56 
57 
57 


40 
47 
54 
02 
10 


XII 2 25 

2 38 
2 50 
3 0,2 
3 14 


XII 6 4 

6 4 
6 S 
6 1 
5 59 


XII 1 23< 

49 S 
31 !j 
13 S 


^31 


57 


18 




5 56 


XI 59 55 S 



Equation- Tables. 



199 



S A TABLE shewing what Time it ought to be by the 
Clock when the Sun's Centre is on the Meridian. 
The first Year after Leap- Year. 



2L 
i 

2 
3 
4 
5 
~6 
7 
8 
9 
10 


September. 


( )ctober. 


November. 


December. J> 


H. M. S. 


H. M. S. 


M. M. 


H M. x 


XI 59 36 

59 17 
58 58 
58 38 
58 18 


XI 49 28 
49 9 
48 51 
48 33 
48 15 


XI 43 46 
43 46 
43 47 
43 48 
43 50 


XI 49 38 
50 01 
50 25 
50 50 
51 15 S 


XI 57 58 
57 38 
57 18 
56 57 
56 37 


XI 47 58 

47 41 
47 24 
47 8 
46 53 


XI 43 53 
43 57 

44 1 
44 7 
44 13 


XI 51 41 ^ 

52 7 I 
52 34 < 
53 01 < 
53 28 <j 


11 
12 
13 
14 

15 


XI 56 16 

55 55 
55 34 
55 13 

54 52 


XI 46 38 
46 24 
46 10 
45 56 
45 44 


XI 44 21 
44 29 
44 38 
44 48 
44 59 


XI 53 56 S 
54 25 
54 54 S 
55 23 J 
55 52 <i 


16 
17 
18 
19 

22 
23 

24 


XI 54 31 
54 11 
53 50 
53 29 
53 8 


XI 45 32 
45 20 
45 9 
44 59 
44 49 


XI 45 13 

45 20 
45 36 
45 50 
46 5 


XI 56 22 S 
56 51 J> 
57 21 S 
57 51 
58 21 ? 


XI 52 47 
52 27 
52 6 
51 46 
51 25 


XI 44 40 
44 31 

44 24 
44 17 
44 10 


XI 46 21 
46 37 
46 54 
47 12 
47 31 


XI 58 51 
59 22 
59 52 5 
XII 22 S 
52 5 


27 
28 
29 

30 


XI 51 5 
50 45 
50 26 
50 6 
49 47 


XI 44 5 

44 
43 56 
43 52 
43 49 


Xi 47 51 
48 11 
48 31 
48 53 
49 15 


XII 121^ 
1 51 S 
2 20 <J 
2 50 S 
3 19 <J 


31 


43 47j 


3 47 ^ 



C c 



200 



Equation-Tables, 



A TABLE shewing what Time it ought to be by the S 
Clock when the Sun's Centre is on the Meridian* 
The second Year after Leap-Year. 



1 


January. 


February. 


March. 


April. ; 


il >i. 'I. 


H. M. S. 


H. M. v 


H. M. S. 


2 
3 
4 
5 


XII 4 15 
4 43 
5 11 
5 38 

6 5 


Xil 14 6 
14 13 
14 19 
14 24 
14 29 


XII ,2 35 
12 23 
12 9 
11 56 
11 42 


XII 3 50 S 
3 32 5 
3 US 

2 56 1; 

2 38 S 


6 
7 
8 
9 
10 


XII 6 31 
6 57 
7 22 
7 47 
8 12 


XII 14 32 
14 35 
14 37 
14 39 
14 39 


XII il 27 
11 13 

10 58 
10 42 
10 26 


XII 2 20 S 

2 3 <; 

1 46 S 
1 29 !j 
1 12 S 


11 
12 
13 
14 

15 


XII 8 35 
8 58 
9 21 
9 43 
10 4 


XII 14 39 
14 38 
14 36 
14 34 
14 31 


XII 10 10 

9 54 
9 37 
9 20 
9 3 


XII 56 
40 ? 
24 S 
9 
XI 59 54 S 


16 
17 
18 
19 

20 


XII 10 24 
10 44 
11 3 
11 22 
11 39 


XII 14 27 
H 22 
14 17 
14 11 
14 4 


XII 8 45 
8 28 
8 10 
7 52 
7 34 


XI 59 39 S 
59 25 > 
59 US 
58 58 I 
58 45 


22 
23 
24 


Xil 1 1 56 
12 12 
12 27 
12 41 
12 55 


XII 13 57 
13 49 
13 40 
13 31 
13 21 


XII 7 15 
6 57 
6 38 
6 20 
6 I 


XI 58 32 
58 20 
58 8 
57 56 
57 45 


i;6 
27 
28 
29 
30 


XII 13 7 
13 19 
13 30 
13 40 

13 50 


Xil 13 10 
12 59 
12 47 


XII 5 42 
5 24 
5 5 

4 46 
4 27 


XI 57 35 
57 25 
57 15 
57 6 

56 58 


31 


13 5ti 




4 y 





Equation* Tables. 



201 



S A TABLE shewing what Time it ought to be by the 
!j Clock when the Sun's Centre is on the Meridian. 


The second Year after Leap- Year. 


f ? 

? C/J 


May. 


June. 


July. 


August. 


H. M. S. 


H. M, S 


H. M ?> 


H M. s. 


S 1 

S 9 

X 

^ 


XI 56 50 

56 43 
56 36 
56 30 
56 24 


XI 57 24 
57 33 

57 42 
57 52 
58 3 


XII 3 22 
3 33 
3 44 
3 55 
4 5 


XII 5 53 

5 49 I 
5 44 
5 39 
5 33 t S 


1 

9 
10 


XI 56 19 
56 15 
56 11 

56 7 
56 5 


XI 58 13 

58 24 
58 35 
58 47 
58 59 


XII 4 16 
4 26 
4 35 
4 44 
4 53 


XII 5 27 ^ 
5 20 ? 
5 13 S 

5 5 1; 

4 56 S 


11 
12 
13 
14 
15 


XI 56 3 
56 1 
56 
56 
56 


XI 59 11 
59 23 
59 37 
59 48 
XII 01 


XII 5 01 
5 9 
5 17 
5 23 

5 30 


XII 4 47 ^ 
4 38 > 
4 27 S 
4 17 ? 
4 5 S 


16 
17 
I 18 
19 
20 


XI 56 1 

56 2 
56 4 
56 7 
56 10 


XII 14 
27 
40 
53 
1 6 


XII 5 36 
5 41 
5 46 
5 50 
5 54 


XII 3 53 C 
3 41 > 
3 28 ? 
3 15 
3 |* 


21 
22 
23 
24 
25 


XI 56 13 
56 17 

56 22 
56 27 
56 32 


XII 1 19 
1 31 

1 44 
1 57 
2 10 


XII 5 57 
6 
6 1 
6 3 

6 4 


xii 2 46 <; 

2 31 S 
2 16 $ 
2 S 
1 44 <J 


^ 26 
J27 
!j 28 
Jj 29 


XI 56 38 
56 45 
56 42 
56 59 
57 7 


XII 2 22 
2 34 
2 46 
2 58 
3 10 


XII 6 4 
6 3 
6 2 
6 1 
5 59 


XII 1 27 \ 
1 10 S 
53 C 
35 S 
17 5 


$ 31 


57 15 




5 56 


XI 59 59 Jj 



202 



Equation- Tables. 



TABLE shewing what Time it ought to be by the 
Clock when the Min's Centre is on the Meridian. 
The second Year after Leap-Year. 



ep 


.leptembtr. 


October. November. 


December J 


H M. >. 


H -xili. M .-5. 


H. M S. S 


i 

3 

4 
5 


XI 59 40 
59 21 
59 2 

58 43 
58 23 


Xi 49 32 

49 14 
48 55 
48 37 
48 20 


XI 43 46 

43 46 
43 46 
43 48 
43 50 


XI 49 32 S 
49 56 <J 
50 20 S 
50 44 <J 
51 9 S 


7 

8 
9 
10 


Xi 58 4 
57 44 
57 23 
57 3 
56 43 


XI 48 3 

47 46 
47 29 
47 14 
46 58 


XI 43 53 

43 . 57 
44 1 
44 7 
44 13 


XI 51 35 S 
52 1 Jj 
52 28 S 
52 55 
53 23 S 


12 
13 
14 
15 


XI 56 22 
56 1 
55 41 
55 20 

54 59 


XI 46 43 
46 29 
46 15 
46 1 
45 48 


XI 44 20 

44 28 
44 37 
44 47 
44 57 


XI 53 51 S 
54 19 J 
54 48 
55 17 
55 46 


16 
17 
18 
19 

20 


XI 54 38 
54 17 
53 56 
53 35 
53 14 


XI 45 36 
45 24 
45 13 
45 2 
44 52 


XI 45 8 
45 20 
45 33 
45 47 
46 2 


XI 56 15 

56 45 
57 14 S 
57 44 J> 
58 14 S 


21 
22 
23 


XI 52 53 
52 32 
52 H 
51 51 
51 30 


XI 44 42 
44 34 
44 26 
44 18 
44 11 


XI 46 17 
46 33 
46 50 
47 7 
47 26 


XI 58 44 
59 14 S 
59 44 <J 
XII 14 S 
44 <I 


26 
27 
28 

30 


Ai 51 10 
50 50 
50 30 
50 11 
49 51 


XI 44 6 

44 
43 56 
43 52 
43 50 


XI 47 45 

48 5 
48 26 
48 47 
49 9 


XIi 1 U* 
1 43 S 
2 12 Sj 

2 42 S 
3 11 < 


31 




43 48 




3 40 



Equation-Tables. 



203 



TABLE shewing what Time it ought to be by the 
Clock when the Sun's Centre is on the Meridian. 



> The third Year alter Leap- Year. 


> 

\" 
\ 


January. 


February. 


March. 


April. 


i. M. ^> 


H. M. :-..jH M. S. 


H. M. S. 


> 1 
\ 2 
> 3 

; 4 

5 s 


Xll 4 
4 3 
5 
5 3 
5 5 


Xll i4 4 
14 11 
14 17 
14 23 
14 28 


Xll 12 38 
12 25 
12 12 
11 59 
11 45 


Xll 3 55 

3 36 
3 18 
3 

2 43 


1 

y 


XII 6 2 
6 5 
7 1 
7 4 
8 


Xll 14 32 
14 35 
14 37 
14 39 

14 40 


XII 11 31 
11 17 
10 2 
10 46 
10 31 


XII 2 25 
2 8 
1 51 
1 34 
1 17 

xii i T 

44 
29 
13 
XI 59 58 


> i; 

12 

^ lo 
14 
15 


Xll 8 3 

8 5 
9 1 
9 3 
9 5 


Xli 14 40 
14 39 
14 37 
14 35 
14 31 


XII 10 14 

9 58 
9 41 

9 24 
9 7 


16 
S l7 
S 18 

S 19 

|S 

S21 

>22 
S23 

24 
25 


XII 10 2 
10 3 
10 5 
11 1 
11 3 


XII 14 27 

14 23 
14 17 
14 11 
14 5 


Xll 8 49 
8 32 
8 14 
7 55 
7 37 


XI 59 43 
59 28 
59 14 
59 
58 47 


Xll .11 5 
12 
12 2 
12 3 

12 5 


All 13 57 
13 49 
13 41 
13 32 
,13 22 


XII 7 19 

7 
6 42 
6 23 
6 4 


XI 58 34 
58 22 
58 10 
57 58 
57 47 


26 
27 
28 

; 29 

S 3C 


Xll 13 
13 1 
13 2 
13 3 

13 4 


Xii 13 12 
13 1 
12 50 


XII 5 46 
5 27 
5 8 

4 50 
4 31 


XI 57 37 
57 27 
57 17 
57 8 
57 


<! 31 


IJ 5 


4 ;3 






204 



Equation-Tables. 



A TABLE shewing what Time it ought to be by the 

Clock when the Sun's Centre is on the Meridian. 

The third Year after Leap-Year. 



o 


May. 


June. 


July. 


August. S 


H M. S.H. M. S. 


M. S.H M s 


5 


XI 56 52 
56 45 
56 38 
56 32 
56 26 


XI 57 22 
57 31 
57 41 
57 51 
58 1 


Xll 3 20 
3 31 
3 42 
3 53 

4 4 


XII 5 54 S 
5 50 <j 
5 46 S 
5 41 <J 
5 35 S 


6 
7 
8 
9 
10 


XI 56 21 
56 17 

56 13 
56 9 
56 6 


XI 58 12 

58 23 
58 34 
58 45 
58 57 


XII 4 14 
4 24 
4 34 
4 43 
4 52 


XII 5 29 S 
5 22 Jj 
5 15 S 

5 7 !j 
4 58 S 


11 

12 

15 


XI 56 4 

56 2 
56 1 
56 
56 


XI 59 8 

59 21 
59 33 
59 45 
59 58 


XII 5 
5 8 
5 15 

5 22 
5 28 


XII 4 49 S 
4 40 
4 29 S 
4 19 ^ 
4 7 S 


17 
18 
19 
20 


XI 56 1 

56 2 
56 4 
56 6 
56 8 


XII 10 
23 
36 
49 
1 1 


Xll 5 34 
5 39 
5 44 
5 48 
5 52 


XII 3 55 < 
3 43 > 
3 30 S 
3 17 > 
3 a] 


21 
22 
23 
24 
25 


XI 56 11 
56 15 
56 20 
56 25 
56 30 


XII 1 14 

1 27 
1 40 
1 53 
2 6 


XII 5 55 
5 58 
6 
6 2 
6 3 


XII 2 48 S 
2 34 J 
2 19 S 

? ^ 


26 
27 
28 
29 
30 


XI 56 36 

56 43 
56 50 
56 57 
57 5 


XII 2 18 
2 31 

2 44 
2 56 
3 8 


XII 6 3 
6 3 
6 2 
6 1 

5 59 


XII 1 31 \ 

1 14 J> 

57 S 
39 S 
22 s 


31 


57 13 




5 57 


4? 



Equation- Tables. 



205 



TABLE shewing what Time it ought to be by the' 
Clock when the Sun's Centre is on the Meridian. 
The third Year after Leap-Year. 



vl 


September. 


v Jctober. 


November. 


December. 


li. M. :>. 


H. M. S. 


H. BE g; 


H. M. S. 


h 

2 

J 5 


XI 59 45 

59 26 
59 7 
58 48 
58 28 


XI 49 37 
49 19 
49 
48 42 
48 24 


XI 43 47 

43 47 
43 47 
43 47 
43 49 


XI 49 27 
49 50 
50 14 
50 38 
51 3 


> 6 

$ 9 
S 10 


XI 58 9 

57 49 
57 28 
57 8 
56 47 


XI 48 7 
47 50 
47 33 
47 17 
47 1 


XI 43 52 
43 55 

43 59 
44 4 
44 10 


XI 51 29 
51 55 
52 21 
52 48 
53 15 


{- 

S 13 

$ 14 
S 15 

s Te 
s l7 

S18 
$19 
S 20 

\~ l 

$ 22 
S 23 
$24 
S25 


XI 56 27 
56 6 
55 45 
55 24 
55 3 


XI 46 46 
46 31 
46 17 
46 3 
45 50 


XI 44 17 

44 25 
44 33 
44 43 
44 53 


XI 53 43 

54 11 
54 40 
55 8 
55 37 


XI 54 42 
54 20 
53 59 
53 38 
53 17 


XI 45 37 

45 25 
45 14 
45 3 

44 53 


XI 45 4 

45 16 
45 29 
45 42 
45 57 


XI 56 7 

56 36 
57 6 
57 36 
58 6 


XI 52 56 

52 36 
52 15 
51 55 
51 35 


XI 44 43 
44 35 
44 27 
44 19 
44 13 


XI 46 12 

46 28 
46 45 
47 3 
47 21 


XI 58 36 
59 6 
59 36 
XII 6 

36 


26 
$27 
S 28 
29 
< 30 

$37 


XI 51 U 

50 54 
50 35 
50 15 
49 56 


XI 44 7 
44 1 
43 57 
43 53 
43 50 


XI 47 40 

48 
48 21 
48 42 
49 4 


XII 1 6 

1 36 
2 6 
2 35 
o 5 




43 48 




3 34 



206 



*#* OBSERVE by a good meridian-line, or by 
a transit-instrument, properly fixed, the moment 
when the Sun's centre is on the meridian; and set 
the clock to the time marked in the preceding 
table for that day of the year. Then if the clock 
goes true, it will point to the time shewn in the 
table every day afterward at the instant when it is 
noon by the Sun, which is when his centre is on 
the meridian. Thus, in the first year after leap- 
year, on the 20th of October, when it is noon by 
the Sun, the true equal time by the clock is only 
44 minutes 49 seconds past XI; and on the last 
day of December (in that year) it should be 3 mi- 
nutcs 47 seconds past XII by the clock when the 
Sun's centre is on the meridian. 

The following table was made from the preced- 
ing one, and is of the common form of a table of 
the equation of time, shewing how much a clock 
regulated to keep mean or equal time is before 
or behind the apparent or solar time every day of 
the year. 



TABLE 



OF THE 



EQUATION OF TIME, 



SHEWING 



How much a Clock should be faster or slower than 
the Sun, at the Noon of every Day in the Year, 
both in Leap- Years and Common Years. 



[ The Asterisks in the Table shew where the Equation 
changes to Slow or Fast.~\ 



Dd 



208 



Equation- Tables. 



S A TABLE of the Equation of Time, shewing ^ 
<> how much a Clock should be faster or slower > 
S than the Sun, every Day of the Year, at Noon, s 


S The Bissextile, or Leap-Year . J 


S 

M 

S y 


Jan. 


Feb. 


March. 


April. 

lvL~sT 


May. 


June. 

"MTsT s 


M. S. 


M. 8. 


M.S. 


M. S. 


P 

< 

S 5 


4 2 
4 30 
4058 
5 7T25 
5 52 


14 3 
14olO 
140*16 

I4?r22 
14 27 


12 30 

12O17 
120 4 
11 ^50 
11 35 


3 42 
3 o24 
3 o 6 
2^48 
2 30 

2 13 
1 >55 
Ig38 
17*21 
1 4 


3 12 

301S 
3C-26 
3^32 
3 37 


2 30 S 
2 C 20^ 
25*11 S 
28- lj 
1 51 S 


s s * 

h 

5 9 
l* 

s 11 
12 

" 
" 

S 16 

S 17 
J 18 

|!9 

S 20 

S 21 
S 22 

J; 23 

S24 

- 

Z 26 

S 27 
$28 
S 29 
^ 30 


6 19 

6 T<45 

?io 

77*35 
8 00 


14 31 
14ET-34 
Hg37 
14^ 38 
14 39 


11 21 
11 2J> 6 
10 50 
107*34 
10 18 


3 42 
32-46 
3350 

n 
3 52 53 

3' 55 


1 40 S 
iS.292 

N il 6* 

I <-i O (^ 

0* 54 S 


8 24 
8 47 
9 10 
9 32 
9 53 

10 14 
10 34 
10 53 
11 12 
11 30 


14 39 
14 38 
14 37 
14 35 
14 32 


10 2 
9 45 
9 28 
9 11 
8 54 


48 
32 
17 
1 
0* 13 


3 57 
3 59 
4 00 
4 00 
3 59 


42 S 
30 
18 S 
5> 
0*8$ 

21 ^ 
0^33 S 

OcT46 <J 
o-59 S 

1 13 ^ 


14 28 
14 24 
14 19 
14 13 
14 7 


8 36 
8 18 

8 00 

7 42 
7 24 


* 28 
42 
Oo~56 
iS- 9 
1 22 


3 58 
3 56 
3 54 
3 51 
3 48 


11 47 
12 3 
12 19 
12 34 
12 48 


14 00 
13 52 
13 44 
13 35 
13 26 


7 6 
6 47 
6 29 
6 10 
5 52 


1 34 
J2L46 
1^57 
2? 8 
2 19 


3 44 
3 40 
3 35 
3 30 
3 24 


1 26s 
1 5T-39 J> 

1^ 
27 s 5 5 
2 17 ? 


13 1 
13 13 
13 25 
13 36 
13 46 


13 16 
13 5 

12 54 

12 42 


5 33 
5 15 

4 56 

4 37 
4 19 


2 29 
2 39 
2 48 
2 56 
3 4 


3 17 
3 10 
3 3 
2 55 

2 47 


2 30 S 
2 42 
2 54 S 
3 6.S 
3 18 Jj 


U 


13 55 




4 00 




2 39 


S 



Equation- Tables. 



209 



*v* * * ,*/ 

S A TABLE of the Equation of Time, shewing S 
t how much a Clock should be faster or slower ![ 
S than the Sun, every Day of the Year, at Noon. S 


The Bissextile, or Leap-Year. s 


|| 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. S 


M. S 


M. S. 


M. S. 


M. S. 


M. S. 


M.S. s 


ij i 

% ; 

!- 

' 

S 8 
S 9 

S 13 
S 17 

s is 
5 19 

S 20 


3 2 

3 4 

3^5 

4 1 


5 51 

5^36 
5 30 


30 

lf$ 

1 48 


10 38 

11 33 
11 51 


16 15 
16 15 

16^1 


10 17 
9 53 S 

9g"29$ 

8 39 Jj 


4 22 

4 P 3 

4 57 


5 23 
55T>16 
5ff 8 
5 r*00 
4 51 


2 8 
22L28 
2 48 
3 % 9 
3 30 


12 8 
12 |-24 
12341 
12$56 
13* 12 


16 7 

1 C W3 

16- 3 
15358 

15^52 
15 46 


8 13 Ij 

7 -47 S 
7320 ^ 

6' 25 


5 5 

5 13 
5 20 
5 26 
5 32 


4 41 
4 31 
4 21 
4 10 
3 58 


3 50 
4 11 
4 32 
4 53 
5 14 


13 27 
13 41 
13 55 
14 8 
14 20 


15 38 
15 29 
15 20 
15 10 
14 59 


5 57 ^ 

5 28 S 
4 .59 Jj 
4 30 S 
4 00 ^ 


5 38 
5 43 
5 48 
5 52 
5 56 


3 46 
3 33 
3 20 
3 6 

2 52 


5 35 

5 56 
6 16 
6 37 
6 58 


14 32 
14 44 
14 54 
5 5 
5 14 


14. 47 
14 34 
14 21 
14 7 
13 52 


3 31 Jj 
3 IS 
2 31 < 
2 1 S 

1 31 I? 
t 


S21 
!* 22 
S23 
!>24 
S 25 

S26 

S 27 
S 28 

^ 29 

S 30 

<! 31 


5 59 
6 1 
6 3 
6 4 
6 4 


2 38 
2 23 
2 7 
1 51 
1 35 


7 19 
7 40 
8 00 
8 20 
8 41 


5 23 
5 31 
5 39 
5 46 
5 52 


3 36 
13 19 
13 2 

12 44 
2 25 


i >s s 

31 S 
1 s 
*29 S 
59 !j 


6 4 
6 4 
6 2 
6 00 
5 58J 


1 18 
1 1 

44 
26 
8 


9 1 
9 21 
9 41 
10 00 
10 19 


5 58 
6 3 

6 7 
6 10 
6 12 


2 5 
1 45 

1 24 
1 2 
40 


1 29 !j 
3 25 s 

s 

3 54 s 


5 55 


0*11 




6 14 









210 



Equation- Tables. 



S A TABLE of the Equation of Time, shewing S 
Jj how much a Clock should be faster or slower v| 


S than the Sun, every Day of the Year, at Noon. S 


<5 The first Year after Leap-Year. 


s o 


Jan. 


Feb. 


March. 


April. 


May. 


June. S 


s v^< 

t tjn 


M. S. 


M: s. 


M. S. 


M. S. 


M. S. 


M. S. s 


s y 












2 33 s 


4 23 


4 9 


12 33 


3 47 


3 11 


5 a 


4 51 


4 16 


12 ^20 


3 -29 


3 r 18 


2 Q 24 S 


Jj 3 


55-19 


4 5"21 


12 5* 7 


3 5 s 10 


3~25 


2 o"14 S 


S 4 


5 46 


4g-26 


11 54 


2 52 


331 


9 x S 

2 9? 4 t 


S 5 


6 13 


4 31 


11 40 


2 35 


3 36 


1 54s 


S - 












V 












C 


S 6 


6 39 


4 34 


11 25 


2 17 


3 41 


1 43s 


S 7 


7 j5"* 4 


4^37 


1 1 P>10 


2 sTOO 


32L45 


lg-33 S 


^ 


7*30 


4*39 


10*55 


Co 


O 
3 3 49 


1322? 


S 9 


1 ~* 54 


4^ 40 


10 ? 39 


i r*26 


3^53 


1 ~. 10 Jj 


S 10 


8 18 


4 40 


10 23 


1 9 


3 ' 55 


0* 58< 


J" 


8 41 


4 39 


10 7 


52 


3 57 


46 S 


S12 


9 4 


14 38 


9 50 


36 


3 59 


34 


S 13 


9 26 


14 36 


9 33 


20 


4 00 


22 s 


S 14 


9 48 


14 33 


9 16 


5 


4 00 


10 S 


^ 15 


10 9 


14 29 


8 58 


0* 10 


4 00 


* 3 s 


v 16 


10 29 


14 25 


8 41 


25 


3 59 


16s 


Fir 


10 48 


14 20 


8 23 


G 3 ! 


3 58 


o 29 s 


< 18 


11 7 


14 15 


8 5 




3 56 


?r42 s 


?19 


11 25 


14 9 


7 47 


1- 6 


3 53 


0$L55 S 


$20 


11 42 


14 2 


7 29 


19 


3 50 


1 8s 


s sT 


11 59 


13 54 


7 10 


32 


3 47 


1 21 


S 22 


12 15 


13 46 


6 52 


|-44 


3 42 


1 ST-34 S 


Jj 23 


12 30 


13 37 


6 33 


3 56 


3 38 


1 g- 47 


S24 


12 44 


13 28 


6 15 


1 2? IT 


3 32 


2 r- oo s 


$25 


12 58 


13 18 


5 56 


2 17 


3 26 


2 13 S 


c 

5 27 


13 10 
13 22 


13 8 
12 57 


5 38 
5 19 


2 28 
2 37 


3 20 
3 13 


2 25 J> 

2 38 S 


s . 28 


13 3o 


12 45 


5 00 


2 46 


3 6 


2 50 S 


^ 29 


13 43 




4 42 


2 55 


2 58 


3 2? 


S30 


13 52 




4 23 


3 3 


2 50 


3 14 


s 












^ 


S 31 


14 




4 5 




2 42 


A 



Equation- Tables. 



211 



S*A TABLE of the Equation of Time, shewing'S 
!j how much a Clock should be faster or slower 
S than the Sun, every Day of the Year, at Noon. S 


S The first Year alter Leap- Year. s 


S s? 


July. 


Aug. 


1 Sept. 


Oct. 


Nov. 


Dec. S 


M.S. 


M. S. 


M.S. 


M. S. 


M. S. 


M. S. I; 


P 

<! 6 

S 8 
S 9 

1 

\\l 

i 

S 19 
J30 

iu 

\ 

S27 
? 28 
S 29 

\H 

S 31 


3 26 

3 n 37 
3~48 
3^58 
4 9 


5 52 

5 -48 
5^43 
5 g-38 
5 32 


24 

?g1 

lg-22 
1 42 


10 32 
10 51 
11 5^ 9 
11 27 

11 45 


16 14 
I6 r 14 
16^13 

16 10 


10 22 ^ 

9^35 !j 
9^10 S 
8 45 s 

s 


4 19 

4 gP 28 

4? 46 
4 55 


5 25 

sflO 
5 r* 2 
4 53 


2 2 
22-22 
2^42 
33 3 
3* 23 


12 2 
12 2M9 
12^35 
12351 
13 ' 7 


16 7 
162L 3 

15? 59 
15^53 
15 ' 47 


8 19 

? ^* S 
62J59 S 
6* 31 < 


5 3 
5 10 
5 17 
5 24 
5 30 


4 44 
4 34 
4 24 
4 13 
4 1 


3 44 
4 5 
4 26 
4 47 
5 8 


3 22 
13 36 
13 50 
14 3 
14 16 


15 39 
15 31 

15 22 
15 12 
15 1 


6 3 S[ 
5 35 S 
5 6 <J 

4 37 S 

4 8 ^ 
c 


5 36 
5 41 
5 46 
5 50 
5 54 


3 49 
3 37 
3 24 
3 10 
2 54 


5 29 
5 5C 
6 1C 
6 31 
6 52 


14 28 
14 40 
14 51 
15 1 
15 11 


14 50 
14 37 
14 24 
14 10 
13 55 


3 38 Ij 
'3 9 S 
2- 39 Ij 
2 9 S 
1 39 


5 57 

6 00 
6 2 
6 3 
6 4 


2 42 
2 27 
2 12 
1 56 
1 40 


7 13 

7 33 
7 54 
8 14 
8 35 


15 20 
15 29 
15 36 
15 43 
15 50 


13 39 
13 23 
13 6 
12 48 
12 29 


1 9 t 
38 S 
8 < 
*22 S 
52 ^ 


6 4 
6 4 
6 3 
6 1 
5 59 


1 23 
1 6 
49 
31 
13 


8 55 
9 15 
9 34 
9 54 
10 13 


15 55 
16 00 
16 4 
16 8 
16 11 


12 9 
11 49 
11 28 
11 7 
10 45 


1 22 s 

2? 50 S 
3 19 S 

3 47 s 


5 56 


0* 5 




16 13 





212 



Equation- Tables. 



I* A 



TABLE of the Equation of Time, shewing 
how much a Clock should be faster or slower 
than the Sun, every Day of the Year, at Noon. 
The second Year alter Leap- Year. 





Jan. 


Feb. 


March 


April. 


May. 


June, s 


$ ? 


M. S. 


M. S. 


M. o. 


M. S. 


M. S. 


M.S. !; 


^ 

s *~ 

\ * 


4 15 
4 43 
55-11 
5 .38 
6 5 


14 6 
14 13 

14~19 
14g-24 
14 28 


12 35 

12 g- 9 
11^56 
11 42 


3 50 
2 38 


3 10 

3^24 
3^30 
3 36 


2 36 1; 

2 O 27 S 
25-17 s 
2 g- 8 S 
1 57 !j 


S 6 

S 8 
S g 

S 10 


6 31 
8 11 


14 32 
14ST-35 
U37 

14 r- 39 
14 39 


11 27 

10~42 
10 26 


2 2C 
1 12 


3 41 

3 -45 
3 49 
3 3 52 
3 ' 55 


! ?f s 


S j j 

jj 12 

\ " 

S 15 


8 35 
8 58 
9 21 
9 43 
10 4 


14 39 
14 38 
14 36 
14 34 
14 31 


10 10 
9 54 
9 37 
9 20 
9 3 


56 
40 
24 
9 
0* 6 


3 57 

3 59 
4 00 
4 00 
4 00 


49 ^ 
37 S 
24 
12 S 
0*1^ 

s 


i 

s 19 

S 20 

S 


10 24 
10 44 
11 3 
11 22 
11 39 


14 27 
14 22 
14 17 
14 11 

14 4 


8 45 

8 27 
8 10 
7 52 
7 34 


21 
35 

0-49 
1 2 
1 15 


3 59 
3 58 
3 56 
3 53 
3 50 


14 5 

o 27 s 

1 " 6 S 


Jj 22 
S 23 

s 24 


11 56 
12 12 
12 27 
12 41 
12 55 


13 57 
13 49 
13 40 
13 31 
13 21 


7 15 
6 57 
6 38 
6 20 
6 1 


1 28 
lg.40 
1 ^52 
23 4 
2* 15 


3 47 
3 43 
3 38 
3 S3 
3 28 


1 19 % 
Ip32 S 

ifyff-l 

2 10 \ 


S2 2 ? 
?28 
S 29 
V 30 


13 7 
13 19 
13 30 
13 40 

13 50 


13 10 
i2 59 

2 47 


5 42 
5 23 
5 5 
4 46 

4 27 


2 25 
2 35 
2 45 
2 54 
3 2 


3 22 
3 15 
3 8 
3 1 
3 53 


2 22 s 
2 34 S 
2 46^ 
2 58 S 
3 10 s 


S31 


13 58 




4 9 




2 45 


s 



Equation- Tables. 



21; 



S A TABLE of the Equation of Time, shewing S 
S how much a Clock should be faster or slower ^ 
S than the Sun, every Day of the Year, at Noon. S 


> The second Year attei- Leap-Year. s 


S 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. ? 


M. S. 


M. S. 


M. S. 


M. S. 


M. b. 


M. S. J> 


L 

h 

S 5 


3 22 

3^33 
3|44 

4 5 


5 53 

5 O49 
5 0*44 
5 39 
5 33 

~5 27 

5^20 
5*13 
5 "* 5 
4 56 


20 
5*58 
1 37 


10 28 

Uo* 5 
117T23 
11 40 


16 14 

168-12 
16 10 
16 7 
162. 3 
15^59 
15^53 
15 47 


10 28 S 
10 4S 
9 0*40 

8 51 J* 


S 10 

s 
fu 

S 15 


4 16 
4^26 

4g35 
4.^44 
4 53 


1 56 

2 37 
2? 57 
3 17 


11 57 
12S.14 
12 3 30 
12 |5 46 

13 2 


8 25 S 
7 -59^ 

7^32 S 

6* 37 S 


5 1 
5 9 
5 17 
5 24 
5 30 


4 47 
4 37 
4 27 
4 17 
4 5 


3 38 
3 59 
4 19 
4 40 
5 1 


13 17 
13 31 
13 45 
13 59 
14 12 


15 40 
15 32 
15 23 
15 13 
15 3 


6 9S 

5 12 S 
4 43 Jj 
4 14 S 


fra 

s 17 
s 18 

S 19 
!j 20 


5 36 
5 41 
5 46 
5 50 
5 54 


3 53 
3 41 
3 28 
3 15 
3 1 


5 22 

5 43 
6 4 
6 25 
6 46 


14 24 
14 36 
14 47 
14 58 
15 8 

Ti" fs 

15 26 
15 34 
15 42 
15 49 


14 52 
14 40 
14 27 
14 13 
13 58 


3 45 S 

3 15$ 
2 46 S 
2 16 S 
1 46 S 


S 21 
S 22 

S23 
S24 
S25 


5 57 
6 00 
6 2 
6 3 
6 4 


2 46 
2 31 
2 16 
2 00 
1 44 


7 7 
7 28 
7 49 
8 9 
8 30 


13 43 
13 27 
13 10 
12 52 
12 34 


1 16 (J 
46 S 
16s 
14 S 

44 ^ 


S 26 

S28 
S 29 
S 30 


6 4 
6 3 
6 2 
6 1 
5 59 


1 27 
1 10 
53 
35 
17 

* 1 


8 50 
9 10 
9 30 
9 49 
10 9 


15 54 
15 59 
16 4 
16 8 
16 11 


12 15 
11 55 
11 34 
11 13 
10 51 


1 13 s 
1^43 S 

2 ~ 42 S 
3 111 


S31 


5 56 




16 12 




3 40 



214 



Equation- Tables. 



S A TABLE of the Equation of Time, shewing S 
S how much a Clock should be faster or slower s 
S than the Sun, every Day of the Year, at Noon. j> 


S The Third Year after Leap-Year. J 


f 


Jan. 


Feb. 


March. 


April. 


May. 


June. S 

"MTsT s 


M. S. 


M. S. 


M. S. 


M. S. 


M. S. 


|j 


4 8 
4^36 
5cT 4 
5 -32 
5 59 


14 4 
14^11 
145*17 
14^23 
14 28 


12 38 
12^25 
11 5*12 
11 -59 
11 45 


3 55 

So*18 
3 -00 
2 43 


3 8 

3 (*< 1 5 

35*22 

o 

3 34 


2 38 <; 

2(^29 S 
25*19 s 

1 59 s 


1 

y 

h 

S 13 
S 14 


6 25 
6^51 

7.^42 
8 6 


14 32 

U07 

14 :* 39 
14 40 


11 31 

10^46 
10 30 


2 25 

2 f 8 

1 ? 34 
1 17 


3 39 
32L43 
3347 
3^51 
3 54 


1 48 <J 

15-37 s 

1 3 26 S 

r sj 


8 30 
8 53 
9 16 
9 38 
9 59 


14 40 
14 39 
14 37 
14 35 
14 31 


10 14 
9 58 
9 41 
9 24 
9 7 


1 1 
45 
29 
13 

0*2 


3 56 
3 58 
3 59 
4 00 
4 00 


051s 
39 J 
27 s 
15 S 

2s 


\IS 

S 19 
S 20 


10 20 
10 39 
10 58 
11 16 
11 34 


14 27 
14 23 
14 17 
14 11 

14 5 


8 49 
8 32 
8 14 
7 56 
7 37 


17 
32 
Oo*46 

ioo 

1 13 


3 59 
3 58 
3 56 
3 54 

3 52 


0* 10 % 
OQ23S 

0-49S 
1 2 


S21 
<j 22 
S 23 
!} 44 
S 25 


11 51 
12 7 
12 22 
12 36 
12 50 


13 57 
13 49 
13 41 
13 32 
13 22 


7 19 
7 00 
6 42 
6 23 
6 4 
5 46 
5 27 
5 8 
4 50 
4 31 


1 26 
1S.38 
1 ^50 

23 2 
2* 13 


3 49 
3 45 
3 40 
3 35 
3 30 


<* b- O CO <O 

' (N rj *O 

faster. 


<J 26 

S 28 
S 2 9 

S 30 


13 3 
13 15 
13 26 
13 37 
13 47 


13 12 
13 1 

12 50 


2 23 
2 33 
2 43 
2 52 
3 00 


3 24 
3 17 
3 10 
S 3 
2 55 


2 18 > 
2 31 S 
2 43 ^ 
2 56 S 
3 8 


13 56 


4 13 




2 47 


J 



Equation-Tables. 



215 



Kt* H* 


S A TABLE of the Equation of Time, shewing S 
5 how much a Clock should be faster or slower lj 


$ than the Sun, every Day of the Year, at Noon. S 


S The third Year ai'ei 1 Leap-Year. S 


S ? 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. s 


v ^ 
s ** 


M.S. 


M. S. 


M.S. 


iVi. S. 


M. S. 


M.S. \ 


S 1 


3 20 


5 54 


0*15 


10 23 


16 13 


10 33 ^ 


S 2 


q o i 




5 50 


34 


10 42 


16 Q 14 


io io s 


S 4 


3 53 


5^46 
5 41 


05-53 


1 ~00 
118 


16R-14 

1613 


9 g-46 Jj 

r* r 


S 5 


4 4 


5 35 


1 32 


1 36 


16 11 


8 57 ^ 


S~6 


4 14 


5 29 


1 51 


11 53 


16 8 


8 31 ^ 


S 7 


4^24 


5^22 


22111 


22110 


1621 5 


8 5" 5 S 


Jj 8 


4|34 


C/J 


232 


12^27 


16 % 1 




S 9 


4 r* 43 


5^ 7 


2? 52 


12^43 


15 p 55 


7 3 12 S 


s 10 


4 52 


4 58 


3 ' 13 


12* 59 


15 ' 49 


6' 45 ^ 


\ 11 


5 00 


4 49 


3 34 


13 14 


15 43 


6 17 J; 


S 12 


5 8 


4 40 


3 54 


13 29 


15 35 


5 49 S 


S 13* 


5 15 


4 29 


4 15 


13 43 


15 27 


5 20 \ 


S 14 


5 22 


4 18 


4 36 


13 57 


15 17 


4 52 S 


S I* 


5 28 


4 7 


4 57 


14 10 


15 7 


4 23 Ij 


16 


5 34 


3 55 


5 18 


14 23 


14 56 


3 54 ^ 


S 17 


5 39 


3 43 


5 40 


14 35 


14 44 


3 24 S 


S 18 


5 44 


3 30 


6 1 


14 46 


14 31 


2 54 \ 


? 19 


5 48 


3 17 


6 22 


14 57 


14 18 


2 24 S 


20 


5 52 


3 3 


6 43 


15 7 


14 3 




s* 1 


5 55 


2 48 


7 4 


15 17 


13 48 


1 24 ^ 


S 22 
Z 23 


5 58 

6 00 


2 34 
2 19 


7 24 

7 45 


15 25 
15 33 


13 32 
13 15 


54 S 
24 ^ 


S24 


6 2 


2 3 


8 5 


15 41 


12 57 


0* 6 S 


fe 


6 3 


1 47 


8 25 


15 48 


12 39 


36^ 


!? 26 


6 3 


1 31 


8 46 


15 53 


12 20 


"i 6 s 


?27 


6 3 


1 14 


9 6 


15 59 


12 00 


1 ^36 S 


5 28 


6 2 


57 


9 25 


16 3 


11 39 


2 g- 6 Jj 


S 29 


6 1 


39 


9 45 


16 7 


11 18 


2^35 S 


!j 30 


5 59 


22 


10 4 


16 10 


10 56 


3 5 \ 


S 












_ ^ 


(,. 


5 57 


4 




16 12 




3 34 t 



Ee 









S A < the S 

Jj i \>iueh \Mll be \\ithin a 
s Prut . N tO the ueuu 
^ 1 ;,i be taster 01 

N : ; i ros 

s 


r*^r*r^s*^r 

Year .\f- ^ 
M invite of the v 
st full Mii.. 
1 than the Sun. s 
s 
s 
s 


^ 


^ F 








x 4 




h 


D C 


3 ^ 




: z X 






^ B)t 




i- * 




ff 


y 


\ 







r 








PJ 


Ij 














S 


> JaS! 


4 


Apr. I 


40 


Axig-U 


*r 


Oct. 3? 


16 ^ 


^ 


i 


<t 








\ 


16 ^ 


s i 
















N 

s 




U 




34 










r 










24 




: 


^r 














\ 1 < 


\t\9f 












1 I ?- 


v 
N 






I 


Sept. .*> 


i 
I 




; 


< 

5 


14| 


U 


s| 


9 




- 


: 

- 


X 


15- 








5 " 




i 


N 


u*T 












v 




S "' 






1 r 






15 


1 


N Mar. 4 


12 P; 












i 


S ^ 


u 













2 N 


r: 














1 ^ 
















5 

w 


N 








6 






N 

" "" S 


S 




4 


4 

c* ii 


10 








x 


s 75 


6 


U 


14 






, 








1- 1 19 






. 



op 



This 

by ihc 



the Moon's /Y/f/v. 217 



CI1 \\\ XV. 

1'lie J/<>''/r.v Sur/licc mountainous : Her Phases de 
serihed: Her l\ith, and the Paths of Jupiter's 
Moo'is delineated: The Proportions <>/ the Diame- 
ters of their O/7;//.v, and those of Saturn's Moons, 
to each other; ami the Diameter of the Sun. 



B 



1M.A I I.. 
VII. 



V looking at the MoonthroUffh an ordinary 
telescope, \\e perceive that her surface is 
diversified \\ ilh long ; tracts of prodiglOUS high mouil- The 
tains aiul deep cavities. Some of her mountains, by Moon's 
e-oinparinj;- their IK i^ht with her diameter (which laJJ^ 
2180 miles,) are ioimd to he three- times as high as ou*. 
the hi-hest mountains on our Ivmh. This rugged- 
ness of the Moon's surface is of great use to us, by 
rdleeting the Sun's light to all sides: for if the Moon 
were smooth and ])olished like a looking- glass, or co- 
\t red with water, she could never distribute the Sun's 
light all round: only, in some positions, she would 
shew us his image-, no bigger than a point, but with 
Mich a lustre as might be hurtful to our e\ 

53 The Moon's surface being so uneven, many 
have wondered why her edge appears not jagged as 
well as the curve bounding the light and dark parts. 
But if we consider, that what we call the edge of the Why no 
Moon's disc is not a single line set round with moun- j^"* JJJ" 
tains, in \\hich case it would appear irregularly in- her edge 
dented, but a large zone, having- many mountains ly- 
ing behind one another from the observer's eye, we. 
shall find that the mountains in some rows will be 
opposite to the \ales in others, and fill up the ine- 
qualities, so as to make her appear quite round ; 
ju:,t as when one looks at an orange, although its 
roughness be very discernible on the side next the 
eye, especially if the Sun or a candle shines ob- 
liquely on that side, yet the line terminating the vi- 
sible part still appears smooth and even. 



;>18 Of the Moon 's Phase*. 



PLATE 
VII. 



254. As the Sun can only enlighten that half of the 
Earth which is at any moment turned toward him, 

The Moon and being withdrawn from the opposite half, leaves it 

twiUht * n darkness; so he likewise doth to the Moon; only 
with this difference, that the Earth being surrounded 
by an atmosphere r and the Moon, as far as we know, 
having none, we have twilight after the Sun sets; 
but the Lunar inhabitants have an immediate transi- 
tion from the brightest sunshine to the blackest dark- 
ness, 177. For, let t r k s w be the Earth, and A* 
B, C, D, E, F, G, H, the Moon, in eight different 

*" ! parts of her orbit. As the Earth turns round its 
axis, from west to east, when any place comes to 
t, the twilight begins there, and when it revolves 
from thence to r, the Sun S rises ; when the place 
comes to s, the Sun sets, and when it comes to iv, 
the twilight ends. But as the Moon turns round 
her axis, which is only once a month, the moment 
that any point of her surface comes to r (see the 
Moon at G) the Sun rises there without any pre- 
vious warning by twilight ; and when the same point 
comes to 5 the Sun sets, and that point goes into 
darkness as black as at midnight. 

The , 255. The Moon beine: an opaque spherical body 

Moon's /r , u . n , ir r iT i 

phases. (f r ner O"*s take oft no more from her roundness 
than the inequalities on the surface of an orange take 
off from its roundness), we can only see that part of 
the enlightened half of her which is toward the Earth. 
And therefore when the Moon is at A, in conjunction 
with the Sun , her dark half is toward the Earth, 
and she disappears, as at a; there being no light on 
that half to render it visible. When she comes to 
her first octant at B, or has gone an eighth part of 
her orbit from her conjunction, a quarter of her en- 
lightened side is seen toward the Earth, and she ap- 
pears horned, as at //. When she has gone a quarter 
of her orbit from between the Earth and Sun to C f , 
she shows us one half of her enlightened side, as at 
c ; and we say, she is a quarter old. At D she is in 
her second octant, and by shewing us more of her 



Of the Moon's Phases. 219 

enlightened side she appears gibbous, as at d. At 
E her whole enlightened side is toward the Earth, 
and therefore she appears round as at e ; when we * 
say it is full Moon. In her third octant at F, part 
of her dark side being toward the Earth, she again 
appears gibbous, and is on the decrease, as at/; At 
G we see just one half of her enlightened side, and 
she appears half- decreased, or in her third quarter, 
as at g. At //we only see a quarter of her enlight- 
ened side, being in her fourth octant, where she ap- 
pears horned, as at h. And at A, having completed 
her course from the Sun to the Sun again, she dis- 
appears; and we say, it is new Moon. Thus, in 
going from A to E, the Moon seems continually to 
increase ; and in going from E to A, to decrease in 
the same proportion; having like phases at equal 
distances from A to E ; but as seen from the Sun 
S, she is always full. 

256. The Moon appears not perfectly round when The t 
she is full in the highest or lowest part of her orbit, 5S^J t 
because we have not a full view of her enlightened always 
side at that time. When full in the highest part bfjjjjji 
her orbit a small deficiency appears on her lower when full, 
edge; and the contrary, when full in the lowest part 

of her orbit. 

257. It is plain by the figure, that when the Moon The P b - 
changes to the Earth, the Earth appears Ml to theE^jf 
Moon ; and vice versa. For when the Moon is at Moon con- 
A, new to the Earth, the whole enlightened side of trary> 
the Earth is toward the Moon ; and when the Moon 

is at , full to the Earth, its dark side is toward her. 
Hence a new Moon answers to -&full Earth, and a 
full Moon to a new Earth. The quarters are also 
reversed to each other. 

258. Between the third quarter and change, theAnagree- 
Moon is frequently visible in the forenoon, even when 

the Sun shines ; and then she affords us an opportu- 
nity of seeing a very agreeable appearance, wherever 
we find a globular stone above the level of the eye, 



nomcnon. 



220 Of the Mootfs Phases. 

as suppose on the top of a gate. For, if the Sun 
shines on the stone, and we place ourselves so as the 
upper part of the stone may just seem to touch the 
point of the Moon's lowermost horn, we shall then 
see the enlightened part of the stone exactly of the 
same shape with the Moon ; horned as she is, and 
inclined in the same way to the horizon. The rea- 
son is plain; for the Sun enlightens the stone the 
same way as he does the Moon : and both being 
globes, when we put ourselves into the above situ- 
ation, the Moon and stone have the same position 
to our eye ; and therefore we must see as much of 
the illuminated part of the one as of the other. 
The nona- 259. The position of the Moon's cusps, or a right 
dee-reef ^ ne touching the points of her horns, is very differ- 
ently inclined to the horizon at different hours of the 
same days of her age. Sometimes she stands, as it 
were, upright on her low r er horn, and then such a 
line is perpendicular to the horizon ; when this hap- 
pens, she is in what the astronomers call the nonage- 
simal degree; which is the highest point of the eclip- 
tic above the horizon at that time, and is 90 degrees 
from both sides of the horizon, where it is then cut 
by the ecliptic. But this never happens when the 
Moon is on the meridian, except when she is at the 
very beginning of Cancer or Capricorn. 
HOW the 260. The inclination of that part of the ecliptic to 
inclination fa horizon in which the Moon is at any time when 
ecliptic horned, may be known by the position of her horns; 
may be for a right line touching their points is perpendicu- 
the n p d osf- lar to the ecliptic. And as the angle which the Moon's 
tion of the orbit makes with the ecliptic can never raise her 
horns' 8 a b ve > nor depress her below the ecliptic, more than 
two minutes of a degree, as seen from the Sun ; it 
can have no sensible effect upon the position of her 
horns. Therefore, if a quadrant be held up, so as that 
one of its edges may seem to touch the Moon's horns, 
the graduated side being kept toward the eye, and 
as far from the eye as it can be conveniently held, the 



Of the Moon's Phases. 221 



PLATE 
VII. 



arc between the plumb-line and that edge of the 
quadrant which seems to touch the Moon's horns, 
will shew the inclination of that part of the ecliptic 
to the. horizon. And the arc between the other 
edge of the quadrant and plumb-line, will shew the 
inclination of a line, touching the Moon's horns, to 
the horizon. 

261. The Moon generally appears as large as the Fig. i. 
Sun ; for the angle v k A^ under which the Moon is why the 
seen from the Earth, is nearly the same with the an- ^ar"aT 
gle LkM, under which the Sun is seen from it. And big as the 
therefore the Moon may hide the Sun's whole disc Sun * 
from us, as she sometimes does in solar eclipses. 

The reason why she does not eclipse the Sun at eve- 
ry change, shall be ex plained hereafter. If the Moon 
were farther from the Earth, as at c, she would ne- 
ver hide the whole of the Sun from us ; for then she 
would appear under the angle N k O, eclipsing only 
that part of the Sun which lies between A* and O ; 
were she still farther from the Earth, as .at X, she 
would appear under the small angle T k W^ like a 
spot on the Sun, hiding only the part y/iFfromour 
sight. 

262. That the Moon turns round her axis in the A proof 
time that she goes round her orbit, is quite demon- of ^ 
strable; for a spectator at rest, without the periphery turning 
of the Moon's orbit, would see all her sides turned roi i her 
regularly toward him in that time. She turns round 35 

her axis from any star to the same star again in 27 
days 8 hours ; from the Sun to the Sun again, in 29|. 
days : the former is the length of her sidereal day, 
and the latter the length of her solar day. A body 
moving round the Sun would have a solar day in eve- 
ry revolution, without turning on its axis; the same 
as if it had kept all the while at rest, and the Sun 
moved round it : but without turning round its axis 
it could never have one sidereal day, because it would 
always keep the same side toward any given star. 



222 



An easy Way of representing 



revoiu- 



Her perio- 263. If the Earth had no annual motion, the Moon 
would go round it so as to complete a lunation, a si- 
dereal, and a solar day, all in the same time. But 
because the Earth goes forward in its orbit while the 
Moon goes round the Earth in her orbit, the Moon 
must go as much more than round her orbit from 
change to change in completing a solar day, as the 
Earth has gone forward in its orbit during that time, 
i. e. almost a twelfth part of a circle. 
Familiarly 264. The Moon's periodical and sy nodical revo- 
represent- \ u ^\ on ma y b e familiarly represented by. the motions 
of the hour and minute-hands of a watch round its 
dial-plate, which. is divided into 12 equal parts or 
hours, as the ecliptic is divided into 12 signs, and 
the year into 12 months. Let us suppose these 12 
hours to be 12 signs, the hour-hand, the Sun, and 
the minute-hand, the Moon ; then the former will go 
round once in a year, and the latter once in a month : 
but the Moon, or minute-hand, must go more than 
round from any point of the circle where it was last 
conjoined with the Sun, or hour-hand, to overtake it 
again : for the hour-hand, being in motion, can ne- 
ver be overtakenby theminute-handat that point from 
which they started at their last conjunction. The first 



A Table 
shewing 
the times 
that the 
hour and 
minute- 
hands of a 
watch are 
in con- 
junction. 



Conj. 


H. 


M. 


S. 


in 


"'' 


vp ts .' 


1 


1 


5 


27 


16 


21 


49.J- 


2 


II 


10 


54 


32 


43 


38-JL S 


3 


III 


16 


21 


49 


5 


27 s S 


4 


IV 


21 


49 


5 


27 


16JL S 


5 


V 


27 


10 


21 


49 


5-1 


6 


VI 


32 


43 


38 


10 


54 e S 


7 


VII 


38 


10 


54 


32 


43V 


8 


VIII 


43 


38 


10 


54 


,TT J 
32_8_ } 


9 


IX 


49 


5 


27 


16 


21 T 9 1 ^ 


10 


X 


54 


32 


43 


38 


lOio ? 


11 


XII 














o 11 s 



Tire Motion of the Sun and Moon. 223 

column of the preceding table shews the number of : 



PLATE 
VII. 



conjunctions which the hour and minute-hand make 
while the hour-hand goes once round the dial- plate ; 
and the other columns shew the times when the two 
hands meet at each conjunction. Thus, suppose 
the two hands to be in conjunction at XII. as they 
always are; then at the first following conjunction 
it is 5 minutes 27 seconds 16 thirds 2i fourths, 49^ 
fifths past I, where they meet : at the second con- 
junction it is 10 minutes 54 seconds 32 thirds 43 
fourths 38^- fifths past II ; and so on. This, though 
an easy illustration of the motions of the Sun and 
Moon, is not precise as to the times of their con- 
junctions; because, while the Sun goes round the 
ecliptic, the Moon makes 12-| conjunctions with 
him; but the minute-hand of a watch or clock makes 
only 11 conjunctions with the hour-hand in one pe- 
riod round the dial-plate. But if, instead of the 
common wheel- work at the back of the dial-plate, 
the axis of the minute-hand had a pinion of 6 leaves 
turning a wheel of 74, and this last turning the hour- 
hand, in every revolution it makes round the dial- 
plate, the minute-hand would make 12-^ conjunc- 
tions with it ; and so would be a pretty device for 
shewing the motions of the Sun and Moon; espe- 
cially, as the slowest moving hand might have a little 
sun fixed on its point, and the quickest, a little 
moon. 

265. If the Earth had no annual motion, the The 
Moon's motion, round the Earth, and her track in Mo n ' s 

, , , T^, motion 

open space, would be always the same. * But as through 
the Earth and Moon move round the Sun, theP ens .pace 
Moon's real path in the heavens is very different e " cl 
from her visible path round the Earth : the latter be- 

* In this place, we may consider the orbits of all the satellites as 
circular, with respect to their primary planets ; because the eccen- 
tricities of their orbits are too small to affect the phenomena here 
described 

F f 



224 The Moods' Path delineated. 



VII. 



PLATE m g i n a progressive circle, and the former in a curve 
of different degrees of concavity, which would al- 
ways be the same in the same parts of the heavens, 
if the Moon performed a complete number of luna- 
tions in a year, without any fraction. 
An idea 266. Let a nail in the end of the axle of a cha- 
jfarut's nt-wheel represent the Earth, and a pin in the nave 
path, and the Moon ; if the body of the. chariot be propped up 
the , so as to keep that wheel from touching the ground, 
and the wheel be then turned round by hand, the pin 
will describe a circle both round the nail and in the 
space it moves through. But if the props be taken 
away, the horses put to, and the chariot driven over 
a piece of ground which is circularly convex ; the 
nail in the axle will describe a circular curve, and 
the pin in the nave will still describe a circle round 
the progressive nail in the axle, but not in the space 
through which it moves. In this case the curve de- 
scribed by the nail, will resemble, in miniature, as 
much of the Earth's annual path round the Sun, as 
it describes while the Moon goes as often round the 
Earth as the pin does round the nail : and the curve 
described by the nail will have some resemblance 
to the Moon's path during so many lunations. 

Let us now suppose that the radius of the circular 
curve described by the nail in the axle is to the radi- 
us of the circle which the pin in the nave describes 
round the axle as 337-|- to 1 ; which is the propor- 
tion of the radius or semi-diameter of the Earth's 
orbit to that of the Moon's ; or of the circular curve 
A 1 2 3 4 5 6 7 B, &c. to the little circle a; and 
then while the progressive nail describes the said 
curve from A to E, the pin will go once round the 
nail with regard to the centre of its path, and in so 
doing, will describe the curve a b c d e. The for- 
mer will be a true representation of the Earth's 
path for one lunation, and the latter of the Moon's 
for that time. Here we may set aside the inequali- 
ties of the Moon's motion, and also those of the 



The Moon's Path delineated. 225 



|. PLATE 
VII. . 



Earth's moving round their common centre of gra- 
vity : all which, if they were truly copied in this 
experiment, would not sensibly alter the figure of 
the paths described by the nail and pin, even though 
they should rub against a plane upright surface all 
the way, and leave their tracks visibly upon it. And 
if the chariot were driven forward on such a con vex 
piece of ground, so as to turn the wheel several 
times round, the track of the pin in the nave would 
still be concave toward the centre of the circular 
curve described by the pin in the axle : as the Moon's 
path is always concave to the Sun in the centre of 
the Earth's annual orbit. 

In this diagram, the thickest curve- line ABCDE, 
with the numeral figures set to it, represents as 
much of the Earth's annual orbit as it describes in 
32 days from west to east ; the little circles at , 6, 
c, d, e, shew the Moon's orbit in due proportion to 
the Earth's ; and the smallest curve abed e f re- 
presents the line of the Moon's path in the heavens 
for 32 days, accounted from any particular new 
Moon at a. The machine Fig. 5th, is for deline- 
ating the Moon's path, and shall be described, with 
the rest of my astronomical machinery in the last . 
chapter. The Sun is supposed to be in the centre 
of the curve A \ 2 3 4 5 6 7 B, &c. asd the small 
dotted circles upon it, represent the Moon's orbit, 
of which the radius is in the same proportion to the ^ P of the 
Earth's path in this scheme, that the radius of the Moon's 
Moon's orbit in the heavens bears to the radius of ^ il to 
the Earth's annual path round the Sun : that is, as Earth's. 
240,000, to 81,000,000*, or as 1 to 337|. 

When the Earth is at A, the new Moon is at a ; 
and in the seven days that the Earth describes the 
curve 1234567, the Moon in accompanying the Fj&> IL 
Earth describes the curve a b ; and is in her first 
quarter at b when the Earth is at B. As the Earth 

* For the true distances, see p. 138. 



226 The Moon's Path delineated. 



describes the curve B 8 9 10 11 12 13 14, the 
Moon describes the curve be; and is at c, opposite 
to the Sun, when the Earth is at C. While the 
Earth describes the curve C 15 16 17 18 19 20 21 
22, the Moon describes the curve cd; and is in her 
third quarter at d when the Earth is at D. And last- 
ly, while the Earth describes the curve D 23 24 25 
26 27 28 29, the Moon describes the curve de ; 
and is again in conjunction at e with the Sun when 
the Earth is at E, between the 29th and 30th day of 
the Moon's age, accounted by the numeral figures 
from the new Moon at A. In describing the curve 
abode, the Moon goes round the progressive Earth 
as really as if she had kept in the dotted circle A, 
and the Earth continued immoveable in the centre 
of that circle. 

The ^ And thus we see that, although the Moon goes 

Motion ai- roun d the Earth in a circle, with respect to the 

ways con- Earth's centre, her real path in the heavens is not 

warVthe vei ^ different m appearance from the Earth's path. 

Sun. To shew that the Moon's path is concave to the 

Sun, even at the time of change, it is carried on a 

little farther into a second lunation, as tof. 

267. The Moon's absolute motion from her change 
to her first quarter, or from a to 6, is so much 
slower than the Earth's, that she falls 240 thousand 
miles (equal to the semi-diameter of her orbit) be- 
hind the Earth at her first quarter in 6, when the 
Earth is at B ; that is, she falls back a space equal 
HOW her to her distance from the Earth. From that time her 
is alter mot * on * s gradually accelerated to her opposition or 
nateiyre- full at c, and then she is come upas far as the Earth, 
!ccti d ra nd k^g regained what she lost in her first quarter 
C<L e ' " from a to b. From the full to the last quarter at d, 
her motion continues accelerated, so as to be just as 
far before the Earth at d, as she was behind it at her 
first quarter in b. But from d to e her motion is re- 
tarded, so that she loses as much with respect to 
the Earth as is equal to her distance from it, or to 
the semi-diameter of her orbit ; and by that means 



The Moons Path, delineated. 227 



PLATE 
VII. 



she comes to e, and is then in conjunction with the 
Sun as seen from the Earth at E. Hence we find, 
that the Moon's absolute motion is slower than the 
Earth's from her third quarter to her first ; and swift- 
er than the Earth's from her first quarter to her 
third , her path being less curved than the Earth's 
in the former case, and more in the latter. Yet it is 
still bent the same way toward the Sun ; for if we 
imagine the concavity of the Earth's orbit to be 
measured by the length of a perpendicular line Cg, 
let down from the Earth's place upon the straight 
line bgd at the full of the Moon, and connecting 
the places of the Earth at the end of the Moon's 
first and third quarters, that length will be about 640 
thousand miles ; and the Moon when new only ap- 
proaching nearer to the Sun by 240 thousand miles 
than the Earth, is the length of the perpendicular 
let down from her place at that time upon the same 
straight line, all which shews that the concavity of 
that part of her path, will be about 400 thousand 
miles. 

26. The Moon's path being concave to the Sun A difficuK 
throughout, demonstrates that her gravity toward *? remov - 
the Sun at her conjunction, exceeds her gravity to- tc 
ward the Earth. And if we consider that the quan- 
tity of matter in the Sun is almost 230 thousand 
times as great as the quantity of matter in the Earth, 
and that the attraction of each body diminishes as 
the square of the distance from it increases, we shall 
soon find, that the point of equal attraction between 
the Earth and the Sun, is about 70 thousand miles 
nearer the Earth than the Moon is at her change. 
It may then appear surprising that the Moon does 
not abandon the Earth, when she is between it and 
the Sun, because she is considerably more attract- 
ed by the Sun than by the Earth at that time. 
But this difficulty vanishes when we consider, that 
a common impulse on any system of bodies aftecfe 



228 The Reason why the Moon does not 

PLATE no t their relative motions; but that they will conti- 
nue to attract, impel, or circulate round one another, 
in the same manner as if there were no such impulse. 
The Moon is so near the Earth, and both of them 
so far from the Sun, that the attractive power of the 
Sun may be considered as equal on both : and there- 
fore the Moon will continue to circulate round the 
Earth nearly in the same manner as if the Sun did 
not attract them at all. For bodies in the cabin of a 
ship, may move round, or impel one another in the 
same manner when the ship is under sail, as when 
it is at rest ; because they are all equally affected by 
the common motion of the ship. If by any other 
cause, such as the near approach of a comet, the 
Moon's distance from the Earth should happen to 
be so much increased, that the difference of their 
gravitating forces toward the Sun should exceed 
that of the Moon toward the Earth ; in that case 
the Moon when in conjunction, would abandon the 
Earth, and be either drawn into the Sun or comet, 
or circulate round about it. 

Fig. in. 269. The curves which Jupiter's satellites de- 
scribe, are all of different sorts from the path describ- 
ed by our Moon, although these satellites go round 
Jupiter as the Moon goes round the Earth. Let 
ABCDE, &c. be as 'much of Jupiter's orbit as he 
describes in 18 days from A to T '; and the curves 
a, 6, c, dj will be the paths of his four moons going 
round him in his progressive motion. 

The abso- Now let us suppose all these moons to set out 
of^uptter fr m a conjunction with the Sun, as seen from Jupi- 
and his ter at A ; then his first or nearest moon will be at c, 
ddLtoeat! ^ s seconc ^ at &> ^ s *h\rd at c, and his fourth at d. 
ed. At the end of 24 terrestrial hours after this conjunc- 
tion, Jupiter has moved to , his. first moon or sa* 
tellite has described the curve a 1, his second the 
curve b 1, his third c 1, and his fourth d 1. The 
next day, when Jupiter is at C, his first satellite has 



abandon the Earth at the Time of her Change. 229 

described the curve a 2, from its conjunction, his PI ^ E 
second the curve b 2, his third the curve c 2, and 
his fourth the curve d 2, and so on. The numeral 
figures under the capital letters shew Jupiter's place 
in his path every day for 18 days, accounted from 
A to T; and the like figures set to the paths of his 
satellites, shew where they are at the like times. 
The first satellite, almost under C, is stationary at 
-f, as seen from the Sun; and retrograde from -f 
to 2 : at 2 it appears stationary again, and thence it 
moves forward until it has passed 3, and is twice 
stationary and once retrograde between 3 and 4. 
The path of this satellite intersects itself every 42 
hours, making such loops as in the diagram at 2. 3. 
5. 7. 9. 10. 12. 14. 16. 18, a little after every 
conjunction. The second satellite , moving slow- 
er, barely crosses its path every 3 clays 13 hours; 
as at 4. 7. 11. 14, 18. making only 5 loops and as 
many conjunctions in the time that the first makes 
ten. The third satellite c, moving still slower, and 
having described the curve c 1. 2. 3. 4. 5. 6. 7, 
comes to an angle at 7, in conjunction with the Sun, 
at the end of 7 days 4 hours ; and so goes on to 
describe such another curve 7. 8. 9. 10. 11. 12. 
13. 14, and is at 14 in its next conjunction. 
The fourth satellite d is always progressive, mak- 
ing neither loops nor angles in the heavens ; 
but comes to its next conjunction at e between Flff ' IIL 
the numeral figures 16 and 17, or in 16 days 18 
hours. In order to have a tolerable good figure of the 
paths of these satellites, I took the following method. 
Having drawn their orbits on a card, in propor- 
tion to their relative distances from Jupiter, I mea- Fig. iv. 
sured the radius of the orbit of the fourth satellite, 
which was an inch and /^ parts of an inch ; then 
multiplied this by 424 for the radius of Jupiter's 
orbit, because Jupiter is 424 times as far from the 
Sun's centre as his fourth satellite is from his cen- 
tre, and the product thence arising was 483 -^ 



230 The Paths of Jupiter's Moons delineated. 

PLATE i, lc hes. Then taking a small cord of this length, 






and fixing one end of it to the floor of a long room 
to by a nail, with a black-lead pencil at the other end 

* drew llie Clirve ^ C A &c. and set off a degree 
an d a half thereon, from A to T ; because Jupiter 
ter's moves only so much, while his outermost satellite 
>ns ' goes once round him, and somewhat more : so thai 
this small portion of so large a circle differs but ve- 
ry little from a straight line. This done I divided 
the space A T'mto 18 equal parts, as A B, B C, 
&c. for the daily progress of Jupiter ; and each 
part into 24 for his hourly progress. The orbit of 
each satellite was also divided into as many equal 
parts as the satellite is hours in finishing its synodi- 
cal period round Jupiter. Then drawing a right 
line through the centre of the card, as a diameter 
to all the four orbits upon it, I put the card upon 
the line of Jupiter's motion, and transferred it to ev- 
ery horary division thereon, keeping always the 
same diameter- line on the line of Jupiter's path ; and 
running a pin through each horary division in the 
orbit of each satellite as the card was gradually trans- 
ferred along the line ABCD, &c. of Jupiter's mo- 
tion, I marked points for every hour through the 
card for the curves described by the satellites, as 
the primary planet in the centre of the card was car- 
ried forward on the line ; and so finished the figure, 
by drawing the lines of each satellite's motion through 
those (almost innumerable) points : by which means, 
and Sa ^ s * s > P erna ps, as true a figure of the paths of these 
turn's.*" satellites as can be desired. And in the same man- 
ner might those of Saturn's satellites be delineated. 
The grand 270. It appears by the scheme, that the three first 
periods^of satellites come almost into the same line of position 
moons!" S every seventh day ; the first being only a little behind 
with the second, and the second behind with the 
3d. But the period of the 4th satellite is so incommen- 
surate to the periods of the other three, that it cannot 



The Pat/is of Jupiter's Moons delineated. 231 



PLATE 
VII. 



be guessed at by the diagram when it would fall 
again into a line of conjunction with them between 
Jupiter and the Sun. And no wonder; for suppos- 
ing them all to have been once in conjunction, it \\ ill 
require 3,087,043,493,260 years to bring them in 
conjunction again. See 73. 

271. In Fig. 4th, we have the proportions of the Fig. IV. 
orbits of Saturn's five satellites, and of Jupiter's four, ?. pro " f 

- - t* iii* portions ox 

to one another, to our Moon's orbit, and to the disc the orbits 
of the Sun. S is the Sun ; M m the Moon's orbit Jj^** 
(the Earth supposed to be at E); /Jupiter j 1. 2. satellites, 
3. 4, the orbits of his four moons or satellites; Sat. 
Saturn ; and 1. 2. 3.4. 5, the orbits of his five 
moons. Hence it appears, that the Sun would much 
more than fill the whole orbit of the Moon ; for the 
Sun's diameter is 763,000 miles, and the diameter 
of the Moon's orbit only 480,000. In proportion to 
all these orbits of the satellites, the radius of Saturn's 
annual orbit would be 2U yards, of Jupiter's orbit 
11, and of the Earth's 2i, taking them in round 
numbers. 

272. The annexed table shews at once what pro- 
portion the orbits, revolutions, and velocities of all 
the satellites bear to those of their primary planets, 
and what sort of curves the several satellites describe. 
For those satellites, whose velocities round their pri- 
maries are greater than the velocities of their prima- 
ries in open space, make loops at their conjunctions, 
5 269 ; appearing retrograde as seen from the Sun 
svhile they describe the inferior parts of their orbits, 
and direct while they describe the superior. This is 
the case with Jupiter's first and second satellites, and 
with Saturn's first. But those satellites, whose velo- 
cities are less than the velocities of their primary pla- 
nets, move direct in their whole circumvolutions ; 
which is the case of the third and fourth satellites of 
Jupiter, and of the second, third, fourth, and fifth 
satellites of Saturn, as well as of our satellite the 
Moon : but the Moon is the only satellite whose 
motion is always concave to the Sun. 

Gg 



232 The Curves described by the secondary Planets. 



The 
Satellites 


Proportion of 
the Radius of 
thePlanet'sOr- 
bit to the Ra- 
dius of the Or- 
bit of each Sa- 
tellite. 


Proportion of 
the Time of 
the Planet's 
Revolution to 
the Revolution 
of each Satel- 
lite. 


Proportion ofS 
the Velocity of? 
each Satellite S 
to the Velocity <J 
of its primary S 
Planet. 

$ 


5 l 

1 


As 5322 to 1 
4155 1 
2954 
1295 
432 


As 5738 to 
3912 
2347 
674 
134 


As5738to5322 S 
3912 4155 ^ 
2347 2954 S 
674 1295 
134 432 S 


$8,1 
1*1. 3 


As 1851 to 
1165 
731 
424 


As 2445 to 
1219 
604 
258 


As 2445 to 1851 S 
1219 1165J; 
604 731 S 
258 424 !j 


S MOOQ 


As 337| to 1 


As 12| to 1 


As 12.Jto337|!j 



There is a table of this sort in De la Cattle's As- 
tronomy, but it is very different from the above, 
which 1 have computed from our English accounts 
of the periods and distances of these planets and 
satellites. 



Of the Harvest-Moon. 233 



CHAP. XVL 

The Phenomena of the Harvest-Moon explained by 
a common Globe. The Years in which the Har- 
vest Moons are least and most beneficialfrom 1751 
to 1861. The long Duration of Moon-light at the 
Poles in Winter. 



T 

J[ 



T is generally believed that the Moon rises No 
about 50 minutes later every clay than on^s 
the preceding : but this is true only \vith regard to equator: 
places on the equator. In places of considerable 
latitude there is a remarkable difference, especially 
in the harvest time, with which farmers were better 
acquainted than astronomers, till of late ; and 
gratefully ascribed the early rising of the full moon 
at that time of the year to the goodness of God, not 
doubting that he had ordered it so on purpose to 
give them an immediate supply of moon-light after 
sun- set, for their greater conveniency in reaping the 
fruits of the Earth. 

In this instance of the harvest-moon, as in many 
others discoverable by astronomy, the wisdom and 
beneficence of the Deity is conspicuous, who really 
ordered the course of the Moon so, as to bestow 
more or less light on all parts of the Earth as their 
several circumstances and seasons render it more or 
less serviceable. About the equator, where there is 
no variety of seasons, and the weather changes sel- 
dom, and at stated times, moon-light is not neces- 
sary for gathering in the produce of the ground; and 
there the Moon rises about 50 minutes later every 
day or night lhan on the former. At considerable 
distances from the equator, where the weather and 
seasons are more uncertain, the autumnal full Moon 
rises very soon after sun-set for several evenings to 



234 Of the Harvest-Moon. 

But re- gether. At the polar circles, where the mild season 
Scm-dine * s ^ ver y s ^ ort duration, tne autumnal full Moon 
to the dis. rises at sun-set from the first to the third quarter. 
tances of And at the poles, where the Sun is for half a year 
from it. absent, the winter full Moons shine constantly with- 
out setting from the first to the third quarter. 
The rea- It is soon said that all these phenomena are owing 
lis 'to the different angles made by the horizon and dif- 
ferent parts of the Moon's orbit ; and that the Moon 
can be full but once or twice in a year in those parts 
of her orbit which rise with the least angles. But 
to explain this subject intelligibly, we must dwell 
much longer upon it. 

274. The* plane of the equinoctial is perpendi- 
cular to the Earth's axis ; and therefore, as the Earth 
turns round its axis, all parts of the equinoctial make 
equal angles with the horizon both at rising and set- 
ting ; so that equal portions of it always rise or set 
in equal times. Consequently, if the Moon's mo- 
tion were equable, and in the equinoctial, at the rate 
of 12 degrees 11 min. from the Sun every day, as 
it is in her orbit, she would rise and set 50 minutes 
later every day than on the preceding ; for 12 deg. 
11 min. of the equinoctial* rise or set in 50 minutes 
of time in all latitudes. 

275. But the Moon's motion is so nearly in the 
ecliptic, that we may consider her at present as 
moving in it. Now the different parts of the eclip- 
tic, on account of its obliquity to the Earth's axis, 
make very different angles with the horizon as they 
rise or set. Those parts or signs which rise with 
the smallest angles set with the greatest, and vice 
versa. In equal times, whenever this angle is least, 
a greater portion of the ecliptic rises than when the 
angle is larger ; as may be seen by elevating the 
pole of a globe to any considerable latitude, and then 

* If a globe be cut quite through upon any circle, the flat 
surface where it is so divided is the plane of that circle. 



Of the Harvest-Moon. 235 



turning it round its axis. Consequently, when the 
Moon* is in those signs which rise or set with the 
smallest angles, she rises or sets with the least dif- 
ference of time ; and with the greatest difference in Fig. HI. 
those signs which rise or set with the greatest angles. 

But, because all who read this treatise may not 
be provided with globes, though in this case it is re- 
quisite to know how to use them, we shall substi- 
tute the figure of a globe; in which FU P is the 
axis, 25 TR the tropic of Cancer, Lt itf the tropic 
of Capricorn, 22 E U >5 the ecliptic touching both 
the tropics, which are 47 degrees from each other, 
and.^fjftthe horizon. The equator being in the 
middle between the tropics, is cut by the ecliptic in 
two opposite points, which are the beginnings of v 
Aries and =^ Libra ; K is the hour-circle with its 
index, F the north pole of the globe elevated to a 
considerable latitude, suppose 40 degrees above the 
horizon ; and P the south pole depressed as much Fi s . HI, 
below it. Because of the oblique position of the 
sphere in this latitude, the eeliptic has the high ele- 
vation N 25 above the horizon, making the angle The differ- 
AT/25 of 73 degrees with it when 25 Cancer is on^ d ^ es 
the meridian, at which time =2= Libra rises in the the eciip- 
east. But let the globe be turned half round its axis, H c and ho * 
till >5 Capricorn comes to the meridian and <v* Aries l ' 
rises in the east, and then the ecliptic will have 
the low elevation NL above the horizon, making 
only an angle NUL of 26J degrees with it; which 
is 47 degrees less than the former angle, equal to 
the distance between the tropics. 

276. In northern latitudes, the smallest angle Least and 
made by the ecliptic and horizon is when Aries rises, 
at which time Libra sets ; the greatest when Libra 
rises, at which time Aries sets. From the rising of 
Aries to the rising of Libra (which is twelve* side- 

* The ecliptic, together with the fixed stars, make 366J 
apparent diurnal revolutions about the Earth in a year ; the 
Sun only 3651. Therefore the stars gain 3 minutes 56 se 



236 



Of the Haw est- Moon.. 



ral hours) the angle increases ; and from the rising 

of Libra to the rising of Aries, it decreases in the 

same proportion. By this article and the preceding 

it appears that the ecliptic rises fastest about Aries, 

and slowest about Libra. 

Result of 277. On the parallel of London, as much of the 
the quan- ecliptic rises about Pisces " 
angifat" 8 an( ^ Aries in two hours as ? 
London, the Moon goes through in s 

six days : and therefore Jj 

while the Moon is in these ^ 

signs, she differs but two S 

hours in rising for six days s 

together; that is, about 20 \ 

minutes later every day or !j 

night than on the preced- 1* 

ing, at a mean rate. But Jj 

in fourteen days afterward, S 9 

the Moon comes to Virgo 

and Libra, which are the 

opposite signs to Pisces \ is 

and Aries; and then shejj 14 

differs almost four times as S J* 

much in rising; namely, s 17 

one hour and about fifteen s 1 8 

minutes later every day or s 19 

night than the former, while ' 

she is in these signs. The ^ ^ 

annexed table shews the s 33 

daily mean difference of 

the Moon's rising and set- 
ting on the parallel ofLo?i- 

don, for 28 days; in which 

time the moon finishes her. 



1 

C/! 


^ <? 
3i 3 


Rising 
Diff.' 


Setting S 
Diff. s 




<t 

y. 


H. M. 


H. M. ^ 


1 


25 13 


5 


50 


2 


26 


10 


43 S 


3 


a 10 


14 


37 Jj 


4 


23 


17 


32 S 


5 


TW A 


16 


o 28 J; 


6 


19 


15 


24 S 


7 


=^ 2 


15 


20 


8 


15 


15 


18 S 


9 


28 


15 


17 ^ 


10 


HI 12 


15 


22 S 


11 


25 


1 14 


30 > 


12 


/ 8 


I 13 


39 S 


1 3 


21 


1 10 


47 > 


14 


X? 4 


1 4 


56 S 


15 


17 


46 


1 5 ^ 


16 


yyy i 


40 


1 8S 


17 


14 


35 


1 12 ? 


18 


27 


30 


1 15 S 


19 


X 10 


25 


1 16 J 


20 


23 


20 


1 17 S 


2] 


cy> <Y 


17 


1 16? 


22 


20 


17 


1 15 S 


23 


3 


20 


1 11 > 


24 


16 


24 


1 15 S 


25 


29 


30 


1 14 Jj 


26 


n is 


40 


1 13 S 


27 


26 


56 


1 7S 


28 


25 9 


I 00 


58 S 



conds upon the Sun every day ; so that a sideral day con- 
tains only 23 hours 56 minutes of mean solar time ; and a 
natural or solar day 24 hours. Hence 12 sideral hours are 
one minute 58 seconds shorter than 12 solur hours. 



Of the Harvest-Moon. 237 



PLATE 
III. 



period round the ecliptic, and gets 9 degrees into 
the same sign from the beginning of which she set 
out. Thus it appears by the table,that when the Moon 
is in *% and =& she rises an hour and a quarter later 
every day than she rose on the former ; and differs 
only 28, 24, 20, 18 or 17 minutes in setting. But, 
when she comes to X and V, she is only 20 or 17 
minutes later in rising ; and an hour and a quarter 
later in setting. 

278. All these things will be made plain by put- 
ting small patches on the ecliptic of a globe, as far 
from one another as the Moon moves from any point 
of the celestial ecliptic in 24 hours, which at a mean 
rate is* 13j degrees; and then, in turning the globe 
round, observe the rising and setting of the patches 
in the horizon, as the index points out the different 
times on the hour-circle. A few of these patches are 
represented by dots at 1 2 3, &c. on the ecliptic, Fig. ni 
which has the position Z/7/when Aries rises in the 

east ; and by the dots 0123, &x. when Libra rises 
in the east, at which time the ecliptic has the posi- 
tion EUv3 : making an angle of 62 degrees with 
the horizon in the latter case, and an angle of no 
more than 15 degrees with it in the former ; suppos- 
ing the globe rectified to the latitude of London. 

279. Having rectified the globe, turn it until the 
patch at 0, about the beginning of x Pisces in the 
half LUI Q the ecliptic, comes to the eastern side 
of the horizon; and then, keeping the ball steady, 
set the hour-index to XII, because that hour may 
perhaps be more easily remembered than any other. 
Then turn the globe round westward, and in that 
time, suppose the patch to' have moved thence- 



* The Sun advances almost a degree in the ecliptic in 24 
hours, the same way that the Moon moves ; and therefore 
the Moon by advancing 13 degrees in that time, goes lit- 
tle more than 12 degrees farther from the Sun than she was 
on the day before. 



238 Of the Harvest-Moon. 

to 1, 13 J degrees, while the Earth turns once round 
its axis, and you will see that 1 rises only about 20 
minutes later than did on the day before. Turn 
the globe round again, and in that time suppose the 
same patch to have moved from 1 to 2 ; and it will 
rise only 20 minutes later by the hour- index than 
it did at 1 on the day or turn before. At the end of 
the next turn suppose the patch to have gone from 
2 to 3 at 7, and it will rise 20 minutes later than it 
did at 2, and so on for six turns, in which time there 
will scarce be two hours difference ; nor would there 
have been so much, if the 6 degrees of the Sun's 
motion in that time had been allowed for. At the 
first turn the patch rises south of the east, at the 
middle turn due east, and at the last turn north of the 
east. But these patches will be 9 hours in setting 
on the western side of the horizon, which shews that 
the Moon's setting will be so much retarded in that 
week in which she moves through these two signs. 
The cause of this difference is evident ; for Pisces 
and Aries make only an angle of 15 degrees with 
the horizon when they rise ; but they make an angle 
of 62 degrees with it when they set. As the signs 
Taurus, Gemini, Cancer, Leo, Virgo, and Libra, 
rise successively, the angle increases gradually which 
they make with the horizon, and decreases in the 
same proportion as they set. And for that reason, 
the Moon differs gradually more in the time of her 
rising every day while she is in these signs, and less 
in her setting : after which, through the other six 
signs, viz. Scorpio, Sagittary, Capricorn, Aquarius, 
Pisces, and Aries, the rising-difference becomes 
less every day, until it be at the least of all, namely, 
in Pisces and Aries. 

280. The Moon goes round the ecliptic in 27 
days 8 hours : but not from change to change in less 
than 29 days 12 hours : so that she is in Pisces and 
Aries at least once in every lunation, and in some 
lunations twice. 



Of the Hai~vest-MooK. 239 

281. If the Earth had no annual motion, the why the 
:Sun would never appear to shift his place in the *jy s is 
ecliptic. And then every new Moon would fall in full in dif- 
the samesign and degree of the ecliptic, and every ^? r ^ t 
full Moon in the opposite: for the Moon would go b ' &ns 
precisely round the ecliptic from change to change. 
-So that if the Moon were once full in Pisces or Aries, 
she would aiways be full when she came round to 
the same sign and degree again- And as the full 
Moon rises at sun- set (because when any point of 
the ecliptic sets, the opposite point rises) she would 
constantly rise within two hours of sun-set, on the 
parallel of London, during the week in which she 
was full. But in the time that the Moon goes 
round the ecliptic from any conjunction or opposi- 
tion, the Earth goes almost a sign forward : and 
therefore the Sun will seem to go as far forward in 
that time, namely, 27| degrees ; so that the Moon 
must go 27 degrees more than round, and as 
much farther as the Sun advances in that interval, 
which is 2^ degrees, before she can be in conjunc- 
tion with, or opposite to the Sun again. Hence it 
is evident that there can be but one conjunction or 
opposition of the Sun and Moon in a year in any Her peri- 
particular part of the ecliptic. This may be fami- odical and 
liarly exemplified by the hour and minute-hands oi revolution 
a watch, which are never in conjunction or oppo- exempiifi- 
sition in that part of the dial-plate where they were ed * 
so last before. And indeed if we compare the 
. twelve hours on the dial-plate to the twelve signs of 
the ecliptic, the hour-hand to the Sun, and the 
minute-hand to the Moon, we shall have a tolerable 
near resemblance in miniature to the motions of our 
great celestial luminaries. The only difference is, 
that while the Sun goes once round the ecliptic, the 
Moon makes \^\ conjunctions with him: but, while 
the hour-hand goes round the dial-plate, the minute - 
hand makes only 11 conjunctions with it; because the 
minute-hand moves slower in respect to the hour- 
Hh 




240 Of the 'Harvest-Mom. 

hand than the Moon does with regard to the Sun, 

ve^t and . 282 ' AS the M n Can nCVer be ^ u11 bllt wnen shfe 

Hunter's opposite to the Sun, and the Sun is never in Vir- 
Moon. go ai.d Libra, but in our autumnal months, it is 
p-'iin that the Moon is never full in the opposite signs, 
Pisces and Aries, but in these two months. And 
thercibre we can have only two full Moons in the 
year, which rise so near the time of sun-set for a 
week together, as above-mentioned. The former 
of these is called the Harvest Moon, and the latter 
the Hunters Moon. 

Why the 283. Here it will probably be asked, why we ne- 
regular ri- ver observe this remarkable rising of the Moon but 
is ne- in harvest, seeing she is in Pisces and Aries twelve 

times * n ^ ie ^ car bes ^ es > an( ^ must then rise with 
in harvest, as little difference of time as in harvest? The answer 
is plain : for in winter these signs rise at noon ; and 
being then only a quarter of a circle distant from 
the Sun, the Moon in them is in her first quarter : 
but when the Sun is above the horizon, the Moon's 
rising is neither regarded nor perceived. In spring 
these signs rise with the Sun, because he is then in 
them ; and as the Moon changes in them at that 
time of the year, she is quite invisible. In sum- 
mer they rise about midnight, and the Sun being 
then three signs, or a quarter of a circle before 
them, the Moon is in them about her third quarter ; 
and when rising so late, and giving but very lit- 
tle light, her rising passes unobserved. And in 
autumn these signs, being opposite to the Sun, 
rise when he sets, with the Moon in opposition, 
or at the full, which makes her rising very conspi- 
cuous. 

284. At the equator, the north and south poles lie 
in the horizon ; and therefore the ecliptic makes the 
same angle southward with the horizon, when Aries 
rise b, as it does northward when Libra rises. Conse- 
quently as the Moon at ail the fore-mentioned patches 
rises and sets nearly at equal angles with the horizon 




Of the Harvest-Moon. 24J 

all the year round, and about 50 minutes later eve- 
ry day or night than on the preceding, there can be 
no particular harvest- moon at the equator. 

285. The farther that any place is from the equa- 
tor, if it be not beyond the polar circle, the angle 
gradually diminishes which the ecliptic and horizon 
make when Pisces and Aries rise : and therefore 
when the Moon is in these signs she rises with a 
nearly proportionable difference later every day than 
on the former ; and is for that reason the more remark- 
able about the full, until we come to the polar cir- 
cles, or 66 degrees from the equator ; in which 
latitude the ecliptic and horizon become coincident 
every day for a moment, at the same sidereal hour 
(or 3 minutes 56 seconds sooner every day than the 
former), and the very next moment one half of the 
ecliptic, containing Capricorn, Aquarius, Pisces, 
Aries, Taurus, and Gemini, rises, and the oppo- 
site half sets. Therefore, while the Moon is going 
from the beginning of Capricorn to the beginning 
of Cancer, which is almost 14 days, she rises at 
the same sidereal hour; and in autumn just at sun-set, 
because all the half of the ecliptic, in which the 
Sun is at that time, sets at the same sidereal hour, 
and the opposite half rises ; that is, 3 minutes 56 
seconds of mean solar time, sooner every day than 
on the day before. So while the Moon is going 
from Capricorn to Cancer, she rises earlier every 
day than on the preceding ; contrary to what she 
does at all places between the polar circles. But 
during the above fourteen days, tae Moon is 24 si- 
dereal hours later in setting ; for the six signs which 
rise all at once on the eastern side of the horizon are 
24 hours in setting on the western side of it ; as 
any one may see by making chalk- marks at the be- 
ginning of Capricorn and of Cancer, and then, 
having elevated the pole 66^ degrees, turn the globe 
slowly round its axis, and observe the rising and 
setting of the ecliptic. As the beginning of Aries 



242 Of the Harvest-Moon* 

is equally distant from the beginning of Cancer and ot 
Capricorn, it is in the middle of that hall oi the 
ecliptic which rises all at once. And when the Sun 
is at the beginning of Libra, he is in the middle of 
the other half. Therefore, when the Sun is in Li- 
bra, and the Moon in Capricorn, the Moon is a 
quarter of a circle before the Sun ; opposite to him, 
and consequently full in Aries, and a quarter of a 
circle hehind him, when in Cancer. But when Li- 
bra rises, Aries sets, and all that half of the eclip- 
tic of w hich Aries is the middle, and therefore, at 
that time of the year, the Moon rises at sun- set 
from her first to her third quarter. 

The bar. 286. In northern latitudes, the autumnal full 

moons re- Moons are in Pisces and Aries > and the vernal full 

guiaron Moons in Virgo and Libra: in southern latitudes, 

of t th e S)deS J ust tne reverse ? because the seasons are contrary. 

equator. But Virgo and Libra rise at as small angles with the 

horizon in southern latitudes, as Pisces and Aries 

do in the northern ; and therefore the harvest- moons 

are just as regular on one side of the equator as 

on the other. 

287. As these signs, which rise with the least 
angles, set with the greatest, the vernal full Moons 
differ as much in their times of rising every night, 
as the autumnal full Moons differ in their times of 
setting ; and set with as little difference as the au- 
tumnal full Moons rise : the one being in all cases 
the reverse of the other. 

288. Hitherto, for the sake of plainness, we 
have supposed the Moon to move in the ecliptic, 
from which the Sun never deviates. But the orbit 
in which the Moon really moves is different from 
the ecliptic : one half being elevated 5^ degrees 
above it, and the other half as much depressed be- 
low it. The Moon's orbit therefore intersects the 
ecliptic in tw T o points diametrically opposite to each 
other ; and these intersections are called the Moon's 
nodes. So the Moon can never be in the ecliptic 



Of the Harvest-Moon. 243 

but when she is in either of her nodes, which is at JJlL^ 
least twice in every course from change to change, 
and sometimes thrice. For, as the Moon goes al- 
most a whole sign more than round her orbit 
from change to change ; if she passes by either 
node about the time of change, she will pass by 
the other in about fourteen days after, and come 
round to the former node two days again before the 
next change. That node from which the Moon be- 
gins to ascend northward, or above the ecliptic, in. 
northern latitudes, is called the ascending node; 
and the other the descending node; because the 
Moon, when she passes by it, descends below the 
ecliptic southward. 

289. The Moon's oblique motion with regard 
to the ecliptic causes some difference in the times 
of her rising and setting from what is already men- 
tioned. For when she is northward of the eclip- 
tic, she rises sooner and sets later than if she mov- 
ed in the ecliptic ; and w ? hen she is southward of 
the ecliptic, she rises later and sets sooner. This 
difference is variable even in the same signs, be- 
cause the nodes shift backward about 19-| degrees 
in the ecliptic every year ; and so go round it con- 
trary to the order of signs in 18 years 225 days. 

290. When the ascending node is in Aries, the 
southern half of the Moon's orbit makes an angle 
of 5-J- degrees less yvith the horizon than the eclip- 
tic does, when Aries rises in northern latitudes: for 
which reason the Moon rises with less difference of 
time while she is in Pisces and Aries, than she 
would do if she kept in the ecliptic. But in 9 
years and 112 days afterward, the descending node 
comes to Aries ; and then the Moon's orbit makes 
an angle 5~ degrees greater with the horizon when 
Aries rises, than the ecliptic does at that time; 
which causes the Moon to rise with greater differ- 
ence of time in Pisces 3nd Aries than if she mov- 
ed in the eclipti.c. 



244 Of the Harvest-Moon. 

291. To be a little more particular, when the 
ascending node is in Aries, the angle is only 9| le- 
grees on the parallel of London when Aries rises. 
But when the descending node comes to Aries, the 
angle is 20^ degrees; this occasions as great a dif- 
ference of the Moon's rising in the same signs eve- 
ry nine years, as there would be on two parallels 
10-f degrees from one another, if the Moon's course 
were in the ecliptic. The following table shews 
how much the obliquity of the Moon's orbit affects 
her rising and setting on the parallel of London, 
from the 12th to the 18th day of her age; suppos- 
ing her to be full at the autumnal equinox : and 
then, either in the ascending node, highest part of 
her orbit, descending node, or lowest part of her 
orbit. Jl/ signifies morning, A afternoon : and the 
line at the foot of the table shews a week's difference 
in rising and setting. 



S ' 


Full in her Ascend- 
ing Node. 


In the highest pt. 
of her Orbit. 


Full in her Descend- 
ing Node. 


In the lowest pt. of \ 
her Orbit. L 


*J 










Rises at 


Sots at 


Rises at 


Sets at 


Rises at 


Sets at 


Rises at 


Sets at S 


S'S 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. S 


s -_ 
















3M 


5 A 15 


3M.-0 


4 A 30 


3Afl5 


4 A 32 


3Af40 


5 A 16 


S 13 


5 32 


4 25 


4 50 


4 45 


5 15 


4 20 


6 


4 15 V 


Sl4 


5 48 


5 30 


5 15 


6 


5 45 


5 40 


6 20 


5 28 S 


S 15 


6 5 


7 


5 4-2 


7 20 


6 15 


6 56 


6 45 


6 32 S 


S16 


6 20 


8 15 


6 2 


8 35 


6 46 


8 


7 8 


7 45 < 


Sir 


6 36 


9 12 


6 26 


9 45 


7 18 


9 15 


7 30 


9 15 S 


Jj 18 


6 54 


10 30 


7 


10 40 


8 


10 20 


7 52 


10 OS 


S Diff. 


13 9 


7 10 


2 30 


7 25 


3 28 


6 40 


2 36 


7 c 



This table was not computed, but only estimated 
as near as could be done from a common globe, on 
which the Moon's orbit was delineated with a black- 
lead pencil. It may at first sight appear erroneous ; 
since as we have supposed the Moon to be full in 
either node at the autumnal equinox, ought by the 



Of the Harvest-Moon. 245 

table to rise just at six o'clock, or at sun-set, on the 
ISthday of her age; being in the ecliptic at that time. 
But it must be considered, that the Moon is only 
14 days old when she is full ; and therefore in both 
cases she is a little past the node on the 15th day, 
being above it at one time, and below it at the other. 

292. As there is a complete revolution of the The peri- 
nodes in 18f years, there must be a regular period j 
of all the varieties which can happen in the rising moon, 
and setting of the Moon during that time. But this 
shifting of the nodes never affects the Moon's rising 
so much, even in her quickest descending latitude, 
as not to allow us still the benefit of her rising nearer 
the time of sun- set for a few day together about the 
full in harvest, than when she is full at any other 
time of the year. The following table shews in what 
years the harvest- moons are least beneficial as to the 
times of their rising, and in what years most, from 
1751 to 1861. The column of years under the let- 
ter L are those in which the harvest- moons are least 
of all beneficial, because they fall about the descend- 
ing node: and those under J/are the most of all 
beneficial, because they fall about the ascending 
node. In all the columns from N to S the harvest- 
moons descend gradually in the lunar orbit, and rise 
to less heights above the horizon. From S to A" 
they ascend in the same proportion, and rise to great- 
er heights above the horizon. In both the columns 
under , the harvest- moons are in the lowest part 
of the Moon's orbit, that is, farthest south of the 
ecliptic, and therefore stay shortest of all above the 
horizon : in the columns under A", just the reverse. 
And in both cases, their risings, though not at the 
same times, are nearly the same with regard to dif- 
ference of time, as if the Moon's orbit were coinci- 
dent with the ecliptic. 



246 



Of the Harvest-Moon. 



Years in which the Harvest- Moons are least bentjicial. 

N L S 

1751 1752 1753 1754 1755 1756 1757 1758 1759 
1770 1771 1772 1773 1774 1775 1776 17.77 1778 
1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 
1807 1808 1809 1810 1811 1812 1813 1814 1815 
1826 1827 1828 1829 1830 1831 1832 1833 1834 t 
1844 1845 1846 1847 1848 1849 1850 1851 1852 

Years in which they are most beneficial. 
S M N 

1760 1761 1762 1763 1764 1765 1766 176? 1768 1769 
1779 1780 1781 1782 1783 1784 1785 1786 1787 
1798 1799 1800 1801 1802 1803 1804 1805 18u6 
1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 
1835 1836 1837 1838 1839 1840 1841 1842 1843 
1853 1854 1855 1856 1857 1858 1859 1860 1861 



The long- 
continu- 
ance of 
moon- 
light at 
the poles. 



293. At the polar circles, when the Sun touches 
the summer-tropic, he continues 24 hours above 
the horizon; and 24 hours below it when he touches 
the winter-tropic. For the same reason the full 
Moon neither rises in summer, nor sets in winter, 
considering her as moving in the ecliptic. For the 
winter full Moon being as high in the ecliptic as the 
summer Sun, must therefore continue as long above 
the horizon ; and the summer full Moon being as 
low in the ecliptic as the winter Sun, can no more 
rise than he does. But these are only the two full 
Moons which happen about the tropics, for all the 
others rise and set. In summer the full Moons are 
low, and their stay is short above the horizon, when 
the nights are short, and we have least occasion for 
moon-light : in winter they go high, and stay long 
above the horizon, when the nights are long, and we 
want the greatest quantity of moon- light. 

294. At the poles, one half of the ecliptic never 
sets, and the other half never rises : and therefore, 
as the Sun is always half a year in describing one 
half of the ecliptic, and as long in going through 



The long Duration of Moon- light at the Poles. 24! 

the other half, it is natural to imagine that the Sun 
continues half a year together above the horizon of 
each pole in its turn, and as long below it ; rising to 
one pole when he sets to the other. This would be 
exactly the case if there were no refraction ; but by 
the atmosphere's refracting the Sun's rays, he be- 
comes visible some days sooner, 183, and contin- 
ues some days longer in sight than he would other- 
wise do : so that he appears above the horizon of ei- 
ther pole before he has got below the horizon of the 
other. And, as he never goes more than 23- de- 
grees below the horizon of the poles, they have 
very little dark night ; it being twilight there as well 
as at all other places, till the Sun is 18 degrees 
below the horizon, 177. The full Moon being al- 
ways opposite to the Sun, can never be seen while 
the Sun is above the horizon, except when the Moon 
fulls in the northern half of her orbit ; for whenever 
any point of the ecliptic rises, the opposite point sets. 
Therefore, as the Sun is above the horizon of the 
north pole from the 20th of March till the 23d of 
September, it is plain that the Moon, when full, be- 
ing opposite to the Sun, must be below the horizon 
during that half of the year. But when the Sun is in 
the southern half of the ecliptic, he never rises to the 
north pole, during which half of the year, every full 
Moon happens in some part of the northern half of 
the ecliptic, which never sets. Consequently, as 
the polar inhabitants never see the full Moon in sum- 
mer, they have her always in the winter, before, 
at, and after the full, shining for 14 of our clays 
and nights. And when the Sun is at his greatest 
depression below the horizon, being then in Capri- 
corn, the Moon is at her first quarter in Aries, full 
in Cancer, and at her third quarter in Libra. And 
as the beginning of Aries is the rising point of the 
ecliptic, Cancer the highest, and Libra the setting 
point, the Moon rises at her first quarter in Aries, 
is most elevated above the horizon, and full in Can- 
cer, and sets at the beginning of Libra in her third 
I i 



248 The long Duration of Moon-light at the Poles. 



PLATE 
VIII. 



quarter, having continued visible for 14 diurnal ro- 
tations of the Earth. Thus the poles are supplied 
one half of the winter-time with constant moon, light 
in the Sun's absence ; and only lose sight of the 
Moon from her third to her first quarter, while she 
gives but very little light, and could be but of lit- 
v. tie, and sometimes of no service to them. A bare 
view of the figure will make this plain : in which let 
8 be the Sun, e the Earth in summer, when its 
jiorth pole n inclines toward the Sun, and E the 
Earth in winter, when its north pole declines from 
him. SEN and NIPS is the horizon of the north 
pole, which is coincident with the equator ; and, in 
both these positions of the Earth, <Y> & V? is the 
Moon's orbit, in which she goes round the Earth, 
according to the order of the letters abed, ABCD. 
When the Moon is at , she is in her third quarter 
to the Earth at e, and just rising to the north pole n; 
at b she changes, and is at the greatest height above 
the horizon, as the Sun likewise is; at c she is in 
her first quarter, setting below the horizon ; and is 
lowest of all under it at c/, when opposite to the 
Sun, and her enlightened side toward the Earth. 
But then she is full in view to the south pole p ; 
which is as much turned from the Sun as the north 
pole inclines toward him. Thus in our summer, 
the Moon is above the horizon of the north pole, 
while she describes the northern half of the ecliptic 
T 25 =3= , or from her third quarter to her first ; and 
below the horizon during her progress through the 
southern half =2= yj v ; highest at the change, most 
depressed at the full. But in winter, when the 
Earth is at E, and its north pole declines from the 
Sun, the new Moon at D is at her greatest depres- 
sion below the horizon A/FiS 1 , and the lull Moon at 
B at her greatest height above it ; rising at her first 
quarter A, and keeping above the horizon till she 
comes to her third quarter C. At a mean state she 
is 123|- degrees above the horizon at B and b, and as 
much below it at D and d, equal to the inclination 



Of the Tides. 249 

of the Earth's axis F. S & or S v$ is, as it were, 
a ray of light proceeding from the Sun to the Earth ; 
and shews that when the Earth is at e, the Sun is 
above the horizon, vertical to the tropic of Cancer; 
and when the Earth is at E, he is below the horizon, 
vertical to the tropic of Capricorn. 

CHAP. XVII. 

Of the Ebbing and Flowing of the Sea. 

HE cause of the tides was discovered by 
KEPLER, who, in his /;/ 1 reduction to the 
Physics of the Heavens, thus explains it : " The The cause 
orb of the attracting power, which is in the Moon, . f 1 the 1 . 

i i r A frxLut i j ' tides dis- 

is extended as far as the Earth ; and draws the wa- coveredby 

ters under the torrid zone, acting upon places where KEPLER. 

it is vertical, insensibly on confined seas and bays, 

but sensibly on the ocean, whose beds are large, 

and the waters have the liberty of reciprocation ; 

that is, of rising and falling." And in the 70th 

page of his Lunar Astronomy " But the cause of 

the tides of the sea appears to be the bodies of the 

Sun and Moon drawing the waters of the sea." 

This hint being given, the immortal Sir ISAAC Their the- 

NEWTON improved it, and wrote so amply on the 01 "?? 115 ?" 

. . c. , r .< . ved by Sir 

subject, as to make the theory or the tides in a ISAAC 
manner quite his own; by discovering the cause of NEWTON - 
their rising on the side of the Earth opposite to the 
Moon. For KEPLER believed, that the presence 
of the Moon occasioned an impulse which caused 
another in her absence. 

296. It has been already shewn, $ 106, that Explain- 
the power of gravity diminishes as the square oft? OI ? th - e 

, \. . P , 4 y Newtoni- 

the distance increases ; and therefore the waters at a n princi- 
Z, on the side of the Earth ABCDEFGH nextP 1 ^- 
the Moon M, are more attracted than the central P L ATR 
parts of the Earth by the Moon, and the central IX * 
parts are more attracted by her than the waters on Tig. I. 
the opposite side of the Earth at n : and there- 



250 Of the Tides. 

PLATE fore the distance between the Earth's centre and 
the waters on its surface under and opposite to the 
Moon will be increased. For, let there be three 
bodies at //, 0, and/).- if they be all equally at- 
tracted by the body M, they will all move equally 
fast toward it, their mutual distances from each 
other continuing the same. If the attraction of M 
be unequal, then that body which is most strongly 
attracted will move fastest, and this will increase its 
distance from the other body. Therefore, by the 
law of gravitation, M \vi\\ attract //more strongly 
than it does 0, by which the distance between H 
and O will be increased : and a spectator on O will 
perceive H rising higher toward Z. In like 
manner, O being more strongly attracted than 
/), it will move farther toward M than D does : 
consequently, the distance between and D will 
be increased ; and a spectator on O, not perceiving 
his own motion, will see D receding farther from 
him toward n : all effects and appearances being the 
same, whether D recedes from O 9 or from /). 
297. Suppose now there is a number of bodies, 
as A, B, C, /), E, F, G, H, placed round O, so 
as to form a flexible or fluid ring : then, as the 
whole is attracted towards M, the parts at H and 
D will have their distance from O increased ; while 
the parts at B and F, being nearly at the same dis- 
tance from Mas O is, these parts will not recede 
from one another ; but rather, by the oblique attrac- 
tion oi'My they will approach nearer to O. Hence, 
the fluid ring will form itself into an ellipse Z I B 
L n K F N Z, whose longer axis n Z produced 
will pass through M, and its shorter axis B F 
will terminate in B and F. Let the ring be filled 
with fluid particles, so as to form a sphere round 0; 
then, as the whole moves toward M, the fluid sphere 
being lengthened at Z and n> will assume an ob- 
long or oval form. If M be the Moon, O the 
Earth's centre, ABCDEFGH the sea covering the 



Of the Tides. 251 

Earth's surface, it is evident, by the above reason- } 
ing, that while the Earth by its gravity falls toward 
the Moon, the water directly below her at B will 
swell and rise gradually toward her : also the water 
at D will recede from the centre (strictly speaking, 
the centre recedes from D), and rise on the opposite 
side of the Earth : while the water at B and JP is 
depressed, and falls below the former level. Hence, 
as the Earth turns round its axis from the Moon to 
the Moon again, in 24| hours, there will be two 
tides of flood and two of ebb in that time, as we 
find by experience. 

298. As this explanation of the ebbing and flow- 
ing of the sea, is deduced from the Earth's con- 
stantly falling toward the Moon by the power of gra- 
vity, some may find a difficulty in Conceiving how 
this is possible, when the Moon is full, or in oppo- 
sition to the Sun ; since the Earth revolves about 
the Sun, and must continually fall toward it, and 
therefore cannot fall contrary ways at the same time : 
or, if the Earth be constantly falling toward the Moon, 
they must come together at last. To remove this 
difficulty, let it be considered, that it is not the cen- 
tre of the Earth that describes the annual orbit round 
the Sun, but the* common centre of gravity of the 
Earth and Moon together : and that while the Earth 
is moving round the 'Sun, it also describes a circle 
round that centre of gravity ; going as many times 
round it in one revolution about the Sun as there 
are lunations or courses of the Moon round the 
Earth in a year : and therefore, the Earth is con- 
stantly falling toward the Moon from a tangent to 
the circle it describes round the said common cen- 
tre of gravity. Let Mbe the Moon, T W part of 

* This centre is as much nearer the Earth's centre than the 
Moon's, as the Earth is heavier, or contains a greater quantity of 
matter than the Moon, namely, about 40 times. It^both bodies 
were suspended on it, they would hang in equilibria. So that divid- 
ing 240,000 miles, the Moon's distance from the Earth's centre, by 
40, the excess of the Earth's weight above the Moon's, the quotient 
will be 6000 miles, which is the distance of the common centre of 
gravity of the Earth and Moon from the Earth's centre. 



252 Of the Tides. 



PLATE the Moon's orbit, and C the centre of gravity of 
the Earth ;ind Moon; while the Moon goes round 
Fig. ii. her orbit, the centre of the Earth describes the cir- 
cle dg around C, to which circle ga k is a tangent: 
and therefore, when the Moon has gone from M to 
a little past W, the Earth has moved from g to e; 
and in that time has fallen toward the Moon, from 
the tangent at a to c ; and so on, round the whole 
circle. 

299. The Sun's influence in raising the tides is 
but small in comparison of the Moon's ; for though 
the Earth's diameter bears a considerable propor- 
tion to its distance from the Moon, it is next to no- 
thing when compared to its distance from the Sun. 
And therefore, the difference of the Sun's attrac- 
tion on the sidfts of the Earth under and opposite 
to him, is much less than the difference of the 
Moon's attraction on the sides of the Earth under 
and opposite to her : and therefore the Moon must 
raise the tides much higher than they can be raised 
by the Sun. 

why the 300. On this theory, so far as we have explained 
n<rt e hiST- fr the tlc ^ es ou ght to be highest directly under and 
est when opposite to the Moon ; that is, when the Moon is 

iiTo^thT ^ ue nort1tt and soutn - But we fi n d, tnat i n p en 

merman, seas, where the water flow sfreely, the Moon M is 
generally past the north and south meridian, as atp, 

Fig. I. when it is high water at Z and at n. The reason 
is obvious; for though the Moon's attraction were 
to cease altogether when she was past the meridian, 
yet the motion of ascent communicated to the wa- 
ter before that time would make it continue to rise 
for some time after ; much more must it do so when 
the attraction is only diminished: as a little impulse 
given to a moving ball will cause it still to move far- 
ther than otherwise it could have done. And as ex- 
perience shews, that the day is hotter about three in 



Of the Tides. 253 

the afternooiTthan when the Sun is on the meridian, PLATE 
because of the increase made to the heat already IX< 
imparted. 

301. The tides answer not always to the same Noral- 
distance of the Moon from the meridian at the same Twer to" 
places ; but are variously affected by the action of her bein 
the Sun, which brings them on sooner when the ^^dis- 
Moon is in her first and third quarters, and keepstancefi-om 
them back later when she is in her second and fourth : 1U 
because, in the former case, the tide raised by the 

Sun alone would be earlier than the tide raised by 
the Moon ; and in the latter case later. 

302. The Moon goes round the Earth in an ellip- 
tic orbit, and therefore, in every lunar month, she 
approaches nearer to the Earth than her mean dis- 
tance, and recedes farther from it . When she is near- Spring 
est, she attracts strongest, and so raises the tides 
most; the contrary happens when she is farthest, be- 
cause of her weaker attraction. When both lumina- 
ries are in the equator, and the Moon in perigeo, or 

at her least distance from the Earth, she raises the 
tides highest of all, especially at her conjunction and 
opposition ; both because the equatorial parts have 
the greatest centrifugal force from their describing 
the largest circle, and from the concurring actions 
of the Sun and Moon. At the change, the attractive 
forces of the Sun and Moon being united, they di- 
minish the gravity of the waters under the Moon, 
and their gravity on the opposite side is diminished 
by means of a greater centrifugal force. At the full, Fi 
while the Moon raises the tide under and opposite 
to her, the Sun, acting in the same line, raises the 
tide under and opposite to him ; whence their con- 
joint effect is the same as at the change; and in both 
cases, occasion what we call the spring tides. But 
at the quarters the Sun's action on the waters at O 
and //diminishes the effect of the Moon's action on 
the waters at Z and N; so that they rise a little un- 
der and opposite to the Sun at and H, and fall as 



254 Of the Tides. 

much under and opposite to the Moon at Z and N; 
making what we call the neap tides, because the Sun 
and Moon then act cross- wise to each other. But, 
strictly speaking, these tides happen not till some 
time after ; because in this, as in other cases, \ 300, 
the actions do not produce the greastet effect when 
they are at the strongest, but some time afterward. 
Not great- 303. The Sun being nearer the Earth in winter 
l ^ an m summer > $ ^05, * s f course nearer to it in 



equnox 

es, and February and October, than in March and Septem- 



ber ; and therefore the greatest tides happen not till 

some time after the autumnal equinox, and return a 

little before the vernal. 
The tides The sea being thus put in motion, would conti- 
ul i" otnue to ebb and flow for several times, even though 
ate i ycea " ge the Sun and Moon were annihilated, or their influ- 
upon the eiice should cease : as if a bason of water were agi- 
tionof the tate< ^' tne water would continue to move for some 
Sun and time after the bason was left to stand still. Or like 
Moon. a p enc iulum, w hich, having been put in motion by 

the hand, continues to make several vibrations with- 

out any hew impulse. 

The lunar 304. When the Moon is in the equator, the tides 

The Tides are ec l lia % high m ^ otn P arts ^ tne ^ unar day, or 
rise 3 to 1 es time of the Moon's revolving from the meridian to 
unequal the meridian again, which is 24 hours 50 minutes. 
the & same m ^ ut as tne Moon declines from the equator toward 
day, and either pole, the tides are alternately higher and lower 
at places having north or south latitude. For one of 
the highest elevations, which is that under the Moon, 
follows her toward the pole to which she is nearest, and 
the other declines toward the opposite pole; each ele- 
vation describing parallels as far distant from the equa- 
tor, on opposite sides, as the Moon declines from it 
to either side ; and consequently, the parallels de- 
scribed by these elevations of the water are twice as 
many degrees from one another, as the Moon is from 
the equator; increasing their distance as the Moon 



Of the Ticks. 255 



increases her declination, till it be at the greatest, 
when the said parallels are, at a mean state, 47 de- 
grees from one another : and on that day, the tides 
are most unequal in their heights. As the Moon re- 
turns toward the equator, the parallels described by 
the opposite elevations approach toward each other, 
until the Moon comes to the equator, and then they 
coincide. As the Moon declines towards the oppo- 
site pole, at equal distances, each elevation describes 
the same parallel in the other part of the lunar day, 
which its opposite elevation described before. 
While the Moon has north declination, the greatest 
tides in the northern hemisphere are when she is 
above the horizon, and the reverse while her decli- 
nation is south. Let N E S Q be the Earth, JV C S Fi ff . Hi* 
its axis, E Q the equator, T 25 the tropic of Can- IV * ^- 
cer, t V5 the tropic of Capricorn, a b the arctic cir- 
cle, edthe antarctic, JVthe north pole, S the south 
pole, Jl/the Moon, F and G the two eminences of 
water, whose lowest parts are at #and d (Fig. III.) 
at AT and S (Fig. IV.) and at b and c (Fig. V.) al- 
ways 90 degrees from the highest. Now when the 
Moon is in her greatest north declination at j\f, the 
highest elevation G under her, is . on the tropic of 
Cancer T 25, and the opposite elevation F on the Fig, lit, 
tropic of Capricorn, t vj ; and these two elevations 
describe the tropics by the Earth's diurnal rotation. 
All places in the northern hemisphere E N Q 
have the highest tides when they come into the po- 
sition b gs Q, under the Moon; and the lowest tides 
when the Earth's diurnal rotation carries them into 
the position a T E, on the side opposite to the 
Moon ; the reverse happens at the same time in the 
southern hemisphere E S Q, as is evident to sight. 
The axis of the tides a C d has now its poles a and 
d (being always 90 degrees from the highest eleva- 
tions) in the arctic and antarctic circles ; and there- 
fore it is plain, that at these circles there is but one tide 

Kk 



Of the Tides. 



PLATE 
IX. 



of flood and one of ebb, in the lunar day. For, when the 
point a revolves half round to />, in 12 lunar hours it 
Fi - 1V - has a tide of flood; but when itcomes tothe same point 
a again in 12 hours more, it has the lowest ebb. In 
seven days afterward, the Moon M comes to the 
equinoctial circle, and is over the equator E Q, when 
both elevations describe the equator ; and in both 
hemispheres, at equal distances from the equator, 
the tides are equally high in both parts of the lunar 
day. The whole phenomena being reversed, when 
Fig. v. the Moon has south declination, to what they W 7 ere 
when her declination was north, require no farther 
description. 

305. In the three last-mentioned figures, the earth 
is orthographically projected on the plane of the me- 
ridian ; but in order to describe a particular pheno- 
menon, we now project it on the plane of the ecliptic, 
rig. vi. Let HZO A'be the earth and sea, FE D the equa- 
tor, T the tropic of Cancer, C the arctic circle, P 
the north pole, and the curves 1, 2, 3, &c. 24 meri- 
dians, or hour-circles, intersecting each other in the 
When poles; AGMis the Moon's orbit, S the Sun, M 
are equal- tne Moon, Zthe water elevated under the Moon, and 
ly high in JVthe opposite equal elevation. As the lowest parts 

da 6 "the 6 of tlie water are ahva } TS 90 degrees from the highest, 
arrive aT when the Moon is in either of the tropics (as at M) 
unequal ^ e l ev ation Z is oil the tropic of Capricorn, and the 

intervals . , , r /-< 

of time ; opposite elevation N on the tropic of Lancer ; the 
andsofce low- water circle HC touches the polar circles at 
C, and the high- water circle E TP 6 goes over 
the poles at P, and divides every parallel of latitude 
into two equal segments. In this case, the tides upon 
every parallel are alternately higher and lower; but 
they' return in equal times : the point T, for example, 
' on the tropic of Cancer (where the depth of the tide 
is represented by the breaclth of the dark shade) has 
a shallower tide of flood at T, than when it revolves 
half round from thence to 6, according to the order 



Of the Tufa. 257 

of the numeral figures ; but it revolves as soon from 
6 to T^as it did from Tto 6. When the Moon is 
in the equinoctial, the elevations Z and A* are trans- 
ferred to the equator at and //, and the high and 
low- water circles are got into each other's former 
places; in which case the tides return in unequal 
times, but arc equally high ii* parts of the lunar day : 
for a place at 1 (under D] revolving as formerly, goes 
sooner from 1 to 11 (under F) than from 11 to 1, 
because the parallel it describes is cut into unequal 
segments by the high- water circle IICO : but the 
points 1 and 11 being equidistant from the pole of 
the tides at C, which is directly under the pole of 
the Moon's orbit MGA, the elevations are equally 
high in both parts of the day. 

306. And thus it appears, that as the tides are go- 
verned by the Moon, they must turn on the axis of 
the Moon's orbit, which is inclined 23~ degrees to 
the Earth's axis at a mean state : and therefore the 
poles of the tides must be so many degrees from the 
poles of the Earth, or in opposite points of the polar 
circles, going round these circles in every lunar day. 
It is true, that according to Fig. IV. when the Moon 
is vertical to the Equator -ECQ, the poles of the 
tides seem to fall- in with the poles of the world A" 
and S; but when we consider that FGH is under 
the Moon's orbit, it will appear, that when the Moon 
is over //, in the tropic of Capricorn, the north pole 
of the tides (which can be no more than 90 degrees 
from under the Moon) must be at C in the arctic 
circle, not at P, the north pole of the Earth ; and 
as the Moon ascends from Hto G in her orbit, the 
north pole of the tides must shift from c to a in the 
arctic circle, and the south pole as much in the an- 
tarctic. 

It is not to be doubted, but that the Earth's quick 
rotation brings the poles of the tides nearer to the 



258 Of the Tides. 

poles of the world, than they would be if the Earth 
were at rest, and the Moon revolved about it only 
once a month; for otherwise the tides would be more 
unequal in their heights, and times of their returns, 
than we find they are. But how near the Earth's 
rotation may bring the poles of its axis and those of 
the tides together, or how far the preceding tides 
may affect those which follow, so as to make them 
keep up nearly to the same heights, and times of 
ebbing and flowing, is a problem more fit to be 
solved by observation than by theory. 



Those who have opportunity to makt obser- 
vations, and choose to satisfy themselves whether 
may ex- the tides are really affected in the above manner by 
latest tne different positions of the Moon, especially as to 
and least the unequal times of their returns, may take this ge- 
neral rule for knowing when they ought to be so af- 
fected. When the Earth's axis inclines to the Moon, 
the northern tides, if not retarded in their passage 
through shoals and channels, nor affected by the 
winds, ought to be greatest when the Moon is above 
the horizon, least when she is below it ; and quite 
the reverse when the Earth's axis declines from her : 
but in both cases, at equal intervals of time. When 
the Earth's axis inclines sidewise to the Moon, both 
tides are equally high, but they happen at unequal 
intervals of time. In every lunation, the Earth's 
axis inclines once to the Moon, once from her, and 
twice sidewise to her, as it does to the Sun every 
year : because the Moon goes round the ecliptic eve- 
ry month, and the Sun but once in a year. In sum- 
mer, the Earth's axis inclines toward the Moon when 
new ; and therefore the day-tides in the north ought 
to be highest, and night- tides lowest, about the 
change : at the full the reverse. At the quarters 
they ought to be equally high, but unequal in their 
returns ; because the Earth's axis then inclines side- 



Of the Tides. 295 

wise to the Moon. In winter, the phenomena are 
the same at full Moon as in summer at new. In au- 
tumn, the Earth's axis inclines sidewise to the Moon 
when new and full ; therefore the tides ought to be 
equally high, and unequal in their returns at these 
times. At the first quarter, the tides of flood should 
be least when the Moon is above the horizon, great- 
est when she is below it; and the reverse at her third 
quarter. In spring, the phenomena of the first quar- 
ter answer to those of the third quarter in autumn ; 
and vice versa. The nearer any time is to either of 
these seasons, the more the tides partake of the phe- 
nomena of these seasons ; and in the middle between 
any two of them, the tides are at a mean state be- 
tween those "Df both. 

308. In open seas, the tides rise but to very small Why the 
heights in proportion to what they do in wide-mouth- ^erln 
ed rivers, opening in the direction of the stream of rivers than 
tide. For, in channels growing narrower gradually, in the se * 
the water is accumulated by the opposition of the 
contracting bank. Like a gentle wind, little felt on 

an open plane, but strong and brisk in a street; es- 
pecially if the wider end of the street be next the 
plane, and in the way of the wind. 

309. The tides are so retarded in their passage The tides 
through different shoals and channels, and otherwise ^diilian- 
so variously affected by striking against capes and ces of the 
headlands, that to different places they happen at all ]^ n the 
distances of the Moon from the meridian ; conse- meridian 
quently at all hours of the lunar day. The tide pro- a * t di ^ c r e " s 
pagated by the Moon in the German ocean when and P why. S ' 
she is three hours past the meridian, takes 12 hours 

to come from thence to London-bridge ; where it ar- 
rives by the time that a new tide is raised in the 
ocean. And therefore when the Moon has north de- 
cimation, and we should expect the tide at London 
to be greatest when the Moon is above the horizon, 
we find it is least; and the contrary when she has 



260 Of the Tides. 

south declination. At several places it is high-water 
three hours before the Moon comes to the meridian ; 
but that tide which the Moon pushes as it were be- 
fore her, is only the tide opposite to that which was 
raised by her when she was nine hours past the op- 
posite meridian. 

The water 310. There are no tides in lakes, because tbey 
hi iakes! 6Sare generally so small, that when the Moon is verti- 
cal she attracts every part of them alike, and there- 
fore by rendering all the water equally light, no part 
of it can be raised higher than another. The Medi- 
terranean and Baltic seas have very small elevations, 
because the inlets by which they communicate with 
the ocean are so narrow, that they cannot in so short 
a time receive or discharge enough to raise or sink 
their surfaces sensibly. 

The Moon 311. Air being lighter than water, and the sur- 
tkies S inthe^ ace ^ ^ e atm osphere being nearer to the Moon 
air. than the surface of the sea, it cannot be doubted 
that the Moon raises much higher tides in the air 
than in the sea. And therefore many have wondered 
why the mercury does not sink in the barometer 
when the Moon's action on the particles of air makes 
them lighter as she passes over the meridian. But 
Wh the we must consider, that as these particles are render- 
mercury ed lighter, a greater number of them is accumulated, 
in the bar- un til the deficiency of gravity be made up by the 
n^Tlffec*. height of the column ; and then there is an eqmli- 
edbythe brium, and consequently an equal pressure upon the 
mercury as before ; so that it cannot be affected by 
the aerial tides. 



Of Eclipses. 261 



CHAP. XVIII. 

Of Eclipses: Their Number and Periods. A large 
Catalogue of Ancient and Modern Eclipses. 

VERY planet and satellite is illuminated A shadow 

by the Sun, and casts a shadow toward wliat * 
that point of the heavens which is opposite to the 
Sun. This shadow is nothing but a privation of light 
in the space hid from the Sun by the opaque body 
that intercepts his rays. 

313. When the Sun's light is so intercepted by Eclipses 
the Moon, that to any place of the Earth the Sun n ^ MOOIJ 
appears partly or wholly covered, he is said to un- what. 
dergo an eclipse ; though, properly speaking, it is 
only an eclipse of that part of the Earth where the 
Moon's shadow or * penumbra falls. When the 
Earth comes between the Sun and Moon, the Moon 
falls into the Earth's shadow ; and having no light 
of her own, she suffers a real eclipse from the in- 
terception of the Sun's rays. When the Sun is 
eclipsed to us, the Moon's inhabitants on the side 
next the Earth (if any such inhabitants there be) see 
her shadow like a dark spot travelling over the Earth, 
about twice as fast as its equatorial parts move, and 
the same way as they move. When the Moon is 
in an eclipse, the Sun appears eclipsed to her, total 
to all those parts on which the Earth's shadow falls, 
and of as long continue as they are in the shadow. 

3 14. That the Earth is spherical (for the hills take A proof 
off no more from the roundness of the Earth, than that the 



grains of dust do from the roundness of a common r and 



arc 

globular 

* The penumbra is a faint kind of shadow all round the perfect bodies. 
shadow of the planet or satellite, and will be more fully explained 
bv and b\\ 



262 Of Eclipses. 

globe) is evident from the figure of its shadow oil 
the Moon ; which is always bounded by a circular 
line, although the Earth is incessantly turning its dif- 
ferent sides to the Moon, and very seldom shews the 
same side to her in different eclipses, because they 
seldom happen at the same hours. Were the Earth 
shaped like a round flat plate, its shadow would only 
be circular when either of its sides directly faced the 
Moon ; and more or less elliptical as the Earth hap- 
pened to be turned more or less obliquely toward the 
Moon when she is eclipsed. The Moon's different 
phases prove her to be round, 254 ; for as she 
keeps still the same side toward the Earth, if that 
side were flat, as it appears to be, she would never 
be visible from the third quarter to the first ; and 
from the first quarter to the third, she would appear 
as round as when we say she is full : because at the 
end of her first quarter the Sun's light would come 
as suddenly on all her side next the Earth, as it does 
on a flat wall, and go off as abruptly at the end of 
her third quarter, 
and that 315. If the Earth and Sun were of equal magni- 

the Sun is tudes.the Earth's shadow would be infinitely extend- 
much Dig- - , . r . ,. J , . 

gertban ed, and every where ot the same diameter; and the 
the Earth, planet Mars, in either of its nodes, and opposite to the 
Moon e Sun, would be eclipsed in the Earth's shadow. Were 
much less, the Earth bigger than the Sun, its shadow would in- 
crease in bulk the farther it extended, and would 
eclipse the great planets Jupiter and Saturn, with all 
their moons, when they were opposite to the Sun. 
But as Mars in opposition never falls into the Earth's 
shadow, although he is not then above 42 millions 
of miles from the Earth, it is plain that the Earth is 
much less than the Sun; for otherwise its shadow 
could not end in a point at so small a distance. If 
the Sun and Moon were of equal magnitude, the 
Moon's shadow would go on to the Earth with an 
equal breadth, and cover a portion of the Earth's sur- 



Of Eclipses. 263 

face more than 2000 miles broad, even if it fell di- 
rectly against the Earth's centre, as seen from the 
Moon; and much more it it fell obliquely on the 
Earth : but the Moon's shadow is seldom 150 miles 
broad at the Earth, unless when it falls very oblique- 
ly on it in total eclipses of the Sun. In annular 
eclipses, the Moon's real shadow ends in a point at 
some distance from the Earth. The Moon's small 
distance from the Earth, and the shortness of her 
shadow, prove her to be less than the Sun. And 
as the Earth's shadow is large enough to cover the 
Moon, if her diameter were three times as large as 
it is (which is evident from her long continuance in 
the shadow when she goes through its centre) it is 
plain that the Earth is much larger than the Moon. 

316. Though all opaque bodies on which the Sun The pri- 
shines have their shadows, yet such is the bulk of * r ypj^j' 
the Sun, and the distances of the planets, that the eclipse 
primary planets can never eclipse one another. A one ano- 
primary can eclipse only its secondaries or be eclips- 
ed by them ; and never but when in opposition to, 

or conjunction with, the Sun. The Sun and Moon 
are so every month : whence one may imagine tkat 
these two luminaries should be eclipsed every month. 
But there are few eclipses in respect to the number 
of new and full Moons ; the reason of which we 
shall now explain. 

317. If the Moon's orbit were coincident with Why 
the plane of the ecliptic, in which the Earth always ^few"^ 
moves, and the Sun appears to move, the Moon's eclipses, 
shadow would fall upon the Earth at every change, 

and eclipse the Sun to some parts of the Earth. In 
like manner, the Moon would go through the raid- 
die of the Earth's shadow, and be eclipsed at every 
full ; but with this difference, that she would be 
totally darkened for above an hour and an half; where- 
as the Sun never was above four minutes totally 
eclipsed by the interposition of the Moon. Butone The 
half of the Moon's orbit is elevated 5~ degrees above Moon's 

T i nodes, 



264 Of Eclipses. 

the ecliptic, and the other half as much depressed 
below it : consequently the Moon's orbit intersects 
the ecliptic in two opposite points called the Moon's 
nodes, as has been already taken notice of, 288. 
When these points are in a right line with the cen- 
tre of the Sun at new or full Moon, the Sun, Moon, 
and Earth, are all in a right line ; and if the Moon 
be then new, her shadow falls upon the Earth ; if 
Limits of full, the Earth's shadow falls upon her. # When the 
echpses. Sun and Moon are more than 17 degrees from ei- 
ther of the nodes at the time of conjunction, the 
Moon is then generally too high or too low in her 
orbit to cast any part of her shadow upon the Earth. 
And when the Sun is more than twelve degrees from 
either of the nodes at the time of full Moon, the 
Moon is generally too high or too low in her orbit to 
go through any part of the Earth's shadow : and in 
both these cases there will be no eclipse. But when 
the Moon is less than 17 degrees from either node 
at the time of conjunction, her shadow or penum- 
bra falls more or less upon the Earth, as she is: more 
or less within this limit.- And when she is less 
than 12 degrees from either node at the time of op- 
position, she goes through a greater or less portion 
of the Earth's shadow as she is more or less within 
this limit. Her orbit contains 360 degrees, of which 
17, the limit of solar eclipses on either side of the 
nodes, and 12, the limit of lunar eclipses, are but 
small portions : and as the Sun commonly passes by 
the nodes but twice in a year, it is'no wonder that 
we have so many new and full Moons without 
eclipses. 



* Tliis admits of some variation : for in apogeal eclipses, the 
solar limit is hut 16 1-2 degrees ; and in perigeal eclipses, it is 18 1-3. 
When tiie full Moon is in her apogee, she will be eclipsed if she be 
within 10 1-2 degrees of the node ; and when she is full in her pe- 
rigee, she will be eclipsed if she be within 12-^ degrees of the 
node. 



Of Eclipses. 265 

To illustrate this, let A B C D be the eliptic, * LATE 
It S T 7 a circle lying in the same plane with the 
ecliptic, and VWXYfat Maoris orbit, all thrown Fi - L 
into an oblique view, which gives them an elliptical 
shape to the eye. One half of the Moon's orbit, as 
V W X, is always below the ecliptic, and the other 
half X Y 7 above it. The points Tand X, where 
the Moon's orbit intersects the circle R S T U, 
which lies even with the ecliptic, are the Mooris 
nodes ; and a right line, as X]P 9 drawn from one Lines of 
to the other, through the Earth's centre, is called the nodes * 
the Line of the nodes, which is carried almost pa- 
rallel to itself round the Sun in a year. 

If the Moon moved round the Earth in the orbit 
R S T U, which is coincident with the plane of the 
ecliptic, her shadow would fall upon the Earth eve- 
ry time she is in conjunction with the Sun, and at 
every opposition she would go through the Earth's 
shadow. Were this the case, the Sun would be 
eclipsed at every change, and the Moon at every 
full, as already mentioned. 

But although the Moon's shadow A" must fall up- 
on the Earth at a, when the Earth is at E, and the 
Moon in conjunction with the Sun, at i, because 
she is then very near one of her nodes, and at her 
opposition n, she must go through the Earth's sha- 
dow /, because she is then near the other node ; yet, 
in the time that she goes round the Earth to her next 
change according to the order of the letters X Y V 
W, the Earth advances from E to c, according to 
the order of the letters E F G If, and the line of 
the nodes VEX being carried nearly parallel to it- 
self, brings the point /of the Moon's orbit in con- 
junction with the Sun at that next change ; and then 
the Moon being at/ is too high above the ecliptic to 
cast her shadow on the Earth : and as the Earth 
is still moving forward, the Moon at her next op- 
position will be at g, too far below r the ecliptic to 



266 Of Eclipses. 

PLATE g O through any part of the Earth's shadow; for by 
that time the point g will be at a considerable dis- 
tance from the Earth as seen from the Sun. 

When the Earth comes to F, the Moon in con- 
junction with the Sun Z is not at &, in a plane coinci- 
dent with the ecliptic, but above it at Y in the high- 
est part of her orbit : and then the point b of her 
shadow goes far above the Earth (as in Fig. II. 
rig. i. which is an edge-view of Fig. I.) The Moon in her 
* nd IL next opposition is not at o (Fig. I.) but at W, where 
the Earth's shadow goes far above her (as in Fig. 
II.) In both these cases the line of the nodes V FX 
(Fig. I.) is about 90 degrees from the Sun, and both 
luminaries are as far as possible from the limits of 
eclipses. 

When the Earth has gone half round the eclip 
tic from E to G, the line of the nodes V G X is 
nearly, if not exactly, directed towards the Sun at 
Z ; and then the new Moon / casts her shadow P 
on the Earth G; and the full Moon/? goes through 
the Earth's shadow L ; which brings on eclipses 
again, as when the Earth \vas at E. 

When the Earth comes to H, the new Moon falls 
not at m in a plane coincident with the ecliptic CD, 
but at JV in her orbit below it : and then her sha- 
dow Q (see Fig. II.) goes far below the Earth. At 
the next full she is not at q (Fig. I.) but at Fin her 
orbit 5^ degrees above q, and at her greatest height 
above the ecliptic CD; being then as far as possi- 
ble, at any opposition, from the Earth's shadow M 
(as in Fig. II.) 

So, when the Earth is at E and G, the Moon is 
about her nodes at new and full ; and in her greatest 
north and south declination (or latitude as it is gene- 
rally called) from the ecliptic at her quarters: but 
when the Earth is at F or H, the Moon is in her 
greatest north and south declination from the ecliptic 
fit new and full, and in the nodes about her quarters, 



Of Eclipses. 267 



PLATE 
X. 



318. The point X where the Moon's orbit cros- 
ses the ecliptic is called the ascending node, because 

the Moon ascends from it above the ecliptic : and JJj, n s 
the opposite point of intersection F"\s called the de- ascending 
scending ?iode, because the Moon descends from it 
below the ecliptic. When the Moon is at F in the 
highest point of her orbit, she is in her greatest 
north latitude : and when she is at /Fin the lowest an d south 
point of her orbit, she is in her greatest south lati- latitude. 
tude. 

319. If the line of the nodes, like the Earth's ax- The nodes 
is, were carried parallel to itself round the Sun, {^ d j*" 
there would be just half a year between the conjunc- motion, 
lions of the Sun and nodes. But the nodes shift 
backward, or contrary to the Earth's annual motion, 

19- degrees every year; and therefore the same Fjg> L 
node comes round to the Sun 19 days sooner every 
year than on the year before. Consequently, from 
the time that the ascending node X (when the Earth 
is atJ passes by the Sun, as seen from the Earth, 
it is only 173 days (not half a year) till the descend- 
ing node V passes by him. Therefore, in whatever 
time of the year we have eclipses of the luminaries the eciips- 
about either node, we may be sure that in 173days^ e s r oon ^ r 
afterward, we shall have eclipses about the other than they 
node. And when at any time of the year the line of ^ h a ( J d be 
the nodes is in the situation V G Jf, at the same time nodes had 
next year it will be in the situation r G s ; the as- not f uch a 
cending node having gone backward, that is, contra- m 
ry to the order of signs, from X to s, and the de- 
scending node from Ftor-, each 19-i degrees. At 
this rate the nodes shift through all the signs and de- 
grees of the ecliptic in 18 years and 225 days; in 
which time there would always be a regular period 
of eclipses, if any complete number of lunations 
were finished without a fraction. But this never 
happens ; for if both the Sun and Moon should 
start from a line of conjunction with either of the 
nodes in any point of the ecliptic, the Sun would 



268 Of Eclipses. 

perform 18 annual revolutions and 222 degrees over 
and above, and the Moon 230 lunations and 85 de- 
grees of the 231st, by the time the node came round 
to the same point of the ecliptic again; so that the 
Sun would then be 138 degrees from the node, and 
the Moon 85 degrees from the Sun. 

A period 320. But, in 223 mean lunations, after the Sun, 
o^ec ips- ^| oon ^ am j no( j eS) have been once in a line of con- 
junction, they return so nearly to the same state 
again, as that the same node, which was in conjunc- 
tion with the Sun and Moon at the beginning of the 
first of these lunations, will be within 28' 12" of a 
degree of a line of conjunction with the Sun and 
Moon again, when the last of these lunations is 
completed. And therefore, in that time, there will 
be a, regular period of eclipses, or return of the 
same eclipse for many ages. In this period, (which 
was first discovered by the Chaldeans J there are 18 
Julian years 11 days 7 hours 43 minutes 20 seconds, 
when the last day of February in leap-years is four 
times included : but when it is five times included, 
the period consists of only 18 years 10 days 7 hours 
43 minutes 20 seconds. Consequently, if to the 
mean time of any eclipse, either of the Sun or 
Moon, you add IS Julian years 11 days 7 hours 43 
minutes 20 seconds, when the last day of Februa- 
ry in leap-years comes in four times, or a day less 
when it comes in five times, you will have the mean 
time of the return of the same eclipse. 

But the falling-back of the line of conjunctions 
or oppositions of the Sun and Moon 2J8' 12" ^vith 
respect to the line of the nodes in every period, will 
wear it out in process of time ; and after that, it will 
not return again in less than 12492 years. These 
eclipses of the Sun, which happen about the ascend- 
ing node, and begin to come in at the north pole 
of the Earth, will go a little southerly at each re- 
turn, till they -go quite off the Earth at the south 









Of Eclipses. 269 

pole ; and those which happen about the descending 
node, and begin to come in at the south pole of the 
Earth, will go a little northerly at each return, till 
at last they quite leave the Earth at the north pole. 

To exemplify this matter, we shall first consider 
the Sun's eclipse, March 21st old stile (April 1st 
new stile) A. D. 1764, according to its mean revolu- 
tions, without equating the times, or the Sun's dis- 
tance from the node ; and then according to its true 
equated times. 

This eclipse fell in the open space at each return, 
quite clear of the Earth, from the creation till 
A. D. 1295, June 13th old stile, at 12 h. 52 m. 59 
sec. post meridiem^ when the Moon's shadow first 
touched the Earth at the north pole ; the Sun being 
then 17 48' 27" from the ascending node. In 
each period since that time, the Sun has come 28' 
12" nearer and nearer the same node, and the 
Moon's shadow has therefore gone more and more 
southerly. Indie year 1962, July 18th old stile, at 
10 h. 36 m. 21 sec. p. m. when the same eclipse will 
have returned 38 times, the Sun will be only 24' 
45" from the ascending node, and the centre of the 
Moon's shadow will fall a little northward of the 
Earth's centre. At the end of the next following 
period, A. D. 1980, July 28th old stile, at 18 h. 
19 m. 41 sec. p. m. the Sun will have receded back 
3' 27" from the ascending node, and the Moon will 
have a very small degree of southern latitude, which 
will cause the centre of her shadow to pass a very 
small matter south of the Earth's centre. After 
which, in every following period, the Sun will be 
28' 12" farther back from the ascending node than 
in the period last before ; and the Moon's shadow- 
will go still farther and farther southward, un- 
til September 12th old stile, at 23 h. 46 m. 22 sec. 
p. m. A. D. 2665; when the eclipse will have com- 
pleted its 77th periodical return, and will go quite 
off the Earth at the south pole (the Sun being then 



270 Of Eclipses. 

17 55' 22" back from the node) ; and it cannot 
come in from the north pole, so as to begin the same 
course over again, in less than 12492 years after- 
ward. And such will be the case of every other 
eclipse of the Sun : for, as there is about 1 8 degrees 
on each side of the node within which there is a 
possibility of eclipses, their whole revolution goes 
through 36 degrees about that node, which, taken 
from 360 degrees, leaves remaining 324 degrees for 
the eclipses to travel in expamum. And as these 
36 degrees are not gone through in less than 77 pe- 
riods, which take up 1388 years, the remaining 324 
degrees cannot be so gone through in less than 12492 
years. For as 36 is to 1388, so is 324 to 12492. 

321. In order to shew both the mean and true 
times of the returns of this eclipse, through all its 
periods, together with the mean anomalies of the 
Sun and Moon at each return, and the mean and 
true distances of the Sun from the Moon's ascend- 
ing node, and the Moon's true latitude at the true 
time of each new Moon, I have calculated the fol- 
lowing tables for the sake of those who may choose 
to project this eclipse at any of its returns, accord- 
ing to the rules laid down in the X Vth chapter ; and 
have by that means taken by much the greatest part 
of the trouble off their hands. All the times are ac- 
cording to the old stile, for the sake of a regularity 
which, with respect to the nominal days of the 
months, does not take place in the new : but by add- 
ing the days difference of stile ; they are reduced to 
the times which agree with the new stile. 

According to the mean (or supposed) equable mo- 
tions of the Sun, Moon, and nodes, the Moon's 
shadow in this eclipse would have first touched the 
Earth at the north pole, on the 13th of June, A. D. 
1295, at 12 h. 52m. 59 sec. past noon on the meri- 
dian of * London; and would quite leave the Earth at the 




Of Eclipses. 271 

south pole, on the 12th of September, A. D. 2665, 
.at 23 h. 46 m. 22 sec. past noon, at the completion 
of its 77th period; as shewn by the first and second 
tables. 

But, on account of the true or unequable motions 
of the Sun, Moon, and nodes, the first coming in 
of this eclipse, at the north pole of the .^arth, was 
on the 24th of June, A. D. 1313, at 3 h. 57 m. 3 
sec. past noon ; and it will finally leave the earth at 
the south pole, on the 31st of July, A. D. 2593, at 
10 h. 25 m. 31 sec. past noon, at the completion of 
its 72d period ; as shewn by the third and fourth ta- 
bles. So that the true motions do not only alter 
the true times from the mean, but they also cut off 
five periods from those of the mean returns of this 
eclipse. 



Mm 



272 



Of E 



<J TABLE I. The mean time of New Afoon, with the mean Anomalies of the ? 
Sun and Moon, and the Sun's mean Distance from the Moon's Ascending * 
J&rde, at the mean time of each periodical Return of the Sun's Eclifise, 
March 21st, I764 n /rom its first coming ufion the Earth since the crea- 
ation, till it falls right against the Earth's centre, according to the Old 



Periodical 
1 Returns. 


f o 


Meantime of 
New 'Moon. 


Sun's mean 
Anomaly. 


Moon's mean KSun'smeandisf ^ 
Anomaly, 'from the Node s 


Month. D. H. M.S. 


s. 0. ' " 


-s. o. ' " 


s. 0. ' S 





1277 


June 2 5 9 39 


il 17 57 41 


1 26 31 42 


18 16 40 S 


1 


1295 


June 13 12 52 59 


11 28 27 38 


1 23 40 19 


17 48 27 


o 


1313 


June 23 20 36 19 


8 57 35 


1 20 48 56 


17 20 15 


3 


1331 


July 5 4 19 30 


19 27 32 


1 17 57 35 


16 52 2 


4 


1349 


July 15 12 2 59 


29 57 29 


1 15 6 10 


16 23 50 * 


5 


136-7 


July 26 19 46 19 


1 10 27 26 


12 14 47 


15 55 37 \ 


6 


1385 


: \ug. 6 3 29 39 


1 20 57 2"3 


9 23 24 


15 27 25 


7 


1403 


Aug. 17 11 12 59 


2 1 27 20 


6 32 1 


14 59 12 


8 


1421 


Aug. 27 18 56 19 


2 11 57 17 


3 40 38 


14 31 


9 


1439 


Sept. 8 2 39 39 


2 22 27 14 


1 49 15 


14 2 47 


LO 


1457 


Sept. 18 10 2 59 


3 2 57 11 


27 57 52 


13 34 35 


LI 


^1475 


Sept. 29 18 6 19 


3 13 27 8 


25 6 29 


13 6 22 


L2 


1493 


Oct. 10 1 49 39 


3 23 57 5 


22 15 6 


12 38 10 


13 


1511 


Oct. 21 9 32 59 


4 4 27 2 


19 23 43 


12 9 57 


14 


1529 


Oct. 31 17 16 19 


4 14 56 59 


16 32 20 


: 11 41 45 J 


15 


154:7 


Nov. 12 59 40 


4 25 26 56 


13 40 57 


Oil 13 32 ? 


16 


150.) 


Nov. 22 8 43 


5 5 56 53 


10 49 34 


10 45 20 J 


17 


1583 


Dec. 3 16 26 20 


5 16 26 50 


7 58 9 


10 17 7 \ 


8 


1601 


Dec. 14 9 40 


5 26 56 47 


O 5 6 48 


9 48 55 J 


9 


1619 


Dec. 25 7 53 


6 7 26 44 


2 15 25 


O 9 20 42 ^ 


10 


1638 


Jan. 4 15 36 20 


6 17 56 41 


11 29 24 2 


8 52 30 > 


11 


1656 


Jan. 15 23 19 40 


6 28 26 38 


11 26, 32 39 


8 24 17 S 


11 


1674 


Jan. 26 7 3 


7 8 56 35 


1 23 41 14 


7 56 5 


J3 


1692 


Feb. 6 14 46 20 


7 19 26 32 


20 49 53 


7 27 52 


14 


1710 


Feb. 16 22 29 40 


7 29 56 29 


17 58 30 


6 59 40 Jj 


15 


1728 


Feb. 28 6 13 


8 10 26 26 


15 7 7 


6 31 27 ? 


-6 


1746 


Mar. 10 13 56 20 


8 20 56 23 


12 15 44 


6 3 15 > 


17 


1764 


Mar. 20 21 39 40 


9 1 26 20 


9 24 21 


5 35 2S 


HB 


1782 


Apr. 1 5 23 


9 11 56 17 


6 32 58 


5 6 50 Jj 


9 


1800 


Apr. 11 13 6 20 


9 22 26 14 


3 41 35 


4 38 37 S 





1818 


Apr. 22 20 49 40 


10 2 56 11 


50 12 


4 10 25 \ 


1 


1836 


Vlay 3 4 33 


10 13 26 8 


10 27 58 49 


3 42 12 Ij 


2 


1854 


May 14 12 16 20 


10 23 56 5 


10 25 7 26 


3 14 S 


3 


1872 


May 24 19 59 40 


11 4 26 2 


10 22 16 3 


2 45 47 !j 


4 


1890 


June 5 3 43 


11 14 55 59 


10 19 24 40 


2 17 35 S 


5 


1908 


June 15 11 26 20 


11 25 25 56 


10 16 33 17 


1 49 22 


6 


1926 


June 26 19 9 40 


5 55 53 


10 13 41 54 


1 21 10 S 


7 


1944 


July 7 2 53 


16 25 50 


10 10 50 31 


52 57 ^ 


8 


1962 


July 18 10 36 21 


26 55 47 


10 7 59 8 


24 45 > 

JL. 



Of Eclipses. 



TABLE II. The mean time of New Moon, with the mean Anomalies of the S 
Sun and Moon, and the Sun's mean Distance from the Moon's dscend- s 
ing Node, at the mean Time of each periodical Return of the Sun' a S 
Eclipse, March 21f, 1764, from the mean Time of its falling riifht 

j J^ . f X~ .',,-.* * O O } 



the Julian, or Old Style. ^ 


|l 


2T ?' 


Mean time oi 
New Moon. 


Sun's mean 
Anomaly. 


Moon's mean 
Anomaly. 


Sun's mean (list. 
from the Node. ^ 


if 


Month. D.H.M.S. 


s. 0. ' ' 


s. o. ' " 


s 0. ' " S 


^ 


19b- 


ju,y 28 18 19 41 


1 7 *o 44. 1U 5 7 45 


1 1 -j 5o 38 Jj 


40 


1998 


Aug, 9231 


1 17 55 41 10 2 16 22 


11 29 23 20 S 


41 


2016 


Aug. 19 9 46 2 


I 28 25 38 9 29 24 59 


11 29 8 


42 


2034 


Aug. SO 17 29.41 


2 8 53 36 9 26 33 36 


11 28 31 55 S 


43 


3052 


Sept. 10 1 13 1 


2 19 25 33 9 23 42 13 


1128 343 Ij 


44 


2070 


Sept. 21 8 56 21 


2 29 55 32 9 20 50 50 


11 27 35 30 S 


45 


2088 


Oct. 1 16 39 41 


3 10 25 27 9 17 59 27 


11 27 7 18 


46 


2106 


Oct. 13 23 1 


3 20 55 24 9 15 8 4 


11 26 39 5 S 


47 


2124 


Oct. 2.3 8 621 


4 1 25 21 9 12 16 41 


11 26 10 53 Jj 


48 


2142 


Nov. 3 154941 


4 1 1 55 18 9 9 25 18 


11 25 42 40 S 


49 


2160 


Nov. 13 23 31 1 


4 22 25 15 9 6 33 36 


11 25 14 28 Jj 


50 


2178 


Nov, 25 71621 


5 2 55 12 9 3 42 33 


11 24 46 15 S 


51 


2196 


Dec. 5 14 59 41 


5 13 25 9 9 51 10 


11 24 18 3 % 


52 


2214 


De<:. 16 22 43 1 


5 23 55 7 8 27 59 47 


11 23 49 50 S 


53 ' 


2232 


Dec. 27 6 26 21 


6 4 25 4[ 8 25 8 24 


11 23 21 38 


54 


2251 


Jan. 7 14 9 41 


6 14 55 1 


8 22 17 1 


11 22 53 25 S 


55 


2269 


Jan. 17 21 53 1 


6 25 24 58 


8 19 2,5 38 


11 22 15 13 ^ 


56 


2287 


Jan, 29 5 36 21 


7 5 54 55 


8 d6 31 15 


11 21 57 S 


57 


2305 


Feb. -8 13 19 41 


7 16 24 52 


8 13 42 52 


11 21 28 48 5 


58 


2323 


Feb. 19 21 3 1 


7 26 54 49 


8 10 51 29 


11 21 35 S 


59 


2341 


Mar. 2 44621 


8 7 24 46 


8806 


11 20 32 23 !j 


60 


2359 


Mar. 13 12 29 42 


8 17 54 43 


8 5 8 43 


11 20 4 10 S 


61 


2377 


Mar. 23 20 13 2 


8 28 24 40 


8 2 17 20 


11 19 35 58 ^ 


62 


2395 


Apr. 4 3 56 22 


9 8 54 37 


7 29 25 27 


11 19 7 45 S ' 


63 


2413 


Apr. 14 11 39 42 


9 19 24 34 


7 26 34 34 


11 18 39 S3 Jj 


64 


2431 


Apr. 2.5 19 23 2 


9 29 54 31 


7 23 43 11 


11 18 11 20 S 


65 


2449 


May 6 3 22 


10 10 24 28 


7 20 51 48 


11 17 43 8 : 


66 


2467 


May 17 10 49 42 


10 20 54 25 


7 18 25 


11 17 14 54 S '' 


67 


2485 


May 27 18 33 2 


11 1 24 22 


7 15 9 2 


11 16 46 43 ? 


68 


2503 


June 8 21622 


11 11 54 19 


7 12 17 39 


11 16 18 31 S 


69 


2521 


June 18 9 59 42 


11 22 24 17 


7 9 26 16 


11 15 50 18 Ij 


70 


2539 


June 29 17 43 2 


2 54 14 


7 6 34 53 


11 15 22 6 < 


71 


2557 


July 10 1 26 22 


13 24 11 


7 3 44 30 


11 14 53 54 ^ ! 


72 


2575 


July 21 9 9 42 


23 54 8 


7 52 7 


11 14 25 41 V 


73 


2593 


July 31 16 53 2 


1 4 24 5 


6 28 44 


11 13 57 28 y 


74 


2611 


Aug. 12 36 22 


1 14 54 2 


6 25 921 


11 13 29 16 S 


75 


2629 


Aug. 22 8 19 42 


1 25 23 59 


6 22 17 58 


11 13 1 3 Jj 


76 


2647 


Sept. 2 16 3 2 


2 5 53 56 


6 19 26 35 


11 12 32 51 S 


77 


2665 


Sept. 12 23 46 22 


2 16 23 53 


6 16 35 12 


11 12 4 38 ^ 



274 



Of Eclipses. 



S TABLE III. The true Time of New Moon, with the Sun's truc\ 


? Distance from the Moon's Ascending Node, and the Moon's true v> 


S Latitude, at the true Time of each periodical Return of the Sun's S 


^ Eclipse, March 2\st, Old Style, A. D. \7 64, from the Time o/J 


S itsjirst coining upon the Earth since the Creation till it falls J 


^ right against the Earth's Centre. ^ 


5 3F 


< 


True lime of 


>un'strueDist. 


Moon's true Lati- Jj 


< a S 
s s 

t a p.-. 


i 

WJ* ^ 


New Moon. 


rom the Node. 


tude North. 






t 


$ y ? 


.-" o 


Month.l). H.M. S. 


s. .0 ' " 


0. ' " Nor. S 


5 o 


i295 


June 13 12 54 32 


18 40 54 


1 33 45 N. A. s 


S i 


1313 


June 24 3 57 3 


17 20 22 


1 29 84 N. A. J 


5 2 


1331 


July 5 10 42 8 


16 29 35 


1 25 20 N. A. s 


J 3 


-1349 


July 15 17 14 15 


15 34 18 


1 20 45 N. A. 


; 4 


1367 


July 26 23 49 24 


14 46 8 


1 16 39 N. A.s 


$ * 


1385 


Aug. 6 6 41 17 


13 59 43 


2 12 43 N. A. S 


\ 6 


1403 


Aug. 17 13 32 19 


13 16 44 


1 9 3 N. A. s 


5 t 


1421 


Aug 27 20 30 17 


12 37 4 


1 5 42 N. A. S 


J 8 


4439 


Sept. 8 3 51 46 


12 1 54 


1 2 41 N. A. s 


5 9 


1457 


Sept 18 10 23 11 


11 30 27 


58 33 N. A. S 


5 io 


1475 


Sept. 29 17 57 7 


11 3 56 


57 43 N. A. s 


I'ii 


1493 


Oct. 16 1 44 3 


10 41 55 


55 49 N. A. 


$12 


1511 


Oct. 21 9 29 53 


10 25 11 


54 28 N. A. ^ 


$13 


1529 


Oct. 31 17 9 18 


10 11 27 


53 12 N. A. S 


5 


1547 


Nov. 12 51 25 


10 1 10 


52 19 N. A. < 


5 15 


1565 


Nov. 22 8 54 56 


9 52 49 


51 46 N. A. > 


i 


1583 


Dec. 3 16 48 17 


9 48 4 


51 11 N. A. ^ 


sir 


1601 


Dec. 4 51 5 


9 43 42 


50 49 N. A. J> 


$18 


1619 


Dec. 25 8 54 59 


9 40 23 


50 31 N. A. s 


I 19 


1638 


Jan. 4 16 56 1 


9 34 57 


50 3 N. A. S 


< 20 


1556 


Jan. 16 54 41 


9 29 24 


49 57 N. A. s 


$21 


1674 


Jan. 26 S 48 24 


9 19 44 


48 44 N. A. S 


\ 22 


1692 


Feb. 6 16 36 28 


9 8 5S 


47 49 N. A. s 


^ 23 


1710 


Feb. 17 8 37 


g 54 20 


46 44 N. A. S 


5 24 


.728 


Feb. 28 7 43 40 


S 34 53 


44 52 N. A. s 


^25 


1746 


Mar. 10 15 14 3- 


8 10 38 


42 46 N. A. S 


$26 


1764 


Mar. 20 22 30 26 


7 42 14 


40 18 N. A. s 


$27 


1782 


Apr. 1 5 37 4 


7 9 27 


37 28 N. A. S 


S 
S ^8 


1800|Apr. 11 12 36 38 


6 35 30 


34 31 N. A. <J 


S 29 


ISIS 


Apr. 22 19 27 34 


5 51 48 


30 43 N. A. S 


< 30 


1836 


May 3 2 12 7 


0555 


26 40 N. A. (J 


S31 


1854 


May 14 8 50 4C 


4 19 45 


22 42 N. A. S 


5 32 


1872 


May 24 15 28 15 


3 26 3 


018 IN. A. <J 


S33 


1890 


June 4 22 8 


2 35 5 


13 34 N. A. S 


S 34 


1908 


- r une 15 4 38 23 


1 41 43 


0854 N. A. -^ 


S 35 


192* 


June 26 11 13 5 


47 38 


4 10 N. A, s 



\ 



Moons, and between the Sun's mean and true distances from the 
node, the Moon's shadow falls even with the Earth's centre two 
periods sooner in this table than in the first. 



Of Eclipses. 



275 



**\, ' .-' 

S TABLE IV. The true Time of New Moon, with the Sun's true ^ 


S Distance from the Moon's Ascending Node, and the Moon's true s 


*> Latitude at each periodical Return of the Sun's E-clipse, March 


5 2lsf, Old Style, A. D. 1764, from its falling right against the S 


J Earth's centre, till it finally leaves the Earth. Jj 


^ T 4 ^ 




True Time of 


Sun's trueDist. 


Moon's true Lati- S 


C r^ rt 

> 


2* 

-> $^ 


Mew Moon 


from the Node. 


tude South. s, 


!i 


1. * 

0> 08 

r 1 " o_ 






s 


Month.D. H. M. S. 


s. ' " 


' " South. !j 


V b 6 


i*44 


Juiy 6 17 50 35 


11 29 55 28 


24 S. A. 


S37 


1962 


July 18 31 38 


11 29 2 35 


5 2 S. A. S 


S 38 


198C 


July 28 7 18 53 


11 28 11 32 


9 29 S. A. Jj 


39 


1998 


Aug. 8 14 12 22 


11 27 26 41 


13 25 S. A.S 


$40 


2016 


Aug. 18 21 14 53 


11 26 42 16, 


17 18 S. A. Jj 


541 


2034 


Aug. 30 4 25 45 


11 26 2 6 


20 48 S. A. S 


S42 


2052 


Sept. 9 11 45 17 


11 25 26 46 


23 53 S. A. ^ 


J 43 


2070 


:iept. 20 19 17 26 


11 24 55 4 


26 39 S. A. S 


^44 


2088 


Oct. 1 2 57 8 


11 24 27 43 


28 58 S. A. 


S45 


210r 


Oct. 12 10 47 39 


11 24 4 38 


031 2 S. A. S 


$46 


2124 


Oct. 22 18 37 40 


11 23 48 28 


32 26 S. A. Jj 


47 


2142 


Nov. 3 2 56 19 


11 23 35 11 


33 53 S. A. S 


S 48 


2160 


Nov. 13 11 11 20 


11 23 22 22 


34 42 S. A. Jj 


J 49 


2178 


Nov. 24 19 36 14 


11 23 18 57 


35 S. A. S 


!J 50 


2196 


Dec. 5449 


11 23 14 40 


35 22 S. A. 


S 51 


2214 


Dec. 16 12 35 48 


11 23 10 43 


35 43 S. A. S 


? 52 


2232 


Dec. 26 20 29 9 


11 23 6 47 


36 1 S. A. Jj 


S 5 3 


2251 


Jan. 7 5 42 9 


11 23 4 27 


36 16 S. A. S 


5 54 


2269 


Jan. 17 14 14 8 


11 23 41 


o 36 35 s. A. !; 


S 5 5 


2287 


Jan. 28 22 43 34 


11 22 53 58 


37 10 S. A. S 


u 


2305 


Feb. 8 7 8 30 


11 22 44 44 


37 59 S. A. lj 


S57 


2323 


Feb. 19 15 7 10 


11 22 31 1 


39 8 S. A. S 


5 58 


2341 


Mar. li 6 5 


11 22 17 46 


40 28 S. A. 


S 59 


2359 


Mar. 13 7 59 17 


11 21 55 29 


42 9 S. A. V 


S 60 


2377 


Mar. 23 15 51 59 


11 21 39 40 


43 41 S. A. ^ 


\H 


2395 


Apr. 3 23 45 7 


11 21 53 


46 58 S. A. S 


S S 62 


2413 


Apr. 14 7 32 40 


11 20 26 22 


49 48 S. A. !; 


!>63 


2431 


Apr. 25 15 12 57 


11 19 47 34 


53 17 S. A. S 


S 64 


2449 


May 5 22 45 14 


11 19 6 22 


56 5.0 S. A. t| 


S65 


2467 


May 17 6 17 30 


11 18 21 16 


1 40 S. A. S 


S 66 


2485 


May 27 13 46 29 


11 17 34 20 


4 42 S. A. ^ 


^67 


2503 


June 7 21 10 31 


11 16 43 17 


9 3 S. A. S 


3 63 


2521 


June 18 4 24 42 


11 15 51 48 


13 26 S. A. s 


S69 


2539 


June 29 11 58 46 


11 15 1 12 


17 43 S. A. S 


^70 


2557 


July 9 19 24 7 


11 14 9 13 


22 6 S. A. s 


s 71 


3575 


July 21 2 52 34 


11 13 19 22 


26 16 S. A. S 


S72 


2593 


July 31 10 25 31 


11 12 13 43 


31 44 S. A. Ij 


S 


2611 


\ug. 11 17 58 39 


11 11 45 13 


36 1 3 S. A. 


S By the true motions ol the Sun, Moon, and nodes, this eclipse S 


^ goes off the Earth four periods sooner than it would have done by Jj 


S mean equable motions. '^ 



276 Of Eclipses. 

From " To illustrate this a little farther, we shall exa- 

S^UT^'S " m " ie somc f th most remarkable circumstances 
disserta- " of the returns of the eclipse, which happened 

edi^es, " Jul y 14 > 1748 ab Ut n00n ' This ecli P se after 

printed 'at " traversing the voids of space from the creation, 

Condon, a t i as t began to enter the Terra Australia Incognita, 

C^VE, " about 88 years after the Conquest, which was the 

Sn the year" last of King STEPHEN'S reign; every Chaldean* 

" period it has crept more northerly, but was still 

" invisible in Britain before the year 1622; when 

" on the 30th of April it began to touch the south 

**- parts of England about 2 in the afternoon its cen- 

" tral appearance rising in the American South Seas, 

" and traversing Peru and the Amazons^ country, 

*' through the Atlantic ocean into Africa, and setting 

<c in the Ethiopian continent, not far from the begin- 

< { ning of the Red Sea, 

" Its next visible period was after three Chaldean 
" revolutions, in 1676, on the first of June, rising 
c< central in the Atlantic ocean, passing us about 9 
" in the morning, with four f digits eclipsed on the 
" under limb ; and setting in the gulph of Cochin- 
" china, in the East -Indies. 

" It being now near the solstice, this eclipse was 
" visible the very next return in 1694, in the even- 
" ing ; and in two periods more, which was in 1730, 
" on the 4th of July, was seen above half eclipsed 
* c just after sun-rise, and observed both at Ifittem- 
" burg in Germany, and Pekin in China, soon af- 
" ter which it went off. 

" Eighteen years more afforded us the eclipse 
" which feli on the 14th of July, 1748. 

" The next visible return will happen on July 25, 
u 1766, in the evening, about four digits eclipsed ; 

* The above period of 18 years, 11 days, 7 hours, 43 minutes, 20 

seconds, was found out by the Chaldeans, and by them called Saros. 

t A digit is the twelfth part of the diameter of the Sun, or Moon 



Of Eclipses. 277 

"and after two periods more, on August 16th, 
" 1802, early in the morning, about five digits, the 
" centre coming from the north frozen continent, by 
" the capes of Norway, through Tartary, China 
" and Japan , to the Ladrone islands, where it goes 
" off. 

" Again, in 1820, August 26, betwixt one and 
" two, there will be another great eclipse at London^ 
" about 10 digits , but happening so near the equi- 
" nox, the centre will leave every part of Britain to 
" the west, and enter Germany & Embden, passing 
" by Venice, Naples, Grand Cairo , and set in the 
" gulf of Bassora near that city. 

" It will be no more visible till 1874, when five 
" digits will be obscured (the centre being now 
<c about to leave the Earth) on September 28. In 
" 1892, the Sun will go down eclipsed at London, 
" and again in 1928 the passage of the centre will be 
" in the expansion, though there will be two digits 
" eclipsed at London, October the 31st of that year; 
" and about the year 2090 the whole penumbra will 
" be worn off; whence no more returns of this eclipse 
" can happen till after a revolution of ten thousand 
" years. 

" From these remarks on the entire revolution of 
" this eclipse, we may gather that a thousand years 
" more or less, (for there are some irregularities that 
" may protract or lengthen this period 100 years), 
" complete the whole terrestrial phenomena of any 
" single eclipse: and since 20 periods of 54 years 
u each, and about 33 days, comprehend the entire 
" extent of their revolution, it is evident that the 
1 : times of the returns will pass through a circuit of 
;c one year and ten months, every Chaldean period 
" being ten or eleven days later, and of the equa- 
;c ble appearances about 32 or 33 days. Thus, 
" though this eclipse happens about the middle of 
" July, no other subsequent eclipse of this period 
i l will return to the middle of the same month again ; 



Of Eclipses. 

" but wear, constantly each period 10 or 11 days 
" forward ; and at last appear in winter, but then it 
<l begins to cease from affecting us. 

" Another conclusion from this revolution may 
* ' be drawn, that there will seldom be any more than 
" two great eclipses of the Sun in the interval of 
" this period, and these follow sometimes next return, 
4C and often at greater distances. That of 1715 re- 
* c turned again in 1733 very great; but this present 
" eclipse will not be great till the arrival of 1820, 
" which is a revolution of four Chaldean periods ; 
" so that the irregularities of their circuits must 
" undergo new computations to assign them ex- 
"actly. 

" Nor do all eclipses come in at the south pole: 
tc that depends altogether on the position of the lu- 
" nar nodes, which will bring in as many from the 
" expansum one way as the other : and such eclips- 
" es will wear more southerly by degrees; contrary 
" to what happens in the present case. 
" The eclipse, for example, of 1736, in Septem- 
" 6er, had its centre in the expansum, and set about 
" the middle of its obscurity in Britain ; it will wear 
" in at the north pole, and in the year 2600, or 
" thereabout, go off in the expansum on the south 
" side of the Earth. 

" The eclipses therefore which happened about 
" the creation are little more than half way yet of 
" their ethereal circuit ; and will be 4000 years be- 
" fore they enter the Earth any more. This grand 
" revolution seems to have been entirely unknown 
" to the ancients. 

pre h sentta- 322 ' " It: is particularly to be noted, that eclipses 

bies agree " which have happened many centuries ago, will not 

ancient** * * ^ e ^ ounc ^ by our present tables to agree exactly with 

observa- ' ' ancient observations, by reason of the great anoma- 

tion. t j- es mtne lunar motions ; which appears an incon- 

" testable demonstration of the non-eternity of the 

" universe. For it seems confirmed by undent- 



Of Eclipses. 279 

" able proofs, that tbe Moon now finishes her period 
" in less time than formerly, and will continue by 
" the centripetal law to approach nearer and nearer 
" the Earth, and to go sooner and sooner round it : 
" nor will the centrifugal power be sufficient to com- 
" pensate the different gravitations of such an as- 
" semblage of bodies as constitute the solar system, 
" which would come to ruin of itself, without some 
" new regulation and adjustment of their original 
" motions*. 

323. " We are credibly informed from the testi- THALES'S 
" mony of the ancients, that there was a total eclipse ecll P se - 

* There are two ancient eclipses of the Moon, recorded by Pto- 
lemy from Hipparchus, which afford an undeniable proof of the 
Moon's acceleration. The first of these was observed at Babylon^ 
December the 22d, in the year before CHRIST 383 : when the Moon 
began to be eclipsed about half an hour before the Sun rose, and the 
eclipse was not over before the Moon set : but by most of our astro- 
nomical tables the Moon was set at Babylon half an hour before the 
eclipse began ; in which case, there could have been no possibility of 
observing it. The second eclipse was observed at Alexandria, Sep.- 
tember the 22d, the year before CHRIST 201; where the Moon rose 
so much eclipsed, that the eclipse must have begun about half an 
hour before she rose ; whereas, by most of our tables, the beginning 
of this eclipse was not till about ten minutes after the Moon rose at 
Alexandria. Had these eclipses begun and ended while the Sun was 
below the horizon, we might have imagined, that as the ancients had 
no certain way of measuring time, they might have been so far mis- 
taken in the hours, that we could not have laid any stress on the ac- 
counts given by them, But, as in the first eclipse the Moon was set, 
and consequently the Sun was risen, before it was over ; and in the 
second eclipse the Sun was set and the Moon not risen, till sometime 
after it began ; these are such circumstances as the observers could 
not possibly be mistaken in. Mr. Struyk, in the following catalogue, 
notwithstanding the express words of Ptolemy, puts down these 
two eclipses as observed at Athens ; where they might have been 
seen as above, without any acceleration of the Moon's motion: 
Athens being 20 degrees west of Babylon^ and 7 degrees west of 
Alexandria. 

Nn 



280 Of Eclipses. 

" of the Sun predicted by THALES to happen in the 
" fourth year of the 48th'* Olympiad, either at Sar- 
" dis or Miletus in Asia, where THALES then re- 
" sided. That year corresponds to the 585th year 
*' before Christ; when accordingly there happened 
" a very signal eclipse of the Sun, on the 28th of 
" Mat/, answering to the present 10th of that monthf, 
" central through North America, the south parts of 

* Each Olympiad began at the time of full Moon next after 
the summer- solstice, and lasted four years, which were of une- 
qual lengths, because the time of full M< on differs 11 days every 
year : so that they might sometimes begin on the next day after the 
solstice, and at other times not till four weeks after it. The first 
Olympiad began in the year of the Julian period 5938, which was 
776 years before the first year of CHRIST, or 775 before the year of 
his birth ; and the hist Olympiad, which was the 293d, began A* D. 
S93. At the expiration of each Olympiad, the Olympic Games were 
celebrated in the Elcan fields, near the river Alfiheus in the Pclo/ion- 
neaus (now Marco) in honour of JUPITER OLYMPUS. See STRAU- 
CHIUS'S Breviarium Chronologicum, p. 247 251. 

t The reader may probably find it difficult to understand why ATr. 
SMITH should reckon this eclipse to have been in the 4th year of the 
48th Olympiad, as it was only in the end of the third year : and al- 
so why the 28th of May, in the 535th year before CHRIST, should 
answer to the present 10th of that month. But we hope the follow- 
ing explanation will remove these difficulties. 

The month of May (when the Sun was eclipsed) in the 585th year 
before the first year of CHRIST, which was a leap-year, fell in the 
latter end of the third year of the 48th Olympiad; and the fourth 
year of that Olympiad beg-in at the summer-solstice following: but 
perhaps Mr. SMITH begins the year of the Olympiad from January, 
in order to make them correspond more readily \vith Julian \ears; 
and so reckons the month of May, when the eclipse happened, to be 
in the fourth year of that Olympiad. 

Tiie place or longitude of the Sun at that time was b 29 43' 17", 
to which same place the Son returned (after 2300 years,) -viz, A. D. 
1716, on May S<* $*> O after noon: so that, with respect to the Sun's 
place, the 9th of May, 1716, answers to the 28th of May in the 585th 
year before the first year cf CHRIST ; that is, the Sun had the same 
longitude on both those days. 



Of Eclipses. 281 

" France, Italy, cc. as far as Athens, or the isles 
** in theJEgean Sea; which is the farthest that even 
" the Caroline tables carry it; and consequently 
" make jt inv bible to any part of Asia, i;i the total 
" character; though I have good reasons to believe 
" that it extended to Babylon, and went down cen- 
" trai over that city. We are not however to ima- 
" gine, that it was set before it passed Sardts and the 
41 Asiatic towns, where the predictor lived; because 
" an invisible eclipse could have been of no service 
<{ to demonstrate his ability in asironomicrj sciences 
" to his countrymen, as it could give no proof of its 
" reality. 

324. "For a further illustration, THUCYDIDES THUCY- 
" relates, that a solar eclipse happened on. a sum- 
" mer's day in the afternoon, in the first year of the 
*' Peloponneslan war, so great that the stars appcar- 
u ed. RIIODIUS was victor in the Olympic games 
u the fourth year of the said war, being also the 
" fourth of the 87th Olympiad, on the 428th year 
tl before CHRIST. So that the eclipse must have 
" happened in the 431st year before CHRIST: and 
" by computation it appears, that on the 3d of An- 
" gust there was a signal eclipse which would have 
" passed over A t hens, central about G in the even- 
" ing, but which our present tables bring no farther 
u than the ancient Syrtes on the African coast, above 
u 400 miles from Athens ; which suffering in that 
u case but 9 digits, could by no means exhibit the 
" remarkable darkness recited by this historian ; the 
" centre therefore seems to have passed Athens about 
u 6 in the evening, and probably might go down 
" about Jerusalem, or near it, contrary to the con- 
" struction of the present tables. I have only ob- 
<c viated these things by way of caution to Nie pre- 
E * sent astronomers, in re-computing ancient eclip- 
" ses ; and refer them to examine the eclipse of Ni- 
' i cias, so fatal to the Athenian fleet*.; that which 

* Before CHRIST 413, dugttst ?r. 



282 Of Eclipses. 

11 overthrew the Macedonian army*, &V." So far 
Mr. SMITH. 

The num. 325. In any year, the number of eclipses of both 
eclises ^ uminar i es cannot be less than two, nor more than 
seyen ; the most usual number is four, and ii is very 
rare to have more than six. For the Sun passes by 
both the nodes but once a year, unless he passes by 
one of them in the beginning of the year ; and when 
he does, he will pass by the same node again a little be- 
fore the year be finished ; because as these points 
move 19-y degrees backward every year, the Sun 
will corne to either of them 173 days after the other, 
319. And when either node is within 17 degrees 
of the Sun at the time of new Moon, the Sun will 
be eclipsed. At the subsequent opposition, the 
Moon will be eclipsed in the other node ; and come 
round to the next conjunction again ere the former 
node be 17 degrees past the Sun, and will therefore 
eclipse him again. When three eclipses fall about 
either node, the like number generally falls about 
the opposite ; as the Sun comes to it in 173 days af- 
terward ; and six lunations contain but four days 
more. Thus there may be two eclipses of the Sun 
and one of the Moon about each of her nodes. But 
when the Moon changes in either of the nodes, she 
cannot be near enough the other node at the next full 
to be eclipsed; and in six lunar months afterward 
she will change near the other node : in these cases 
there can be but two eclipses in a year, and they will 
be both of the Sun. 

326. A longer period than the above mentioned, 
320, for comparing and examining eclipses which 
happened at long intervals of time, is 557 years 21 
days 18 hours 30 minutes 11 seconds, in which 
time there are 6890 mean lunations : and the Sun 
and node meet again so nearly as to be but 11 se- 
conds distant ; but then it is not the same eclipse that 
returns, as in the shorter period above-mentioned. 

* Before CHRIST 168, June 21. 



Of Eclipses. 233 

327. We shall subjoin a catalogue of eclipses 
recorded in history, from 721 years before CHRIST 
to A. D. 1485 ; of computed eclipses from 1485 to 
1700: and of all the eclipses visible in Euro/whom 
1700 to 18CO. From the beginning of the cata- 
logue to A. /). 1485, the eclipses are taken from 
STRUYK'S Introduction to Universal Geography, An ac- 
as that indefatigable author has, with much labour, ^"'^ f w , 
collected them from Ptolemy, Timcydidcs, Pin- ing- cata- 
ta?'c/i 9 Calvisius, Xenophon, Jjiodorus Siculus, Jus- lo ue of 
tin, Polybius, Titus Livius, Cicero, Lucanus, The-* 
ophanes* Dion, Cassias, and many others. From 
1485 to 1700 the eclipses are taken from Ricciolus's 
Almagest: and from 1700 to 1800 from L?Art dc 
verifier les Dates. Those from Struyk have all the 
places mentioned where they were observed : Those 
from the French authors, viz. the religious Benedict 
tines of the congregation of St. Maur, are fitted to 
the meridian of Paris: And concerning those from 
Ricciolus, that author gives the following account : 

" Because it is of great use for fixing the cycles 
or revolutions of eclipses, to have at hand, without 
the trouble of calculation, a list of successive eclip- 
ses for many years, computed by authors of ephe- 
mcrides, although from tables not perfect in all re- 
spects, I shall, for the benefit of astronomers, give a 
summary collection of such. The authors I extract 
from are : an anonymous one w ho published ephe- 
meridesfrom 1484 to 1506 inclusive: Jacobus Ptlau- 
men and Jo. St&flerinus, to the meridian of Vim, 
from 1507 to 1534: Lucas Gauricus, to the latitude 
of 45 degrees, from 1534 to 1551 : Peter Appian, 
to the meridian of Lei/sing, from 1538 to 1578 : Jo. 
Sttfflerus, to the meridian of Tubing, from 1543 to 
1554 : Petrus Pitatus, to the meridian of Venice, 
from 1554 to 1556: Georgius Joachimus Rheticus, 
for the-y^ar 1551 : Nicholas Simus,lo the meridian 
of Bologna, from 1552 to 1568 : M. ichael Mastlin, 
to the meridian of Tubing, from 1557 to 1590: Jo. 



Stadius, to the meridian of Antwerp, from 1554 to 
1574 : Jo. Antoninus Maginus^ to the meridian of Ve- 
nice^ from 1581 to 1630 : David Origan to the meri- 
dian of Franckfort on the Oder, from 1595 to 1664 : 
Andrew Argol,\a the meridian of Home, from 1630 to 
1700 : Franciscus Montchrunus, to the meridian of 
Bologna, trom 1461 to 1660: Among which, Sta- 
dius, Mtfstlin,and Maginus, used the Prutenic tables; 
Origan the Prutenic and Tychonic; Montebrunus\hz 
Lansbergian, as likewise those of Durat. Almost 
all the rest the Alphonstne. 

" But that the places may readily be known for 
which these eclipses were computed, and from what 
tables, consult the following list, in which the years 
inclusive are also set down : 

From To 

1485 1506 The place and author unknown. 

1507 1553 Ulm in Suabia, from the Alphonsine. 

1554 1576 Antwerp, from the Prutenic. 

1577 1585 Tubing, from the Prutenic. 

1586 1594 Venice, from the Prutenic. \Jenic. 

1595 1600 Franckfort on the Oder, from the Pru- 

1601 1640 Franc/cfortQnthcOderJromthtTychonic 

1641 1660 Bologna, from the Lansbcrgian* 

1661 1700 Rome, from the Tychonic" 

So far RICCIOLUS. 

JY. B. The eclipses marked with an asterisk are 
not in Rice 10 LUS'S catalogue, but are supplied from 
L'Art de verifier les Dates. 

From the beginning of the catalogue to A.D. 1700, 
the time is reckoned from the noon of the day men- 
tioned to the noon of the following day : but from 
1700 to 1800 the time is set down according to our 
common way of reckoning. Those markedhjPfto 
and Canton are eclipses from the Chinese chronology 
according to STRUYK ; and throughout the table this 
mark signifies Sun y and 3 Moon. 






Of Eclipses. 



285 



STRUYK's CATALOGUE OF ECLIPSES. 



JJff. 


jLcii;>s /a ul Uie iuu 




4. and D. 


JHidiilu 


Digits 


Chr. 


and Moon seen ut 






H. M 


eclipsed. 


721 


Babylon 


3 


March 1910 34 


Total 


720 


Babylon 


5 


March 8. 


11 56 


1 5 


720 


Babylon 


^) 


icpt. 1 


10 18 


5 4 


621 


Babylon 


D 


Apr. 21 


18 2 ; 


2 36 


523 


Babylon 


D 


July 16 


13 47 


7 24 


502 


Babylon 


3 


Nov. 19 


12 21 


1 52 


491 


Babylon 


5 


April 25 


12 1? 


1 44 


431 


Athens 





Aug. 3 


6 35 


11 


425 


Athens 


"2 


Oct. 9 


6 45 


Total 


424 


Athens 




March 20 


20 ir 


9 


413 


Athens 


if 


Aug. 27 


10 lo 


Total 


406 


Athens 


3> 


Apr. 15 


8 50 


Total 


404 


Athens 


(v) 


Sept. 2 


21 12 


8 40 


403 


Pekin 


(v) 


Aug. 28 


5 53 


10 40 


394 


Gnide 





Aug. 13 


22 17 


11 


383 


Athens 


J) 


Dec. 2i 


19 o 


2 1 


382 


Athens 


D 


June 18 


rt 54 


6 15 


382 


Athens 


~j) 


Dec. 12 


10 21 


Total 


364 


1'hebes 


p 


July K 


23 51 


6 10 


357 


Syracuse 





Feb. 28 


22' 


3 33 


357 


Zant 


D 


Aug. 29 


7 2 


4 21 


340 


Zant 





Sept. 14 


18 - 


9 


331 


Arbela 


j 


Sept. 20 


20 i 


Total 


310 
219 


Sicily Island 
Mysia 





Aug. 14 
March 19 


-20 5 
14 5 


10 22 
Total 


218 


Pergamos 


2 


Sept. 1 


rising 


Total 


217 


Sardinia 


(v) 


Feb. 11 


1 57 


9 6 


203 


Frusini 


S 


May 6 


2 5? 


5 40 


202 


Cumis 


(B 


Oct. 18 


22 24 


1 


201 


Athens 


D 


Sept. 22 


7 14 


. 8 58 


200 


Athens 


D 


March 19 


13 < 


Total 


200 


Athens 


3 


Sept. 11 


14 4^ 


Total 


198 


H.OTOC 


f?\ 


Aue* 9 


9 




190 


Rome 
Rome 


1 


JT-ug. y 

March 15 
July 16 


18 ~ 
20 St. 


11 

10 43 


174 


Athens 


D 


April 30 


14 3> 


7 1 


168 


Macedonia 


J) 


June 2] 


8 2 


Total 


141 


Rhodes 


^) 


Jan. 27 


10 I 


3 26 


104 


Rome 





July IS 


22 


11 52 


' 63 


Rome 


j) 


Oct. 27 


6 2. 


Total 


60 


Gibraltar 


i 


March 16 


settiiu 


Central 


54 


Canton 




May 9 


3 4i 


Total 


51 


Rome 




March 7 


2 1^ 


9 


48 


Rome 


D 


Jan. 18 


10 ( 


Total 


45 


ilome 


J 


Nov. 6 


4 - 


Total 


36 


Rome 





May 19 


3 5: 


6 47_ 



Of Eclipses. 

STRUYK's CATALOGUE OF ECLIPSES. 



Wei: 

Chr. 


eclipse* oi tlie bun 
and Moon seen at 




M. and D. 


Middle 
H. M 


iJlglt.S * 

eclipsed. 


31 


Rome 


*-y\ 


Aug. 20 


setting 


Gr. Eel. 


29 


Canton 


v) 


Jan. 5 


4 2 


11 


28 


Pekin 





June 18 


23 48 


Total 


26 


Canton 





Oct. 23 


4 16 


11 15 


24 


Pekin 


3? 


\pril 7 


4 11 


2 


16 


Pekin 


(v) 


Nov. 1 


5 13 


2 8 


2 


Canton 





Feb. 1 


20 8 


11 42 


Aft. 












Chr. 












1 


Pekin 




June 10 


1 10 


U 43 


SjRome 




March 28 


4 15 


4 45 


14 Pannonia 


J 


Sept. 26 


17 15 


Total 


27jCanton 




July 22 


8 56 


Total 


SOCanton 





Nov. ir, 


19 20 


10 30 


40:pekin 


(v) 


-\pril 30 


5 50 


7 ot 


45 Rome 


(y) 


July 31 


.2 1 


5 17 


46 Pekin 





July 21 


.22 .55 


2 10 


46 Rome 


3 


Dec. .'U 


9 5: 


Total 


49 Pekin 


(v) 


lay 2i> 


7 16 


10 8 


53; Canton 





viarch 8 


20 4 C - 


11 6 


55| Pekin 


(v) 


July 12 


1 5u 


6 40 


56i Canton 


/v} 


Ice. 2o 


28 


9 20 


59|R')me 





\pril SO 


3 8 


10 38 


60 Canton 





Oct. 13 


3 31 


10 SO 


65 Canton 





Dec. 15 


21 50 


lO 23 


691 Rome 


J) 


Oct. 18 


10 43 


10 49 


70 Canton 
71 Rome 




3) 


Sept. 2i 
March 4 


31 13 

8 32 


8 26 
6 (j 


95jEphesus 
125 Alexandria 


f 


Mav 21 
April 5 




1 . 
1 44 


9 16 


133 


Alex Adda 


D 


VTay 6 


11 44 


Total 


134 


Alexandria 


D 


Oct. 2C 


LI 


!0 19 


136 


Alexandria 


D 


\Iarch 5 


1 5 56 


5 17 


237 


Bologna 




april 12 





Total 


238 


Rome 




Vpril 1 


20 20 


8 45 


290 


Carthage 




May 15 


3 20 


i 1 20 


304 


Rome 


3 


Aug. S3 


9 36 


fotal 


316 


Constantinople 





Dec. 30 


19 53 


2 18 


334 


Toledo 





July 17 


atnoo- 


Central 


348 


Constantinople 





Oct. 


19 2^ 


3 f; 


360 


Ispahan 





Aug. 27 


;8 ( 


Central 


364 


Alexandria 


5 


tfov. 25 


!5 24 


l'oU| 


401 


Rome 


Tj 


[nne 1" 




t'otal 


'401 


Rome 


M 

3 


Dec. 6 


32 1-v 


<'otal 


402 


ilome 


3 


June 1 


8 4., 


10 2 



Of Eclipses. 
STRUYK's CATALOGUE OF ECLIPSES* 



387 



Aft. 
Chr, 


Eclipses of the Sun 
and Moon seen at 




M.andD. 


Middle 
H. M 


Digits "S 
eclipsed. J 


402 


Rome 




Nov. 10 


20 33 


10 30 S 


447 


Compostello 




Dec. 23 


46 


1 S 


451 


Compostello 




April 1 


16 34 


19 52 h 


451 


Compostello 


3 


Sept. 26 


6 30 


2? 


458 


Chares 





May 27 


23 16 


18 53 S 


462 


Compostello 


D 


March 1 


13 2 


11 11 \ 


464 


C haves 


^ 


July 19 


19 1 


10 15 ? 


484 


Constantinople 


3 


Jan. 13 


19 53 


10 0? 


486 


Constantinople 


o 


May 19 


1 10 


5 15 S 


497 


Constantinople 


5 


April 18 


6 5 


17 57 {> 


512 


Constantinople 


\-) 


June 25 


23 8 


1 50 ? 


538 


England 


} 


Feb. 14 


19 


8 23 ? 


540 


London 


v) 


June 19 


20 15 


8 S 


577 


Tours 


5 


Dec. 10 


17 28 


6 46 > 


581 


Paris 


D 


April 4 


^3 33 


6 42 w 


582 


Paris 


D 


Sept. 17 


12 41 


Total S 


590 


Paris 


D 


Oct. 18 


6 30 


9 25 S 


592 


Constantinople 




Marchl8 


22 6 


10 < 


603 


Paris 





Aug. 12 


3 3 


11 20 S 


622 


Constantinople 


D 


Feb. 1 


11 28 


Total S 


644 


Paris 





Nov. 5 


30 


9 53 Ij 


680 


Paris 


D 


June 17 


12 30 


Total c 


683 


Paris 


D 


April 16 


11 30 


Total S 


693 


Constantinople 





Oct. 4 


23 54 


11 54 J 


736 


Constantinople 




Jan. 13 


7 


Total J 


718 


Constantinople 




June 3 


1 15 


Total C 


733 


England 




Aug. 13 


20 


11 IS 


734 


England 


D 


Jan. 23 


14 


Total S 


752 


England 


J) 


July 30 


13 


Total ? 


753 


England 





June 8 


2<J 


10 35 S 


753 


England 


D 


Jan. 23 


13 


Total S 


760 


England 





Aug. 15 


4 


8 15 


760 


London 


D 


Aug. 30 


5 50 


10 40 c 


764 


England 





June 4 


at noon 


7 15 S 


770 


London 


^) 


Ftb. 14 


7 12 


Total S 


774 


Rome 


^) 


Nov. 22 


14 37 


11 58 > 


784 


London 


j) 


Nov. 1 


14 ^ 


Total C 


787 
796 


Constantinople 
Constantinople 




D 


Sept. 14 
March27 


20 43 
16 22 


9 47 S 
Total S 


800 


Rome 


D 


Jan. 15 


9 


10 17 J; 


807 
807 


Angoulesme 
Paris 



D 


Ffeb. 10 
Feb. 25 


21 24 
13 43 


9 42? 
Total S 


807 


Paris 


D 


Aug. 21 


10 20 


Total 


809 


Paris 





July 15 


21 33 


8 8? 


809 


Paris 




Dec. 25 


8 


Total s 


810 
f^*r 


Paris 
s~*r-rj*s*^j*s>fjrsj 


j> 
VT.J 


June 20 
ns*s*j*j-*r 


8 
^s**r*r 


Total S 
.r-r,/--rr < \)* 



Go 



Of Eclipses. 
STRUYK's CATALOGUE OF ECLIPSES. 



S Aft. I 
S Chr. 


Eclipses of the Sun 
and Moon seen at 


1 


Viand D. 


Middle 

i. M. 


Digits S 
eclipsed P 


s 810 Paris 


3> Nov. 30 


12 


Total S 


S 810 


'aris 


D Dec. 14 


8 


Total S 


J 812 


Constantinople 


R 


May 14 


2 13 


9 J 


2 813 


Cappadocia 




May 3 


7 5 


10 35 ^ 


S 81? 


Paris 


5 


Feb. 5 


5 42 


Total S 


S 818 


Paris 


p 


July 6 


18 


6 35 


820 


Paris 


Hi 


Nov. 23 


6 26 


Total L 


^' 824 


Paris 


D 


March IB 


7 55 


Total s 


S 828 


Paris 


D 


June 30 


5 


Total S 


S 828 


Paris 


D 


Dec. 24 


13 45 


Total { 


831 


Paris 


D 


April 30 


6 19 


11 8? 


S 831 


Paris 




May 15 


23 


4 24 S 


7 

S 831 


Paris 


? 


Oct. 24 


11 18 


Total S 


V 832| Paris 




April 18 


9 


Total 2 


J 84 Oi Paris 


*,) 


May 4 


23 22 


9 20 S 


^ 841j Paris 
S 842 Paris 




D 


Oct. 17 
March 29 


18 5fc 
14 38 


5 24 S 
Total 


S 843] Paris 


D 


March 19 


7 1 


Total 5 


< 861 


Paris 


D 


March 29 


15 7 


Total S 


S 878 


Paris 


D 


Oct. 14 


16 


Total 


S 878 


Paris 




Oct. 29 


1 


11 14 J 


i 883 


Arracta 


5 


July 23 


7 44 


11 ? 


S 889 


Constantinople 


/77" 


April o 


17 52 


23 S 


S 891 


Constantinople 


S 


Aug. 7 


23 48 


10 30 J 


> 501 


Arracta 


J 


Aug. 2 


15 7 


Total s 


5 904 


London 


5 


May 3 


11 47 


Total S 


S 904 


London 


D 


Nov. 2 


9 C 


Total J 


S 912 


London 


D 


Jan. 


15 11 


Total c 


926 


Paris 




March 31 


15 17 


Total S 


5 934 


Paris 





April 16 


4 30 


11 36 J 


S 939 


Paris 




July 18 


19 45 


10 7 


S 955 


Paris 


T) 


Sept. 4 


11 18 


Total s 


J 961 


Rh ernes 


S 


May 16 


20 13 


9 18 S 


< 970 


Constantinople- 




May 7 


18 Sfr 


11 22 


S 976 


London 


5 Jul y to 


15 7 


Total t 


V 985 


Messina 





July 2i 


3 52 


4 10 S 


^ 98? 


Constantinople 


P"- 


May 2S 


6 54 


8 40 S 


^ 99C 


Fulda 


5 


April li 


10 22 


9 5 > 


S 99C 


Fulda 




Oct. 6 


15 4 


1 10 <J 


* 99C 


Constantinople 


i 


Oct. 21 


45 


10 5 S 


{ 995 


Augsburga 


3) 


July 14 


11 27 


Total 


c iocs 


Ferrara 


3 


Oct. 


11 56 


Total J 


S 101C 


Messina 


j) 


March 1 


5 41 


9 12? 


S 1016 


N 5 meg-uen 




Nov. 1C 


16 39 


Total j 


5 1017 


Niiriegr.en 


K 


Oct. 22 


2 8 


6 rs 


s io^c 


Cologne 


5 


Sept. 411 3S 


Total s 



Of Eclipses. 
STRUYK's CATALOGUE OF ECLIPSES. 



589 



* 



my* 



S Aft.] 
S Ch'-. 


Eclipses of the Sun 
and Moon seen at 




M.amlD. 


Middle 

H. M. 


Digits 'S 
eclipsed. S 


S 1023 


London 





Jan. 23 


2:3 29 


11 S 


S 1030 


Rome 


'^ 


Feb. 20 


11 43 


Total S 


J 1031 


Paris 


J) 


Feb. 9 


11 51 


Total S 


S 1033 


Paris 


D 


Dec. 8 


11 11 


9 17 


S 1034 


Milan 


D 


June 4 


9 8 


Total s 


J 1037 


Paris 




Apr. 17 


20 45 


10 45 S 


J 1039 


Auxerre 


/v"j 


Aug. 21 


23 40 


11 5J; 


S 104'J 


Elome 


D 


Jan. 8 


16 39 


Total t 


S 1044 


Aaxerre 


j) 


Nov. 7 


16 12 


10 IS 


J 1044 


Cluny 





Nov. 21 


22 12 


11 -S 


2 1056 


Nurembui'g 




April 2 


12 9 


Total 


S 1063 


Rome 


D 


Nov. 8 


12 16 


Total ^ 


S 1074 


Augsburgh 
Constantinople 


D 

D 


Oct. 7 
Nov. 29 


10 13 
11 12 


Total S 
9 36^ 


S 1082 


Condon 




May 14 


10 32 


10 2 ? 


S 1086 


Constantinople 





Feb. 16 


4 .7 


Total s 


S 1089 


Naples 


j) 


June 25 


6 6 


Total S 


J 1093 


Augsburgh 





Sept. 22 


22 35 


10 12 r> 


S 1096 


Gembluors 


D 


Feb. 10 


16 4 


Total ^ 


S 1096 


Augsburgh 


D 


Aug. 6 


8 21 


Total S 


J 1098 
c 1099 


Augsburgh 
Naples 




D 


Dec. 25 
Nov. 30 


1 25 
4 58 


12 S 
T-otal J 


S 1103 


Rome 


D 


Sept. 17 


10 18 


Total t 


S 1106 


irfurd 


D 


July 17 


11 28 


11 54 S 


J 1107 


Naples 


D 


Jan. 10 


13 16 


Total S 


J 1109 


Erfurd 





May 31 


1 30 


10 20 J 


s mo 


Condon 


3 


May 5 


10 51 


Total <J 


S 1113 


ferusalem 




March 18 


19 


9 12 S 


? 1114 


l.ondon 


5 


Aug. 17 


15 5 


Total S 


S 1117 


Triers 


5 


June 15 


13 26 


Total J 


S 1117 


Triers 


D 


Dec. 10 


12 51 


Total t 


J 1110 


Naples 


D 


Nov. 20 


15 46 


4 US 


< 1121 


Triers 


D 


Sept. 27 


16 47 


Total S 


S H22 


Prague 


D 


March 24 


11 20 


3 49? 


S 1124 


irfurd 




Feb. 1 


6 43 


8 39 S 


J* 1124 


London 





Aug. 10 


23 29 


9 58 S 


C 1132 


irf'urd 


D 


March 3 


8 14 


Total ? 


S 1133 


Prague 


D 


Feb. 20 


16 41 


3 23 <J 


J 1135 


London 


D 


Dec. 22 


20 11 


Total S 


J 1142 


Rome 


D 


Feb. 1 1 


14 17 


8 30 S 


S H43 


Rome 




Feb. 1 


6 36 


Total h 


S 1147 


Auranches 





Oct. 25 


22 38 


7 20 ^ 


J 1149 


Bary 


5 


March 25 


13 54 


5 29 S 


2 1151 


Eimbeck 


3) 


Aug. 28 


12 4 


4 29 J 


S 1153 


Augsburgh 





Jan. 26 


42 


11 > 


S 1154 


Paris 


D 


June 36 


16 1 


Total s 



290 



Of Eclipses. 
STRUYK's CATALOGUE OF ECLIPSES. 



S Aft. 
ijChr. 


Eclipses of the Sun 
and Moon seen at 




M.andD. 


Middle 

H. M. 


Digits S 
eclipsed. > 


S 1154 


^aris 


D 


Jec. 2 1 


8 30 


4 22^ 


Jj 1155 


Auranches 


D 


une 16 


8 45 


53 S 


5 1160 


tome 


D 


Aug. 18 


7 53 


6 49 > 


S 1161 


tome 


D 


Vug. 7 


8 11 


Total c 


S 1162 


irfurd 


D 


Feb. 1 


6 40 


5 56 S 


> 1162 


irfurd 




July 27 


21 30 


4 11 S 


? 1163 
S H61 


Vlont Gassini 
Milan 


f 


July 3 
June 6 


7 46 
10 


2 0? 
Total S 


S 1168 


Condon 




Sept 18 


14 


Total S 


J nr2 


Cologne 


3) 


Jan. 11 


13 31 


Total J 


? lire 


\uranches 


D 


April 25 


7 2 


8 6? 


s lire 


Auranches 


D 


Oct. 19 


11 20 


8 53 S 


S lira 


Cologne 


D 


March 5 


setting 


7 52 S 


? iirs 


Auranchea 


D 


Aug. 29 


13 52 


5 31 J 


< iirs 


Cologne 





Sept. 12 




10 51 s 




S nr9 


Cologne 




Aug. 18 


14 28 


Total S 


> 1180 


Auranches 





Jan. 28 


4 14 


10 34 J 


$1181 


Auranches 


(& 


July 13 


3 15 


3 48 ^ 


S 1181 


Aaranches 


j) 


Dec. 22 


8 58 


4 40 S 


S 1185 


themes 





May 1 


1 53 


9 OS 


J 1186 


[Cologne 




April 5 


6 


Total S 


? 11S6 


Frankfort 





April 20 


7 19 


4 OS 


s H87 


Paris 


D 


March25 


16 17 


8 42 J 


s ii8r 

J Ild9 


England 
England 




Sept. 3 
Feb. 2 


21 54 
10 


8 6? 
9 S 


5 1191 


England 


ATi 
W 


June 23 


20 


11 32 > 


S H92 


France 


D 


Nov. 20 


14 


6 -^ 


S1193 


France 


D 


Nov. 10 


5 27 


Total S 


> 1194 


London 





April 22 


2 15 


6 49 S 


v 1200 


London 


D 


Jan. 2 


17 2 


4 35 > 


S1201 


London 




June 17 


15 4 


Total s 


S 1204 


England 


D 


April 15 


12 39 


Total S 


? 1204 


Saltzburg 


D 


Oct. 10 


6 32 


Total S 


S 1207 


Rhemes 





Feb. 27 


10 50 


10 20 J 


S 1208 


Rhemes 


D 


Feb. 2 


5 10 


Total ? 


S 1211 


Vienna 




Nov. 21 


13 57 


Total S 


? 1215 


Cologne 


D 


4archl6 


15 35 


Total S 


C 1216 


icre 





leb. 18 


21 15 


11 36 J 


S 1216 


Acre 


D 


/larch 5 


9 28 


7 4? 


J 1218 


Damictta 


D 


July 9 


9 46 


11 31 S 


< 1222 


Rome 


D 


Jet. 22 


14 28 


Total J 


S 1223 


Colmar 




April 16 


8 13 


11 ? 


S 122 H 


Naples 




Dec. 27 


9 55 


9 19 w 


> U30 


Naples 




May 13 


17 


Total S 


J 1230 


London 




Nov. 21 


13 21 


9 34 J 


?>>2 


Rhemes 





Oct. 15 


4 29 


4 25 I 



Of Eclipses, 
STRUYK's CATALOGUE OF ECLIPSES. 



291 



s'Aft. 1 
S Chr, 


Eclipses of the Sun 
and Moon seen at 




M.andD. 


Middle 
H. M. 


Digits 'S 
eclipsed. / 


s 




__ 






s 


S 1245 


Rhemes 





uly 27 


17 47 


6 s 


> 1248 


London 


3) 


une 7 


8 49 


Total S 


S 1255 


London 


D 


luly 20 


9 47 


Total < 


> 1255 


Constantinople 


(v) 


Dec. 30 


2 52 


Annul. 


S 1258 


Augsburgh 


5 


May IS 


I 17 


Total s 


^ 1261 


Vienna 


X.V 


March 3 1 


22 40 


9 8S 


< 1262 


Vienna 


D 


March 7 


5 50 


Total s 


? 1262 


Vienna 


D 


\ug. 30 


14 39 


Total ^ 


S 1263 


Vienna 


3) 


Feb. 24 


6 52 


6 29 S 


!> 1263 


Augsburgh 




Aug. 5 


3 24 


11 17S 


S 1263 


Vienna 


D 


Aug. 20 


7 35 


9 7s 


I* 1265 


Vienna 


D 


Dec. 23 


16 25 


Total S 


S 126* 


Constantinople 




May 24 


23 11 


11 40 < 


Ij 1270 


Vienna 





March 22 


18 47 


10 40 > 


S 1272 


Vienna 


D 


Aug. 10 


7 27 


8 53 S 


ij 1274 


Vienna 


D 


Jan. 23 


10 39 


9 25 Jj 


S 1275 


Lauben 


D 


Dec. 4 


6 20 


4 29 S 


^ 1276 


Vienna 


]) 


Nov. 22 


15 


Total ^ 


S 1277 


Vienna 


D 


May 18 


. 


Total S 


<J 1279 


Franckfort 


(v) 


April 12 


6 55 


10 6 J 


S 1280 


London 


D 


March 17 


12 12 


Total S 


^ 1284 


Reggio 


D 


Dec. 23 


16 H 


9 13 J; 


S 1290 


Wittemburg 


CD 


Sept. 5 


19 37 


10 30 S 


S 1291 


London 


j 


Feb. 14 


10 2 


Total s 


S 1302 


Constantinople 


D 


Jan. 14 


10 25 


Total S 


? 1307 


Ferrara 


(v) 


April 2 


22 18 


54 S 


S 1309 


London 


D 


Feb. 24 


17 44 


Total > 


S 1309 


Lucca 


D 


Aug. 21 


10 32 


Total S 


S J310 


Wittemburg 





Jan. 3 1 


2 2 


10 10 ^ 


S 1310 


Torcella 


D 


Feb. 14 


4 8 


10 20 S 


S 1310 


Torcella 


D 


Aug. 10 


15 33 


7 16 Jj 


S 1312 Wittemburg 
S 1312;Plaisance 


D 


July 4 
Dec. 14 


19 49 

7 19 


3 23 S 
Total Ij 


S 1313 Torcello 


D 


Dec. 3 


8 58 


9 34 S 


S 1316 


Modena 


D 


Oct. 1 


14 55 


Total JJ 


S 1321 


Wittemburo; 




June 25 


18 1 


11 17 S 


J 1323 Florence 


D 


May 20 


15 24 


Total > 


S 1324 


Florence 


D 


May 9 


6 3 


Total S 


S 1324 


Wittemburg 




April 23 


6 35 


8 8 


Jj 1327!Constantinople 


D 


Aug. 31 


18 26 


Total \ 


S 1328 Constantinople 




Feb. 25 


13 47 


11 S 


$ 13 30; Florence 


3) 


June SO 


15 10 


7 34 Sj 


S 1330 Constantinople 


(D 


July 16 


4 5 


10 43 S 


Ij 1330 Prague 




Dec. 25 


15 49 


Total 


S 1331 Prague 


(D 


Nov. 29 


20 26 


7 41 S 


S 1 331 1 Prague 




Dec. 14 


18 


11 



292 



Of Eclipses, 

S TRUYK's CATALOGUE OF ECLIPSES. 

%# 



S Aft. 
S Chr. 


Eclipses of the Sun 
and Moon seen at 




M.andD. 


Middle 
H. M. 


Digits S 
eclipsed. Jj 


S 1333 


Wittemburg 





viay 1 4 


3 


10 18 !j 


S 1334 


Cesena 


D : April 19 


10 33 


Total S 


S 1341 


Constantinople 


D Nov. 23 


12 23 


Total s 


1341 


Constantinople 


;DCC. 8 


22 15 


6 30 S 


S 1342 


Constantinople 


D May 20 


14 27 


Total s 


S 1344 


Alexandria 


Oct. 6 


18 40 


8 55 J 


S 1349 


Wittemburg 


D June 30 


12 20 


Total < 


S 1354 


Wittemburg 


-Jept. 16 


20 45 


8 43 S 


5 1356 


Florence 


J> Feb. 16 


11 43 


Total <. 


S 1361 


Constantinople 





May 4 


22 15 


8 54 S 


S 1367 


Sienna 


D 


Jan. 16 


8 27 


Total s 


S 1389 


Eugibio 




Nov. 3 


17 5 


Total S 


S 1396 


Augsburgh 


Jan. 1 1 


16 


6 22 ^ 


5 1396 


Augsburgh 


D June 21 


11 10 


Total S 


S 1399 


Forli 


Oct. 29 


43 


9 -~\ 


S 1406 


Constantinople 


D : June 1 


13 


10 31 S 


5 1406 


Constantinople 


June 15 


18 1 


11 38 < 


Jj 1408 


Forli 


Oct. 18 


21 47 


9 32 S 


? 1409 


Constantinople 


.April 15 


3 1 


10 48 s 


J 1410 


Vienna 


3 ! March 20 


13 13 


Total S 


S 1415 


Wittemburg 


June 6 


6 43 


Total s 


J 1419 


Franckfort 





March 25 


22 5 


1 45 


? 142] 


Forli 


J 


Feb. 17 


8 C 2 


Total \ 


S 1422 


Forli 


J 


Feb. 6 


8 26 


11 7$ 


S 1424 


Wittemburg 





June 26 


3 57 


11 20 S 


S 1431 


Forli 





Feb. 12 


2 4 


1 39 


^ 1433 


Wittembiirer 





June 1 7 


5 


Total S 


S 1438! Wittemburg 
S 1442 Rome 




D 


Sept. 18 
Dec. 17 


20 59 
3 59 


8 7S 
Total S 


S 1448 


Tubing 





Aug. 28 


22 23 


8 53 \ 


S 1450 


Constantinople 


D 


July 24 


7 19 


Total S 


S 1457 


Vienna 


D 


Sept. 3 


11 17 


Total 


<J 1460 


Austria 


D 


July 3 


7 31 


5 23 ? 


S 1460 


Austria 





July 17 


17 32 


11 19 


Jj 1460 


Vienna 


D 


Dec. 27 


13 30 


Total ,S 


S 1461 


Vienna 


D 


June 22J11 50 


Total J[ 


J 1461 


Rome 


1*L 


Dec. 17 




Total S 


S 1462 


Viterbo 


D 


June 1 1 


15 


7 38 J 


Jj 1462 


Viterbo 





Nov. 2 1 


10 


2 6 S 


S 1464 


Padua 


D 


April 21 


12 43 


Total ^ 


5 1465 


Rome 





Sept. 20 


5 15 


8 46 S 


S 1465 


Rome 


D 


Oct. 4 


5 12 


Total 


^ 1469 


Rome 


D 


Jan. 27 


7 9 


Total S 


S 1485 

, 


Nurimburg 




March 16 


3 53 


11 



\ 



Of Eclipses. 



1293 



All the following ECLIPSES, are taken from RICCIOLUS, except those 
marked with an Asterisk, which are from L'Art de -verifier les Dates. 



>' Aft. 
S Chr. 
S 




M. & D. 


Middle 
H. M. 


Digits 
eclipsed 


Aft. 
Chr. 




M. & D. 


Middle 
H. M. 


Digits "s 

eclipsed \ 


V 1486 


D 


Feb. 1 8 


5 41 


Total 


1508 





May 29 


6 


* S 


Jj 1486 





March 5 


17 43 


9 


1508 


i> 


June 12 


17 40 


Total J; 


S 1487 


D 


Feb. 7 


15 49 


Total 


1509 




June 2 


11 11 


7 OS 


^ 1487 





July 2( 


2 6 


7 


1509 


0Nov. 11 


22 


s 


S 1488 


D 


Jan. 28 


6 


# 


1510 


y 


Oct. 16 


19 


* V 


1488 





July 8 


1 7 St. 


4 


1511 


D 


Oct. 6 


11 50 


Total 5 


S 1489 


J 


Dec. 7 


17 41 


Total 


1512 




Sept. 25 


3 56 


Total S 


J; 149G 





May 19 


Noon 


* 


1513 





March 7 


30 


6 ^ 


S 1490 


j) 


June 2 


10 f 


Total 


1513 





July 30 


1 


* S 


> 149C 


3 


Nov. 26 


18 25 


Total 


1515 


D 


Jan. 29 


15 18 


Total 


S 1491 





March 8 


2 19 


9 


1516 




Jan. 1 9 


6 


Total S 


Jj 1491 




Nov. 15 


18 


* 


1516 


D 


July 1 3 


11 37 


Total < 


S 1492 





April 26 


7 


* 


15 1C 





Dec. 23 


3 47 


3 S 


> 1492 





Oct. 20 


23 


* 


1517 




June 1 8 


16 


S 


S 1493 


3) 


April 21 


14 


Total 


1517 


D 


Nov. 27 


19 


s 


> 1493 





Oct. 1C 


2 40 


8 


1518 




May 24 


11 19 


9 11 S S 


S 1494 





March 7 


4 12 


4 


1518 





June 7 


17 56 


11 OS 


^ 1494 


3 


March 2 1 


14 38 


Total 


1519 





May 28 


1 


* S 


S 1494 


D 


Sept. 14 


19 45 


Total 


1519 


5) 


Oct. 23 


4 33 


6 S 


!j 1495 


3> 


March 10 


16 


* 


1519 


D 


Nov. 6 


6 24 


Total s 


S 1495 




Aug. 19 


17 


# 


152015 


May 2 


7 


* S 


<J 1496 


5' 


Jan. 29 


14 


* 


1520 


fe 


Oct. 1 1 


5 22 


3 s 


S 1497, 


]) 


Jan. 18 


6 38 


Total 


1520 


3 


Oct. 25 


19 


* S 


Jj 1497 





July 29 


3 2 


3 


1520 


3 


March 2 1 


17 


* / 


S 1499 


5 


June 22 


17 


* 


1521 





April 6 


19 


* S 


,5 1499 





Aug. 23 


18 


* 


1521 





Sept. 50 


3 


* s 


S 1499 


D 


Nov. 1 7 


10 


# 


1522 


D 


Sept. 5 


12 17 


Total S 


^ 1500 





March 27 


In the 


Night 


1523 


3 


March 1 


8 26 


Total s 


S 1500 


3 


April 1 1 


At 


Noon 


1523 


3 


Aug. 25 


15 24 


Total Jj 


<J 1501 


3 


Oct. 5 


14 2 


10 


1524 





Feb. 4 


1 




S 1502 


3 


May 2 


17 49 


Total 


1524 


3> 


Aug. 16 


16 


* S 


1502 





Sept. 30 


19 45 


10 


1525 


Jan 23 


4 


* V 


S 1503 


D 


Oct. 15 


12 20 


2 


1525 


D 


July 4 


10 10 


Total > 


^ 1503 


D 


March 12 


9 


* 


I52o 


5 


Dec. 29 


10 46 


Total ? 


^ 1503 





Sept. 19 


22 r 


* 


1526 


D 


Dec. 18 


10 30 


Total S 


S 1504 


D 


Feb. 29 


13 26 


Total 


1527 





Jan. 2J 3 





S 1504 





March 16 


3 


# 


1527 




Dec. 710 




\ 1505 


5 


Aug. 14 


8 18 


Total 


1528 





May 17 


20 


* S 


lj 1506 


3 


Feb. 7 


15 


* 


1529 


D 


Oct. 1 6 


20 23 


11 55 ^ 


S 1507 





July 20 


3 11 


2 1530 





March 28 


13 23 


8 4s 


!j 1506 


/*~'S 


Aug. 3 


10 


* 


1530 


3 


Oct. 6 


12 1 


Total ^ 


S 1507 





Jan. 12 


19 


* 


153 


3 


April 1 


7 


* S 


^ 1508 





Jan. 2 


4 


* 


1532 





Aug. 30 


40 


S 
S 



Of Eclipses. 
'RICCIGLUS's CATALOGUE OF ECLIPSES. 



S Aft. 
S Chr. 




M. Sc D. 


Middle 
H. M. 


Digits 
eclipsed 


Aft. 
Chr. 




M. Sc D 


Middle 
H. M. 


Digits 
eclipsed 


S 1533 


3 


Aug. 4 


11 50 


Total 


1556 


(V) 


Nov. 1 


18 


9 41 


S 1533 





Aug. 19 


17 


* 


1556 


3 


Nov. 1 6 


12 44 


6 55 


S 1534 





Jan. 14 


1 42 


5 45 


1557 


(Vf 


Oct. 20 


20 


* 


S 1534 


3 


Jan. 29 


14 25 


Total 


1558 


3 


April 2 


11 


9 50 S 


Ij 1535 





June 30 


Noon 


* 


1558 





April 18 


1 


* S 


S 1535 


3 


July 14 


8 


* 


1559 


3 


April 16 


4 50 


Total J 


lj 1535 





Dec. 24| 2 


# 


1560 


3 


March 11 


15 40 


4 13 <| 


S 1536 





June 18 


2 2 


8 


1560 




Aug. 21 


1 


6 22 5 


^ 1536 


D 


Nov. 27 


6 24 


10 15 


1560 


3 


Sept. 3 


7 


* S 


S 1537 


3 


May 24 


8 3 


Total 


1561 





Feb. 13 


29 


* 


1537 





June 7 


8 


* 


1562 


Feb. 3 


5 


S 


S 1537 


3 


Nov. 16 


14 56 


Total 


1562 


3 July 15 


15 50 


Total J 


^ 1538 


3 


May 1 3 


14 24 


2 


1563 


(v)!Jan. 22 


19 


* 


S 1538 


3 


Nov. 6 


5 31 


3 37 


1563 





June 20 


4 50 


8 38^ 


1539 





April 8 


4 33 


9 


1563 


3 


July 5 


8 4 


11 34 i 


S 1540 





April 6 


17 15 


Total 


1565 





March 7 


12 53 


^ 


!j 1541 


3 


March 1 1 


16 34 


Total 


1565 


3 May 14 


16 


I 


S 1541 





Aug. 21 


56 


3 


1565 


^ I Nov. 7 


12 46 


11 46 J 


^ 1542 


3 


March 1 


8 46 


1 38 


1566 


3>|Oct. 28 


5 38 


Total ^ 


S 154* 





\ug. 10 


17 


* 


1567 


April 8 


23 4 


6 34 s 


Ij 1543 


3 


July 15 


16 


* 


1567 


D 


Oct. 17 


13 43 


2 40 S 


S 1544 


3 


Jan. 9 


18 13 


Total 


1568 





March 28 


5 


5 


S 1544 





Jan. 23 


21 16 


11 17 


1569 


3 


March 2 


15' 18 


Total J 


S 1544 


3 


July 4 


8 31 


Total 


1570 


3 


Feb. 20 


5 46 


Total < 


5 1544 


3 


Dec. 28 


18 27 


Total 


1570 


3 


Aug. 15 


9 17 


Total J 


!j 1545 





June 8 


20 48 


3 45 


157. 




Jan. 25 


4 


* V 


S 1545 




Dec. 17 


18 * 


1572 




Jan. 14 


19 


< 


Jj 1546 


<- 


May 30 


5 ( * 


1572 


| 


fune 25 


9 


5 26 V 


S 1546 


Cv 


Nov. 22 


23 * 


1573 




June 28 


18 


* < 


!j 1547 


3 


May 4 


27] 8 1573 


v? 


Nov. 24 


4 


* \ 


S 1547 


3 


)ct. 28 


4 56J11 34 


1573 





Dec. 8 


6 51 


Total I 


> 1547 




\ T ov. 12 


2 9 


9 30 


1574 


3 


Nov. 13 


3 50 


5 21 V 


S 1548 


S 


Ypril 8 


3 


* 


1575 





May 19 


8 - 


6 


!j 1548 


3 


April 22 


11 24 


Total 


J157o 


T) 


Nov. 2 


5 


* 


S 1549 


3 


April 1 


15 19 


2 


1576 


3 


Oct. 7 


9 45 


< 


!j 15-49 


^ 


Oct. C 


6 


* 


1577 


3 


April 2 


8 33 


Total < 


S 1550 





iVLirch 10 


20 


* 


1577 


3 


Sept. 26 ! 3 4 


Total .' 


*ij 1551 


3 


Feb. 20 


8 21 


Total 


1578 


3 


;:cpt. 1513 4 


2 20 < 


S 1551 


;v) 


Au-. 31 


2 


1 52 


1579 





i'eb. 15 


5 41 


8 36 < 


vj 1553 





Jan. 12 


22 54 


1 22 


1579 


(S 


Aug. 20 


19 


; 


S 1553 





July 10 





# 


1530 


3 




10 7 


Total ; 


^ 1553 


3 


July 24 


16 


31 


1581 


3 


Jan. 19 


9 22 


Total ( 


S 1554 





Jr. lie 29 


6 - 


* 


1581 


3 


July 15 


17 51 


Total | 


S . l ^54 


-i' 


Dec. t 


13 7 


10 12 


1582 


3 


Jan. 8 


10 29 


53, 


S 1 555 


3 


June 4 


15 C 


Total 


1582 


a 


June 9 


17 5 


r s 


^ 1 5 5 5 j 5 o 


Nov. 13 


.19 


* 


1583 


3 


Nov. 28 21 51 


Total 



Of Eclipses. 



RICCIOLUS's CATALOGUE OF ECLIPSES. 



2?& 


JChr. 




M. Sc D. 


Middle 
H. M. 


Digits 

eclipsed. 


Aft. 
Chr. 


|M. & D. 


Middle 
II. M. 


Digits S 

eclipsed ^ 


Ij 1584 





May 9 


18 20 


3 36 


1601 


D; June 15 


6 18 


4 52 


S 1584 


D 


Nov. 17 


14 15 


Total 


1601 


June 29 


China 


4 29 S 


5 1585 





April 2 


7 53 


11 7 


1601 


D Dec. 9 


7 6 


10 53 s 


S 1585 


D 


May 13 


5 9 


6 54 


1601 


a 


Dec. 24 


2 46 


9 52 S 


Ij 1586 


D 


Sept. 27 


8 


# 


1602 





May 21 Green] 


241s 


S 1586 


(? 


Oct. 12 


Noon 


# 


1602 


3 


June 4 


7 18 


Total S 


Ij 1587 


5 


Sept 10 


9 28 


10 2 


1602 





June 1 9 


N.Gra. 


5 43 s 


S 1588 





Feb. 26 


1 23 


1 3 


1602 





Nov. 1 3 


Magel. 


3 S 


ij 1588 


3 


March 12 


14 14 


Total 


1602 


3) 


Nov. 28 


10 2 


Total s 


S 1588 


3> 


Sept. 4 


17 30 


Total 


1603 





May 10 


China 


11 2lS 


^ 1589 





Aug. 10 


18 


# 


1603 


3> 


May 24 


11 41 


7 59 S 


S 1589 


3) 


Aug. 25 


8 1 


3 45 


1603 





Nov. 3 


Rom. I. 


11 17 J> 


> 1590 





Feb. 4 


5 


# 


1903 


D 


Nov. 18 


7 31 


3 26 S 


S 1590 


3 


July 16 


17 4 


3 54 


1604 





April 20 


Arabia 


9 32 J 


> 1590 





July 30 


19 57 


10 27 


1604 





Oct. 22 


Peru 


6 49 S 


S 1591 


3) 


Jan. S 


6 21 


9 40 


1605 


D 


April 3 


9 19 


11 49 


!j 1591 


3) 


July 6 


5 8 


Total 


1605 





April 1 8 


Madag. 


5 31 S 


S 1591 


/ r*-. 


July 20 


4 2 


I 


1605 


3> 


Sept. 27 


4 27 


9 26 ^ 


^ 1591 


3 


Dec. 29 


16 11 


Total 


1605 





Oct. 12 


2 32 


9 24 S 


S 1592 


3) 


June 24 


10 13 


8 58 


1606 





March 8 


Mexico 


6 


!j 1592 


j) 


Dec. 18 


7 24 


5 54 


1606 


5 


March 24 


11 17 


Total S 


S 1593 





May 30 


2 30 


2 38 


1606 





Sept. 2 


Magel. 


6 40 J; 


^ 1594 





May 1 9 


14 58 


10 23 


1606 





Sept. 2 


Magel. 


6 40 S 


S 1594 


D 


Oct. 28 


19 15 


9 40 


1606 


3 


Sept. 16 


15 6 


Total. $ 


% 1595 





April 9 


Ter.de 


Fucgo 


1607 





Feb. 25 


21 48 


1 13 S 


S 1595 


J) 


April 24 


4 12 


Total 


1607 


3> 


March 13 


6 36 


1 22 Jj 


S 1595 





May 7 


o 


# 


1607 





Sept. 5 


15 40 


4 7 < 


1595 





Oct. 3 


2 4 


5 18 


1608 





Feb. 15 


at the 


Antipo. Jj 


S 1595 


]) 


Oct. 18 


20 47 


Total 


1608 


3 


July 27 


30 


1 53 S 


S 1596 





March 28 


In 


Chili 


1608 





Aug. 9 


4 39 


40 ^ 


S 1596 


D 


April 12 


8 52 


6 4 


1609 


j) 


Jan. 19 


15 21 


10 32 S 


> 1596 





)ept. 21 


In 


China 


1609 





Feb. 4 


Fuego 


5 22 i; 


S 1596 


3) 


)ct. 6 


21 15 


3 33 


1609 


D 


July 16 


12 8 


Total S 


> 1597 




vlarch 16 


St. Pet. 


Isle 


1609 





July 30 


Canada 


4 10 % 


S 1597 





*>ept. 1 1 


Picora 


9 49 


1609 





Dec. 26 


19 


5 50 ^ 


Jj 1598 


3) 


Feb. 20 


18 12HO 55 


1610 


3) 


Jan. 9 


1 31 


Total 5 


S 1598 





March 6 


22 12 


11 57 


1610 





June 20 


Java 


10 46 S 


% 1598 


j) 


Aug. 1 6 


1 15 


Total 


1610 


D 


July 5 


16 58 


11 1S2 


S 1596 





Aug. 3 1 


Magel. 


S 34 


1610 





Dec. 15 


Cyprus 


4 50 J 


Ij 1599 


9 


Feb. 10 


18 21 


Total 


1610 


3) 


Dec. 29 


16 47 


4 23 s 


S 1599 





July 22 


4 31 


8 18 


1611 





June 10 


Calilbr. 


11 30 S 


I} 1599 


3) 


Aug. 6 




Total 


1612 


]) 


May 14(10 38 


7 22 v 




S 1600 





Jan. 15 


Java 


11 48 


1612 





lay 29 


23 38 


r H s 


Ij 1600 


3) 


Jan. 30 


6 40 


2 5* 


16 i 2 


D 


.'ov. 8 


3 22 


9 49 > 


S 1600 
% 1601 






July 10 
Jan. 4 


2 10 
Ethiop. 


5 39 
9 40; 


1612 
1613 







Nov. 22 
April 20 


Magel. 
Magel. 


*. m O's 

lanica. 


fV ^ 

** ^ *J 



Pp 



296 Of Eclipses. 

RICClOLUS's CATALOGUE OF ECLIPSES. 



S*Aft. 

S Chr. 


"./- 


r*rj~*r^^- 

M.and D. 


./-v./'V^/^/^ 

Middle 
M. M. 


\y-,r\yx/-,x'-*--rx 

Digits fiAft. 
eclipsed. .Chr 

1 1 


^r-s 


-^^rv-A^-. 

M.and D. 


Mldle Dig-its S 
I. M.' eclipsed. V 


S 1613 


jj 


May 4 


35 


Total 


1625 





./iarch b 


Florida 


S 1613 


<) 


May 19 


East 


Partary 


1625 


J) 


viarcn23 


14 11 2 11 S 


? 1613 


4 .'0 


Oct. 13 


South 


Arm r. 


1625 




ept. 


St. Pe'ter's Isle S 


^1613 


f 


Oct. 28 


4 19 


Total 


1625 


~) 


,ept. 16 


11 41 5 6 c 


S 1614 


w 


April fc 


N. Gui. 


8 44 


1626 


3 


i-'eb. 25 


Madag 8 27 S 


5 1614 


~j) 


April 23 


17 36 


5 25 


1626 


^ 


Aug. 7 


7 48 


25 S 


J 1614 




Oct. 3 


57 


5 2 


1626 





Aug. 21 


In 


Mexico J 


S 1614 
S 1615 
J 1615 


T) < )ct. 17 

(f) March 29 
^ Sept. 22 


4 58 
Goa 

Salom 


4 56 

10 38 
Isle 


1627 
1627 
1627 


5 


Jan. 30 
I-eb. 15 
July 27 


11 38 
Magel 
9 4 


10 21 <; 

Itnica < 
Total S 


SifilS* 


M .rch 3 


I 58 


Total 


16,7 


S) 


/\ug. 11 


Tenduc 


10 J 


S 1616 




March 17 


Mexico 


6 47 


1628 





.ian. 6 


'1 'endue 


5 40 t 


S 1616 




Aug. 26 


15 35 


Total 


1628 




Jan, 20 


10 11 


Total S 


J 16]6 




Sepr. 10 


Ma gel. 


10 33 


[62i 


.'?: 


July 1 


C.Good 


Hope S 


S 1617 


'' 7 ) 


Feb. 5 


Mage! 


anica 


1 Si 


5" 


July 16 


11 26 


Total J 


S 1617 
> 1617 


j> 

<-.-> 


Feb. 20 
March 6 


1 49 

22 


Total 


1621 

162v 





Oec. 25jlnEug 
Ian. 91 36 


and ? 
4 27 "S 


c 1617 


i 


Aug. 1 


Biarmia 


# 


1629 


.T f 


June 11 


Gange 


J.1 25 S 


S 1617 




Aue. 16 


8 22 


Total 


1629 


Dec. H 


Peru 


10 14 J 


S 1618 


f'janT 26 


Maarei 


.anica 


1630J T) 


May 25 


17 56 


6 s 


J 1618 


(Feb. 9 


3 29 


2 57 


1630 





lune 10 


7 47 


9 8 S 


^ 1618 


D 


July 21 


Mexico 




16,j(j 


2 


\ r ov. 19 


11 24 


9 27 S 




S 1619 


S 


Jan. 15 ! Caliior 


aia 


1630 


';'.' 


Dec. 3 


N. Gui. 


10 10 t 


S 1619 


v^/ 


June 2G 


12 40 


5 10 


1631 





-vpril 30 


Antar. 


Circle s 


J 1619 





Jaly 11 


Africa 


11 39 


163 




Way 15 


8 15 


Total S 


< 1619 


5 


Dec. 20 


15 53 


10 47 


163 1 





Oct. 24 


C.Good 


Hope J 


S 1620 





May 31 


Arctic 


Circle 


1631 


"D 


Mov. 8 


12 


1- Total ^ 


S 1620 


5 


June 14 


13 47 


Total 


1632 





Apr. 19 


C.Good 


Hope S 


J 1620 





June 29 


Mattel. 


7 20 


1632 


D 


May 4 


1 24 


6 35 S 


S 1620 


} (Dec. 9 


6 39 


Total 


1532 





Oct. 13 


Mexico 


8 37 J 


S 16^0 


fv) 


Dec. 23 


Mag?l 


lanica 


1532 




< )ct. 17 


12 2.3 


5 31 c 


J 1621 


3) 


May 20 


14 54 


10 44 


1633 




npril 8 


5 14 


4 30 S 


< 1621 


5 


June 3 


19 42 


9 53 


1633 




Oct. 3 


Maldiv. 


Total S 


S 1621 
S 1621 


3 


Nov. 13 
Nov. 2.s 


Mage) 
15 43 


lanica 
3 2H 


1634 
i 'i34 


1 


March 14 
March 28 


9 35 
Japan 


11 18 y 
10 19 w 






May 10 


C. Yen! 


U J* 


Io.i4 


3) ISept. 7 


5 


Total S 


lj 1622 


^) 


Nov. 2 


Malar 


c i In. 


1634 




Sept. 22 


C.G.FL 


9 54 J> 


S 1623 


5 


\pril 1 4 


7 19 


10 5'i 


1635 




Feb. 17 


Antar. 


Circle <J 


S 1523 





April 29 






1635|5 


March 3 


9 26 


Toial S 






J 1623 




Oct. ft 


22 


8 35 


1 o.>5 (v) 


March U 


.vlexico 


16 S 


^ 1623 


(V) 


Oct. 23 


Califor. 


10 46'|1635|(3 


Aug. 12 


Iceland 


5 07 


S 1624 


May 18 


N. Zem. 


6 163.5! J 


Aug. 27 


16 4 


Total < 


1S24 
J 1624 


1 


\pril 3 
April 17 


7 9 
Ant'.r. 


Total 1636; 
Circle ; 1636 ^ 


Feb. 
Feb. 20 


In 

11 34 


Peru S 
3 23 S 


S 

S 1624 





Sept. 12 


Mag.-! 


i mica \ 1636 (v) 


\ug-. 


Tartan 


U 20^ 


S 1624 


5 


Sept. 2C 


8 5J 


Total .1636 j> 


Aug. 1- 


34 


1 25 J 



CJf Eclipses. 
KICCIOLUS's CATALOGUE OF ECLIPSES. 



J Aft. 
S Chr. 




M. & D. 


Middle 
H. M. 


Digits j|Aft. 
eclipsed Chr. 





5 




D 


5 

j> 


3) 

D 




I 

9 

5 










D 


D 


i 

ij 


M.anclD. 


Middle 
II. M. 


Digits Jj 
eclipsed ? 


Ij 1637 
J 1637 
<J 1637 
J* 1638 
S 1638 
jj 1638 
S 163h 
> 1638 
S 1639 
163 
S 1639 
|> 1639 
S 1639 
> 1640 
S 16K, 
Jj 164t 
S 1641 

Jj i64i 

S 1641 
> 1642 
S 1642 
1642 
S 1642 
Jj 1643 
S 1643 
Jj 1643 
S 1643 
Ij 1644 
S 1644 
Ij 1645 
S 1645 
Ij 1645 
S 1645 
.tj 1646 
S 1646 
' 
J 16-1-6 
3 1647 
S 1647 
<; 1647 
S 1547 
,J 1648 
S 1648 
? 1648 
S 1648 
S 1649 





j) 


J) 


J) 




J) 






J 


J) 

j) 

J) 

1) 



3 


D 


v.'L-' 

f> 




D 

3) 




Jan. 26 

uiy 21 
Dec. 31 
1 ji. 14 
,une 25 
July 11 
Dec. 5 
Dec. 20 
Jan. 4 
J une 1 
June 15 
S r ov. 24 
Dec. 9 
May 20 
Nov. 1 3 
April 25 
May 9 
Oct. 18 
Nov. 2 
March 30 
April 1 4 
Sept. 2.) 
Oct. 7 
March 19 
April 3 
Sept. 1 2 
Sept. 27 
March 8 
Aug. 3 1 
Feb. 10 
Feb. 26 
Aug. 7 
Aug. 21 
Jan. 1 6 
fcarj. 30 
Uily 12 
July 27 

s 

20 

' ': \ i V 2 

Dec. 25 

5 
'ime 20 
NOV. 29 
Dec. 13 

May 25 


Cain 
Jucutan 

44 
Persia 

20 17 
C Mag 
ellan 
15 16 
Tartary 
5 29 
2 41 
Magel. 
11 57 
NT.Spa. 
Peru 2 
I 
Peru 
8 19 
18 46 
Estod. 
14 31 
Magei 
16 45 
13 53 
.31 10 
17 
7 38 
6 20 
IS 10 
7 45 
Rom. I. 
2 4 
35 
Str.of 
18 1 i 
6 57 
6 
12 10 
9 43 
9 
13 3f> 
55 
1 3 2.3 
19 17 
21 48 
15 20 


boya 

10 45 
9 45 
Total 

9 5 
2 10 
Total 
30 
10 40 
11 9 
11 
3 46 
10 30 
10 3o 
9 4, 
10 16 
6 31 


j 1649 
J1649 
|1649 
1650 
1650 
1650 
1 650 
1651 
1651 
1652 
1652 
1652 
1652 
1653 
1653 
1653 
1 65 3 
165* 
1654 
1654 
1654 
1655 
1655 

165;> 

165 
1655 

1657 
1657 
1658 
165ft 
1658 
1658 
1 6 5 9 
1659 
1 659 
1659 
1060 
1660 
1660 
1 660 
1661 
1661 


June 9 
Nov. 4 
Nov. 1 8 
April 30 
May 1 5 
Oct. 24 
Nov. 7 
April 1' 
Oct. l-l 
:h 24 
April 7 
Sept. ir 

' } P *~ c "* 

i-'eb. 27 
March 13 
Aug. 22 
Sept. 6 
Feb. 16 
MiiTcii 2 
Aug. 1 1 
Aug. 27 
Feb. 6 
\g. 1 

Jan. 1 1 
July 6 
juiy 21 
Dec. 30 
11 
j'une 25 
Dec. 4 
Dec, 2( 
May 3 1 
June M 
Nov. 9 
Nov. 24 

n 

M;ty 20 
Oct. 29 
Nov. 1 l- 
April 21 
Oct. 3 
Oct. 18 
Nov. 2 
vlarch 29 
April R 


ArctC. 

2 10 
19 56 
5 5 4 
8 37 
17 17 
20 29 
Tube". 
'2 15 
1 6 52 
22 40 
7 27 
5 2 


4 
3 16 S 
Total <J 

8 50 S 
9 59 t[ 


1 7 '$ 


v 


23 45 
9 10 
19 25 
22 24 
1 1 40 
2 37 
14 19 
16 
9 4 
3 17 
11 43 
23 30 
11 20 
9 35 
20 O 

r 47 

16 
22 58 
3 56 
11 36 
8 34 
17 4 
16 16 
4 25 
11 58 
22 34 
32 
3 4c 
22 32 
4 28 


Total 5 

s 


3 14 s 
2 28 
1 53 Ij 
4 20 Jj 

* S 
10 s 
Total ^ 
i 


4 
Total 
ianica 
Total 


3 <; 


6 


Total S 




8 52 
10 46 
Total 
4 40 
Anian 
Total 


Total -*J 

S 


10 S 

s 


Total 


8 5> 

s 


4 47 


5 5 2 % 

9 51 ^ 
Total s 




4 28 


Total S 


7 40 
Total 


S 


s 



29S 



Of Eclipses. 



RICCIOLUS's CATALOGUE OF ECLIPSES. 



5 Aft. 
S Ciu. 




M.andD. 


Middle 
H. M. 


i ;is 
eclipsed. 


Aft. 
Chr. 




M.andD 


Middle 
H. M. 


Digits S 
eclipsed <* 


S 1661 
5 1661 
S 1662 
^ 166. 
V iiv-3 
S i663 
S 1663 
Jj 1663 
S 1664 
! 1664 
S 1664 
!j 1664 
S 166.3 
Jj 166., 
S 1665 
!j 1660 
S 166& 
\ 1667 
S 1667 
!j 1667 
S 1668 
!j 1668 
S 1668 
!> 1668 
S 1669 
^ 1669 
S 1670 
I] 1670 
S 1670 
!j 1670 
S 1671 

S 1671 
lj 1672 

S 1672 

S 

S 1672 
S 1673 

! i 

S 167:; 

J 1675 
V 1676 



3) 



& 

3> 







.- , 

3 

3 









3 





f 




3 




3 



3 


j 

* .'-' 


Sept. 23 
Oct. 7 
March 19 

Feb. 2 1 
a . 
Aug. 18 
Sept. 1 
Jan. 27 
Feb. 1 1 
h:;y 22 
Aug. 20 
Jan. 3i 
July 12 
July 26 
Jan. 4 
July 1 
June 5 
July 21 
N T ov. 25 
Mav 10 
May 25 
Kov. 4 
Nov. 1 8 
April 29 
Oct. 24 
April 1 9 
Sept. 10 
Sept. 28 
Oct. 13 
April 8 
Sept. 2 
Sept. 1 8 
Feb. 28 
March 13 

up\. C 
Feb. 6 
Aug. 1 1 

Jan. 21 
' . b. 
July 17 
Jan. 11 
'"'ii 2^ 
July 6 
June 1C 


1 36 
14 51 
15 8 
1 8 
16 11 
5 47 
8 45 
8 8 
20 40 
3 16 
14 48 
22 10 
18 47 
7 48 
13 31 
31 33 
19 
Noon 
2 32 
11 30 
Setting 
16 26 
2 53 
3 54 
13 18 
10 13 
7 
19 
15 45 
12 5 
23 29 
21 25 
7 44 
3 38 
3 17 
6 43 
18 5--. 
7 29 
21 44 
18 22 
9 4 
9 40 
8 29 
;o 36 
16 31 
21 26 


1 1 1 9 

7 4 

3 14 


676 

1671 

1677 
167W 
1678 
1679 
1 679 
1680 
1680 
1680 
1681 
1681 
1681 
1682 
1682 
1683 
1683 
1683 
1684 
1684 
1684 
1684 
,1685 
1685 
1685 
J1686 
il686 
',1686 
11687 
1687 
i!687 
,1688 

'1688 

1689 
169G 
1690 
1690 
1690 
1691 
169; 
1692 
1692 
1692 


3 


3 
3 
3 

3 


3 

3 

3 


3 



3 

3 


3 

3 
3 

3 

3 


3 





3 




June 25 
Dec. 4 
Nov. 24 
May 16 
May 6 
Oct. 29 
April 10 
May 25 
March 29 
Sept. 22 
March 4 
March 19 
Aug. 28 
Sept. 11 
Feb. 2 1 
Aug. 16 
Jan". 27 
Feb. 9 
Aug. 6 
Jan. 1 6 
June 26 
July 12 
Dec. 21 
Jan. ' 4 
June 16 
Dec. 10 
May 2 1 
June 6 
Nov. 29 
May 1 1 
May 26 
April 15 
April 2: 
Oct. 9 
Oct. 25 
April 4 
Sept. 28 
March 10 
March 24 
Sept. 3 
Sept. 1 8 
Feb. 27 
Aug. 23 
Feb. 2 
Feb. If 
July 27 


6 26 
20 52 
12 5 
16 25 
5 30 
9 17 
21 
11 53 
23 22 
7 57 
Noon 
13 43 
15 22 
15 43 
12 28 
18 56 
I 35 
3 39 
20 36 
6 34 
15 18 
4 26 
11 18 
16 
6 
11 26 
17 9 
Noon 
12 22 

14 
7 4 
16 27 
Noon 
19 4C 
7 42 
15 46 


L 


S 

8 15 S 

Total 


1 i;tai 








S 




~ S 


4 34 


10 35 !j 

Total 
Total S 
10 30 5 

s 


10 


11 10 




s 

~ s 




9 32 
9 50 
6 45 

9 7 


1 35 > 
Total s 
9 45 S 

Total S 
Total $ 
6 49 5 

S 

'Total < 
Total ^ 


Total 






11 14 

2 42 
17 30 
5 51 
3 20 
17 31 
16 9 


5 43 S 


11 21 

'i otai 
Total 

TotaJ 

4 3-1 


S 


E^! 

Total ^ 



Of Eclipses, 



299 



RICCIOLUS's CATALOGUE OF ECLIPSES. 



s'Aft. 
\ Chr. 




M.andD. 


Middle 
H. M. 


Digits, 

eclipsedj 


Aft. 
Chr. 




M.andD. 


Middle 
II. M. 


Di-its S 
eclipsed JJ 


> 1693 

t 1 fiQ^ 


5 

Tk 


Jan. 21 


17 2j 


1 oUii 


1696 
1 fiQ7 




/rr. 


Nov. 23 

A i-ji'i 1 2() 


17 32 

U<IO 


S 


> 1694 
S 1694 

S 1 fiQ/l 


J> 

D 



TV 


Jan. 1 1 
June 22 

liilv 6 


Noon 

4 22 
13 51 


6 22 

a 47 


1697 
1697 
1698 


W 

3 

3 

^ 


May 5 
Oct. 29 
\nril 10 


18 27 
8 44 
9 13 


88 45 


C 1 AQ 5 


J 

,V,N 


Vlav 1 1 


fi ^ 




1 fiQR 


^ 

/TT-, 


Ort ^ 


15 9 9 


I 


1695 


^> 

7i 


May 28 


Noon 




1699 


(i) 

^ 


March 15 


8 14 


9 7^ 


S 1695 

i 1 fiO S 


Ji 

D 
r^ 


Nov. 20 
DPP 5 


8 
17 7 


6 55 


1699 
1 fiQQ 


JJ 




March 30 

Cif*nt c 


22 

23 22 


_| 


S 1696 

7 i cq r 


w 

j) 

'.t\ 


May 16 

IVTnv ^0 


12 45 
1 9 ifi 


Total 


1699 
1 7nn 


3 



Sept. 23 


22 38 
9O 1 1 


9 58 S 


S 1696 




5 


Nov. 8 


17 30 


Total 


1700 


3 
3 


Aug. 29 


1 42 


S 

' S 



The Eclipses from STRUYK were observed ; those from RICCIOLUS 
calculated : the following from L?Art de -verifier les Dates are only those 
which are visible in Eurojie for the present century : those which arc 
tota,! are marked with a T. ; and M. signifies Morning, A. Afternoon. 



VISIBLE ECLIPSES FROM 



*.< 



1700 TO 1800. 

# 



5 Aff 




Months 


Time ot 


Aft 


| Months 


Time of S 


^ jfVlL* 

^Chr. 

s 




and 
Days. 


the Day 

or Night. 


\l\>* 

Chr. 




and 
Days. 


the Day s 
or Night. S 


S 1701 


J 


Feb. 22 


11 A. 


1715 





May 3 


9 M.T. S 


S 1703 


3 


Jan. 3 


7 M. 


1715 


D 


Nov. 1 1 


5 M. s 


S 1703 


2 


June 29 


i M.y. 


1717 




March 27 


3 M. 


lj iros 


3 


Dec. 23 


7 M.T. 


1717 


3 


May 20 


6 A. ^ 


S 1704 


3 


Dec. 11 


7 M. 


1718 




Sept. 9 


8 A. T. \ 


vj 1706 


j) 


April 28 


2 M. 


1719 


j) 


Aug. 29 


9 A. 5 


S 1706 





May 12 


10 M. 


1721 


j 


Jan. 13) 3 A. 


^ 1706 


3 


Oct. 2 1 


7 A. 


1722 


3 


June 29 


3 M. S 


S 1707 




April 17 


2 M.2". 


1722 





Dec. 8 


3 A. S 


S 1708 


3 


April 5 


6 M. 


1722 


3 


Dec. 22 


4 A. S 


^ 1708 





Dec. 14 


8 M. 


1724 





May ~2 


7 A.T. J> 


^ 1708 


3 


Sept. 29 


9 A. 


1724 




Nov. 1 


4 M. S 


S 1709 


^~- 


March 1 1 


2 A. 


1725 


3 


Oct. 21 


7 A. J; 


Ij 1710 




Feb. 1 3 


11 A. 


1726 





Sept. 25 


6 A. S 


S 1710 





Feb. 28 


1 A. 


1726 


3 


Oct. 1 1 


5 M. !; 


S 1711 





July 15 


8 A. 


1727 





Sept. 15 


7 M. S 


S 1711 


3 


July 29! 6 A.T. 


1729|3 


Feb. 1 3 


.6 A.T. S 


S 1712 


3> 


Jan. 23 8 A. 


|1729 


3 


Aug. 9 


1 M. < 


S 1713 


3 


June 8 6 A. 


|l730 


3 


Feb. 4 


4 M. S 


<, 1713 


3 


Dec. 2, 4 M. 


! 173l 


3 


June 20 


2 M. i 


, s -f/ 



9f Eclipses* 

VISIBLE ECLIPSES FROM 1700 TO 



5 Ait. 




Months 
and 


Time of 
the Day 


Aft. 

01 Kr 




Months 
and 


Time ol S 
ne Day v, 


\ 




Days. 


or Night. 


onr. 




Days. 


or Night. S 




S 1732 


D 


Dec. 1 


10 A.T. 


17 9 4 





\pril l 


o M. J 


^ 1733 





May 13 


7 A. 


1764 


J> 


\pril 16 


1 M. s 


S 1733 


D 


May 28 


r A. 


1765 





March 2 1 


2 A. J 


1735 


D 


Oct. 2 


I M. 


1765 


(j 


Aug. 16 


5 A. s 


S 1736 


3 


March 2 6 


12 A.r. 


1766 


j 


eh. 24 


7 A. S 


^ 1736 


D 


Sept. 20 


3 M.T. 


1766 


(''" 


Aug. 5 


7 A. s 


S 1736 





Oct. 4 


6 A. 


1768 


J 


an. 4 


5 M. S 


i 1737 





March 1 


4 A. 


1768 


J) 


'une 30 


4 M.T. s 


S 1737 

A 


D 


Sept. 9 


4 M. 


1768 


J 


Dec. 23 


4 A.T. S 


? 1738 





\ug. 15 


1 1 M. 


1769 


<V 


kme 4 


8 M. S 


S 173, 


5 


Jan. 24 


11 A. 


1769 


3 


Dec. 13 


7 M. J 


\ 173? 





Aug. 4 


5 A 


1770 





yiov. 17 


10 M. s 


S 1731' 





)ec. 30 


9 M. 


1771 


5 


April 28 


2 M. X 


lj 174( 


3) 


Jan. 13 


11 A.T. 


1771 


5 


Oct. 23 


5 A. J; 


S 174! 


j> 


Jan. 1 


12 A. 


1772 


]> 


Oct. ' 1 1 


6 A.T. S 


<| 174^ 


D 


Nov. 2 


3 M.T. 


1772 




Oct. 2f 


I/) M. $ 


<, 174-; 


D 


Aug. 26 


9 A. 


1773 


S3 


March 23 


5 M. S 


Ij 1746 


D 


Aug. 30 


12 A. 


1773 


j) 


Sept. 50 


7 A. Jj 


S 1747 


3) 


Feb. 14 


5 M.T. 


1774 




March 11 


10 M. c 


Jj 1748' 




July 25 


11 M. 


1776 


j) 


July 31 


1 M.T. S 


S 1748 


3 


Aug. 8 


12 A. 


177C 


\L 


Aug. 14 


5 M. 5 


S . 1749 


D 


Dec. 23 


8 A. 


1777 





Jan. 9 


5 A. S 


^ 1750 


{"?} 


Jan. 8 


9 M. 


1778 


/v)Uune 2< 


4 A. ^ 


S 1750 


j) 


June 19 


9 A.r. 


1778 


J> 


Dec. 4 


6 M. S 


I! 1750 


D 


Dec. IS 


7 M. 


1779 


3 


May 30 


5 M.T, % 


S 1751 


j> 


June 9 


2 M. 


1779 





June 14 


8 M. S 


<J 175i 


3) 


Dec. 2 


10 A. 


1779 


J) 


Nov. 23 


s A. J; 


S 175*2 




May 13 


8 A. 


1780 





Oct. 27 


6 A. S 


v 1753 


5 


Apr. 17 


7 A. 


1780 


J) 


Nov. 12 


4 M. 5 


S 1753 





Oct. 26 


10 M. 


1781 





April 25 


6 A. S 


S 1755 


j) 


March 28 


1 M. 


1782 





Oct. 17 


8 M. J; 


S 1757 


D 


Feb. 4 


5 M. 


1782 


5 


April 1~ 


7 A. S 


< 1757 


j) 


July 30 


12 A. 


1783 


D 


March Ib 


9 A.r. J; 


J 1758 


5 


Jan. 24 


7 M.T. 


1783 


2) 


Sept. l.( 


11 A.7\S 


S 1758 





Dec. 30 


7 M. 


1784 


3 


March 7 


3 M. < 


S 1759 





June 24 


r A. 


1785 





:-'cb. 9 


1 A. S 


$ 1759 





Dec. 19 


2 A. 


1787 


j) |Jan. 3 


12 A.T. ^ 


S 176C 




May 29 


9 A. 


1787 


(v)Jan. 19 


10 M. S 


<J 176C 





June 1 3 


7 M. 


1787 





June 15 


5 A. < 


S 176C 


D 


Nov. 22 


9 A. 


1787 


5 


Dec. 24 


3 A. S 


^1761 


5 


May 18 


11 A.T. 


1788 


(v". 


June 4 


9 M. s 


SI W i*r 
1 7 0^ 


D 


May 8 


4 M. 


1789 


j 


i\ov. 2112 A. S 


176L 





Oct. 1 7 


8 M. 


1790 


5 


April 28J12 A.T. $ 


S 176: 


3) 


Nov. 1 


8 A. 


m>c 


D 


Oct. 2: 


i M.r. s 


S 176: 





April 1 3 


8 M. 


1791 





April t 


1 A. < 



VISIBLE ECLIPSES FROM 1700 TO 



$ Aft. 
Chr. 

s 


D 

D 

J 


Months 
and 
Days. 


Time of 
the Day 

or Night. 


Aft. 
Chr. 


D 

a 

D 

D 


Months 
and 
Days. 


Time of S 
the Day < 

or Night. S 


S 1791 
Ij 1792 
S 1793 
S 1793 
S 1794 
S 1794 
S 1794 


Oct. 12 
Sept. 16 
Feb. 25 
Sept. 5 
Jan. 31 
Feb. 14 
Aug. 25 


3 M. 
11 M. 
10 A. 
3 A. 
4 A. 

11 ^.T. 

5 A. 


1795 
1795 
1795 
1797 
1797 
1798 
J800 


Feb. 4 
July 16 
July 31 
June 25 
Dec. 4 
May 27 
Oct. 2 


1 M. S 
9 M. ^ 

8 A. S 
S A. Z 
6 M. S 

7 A.r. 

11 A. S 



328. A List of Eclipses, and historical Events, 
which happened about the same Times, from Rio 



But according to an old calen* 
Jar, this eclipse of the Sun was on 
the 21st of April, on which day 
the foundations of Rome were laid; 
if we may believe Taruntius Fir- 



Before CHRIST. 



'54 



721 
585 



March 19 

May 28 



4.63 



July 



6 

Nov. 19 

April 30 



A total eclipse of the Moon. The 
Assyrian Empire at an end; thej&z- 
bylonian established. 

An eclipse of the Sun foretold by 
THALES, by which a peace was 
brought about between the Medes 
and Lydians. 

An eclipse of the Moon, which 
was followed by the death of CAM- 

UYSES. 

An eclipse of the Moon, which 
was followed by the slaughter of 
the Sabines, and death of Valerius 
Public 'o/a. 

An eclipse of the Sun. The 
Persia?! war, and the falling. off of 
the Persians from the Egyptians. 



eclipse. 



302 



Of Eclipses. 



Before CHRIST. 
April 25 



An eclipse of the Moon, which 
was followed by a great famine at 
Rome ; and the beginning of the 
Peloponnesian war. 

431 August 3 A total eclipse of the Sun. A 
comet and plague at Athens*. 

413 August^l A total eclipse of the Moon. Ni- 
dus with his ship destroyed at Sy- 
racuse. 

394 August 14 An eclipse of the Sun. The 
Persians beat by Conon in a sea-en- 
gagement. 

168 June 21 A total eclipse of the Moon. The 
next day Perseus King of Macedo- 
nia was conquered by Paulus Emi- 
. lius. 

After CHRIST. 

59 April 30 j An eclipse of the Sun. This is 
reckoned among the prodigies, on 
iccount of the murder of Agrippi- 
nus by Nero. 

237 April 12 A "total eclipse of the Sun. A 
sign that the reign of the Gordiani 
vould not continue long. A sixth 
persecution of the Christians. 
306 July 27 An eclipse of the Sun. The stars 
were seen, and the Emperor Con- 
stantius died. 

840 May 4 A dreadful eclipse of the Sun. 
And Lewis the Pious died within 
six months after it. 

1009 An eclipse of the Sun. And 

Jerusalem taken by the Saracens. 
1133 August 2 A terrible eclipse of the Sun. The 
stars were seen. A schism in the 
church, occasioned by there being 
three Popes at once. 

* This eclipse happened in the first year of the Pelopon- 
nesian war. 



Of Eclipses. 303 

329. I have not cited one half of RicciOLUs'sThesuper, 
list of portentous eclipses; and for the same reiason^ 1 ^ 
that he declines giving any more of them than what the anci- 
that list contains ; namely, that it is most disagree- 

able to dwell any longer on such nonsense, and a 
much as possible to avoid tiring the reader: the 
superstition of the ancients may be seen by the few 
here copied. My author farther says, that there were 
treatises written to shew against what regions the 
malevolent effects of any particular eclipse was aim- 
ed ; and the writers affirmed, that the effects of an 
eclipse of the Sun continued as many years as the 
eclipse lasted hours ; and that of the Moon as many 
months. 

330. Yet such idle notions were once of no small Very for- 
advantage to CHRISTOPHER COLUMBUS, who, in^cffor 
the year 1493, was driven on the island of Jamaica, CHRISTO- 
where he was in the greatest distress for want of PHER 

1 r i COLUM- 

provisions, and was moreover refused any assistance Bus> 
from the inhabitants ; on which he threatened them 
with a plague, and told them, that in token of it, 
there should be an eclipse. This accordingly fell 
on the day he had foretold, and so terrified the Bar- 
barians, that they strove, who should be first in 
bringing him all sorts of provisions ; throwing them 
at his feet, and imploring his forgiveness. RICCIO- 
i.us's Almagest, Vol. I. 1. v, c. ii. 

331. Eclipses of the Sun are more frequent than Why-there 
those of the Moon, because the Sun's ecliptic- limits ^.^ )re 
are greater than the Moon's, 317: yet we have eclipses of 
more visible eclipses of the Moon than of the Sun, the Moon 
because eclipses of the Moon are seen from all parts the'sun, 
of that hemisphere of the Earth which is next her, 

and are equally great to each of those parts ; but the 
Sun's eclipses are visible only to that small portion 
of the hemisphere next him whereon the Moon's 
shadow falls, as shall be explained by and by at 
large. 

^ 332. The Moon's orbit being elliptical, and the 
Earth in one of its focuses, she is once at her least 

Qq 



304 Of Eclipses. 

Plate XL distance from the earth, and once at her greatest, 
Fig. L in every lunation. When the Moon changes at her 
least distance from the Earth, and so near the node 
that her dark shadow falls upon the Earth, she ap- 
pears big enough to cover the whole * disc of the 
Sun from that part on which her shadow falls ; and 
Total and the Sun appears totally eclipsed there, as at A, for 
an ! mlar -some minutes : but when the Moon changes at her 

eclipses of ,. .. . ,^ , , 

the Sun. greatest distance from the Earth, and so near the 
node that her dark shadow is directed toward the 
earth, her diameter subtends a less angle than the 
Sun's ; and therefore she cannot hide his whole disc 
from any part of the Earth, nor does her shadow 
reach it at that time ; and to the place over which 
the point of her shadow hangs, the eclipse is annu- 
lar, as at B ; the Sun's edge appearing like a lumi- 
nous ring all around the body of the Moon. When 
the change happens within 17 degrees of the node, 
and the Moon at her mean distance from the Earth, 
the point of her shadow just touches the Earth, and 
she eclipses the Sun totally to that small spot whereon 
her shadow falls ; but the darkness is not of a mo- 
ment's continuance. 

The long-- 333. The Moon's apparent diameter, when largest, 
estdura- exceeds the Sun's when least, only 1 minute 38 
taTecHp-" seconds of a degree : and in the greatest eclipse of 
ses of the the Sun that can happen at any time and place, the 
total darkness continues no longer than while the 
Moon is going 1 minute 38 seconds from the Sun 
in her orbit; which is about 3 minutes and 13 se- 
conds of an hour. 

To how 334. The Moon's dark shadow covers only a spot 
much of on the Earth's surface, about ISO English miles 
the Surf 1 broad, when the Moon's diameter appears largest, 

may be to- 
tally or * Although the Sun and Moon are spherical bodies, as 
eclipsed seen * rom t ^ ie ^ artn tne y appear to be circular planes ; and 
at once so WC11 M the Earth do. ii it were seen from the Moon, i he 

apparently flat surfaces of the Sun and Moon are called their 

discs by astronomers, 



Of Eclipses* 305 

and the Sun's least ; and the total darkness can ex- Plate XL 
tend no farther than the dark shadow covers. Yet 
the Moon's partial shadow or penumbra may then 
cover a circular space 4900 miles diameter, within 
all which the Sun is more or less eclipsed, as the 
places are less or more distant from the centre of the 
penumbra. When the Moon changes exactly in the 
node, the penumbra is circular on the Earth at the 
middle of the general eclipse ; because at that time 
it falls perpendicularly on the Earth's surface : but 
at every other moment it falls obliquely, and will 
therefore be elliptical, and the more so, as the time 
is longer before or after the middle of the general 
eclipse; and then, much greater portions of the 
Earth's surface are involved in the penumbra. 

335. When the penumbra first touches the Earth, Duration 
the general eclipse begins : when it leaves the Earth, of general 
the general eclipse ends : from the beginning to the cuiar edp- 
end the Sun appears eclipsed in some part of theses. 
Earth or other. When the penumbra touches any 
place, the eclipse begins at that place, and ends when 

the penumbra leaves it. When the Moon changes 
in the node, the penumbra goes over the centre of 
the Earth's disc as seen from the Moon ; and con- 
sequently by describing the longest line possible on 
the Earth, continues the longest upon it; namely, 
at a mean rate, 5 hours 50 minutes : more, if the 
Moon be at her greatest distance from the Earth, 
because she then moves slowest ; less, if she be at 
her least distance, because of her quicker motion. 

336. To make the last five articles and several Fig. I/, 
other phenomena plainer, let S be the Sun, E the 
Earth, M the Moon, and AMP the Moon's orbit. 
Draw the right line We 12 from the western side 

of the Sun at W^ touching the western side of the 
Moon at c, and the Earth at 12 : draw also the right 
line Vd 12 from the eastern side of the Sun at V> 
touching the eastern side of the Moon at r/, and the 



306 Of Eclipses. 

The ^ Earth at 12 : the dark space ce 12 d included be* 
dariTsha- tween those lines in the Moon's shadow, ending in 
dow, a point at 12, where it touches the Earth ; because 
in this case the Moon is supposed to change at M 
in the middle between A the apogee, or farthest 
point of her orbit from the Earth, and P the peri- 
gee, or nearest point to it. For, had die point P 
been at J/, the Moon had been nearer the Earth ; 
and her dark shaded at e would have covered a 
space upon it about 180 miles broad, and the Sun 
would have been totally darkened, as at.// (Fig. I,) 
with some continuance : but had the point A (Fig. 
II,) been at J/, the Moon would have been farther 
from the Earth, and her shadow would have ended 
in a point about e, and therefore the Sun would have 
andpe- appeared, as at./? (Fig. L), like a luminous ring all 
numbra* around the Moon. Draw the right lines W ' Xdh 
and PXcg) touching the contrary sides of the Sun 
and Moon, and ending on the Earth at a and b: 
draw also the right line S XM 12, from the centre 
of the Sun's disc, through the Moon's centre, to 
the Earth at 12 ; and suppose the two former lines 
WXdh and VXcg to revolve on the line SXM 
12 as an axis, and their points a and b will describe 
the limits of the penumbra TT on the Earth's sur- 
face, including the large space a b 12 a, within 
which the Sun appears more or less eclipsed, as the 
places are more or less distant from the verge of 
the penumbra a b. t 

Digits, Draw the right line y 12 across the Sun's disc, 
what. perpendicular to SXM, the axis of the penumbra: 
then divide the line y 12 into twelve equal parts, as 
in the figure, for the twelve * digits of the Sun's 
diameter : and at equal distances from the centre of 
the penumbra at 12 (on the Earth's surface YY) to 
its edge a b, draw twelve concentric circles, as 
marked with the numeral figures 1, 2, 3, 4, &c. and 

* A digit is a twelfth part of the diameter of the Sun or 
Moon. 



Of Eclipses. 307 



remember that the Moon's motion in her orbit 
A M P is from west to east, as from s to t. Then, 

To an observer on the Earth at b, the eastern T 
limb of the Moon at d seems to touch the western 
limb of the Sun at PF, when the Moon is at M; eclipse. 
and the Sun's eclipse begins at , appearing as at 
A in Fig, III, at the left hand ; but at the same 
moment of absolute time to an observer at a in 
Fig. II, the western edge of the Moon at c leaves 
the eastern edge of the Sun at F, and the 'eclipse 
ends, as at the right hand C of Fig. III. At the 
very same instant, to all those who live on the cir- 
cle marked 1 on the Earth E in Fig. II. the Moon 
M cuts off or darkens a twelfth part of the Sun 5, 
and eclipses him one digit, as at ] in Fig. Ill : to 
those who live on the circle marked 2 in Fig. II, 
the Moon cuts off two twelfth parts of the Sun, 
as at 2 in Fig. Ill : to those on the circle 3, three 
parts; and so on to the centre at 12 in Fig. II, 
where the Sun is centrally eclipsed as at B in the 
middle of Fig. Ill ; under which figure there is a 
scale of hours and minutes, to shew, at a mean rate, Fl S- n 
how long it is from the beginning to the end of a 
central eclipse of the Sun on the parallel of London ; 
and how many digits are eclipsed at any particular 
time from the beginning at A to the middle at B, or 
the end at C. Thus, in 1 6 minutes from the be- 
ginning, the Sun is two digits eclipsed ; in an hour 
and five minutes, eight digits; and in an hour and 
thirty-seven minutes, 12 digits. 

337. By Fig. II, it is plain, that the Sun is total- FL 
ly or centrally eclipsed but to a small part of the 
Earth at any time ; because the dark conical shadow 
e of the Moon M falls but on a small part of the 
Earth : and that a partial eclipse is confined at that 
time to the space included by the circle a , c: 
which only one half can be projected in the figure, 
the other half being supposed to be hid by the con- 
vexity of the Earth E ; and likewise, that no parr 



308 Of Eclipse*. 

Plats XL of the Sun is eclipsed to the large space TT of the 
Earth, because the Moon is not between the Sun and 
cit%Tthe an y thatpart of the Earth: and therefore to all that 
Moon's ie part the eclipse is invisible. The Earth turns east* 
shadow on warc j on its axis, as from g to /;?, which is the same 
lt way that the Moon's shadow moves; but the Moon's 
motion is much swifter in her orbit from s to / : and 
therefore, although eclipses of the Sun are of longer 
duration on account of the Earth's motion on its 
axis than they would be if that motion was stopt, yet 
in four minutes of time at most the Moon's swifter 
motion carries her dark shadow quite over any place 
that its centre touches at the time of greatest obscu- 
ration. The motion of the shadow on the Earth's disc 
is equal to the Moon's motion from the Sun, which 
is about 30-^ minutes of a degree every hour at a 
mean rate; but so much of the Moon's orbit is equal 
to SO- degrees of a great circle on the Earth, 32O; 
and therefore the Moon's shadow goes 30- degrees 
or 1 830 geographical miles on the Earth in an hour, 
or 30] miles in a minute, which is almost four times 
as swift as the motion of a cannon ball. 
Figr- iv. 338. As seen from the Sun or Moon, the Earth's 
axis appears differently inclined every day of the year, 
on account of keeping its parallelism throughout its 
annual course. Let , D, 0, N 9 be the Earth at the 
two equinoxes, and the two solstices, NS its axis, N 
the north pole, 5 the south pole, JE Q the equator, 
T the tropic of Cancer, t the tropic of Capricorn, 
and ABC the circumference of the Earth's enlight- 
ened disc as seen from the Sun or new Moon at these 
Phenome. times. The Earth's axis has the position N E S at 
Earti^as 6 t ^ le verna ^ equinox, lying toward the right hand, as 
seen from seen from the Sun or new Moon ; its poles A' and S 
the su nol *beimr then in the circumference of the disc ; and the 

new Moon o i i- 

atdifferent equator and all its parallels seem to be straight lines, 

times of b ecaus e their planes pass through the observer's eye 

looking down upon the Earth from the Sun or Moon 

directly over E, where the ecliptic F G intersects the 



Of Eclipses. 309 

equator JE Q.-> At the summer solstice, the Earth's 
axis has the position NDS; and that part of the eclip- 
tic FG, in which the Moon is then new, touches the 
tropic of Cancer T at D. The north pole N at that 
time inclining 23 * degrees toward the Sun, falls so ' 
many degrees within the Earth's enlightened disc; 
because the Sun is then vertical to Z), 23V degrees 
north of the equator M Q; and the equator, with all 
its parallels seem elliptic curves bending downward, 
or toward the south pole, as seen from the Sun: 
which pole, together with 237 degrees all round it, 
is hid behind the disc in the dark hemisphere of the 
Earth. At the autumnal equinox, the Earth's axis 
has the position NOS 9 lying to the left hand as seen 
from the Sun or new Moon, which are then vertical 
to 0, where the ecliptic cuts the equator O. Both 
poles now lie in the circumference of the disc, the 
north pole just going to disappear behind it, and the 
south pole just entering into it ; and the equator with 
all its parallels seem to be straight lines, because their 
planes pass through the observer's eye, as seen from 
the Sun, and very nearly so as seen from the Moon. 
At the winter solstice, the Earth's axis has the position 
NNS ; when its south pole S inclining 23J degrees 
towards the Sun, falls 23 degrees within the enlight- 
ened disc, as seen from the Sun or new Moon, which 
are then vertical to the tropic of Capricorn /, 23] de- 
grees south of the equator JE O; and the equator with 
all its parallels seem elliptic curves bending upward ; 
the north pole being as far behind the disc in the 
dark hemisphere, as the south pole is come into the 
light. The nearer that any time of the year is to 
the equinoxes or solstices, the more it partakes of the 
phenomena relating to them. 

339. Thus it appears, that from the vernal equi- 
nox to the autumnal, the north pole is enlightened ; 
and the equator and all its parallels appear elliptical 
as seen trom the Sun, more or less curved as the 
time is pearer to or farther from the summer sol- 



310 Of Eclipses. 

Plate XL st | ce . and bending downward, or toward the south 

Var-.pis pole; the reverse of which happens from the au- 

ofthe'' tumna l equinox to the vernal. A little consideration 

Earth's will be sufficient to convince the reader, that the 

teeiifVom ^ artn ' s ax * s inclines toward the Sun at the summer 

the Sun at solstice ; f rom the Sun at the winter solstice ; and 

tlme^'of- sidewise to the Sun at the equinoxes ; but toward 

the year, the right hand, as seen from the Sun at the vernal 

equinox ; and toward the left hand at the autumnal, 

From the winter to the summer solstice, the Earth's 

'axis inclines more or less to the right hand, as seen 

from the Sun ; and the contrary from the summer: 

to the winter solstice. 

jfow these 340. The different positions of the Earth's axis, 
affect solar as seen ^ rom tne ^ un at different times of the year, 
eclipses, affect solar eclipses greatly with regard to particular 
places ; yea so far as would make central eclipses 
which fall at one time of the year, invisible if they 
had fallen at another ; even though' the Moon should 
always change in the nodes, and at the same hour of 
the day : of which indefinitely various affections, we 
shall only give examples for the times of the equi- 
noxes and solstices. 

Fig. iv. In the same diagram, let FG be part of the eclip- 
tic, and IK, i k, i k, i k, part of the Moon's orbit ; 
both seen edgewise, and therefore projected into right 
lines ; and let the intersections TV, 0, ), , be one 
and the same nodes at the above times, when the 
Earth has the forementioned different positions; and 
let the space included by the circles, P, /, p, p, be 
the penumbra at these times, as its centre is passing 
over the centre of the Earth's disc. At the winter 
solstice, when the Earth's axis has the position 
N N 6\ the centre of the penumbra P touches the 
tropic of Capricorn / in N at the middle of the ge- 
neral eclipse ; but no part of the penumbra touches 
the tropic of Cancer T. At the summer solstice, 
when'the Earth's axis has the position ND S (i D k 



Of Eclipses. 

being then part of the Moon's orbit, whose node is 
at Z)), the penumbra p has its centre at I), on the 
tropic of Cancer T 9 at the middle of the general 
eclipse, and then no part of it touches the tropic of 
Capricorn /. At the autumnal equinox, the Earth's 
axis has the position N S (i k being then part 
of the Moon's orbit), and the penumbra equally in- 
eludes part of both tropics 7" and t at the middle of 
the general eclipse : at the vernal equinox it does 
the same, because the Earth's axis has the position 
N E S : but in the former of these two last cases, 
the penumbra enters the Earth at A, north of the 
tropic of Cancer T, and leaves ii at m, south of the 
tropic of Capricorn /; having gone over the Earth 
obliquely southward, as its centre described the line 
AOm: whereas, in the latter case, the penumbra 
touches the Earth at ;;, south of the equator JE 6>, 
and describing the line n E q (similar to the former 
line AOm in open space) goes obliquely northward 
over the earth, and leaves it at ^, north of the equa- 
tor. 

In all these circumstances, the Moon has been 
supposed to change at noon in her descending node : 
had she changed in her ascending node, the pheno- 
mena would have been as various the contrary way, 
with respect to the penumbra's going northward or 
southward over the Earth. But because the Moon 
changes at all hours, as often in one node as in the 
other, and at all distances from them both at differ- 
ent times as it happens, the variety of the phases of 
eclipses are almost innumerable, even at the same 
places; especially considering how variouslv the 
same places are situate on the enlightened disc of the 
Earth, with respect to the penumbra's motion, at the 
different hours when eclipses happen. 

341. When the Moon changes 17 degrees short HOW 
of her descending node, the penumbra P \ 8 just | n . ; 1( , h e ( '' 

touches the northern part of the Earth's disc, near uumbr* 

i) j. folia MI tW 



Of Eclipses. 



distances Moon appears to touch the Sun, but hides no part 

fcodes the ^ ki m * rom ^g^ ^ ac * tne change been as far 
short of the ascending node ; the penumbra would 
have touched the southern part of the disc near the 
south pole S. When the Moon changes 12 degrees 
short of the descending node, more than a third part 
of the penumbra P 1 2 falls on the northern parts of 
the Earth at the middle of the general eclipse : had 
she changed as far past the same node, as much on 
the other side of the penumbra about P would have 
fallen on the southern part of the Earth ; all the rest 
in the expansion or open space. When the Moon 
changes 6 degrees from the node, almost the whole 
penumbra P 6 falls on the Earth at the middle of the 
general eclipse. And lastly, when theMoon changes 
in the node at A 7 , the penumbra P N takes the long- 
est course possible on the Earth's disc ; its centre 
falling on the middle of it, at the middle of the ge- 
neral eclipse. The farther the Moon changes from 
either node, within 1 7 degrees of it, the shorter is 
the penumbra's continuance on the Earth, because 
it goes over a less proportion of the disc, as is evi- 
dent by the figure. 

Earth's 342> T ^ e nearer tnat tne penumbra's centre is to 

diumai the equator at the middle of the general eclipse, the 

lengthens ^ on g er * s tne duration of the eclipse at all those 

the dura- places where it is central ; because, the nearer that 

hrecfi *~ * n y P* ace ^ to t ^ le equator the greater is the circle 

ses, which it describes by the Earth's motion on its axis ; and 

mltthe^o s 5 t ^ ie P^ ace m ving quicker, keeps longer in the 

tar circles, penumbra, whose motion is the same way with that 

of the place, though faster, as has been already 

mentioned, 337. Thus (see the Earth at D and 

the penumbra at 12) while the point b in the polar 

circle a b c d is carried from b to c by the Earth's 

diurnal motion, the point d on the tropic of Cancer 

T is carried a much greater length from d to D : 



Of Eclipses. 

and therefore, if the penumbra's centre should go one 
time over c, and another time over D, the penumbra 
will be longer in passing over the moving-place d, 
than it was in passing over the moving-place b. Con- 
sequently, central eclipses about the poles are of the 
shortest duration ; and about the equator of the 
longest. 

343. In the middle of summer, the whole frigid 

.... . .17 7 v i ens the du- 

zone, included by the polar circle ab <:<:/, is enhght- ration of 
ened ; and if it then happens that the penumbra's * 
centre passes over the north pole, the Sun will be within * 
eclipsed much the same number of digits at a as at these c! *- 
c ; but while the penumbra moves eastward over r/ ' 
it moves westward over a 9 because, with respect to 
the penumbra, the motions of a and c are contrary: 
for c moves the same way with the penumbra toward 
d, but a moves the contrary way toward b; and there- 
fore the eclipse will be of longer duration at c than 
at a. At a, the eclipse begins on the Sun's eastern 
limb, but at <:, on his western : at all places lying 
without the polar circles, the Sun's eclipses begin 
on his western limb, or near it, and end on or near 
his eastern. At those places where the penumbra 
touches the earth, the eclipse begins with the rising 
Sun, on the top of his western or uppermost edge; 
and at those places where the penumbra leaves the 
Earth, the eclipse ends with the setting Sun, on the 
top of his eastern edge, which is then the uppermost, 
just at its disappearing on the liorizon. 
344.IftheMoonweresurroundedbyanatmosphereTbeMoof> 

of any considerable density, it would seem to touch 
the Sun a little before the Moon made her appulse 
to his edge, and we should see a little faintness on 
that edge before it was eclipsed by the Moon: but 
as no such faintness has been observed, at least so 
far as I have ever heard, it seems plain, that the 
Moon has no such atmosphere as that of the Earth. 
The faint ring of light surrounding the Sun in to- 



314 Of Eclipses. 

Plate XL tal eclipses, called by CASSINI la Chevelure du 
Sohil, seems to be the atmosphere of the Sun ; be- 
cause it has been observed to move equally with the 
Sun, not with the Moon. 

345. Having said so much about eclipses of the 
Sun, we shall drop that subject at present, and pro- 
ceed to the doctrine of lunar eclipses: which, being 
more simple, may be explained in less time. 

fte 'Moon' f ^ ^ at tne Moon can never be eclipsed but at the 
time of her being full, and the reason why she is 
not eclipsed at every full, has been shewn already. 

Fig. ii. 3)6, 317. Let S be the Sun, E the Earth, RR 
the Earth's shadow, and B the Moon in opposition 
to the Sun : in this situation the Earth intercepts 
the Sun's light in its way to the Moon : and when 
the Moon touches the Earth's shadow at v, she be- 
gins to be eclipsed on her eastern limb #, and con- 
tinues eclipsed until her western limb y leaves the 
shadow at iv; at B she is in the middle of the 
shadow, and consequently in the middle of the 
eclipse. 

346. The Moon when totally eclipsed is not in- 
visible, if she be above the horizon, and the sky be 
clear ; but appears generally of a dusky colour like 
tarnished copper, which some have thought to be 

why the the Moon's native light. But the true cause of her 
Moon is b em pp visible is the scattered beams of the Sun, bent 

visible in a . P. , , , . , , 

total into the Earth s shadow by going through the atmos- 
?ciipse. phere; which, being more dense near the Earth than 
at considerable heights above it, refracts or bends 
theSun's rays more inward, 179; and those which 
pass nearest the Earth's surface, are bent more than 
those rays which go through higher parts of the at- 
mosphere, where it is less dense, until it be so thin 
or rare as to lose its refractive power. Let the 
circle fg h /, concentric to the Earth, include the 
atmosphere, whose refractive power vanishes at the 
heights /and /'; so that the rays W fw and Vi v 



Of Eclipses. 31.5 

go on straight without suffering the least refraction. Ptat* XL 
But all those rays which enter the atmosphere, be- 
tween f and , and between / and /, on opposite 
sides of the Earth, are gradually more bent inward as 
they go through a greater portion of the atmosphere, 
until the rays W k and V I touching the Earth at m 
and ?2, are bent so much as to meet at q, a little 
short of the Moon ; and therefore the dark shadow 
of the Earth is contained in the space m o q p ??, 
where none of the Sun's rays can enter : all the rest 
R R, being mixed by the scattered rays which are 
refracted as above, is in some measure enlightened 
by them ; and some of those rays falling on the 
Moon, give her the colour of tarnished copper, or 
of iron almost red-hot. So that if the Earth had no 
atmosphere, the Moon would be as invisible in to- 
tal eclipses as she is when new. If the Moon were 
so near the Earth as to go into its dark shadow, sup- 
pose about p o, she would be invisible during her 
stay in it ; but visible before and after in the fainter 
shadow R R. 

347, When the Moon goes through the centre of why the 
the Earth's shadow, she is directly opposite , to the ,;'^'"j. e 
Sun : yet the Moon has been often seen totally eclips- sometimes 
ed in the horizon when the Sun was also visible i 

the opposite part of it : for, the horizontal refraction MOOU 
being almost 34 minutes of a degree, 181, and the 
diameter of the Sun and Moon being each at a mean 
state but 32 minutes, the refraction causes both lu- 
minaries to appear above the horizon when they are 
really below it, 1 79. 

348. When the Moon is full at 12 degrees from 
either of her nodes, she just touches the Earth's sha- 
dow, but enters not into it. Let G H be the eclip- 
tic, ef the Moon's orbit where she is 12 degrees 
from the node at her full ; c d her orbit where she is 
6 degrees from the node; a b her orbit where she is 
full in the node; A B the Earth's shadow, and M 



516 Of Eclipses. 

Duration the Moon. When the Moon describes the line ef y 
ccH^sesoV S ^ e J ust toucnes tne shadow, but does not enter into 
the Moon, it ; when she describes the line c d, she is totally, 
though not centrally immersed in the shadow ; and 
when she describes the line a b, she passes by the 
node at M in the centre of the shadow ; and takes 
the longest line possible, which is a diameter, through 
it: and such an eclipse being both total and central 
is of the longest duration, namely, 3 hours 57 mi- 
nutes 6 seconds from the beginning to the end, if 
the Moon be at her greatest distance from the Earth; 
and 3 hours 37 minutes 26 seconds, if she be at 
her least distance. The reason of this difference 
is, that when the Moon is farthest from the Earth, 
she moves the slowest ; and when nearest to it, the 
quickest. 

Digits. 349. The Moon's diameter, as well as the Sun's, 

is supposed to be divided into twelve equal parts, 

called digits ; and so many of these parts as are 

darkened by the Earth's shadow, so many digits is 

the Moon eclipsed. All that the Moon is eclipsed 

above 12 digits, shew, how far the shadow of the 

Earth is over the body of the Moon, on that edge 

to which she is nearest at the middle of the eclipse. 

why the 350. It is difficult to observe exactly either the 

anTendof Beginning or ending of a lunar eclipse, even with a 

a lunar good telescope ; because the Earth's shadow is so 

? cli P s faint and ill-defined about the edges, that when the 

is so tlifa- ^ . . 1 i 

cult to be Moon is either just touching or leaving it, the ob- 
1 " scurat i n *' k r * irn b * s scarce sensible ; and there- 



aervation" fore the nicest observers can hardly be certain to se- 
veral seconds of time. But both the beginning and 
ending of solar eclipses are visibly instantaneous : 
for the moment that the edge of the Moon's disc 
touches the Sun's, his roundness seems a little broken 
on that part ; and the moment she leaves it, he ap- 
pears perfectly round again. 

The use of 351. In astronomy, eclipses of the Moon are of 
fn'llrtro- g r eat use for ascertaining the periods of her motions ; 

no my, 



Of Eclipses. 317 



especially such eclipses as are observed to be alike i 
ull circumstances, and have long intervals of ti 
between them. In geography, the longitudes 
places are found by eclipses, as already shewn in the 
eleventh chapter. In chronology, both solar and lu- 
nar eclipses serve to determine exactly the time of 
any past event: for there are so many particulars ob- 
servable in every eclipse, with respect to its quanti- 
ty, the places where it is visible (if of the Sun,) and 
the time of the day or night ; that it is impossible 
there can be two solar eclipses in the course of ma- 
ny ages which are alike in all circumstances. 

352. From the above explanation of the doctrine The dkrk - 
of eclipses, it is evident that the darkness at our SA-"ur S s a A . 
VIOUR'S crucifixion was supernatural. For he suf- VJOUR'S 
fered on the day on which the passover was eaten by 
the Jews, on which day it was impossible that 
Moon's shadow could fall on the Earth; for the Jews 
kept the passover at the time of full Moon: nor does 
the darkness in total eclipses of the Sun last above 
four minutes in any place, 333, whereas the dark- 
ness at the crucifixion lasted three hours, Matt. 
xxviii. 15. and overspread at least all the land of 
Judea. 



The Construction of the following Tables* 



CHAP. XIX. 

Shewing the Principles on which the following Astro- 
nomical Tables are constructed, and the Method of 
co. I dilating the Times of New and Full Moons and 
Eclipses by them. 



353 nearer that any object is to the eye of 

JL an observer, the greater is the angle un- 
der which it appears : the farther from the eye, the less. 

The diameters of the Sun and Moon subtend dif- 
ferent angles at different times. And at equal in- 
tervals of time, these angles are once at the greatest, 
and once at the least, in somewhat more than a com- 
plete revolution of the luminary through the eclip- 
tic, from any given fixed star to the same star 
again. This proves that the Sun and Moon are 
constantly changing their distances from the Earth ; 
and that they are once at their greatest distance and 
once at their least, in little more than a complete re- 
volution. 

The gradual differences of these angles are not 
what they would be, if the luminaries moved in 
circular orbits, the Earth being supposed to be 
placed at some distance from the centre : but they 
agree perfectly with elliptic orbits, supposing the low- 
er focus of each orbit to be at thecentre of the Earth.* 

The farthest point of each orbit from the Earth's 
centre is called the apogee, and the nearest point is 
called the perigee. These points are directly oppo- 
site to each other. 

Astronomers divide each orbit into 12 equal parts 
called signs ; each sign into SO equal parts, called 
degrees ; each degree into 60 equal parts, called mi- 
nutes ; and every minute into 60 equal parts, called 
seconds. The distance of the Sun or Moon from 

* The Sun is in the focus of the Earth's orbit, and the 
Earth in or near that of the Moon's orbit. 



The Construction of the following Tables. 519 

any given point of its orbit, is reckoned in signs, 
degrees, minutes, and seconds. Here we mean the 
distance that the luminary has moved through from 
any given point ; not the space it is short of it in 
coming round again, though ever so little. 

The distance of the Sun or Moon from its apo- 
gee at any given time is called its mean anomaly : 
so that, in the apogee, the anomaly is nothing ; in 
the perigee, it is six signs. 

The motions of the Sun and Moon are observed 
to be continually accelerated from the apogee to the 
perigee, and as gradually retarded from the perigee 
to the apogee ; being slowest of all when the mean 
anomaly is nothing, and swiftest of all when it is 
six signs. 

When the luminary is in its apogee or its perigee, 
its place is the same as it would be, if its motion 
were equable in all parts of its orbit. The sup- 
posed equable motions are called mean ; the unequa- 
ble are jusfry called the true . 

The mean place of the Sun or Moon is always for- 
warder than the true place*, while the luminary is 
moving from its apogee to its perigee; and the true 
place is always forwarder than the mean, while the 
luminary is moving from its perigee to its apogee. 
In the former case, the anomaly is always less than 
six signs ; and in the latter case, more. 

It has been found, by a long series of observa- 
tions, that the Sun goes through the ecliptic, from 
the vernal equinox to the same equinox again, in 
365 days 5 hours 48 minutes 55 seconds : from the 
first star of Aries to the same star again, in 365 days 
6 hours 9 minutes 24 seconds: and from his apogee 
to the same again, in 365 days 6 hours 14 minutes 
seconds. The first of these is called the solar 

* The point of the ecliptic in which the Sun or Moon is at any 
given moment of time is called \hefilace of the Sun or Moon at 
that time. 

S s 



The- Construction of lhc following Tables. 

ijcar> the second the sidereal year, and the third the 
anomalistic year. So that the solar year is 20 minutes 
29 seconds shorter than the sidereal; and the sidereal 
year is 4 minutes 36 seconds shorter than the ano- 
malistic. Hence it appears that the equinoctial 
point, or intersection if the ecliptic and equator at 
the beginning of Aries, goes backward with respect 
to the fixed stars, and that the Sun's apogee goes 
forward. 

It is also observed, that the Moon goes through 
her orbit from any given fixed star to the same star 
again, in 27 days 7 hours 43 minutes 4 seconds at 
a mean rate : from her apogee to her apogee again, 
in 27 days 13 hours 18 minutes 43 seconds: and 
from the Sun to the Sun again, in 29 days 12 hours 
44 minutes 3-fs seconds. This shews, that the Moon's 
apogee moves forward in the ecliptic, and that at a 
much quicker rate than the Sun's apogee does; 
since the Moon is 5 hours 55 minutes 39 seconds 
longer in revolving from her apogee to her apogee 
again, than from any star to the same star again. 

The Moon's orbit crosses the ecliptic in two op- 
posite points, which are called her nodes : and it is 
observed that she revolves sooner from any node to 
the same node again, than from any star to the same 
star again, by 2 hours 38 minutes 27 seconds; which 
shews that her nodes move backward, or contrary 
to the order of signs, in the ecliptic. 

The time in which the Moon revolves from the 
Sun to the Sun again (or from change to change) is 
called a lunation\ which, according to Dr. POUND'S 
mean measures, would always consist of 29 days 12 
hours 44 minutes 3 seconds 2 thirds 58 fourths, if 
the motions of the Sun and Moon were always equa- 
ble*. Hence, 12 mean lunations contain 354 days 

* We have thought proper to keep by Dr. Pound's length of a 
mean lunation, because his numbers come nearer to the times of the 
ancient eclipsesj than Mayer's do, without allowing for the Moon% 
acceleration* 



The Construction of the following Tables. 321 

3 hours 48 minutes 36 seconds 3 5 thirds 40 fourths, 
which is 10 days 21 hours 11 minutes 23 seconds 
24 thirds 20 fourths less than the length of a com- 
mon Julian year, consisting of 365 days 6 hours ; 
and 13 mean lunations contain 383 days 21 hours 
32 minutes 39 seconds 38 thirds 38 fourths, which 
exceeds the length of a common Julian year, by 18 
days 15 hours 32 minutes 39 seconds 38 thirds 38 
fourths. 

The mean time of new Moon being found for any 
given year and month, as suppose for March 1700, 
old style, if this mean new Moon falls later than the 
llth day of March, then 12 mean lunations, added 
to the time of this mean new Moon, will give the 
time of the mean new Moon in March 1701, after 
having thrown off 365 days. But when the mean 
new Moon happens to be before the llth of March, 
we must add 13 mean lunations, in order to have 
the time of mean new Moon in March the year fol- 
lowing ; always taking care to subtract 365 day sin 
common years, and 366 days in leap-years, from 
the sum of this addition. 

Thus, A. D. 1700, old style, the time of mean 
new Moon in March, was the 8th day, at 16 hours 
11 minutes 25 seconds after the noon of that day 
(viz. at 11 minutes 25 seconds past IV in the morn- 
ing of the 9th day, according to common reckon- 
ing). To this we must add 13 mean lunations, or 
383 days 21 hours 32 minutes 39 seconds 38 thirds 
38 fourths, and the sum will be 392 days 13 hours 
44 minutes 4 seconds 38 thirds 3 8 fourths; from 
which subtract 365 days, because the year 1701 
is a common year, and there will remain 27 days 
13 hours 44 minutes 4 seconds 38 thirds 38 fourths 
for the time of mean new Moon in March, A. D. 
1701. 

Carrying on this addition and subtraction till 
A. D. 1703, we find the time of mean new Moon 
in March that year, to be on the 6th day at 7 hours 



322 The Construction of the following Tables. 

21 minutes 17 seconds 49 thirds 46 fourths past 
noon ; to which add 13 mean lunations, and the sum 
will be 390 days 4 hours 53 minutes 57 seconds 28 
thirds 20 fourths ; from which subtract 366 days, 
because the year ] 704 is a leap-year, and there will 
remain 24 days 4 hours 53 minutes 57 seconds 28 
thirds 20 fourths for the time of mean new Moon in 
March, A. D. 1704. 

In this manner was the first of the following tables 
constructed to seconds, thirds, arid fourths; and then 
written out to the nearest second. The reason why 
we chose to begin the year with March* was to avoid 
the inconvenience of adding a day to the tabular time 
in leap-years after February, or subtracting a day 
therefrom in January and February in those years ; 
to which all tables of this kind are subject, which 
begin the year with January, in calculating the times 
of new or full Moons. 

The mean anomalies of the Sun and Moon, and 
the Sun's mean motion from the ascending node of 
the Moon's orbit, are set down in Table III. from 
one to 13 mean lunations. These numbers, for 13 
lunations, being added to the radical anomalies of the 
Sun and Moon, and to the Sun's mean distance from 
the ascending node, at the time of mean new Moon 
in March 1700, (Table I.) will give their mean ano- 
malies, and the Sun's mean distance from the node, 
at the time of mean new Moon in March 1701 ; 
and being added for 12 lunations to those for 1701, 
give them for the time of mean new Moon in March 
1702. And so on, as far as you please to continue 
the table (which is here carried on to the year 1800), 
always throwing off 12 signs when their sum ex- 
ceeds 12, and setting down the remainder as the 
proper quantity. 

If the numbers belonging to A. D. 1700 (in Ta- 
ble I.) be subtracted from those belonging to 1800, 
we shall have their whole differences in 100 com- 
plete Julian years ; which accordingly we find to be 



The Construction of the following Tables. 

4 days 8 hours 10 minutes 52 seconds 15 thirds 40 
fourths, with respect to the time of mean new 
Moon. These being added together 60 times, (al- 
ways taking care to throw off a whole lunation when 
thQ days exceed 29|) making up 60 centuries, or 
6000 years, as in Table VJ. which was carried on 
to seconds, thirds, and fourths; and then written 
out to the nearest second. In the same manner 
were the respective anomalies and the Sun's distance 
from the node found, for these centurial years ; and 
then (for want of room) written out only to the near- 
est minute, which is sufficient in whole centuries. 
By means of these two tables, we may find the time 
of any mean new Moon in March y together with 
the anomalies of the Sun and Moon, and the Sun's 
distance from the node, at these times, within the 
limits of 6000 years, either before or after any giv- 
en year in the 18th century; and the mean time of 
any new or full Moon in any given month after 
March, by means of the third and fourth tables, 
within the same limits, as shewn in the precepts for 
calculation. 

Thus it would be a very easy matter to calculate 
the time of any new or full Moon, if the Sun and 
Moon moved equably in all parts of their orbits. 
But we have already shewn that their places are ne- 
ver the same as they would be by equable motions, 
except when they are in apogee or perigee ; which 
is when their mean anomalies are either 'nothing, or 
six signs : and that their mean places are always for- 
warder than their true places, while the anomaly is 
less than six signs ; and their true places are for- 
warder than the mean, while the anomaly is more. 

Hence it is evident, that while the Sun's anomaly 
is less than six signs, the Moon will overtake him, 
or be opposite to him, sooner than she could if his 
motion were equable ; and later while his anomaly 
is more than six signs. The greatest difference that 
can possibly happen between the mean and true time 



324 The Construction of the following Tables. 

of new or full Moon, on "account of the inequality 
of the Sun's motion, is three hours 48 minutes 
28 seconds : and that is, when the Sun's anomaly 
is either 3 signs 1 degree, or 8 signs 29 degrees ; 
sooner in the first case, and later in the last. In all 
other signs and degrees of anomaly, the difference 
is gradually less, and vanishes when the anomaly is 
either nothing or six signs. 

The Sun is in his apogee on the 30th of June, 
and in his perigee on the 30th of December , in the 
present age ; so that he is nearer the Earth in our 
winter than in our summer. The proportional dif- 
ference of distance, deduced from the difference of 
the Sun's apparent diameter at these times, is as 
983 to 1017. 

The Moon's orbit is dilated in winter, and con- 
tracted in summer ; therefore the lunations are long- 
er in winter than in summer. The greatest differ- 
ence is found to be 22 minutes 29 seconds ; the lu- 
nations increasing gradually in length while the Sun 
is moving from his apogee to his perigee, and de- 
creasing in length while he is moving from his pe- 
rigee to his apogee. On this account the Moon 
will be later every time in coming to her conjunc- 
tion with the Sun, or being in opposition to him, 
from December till June^ and sooner from June to 
December, than if her orbit had continued of the 
same size all the year round. 

As both these differences depend on the Sun's 
anomaly, they may be fitly put together into one ta- 
ble, and called The annual, or first equation of the 
mean to the true* syzygy (see Table VII.) This 
equational difference is to be subtracted from the 
time of the mean syzygy when the Sun's anomaly 
is less than six signs, and added when the anomaly 
is more. At the greatest, it is 4 hours 10 minutes 
57 seconds, viz. 3 hours 48 minutes 28 seconds. 

* The word syzygy signifies both the conjunction and opposition 
of the Sun and Moon/ 



The Construction of the following. Tables. 325 

i 

on account of the Sun's unequal motion, and 22 
minutes 29 seconds, on account of the dilatation of 
the Moon's orbit. 

This compound equation would be sufficient for 
reducing the mean time of new or full Moon to the 
true time, if the Moon's orbit were of a circular 
form, and her motion quite equable in it. But the 
Moon's orbit is more elliptical than the Sun's, and 
her motion in it so much the more unequal. The 
difference is so great, that she is sometimes in con- 
junction with the Sun, or in opposition to him, soon- 
er by 9 hours 47 minutes 54 seconds, than she 
would be if her motion were equable ; and at other 
times as much later. The former happens when 
her mean anomaly is 9 signs 4 degrees, and the lat- 
ter when it is 2 signs 26 degrees. See Table IX. 

At different distances of the Sun from the Moon's 
apogee, the figure of the Moon's orbit becomes dif- 
ferent. It is longest of all, or most eccentric, when 
the Sun is in the same sign and degree either with 
the Moon's apogee or perigee ; shortest of all, or 
least eccentric, when the Sun's distance from the 
Moon's apogee is either three signs or nine signs ; 
and at a mean state when the distance is either 1 
sign 15 degrees, 4 signs 15 degrees, 7 signs 15 de- 
grees, or 10 signs 15 degrees. When the Moon's 
orbit is at its greatest eccentricity, her apogeal dis- 
tance from the Earth's centre is to her perigeal 
distance from it, as 106 7 is to 933 ; when least ec- 
centric, as 1043 is to 957; and when at. the mean 
state, as 1055 is to 945. 

But the Sun's distance from the Moon's apogee 
is equal to the quantity of the Moon's mean ano- 
maly at the time of new Moon, and by the addition 
of six signs, it becomes equal in quantity to the 
Moon's mean anomaly at the time of full Moon. 
Therefore, a table may be constructed so as to answer 
all the various inequalities depending on the different 
eccentricities of the Moon's orbit In the syzygies ; 
and called The second equation of the mean to the true 



326 The Construction of the following Tables. 

syzygy (see Table IX.) and the Moon's anomaly, 
when equated by Table VIII. may be made the 
proper argument for taking out this second equa- 
tion of time, which must be added to the former 
equated time, when the Moon's anomaly is less than 
six signs, and subtracted when the anomaly is more. 
There are several other inequalities in the Moon's 
motion, which sometimes bring on the true syzygy 
a little sooner, and at other times keep it back a 
little later than it would otherwise be ; but they are 
so small, that they may be all omitted except two ; 
the former of which (see Table X.) depends on the 
difference between the anomalies of the Sun and 
Moon in the syzygies, and the latter (see Table 
XL) depends on the Sun's distance from the Moon's 
nodes at these times. The greatest difference aris- 
ing from the former, is 4 minutes 58 seconds; and 
from the latter, 1 minute 34 seconds. 

Having described the phenomena arising from the 
inequalities of the solar and lunar motions^ we 
shall now shew the reasons of these inequalities. 

In all calculations relating to the Sun and Moon, 
we consider the Sun as a moving body, and the 
Earth as a body at rest j since all the appearances 
are the same, whether it be the Sun or the Earth that 
moves. But the truth is, that the Sun is at rest, and the 
Earth moves round him once a year, in the plane 
of the ecliptic. Therefore, whatever sign and de- 
gree of the ecliptic the Earth is in, at any given 
time, the Sun will then appear to be in the oppo- 
site sign and degree. 

The nearer that any body is to the Sun, the more 
it is attracted by him; and this attraction increases 
as the square of the distance diminishes ; and vice 
versa. 

The Earth's annual orbit is elliptical, and the Sun 
is placed in one of its focuses. The remotest point 



The Construction of the following Tables. 327 

of the Earth's orbit from the Sun is called The 
earth* s aphelion; and the nearest point of the Earth's 
orbit to the Sun, is called The Earth's perihelion. 
When the Earth is in its aphelion, the Sun appears 
to be in its apogee ; and when the Earth is in its pe- 
rihelion, the Sun appears to be in its perigee. 

As the Earth moves from its aphelion to its pe- 
rihelion, it is constantly more and more attracted 
by the Sun ; and this attraction, by conspiring in 
some degree with the Earth's motion, must neces- 
sarily accelerate it. But as the Earth moves from 
its perihelion to its aphelion, it is continually less 
and less attracted by the Sun ; and as this attrac- 
tion acts then just as much against the Earth's 
motion, as it acted for it in the other half of the 
orbit, it retards the motion in the like degree. 
The faster the Earth moves, the faster will the 
Sun appear to move ; the slower the Earth moves, 
the slower is the Sun's apparent motion. 

The Moon's orbit is also elliptical, and the Earth 
keeps constantly in one of its focuses. The Earth's 
attraction has the same kind of influence on the 
Moon's motion, as the Sun's attraction has on the 
motion of the Earth : and therefore, the Moon's 
motion must be continually accelerated while she 
is passing from her apogee to her perigee ; and as 
gradually retarded in moving from her perigee to 
her apogee. 

At the time of new Moon, the Moon is nearer 
the Sun than the Earth is at that time, by the whole * 
semidiameter of the Moon's orbit ; which, at a 
mean state, is 240,000 miles ; and at the full, she 
is as much farther from the Sun than the Earth 
then is. Consequently, the Sun attracts the Moon 
more than it attracts the Earth in the former case, 
and less in the latter. The difference is greatest 
when the Earth is nearest the Sun, and least when 
it is farthest from him. The obvious result of this 
is, that as the Earth is nearest to the Sun in winter, 

Tt 



The Construction of the following Tables. 

and farthest from him in summer, the Moon's or.- 
bit must be dilated in winter, and contracted in 
summer. 

These are the principal causes of the difference 
of time, that generally happens between the mean 
and true times of conjunction or opposition of the 
Sun and Moon. As to the other two differences, 
'viz. those which depend on the difference between 
the anomalies of the Sun and Moon, and upon the 
Sun's distance from the lunar nodes, in the syzy- 
gies, they are owing to the different degrees of at- 
traction of the Sun and Earth upon the Moon, at 
greater or less distances, according to their respec- 
tive anomalies, and to the position of the Moon's 
tiodes with respect to the Sun. 

If ever it should happen, that the anomalies of 
both the Sun and Moon were either nothing or six 
signs, at the mean time of new or full Moon, and 
the Sun should then be in conjunction with either 
of the Moon's nodes, all ^he above-mentioned 
equations would vanish, and the mean and true 
time of the syzygy would coincide. But if ever 
-this circumstance did happen, we cannot expect; 
the like again in many ages afterward. 

Every 49th lunation (or course of the Moon 
from change to change) returns very nearly to the 
same time of the day as before. For, in 49 mean 
lunations there are 1446 days 23 hours 58 minutes 
29 seconds 25 thirds, which wants but 1 minute 
SO seconds 34 thirds of 1477 days. 

In29530590851 08 days,thereare lOOQOQOOOOOO 
mean lunations exactly : and this is the smallest 
number of natural days in which any exact num- 
ber of mean lunations will be completed. 



Astronomical Tables. 



129 



S 'TABLE I. The mean Time of JVew Moon in March, Old Style, S 
Ij with the mean Anomalies of the Sun and Moon, and the Sun'smean ^ 
S Distance from the Moon's Ascending Node, from A. D. 1700 to S 
S A. D. 1800 incliifiiue. S 


Y.ofChr. 


Mean New Moon 
in March. 


Sun's mean 
Anomaly. 


Moon's mean 
Anomaly. 


Sun'smeanDist. ? 
from the Node. ^ 


D. H. M. S. 


SO 7 " 


s ' " 


- S 


S 1700 
\ 1701 
S 1702 
<5 1703 
S 1704 


8 16 11 25 
27 13 44 5 
16 22 32 41 
6 7 21 18 
24 4 53 57 


8 19 58 48 
9 8 20 59 
8 27 36 51 
8 16 52 45 
9 5 14 54 


1 22 30 37 
28 7 42 
11 7 55 47 
9 17 43 52 
8 23 20 57 


6 14 31 7 S 
7 23 14 8 <J 
8 1 16 55 S 
8 9 19 42 ^ 

9 18 2 43 < 


S 1705 

% if oe 

S 1707 
vj 1708 


13 13 42 34 
2 22 31 11 
31 20 3 50 
10 4 52 27 


8 24 30 47 
8 13 46 39 
9 2 8 50 1 

8 21 24 43 


7392 
5 12 57 7 
4 18 34 13 
2 28 22 18 


9 26 5 30 S 
10 4 8 17 Jj 
11 12 51 18 S 
11 20 54 5 


^ 1709 
S 1710 
!j 1711 
S 1712 


29 2 25 7 
18 11 13 43 
7 20 2 20 
25 17 34 59 


9 9 46 54 
8 29 2 47 
8 18 18 39 
9 6 40 51 


2 3 59 24 
13 47 3C 
10 23 35 36 
9 29 12 42 


29 37 6 > 
1 7 39 54 S 
1 15 42 41 
2 14 25 43 < 


S 1713 
> 1714 
S 1715 
J.1716 


15 2 23 36 
4 11 12 13 
23 8 44 52 
11 17 33 29 


8 25 56 43 
8,15 12 35 
9 3 34 47 
8 22 50 39 


8 9 47 
6 ,18 48 5? 
5 24 25 57 
4 4 14 2 


3 2 28 30 
3 10 31 17 S 
4 19 14 IS S 
4 27 17 5 S 


S 1717 
$1718 

S 1719 
Ij 1720 


1 2 22 5 
19 23 54 45 
9 8 43 22 
27 6 16 1 


8 12 6 32 
9 28 44 
3 19 44 37 
9 8 6 49 


2 14 2 8 
1 19 39 13 
11 29 27 18 

115 4 24 


5 5 19 52 S 
6 14 2 54 ^ 
6 22 5 41 S 
8 43 43 J 


S 3722 
!j 1723 
S 1724 


16 15 4 38 
5 23 53 14 
24 21 25 54 
13 6 14 31 


8 27 22 4J 
8 16 38 33 
9 5 45 
8 24 16 37 


9 14 52 29 
7 24 40 34 
7 17 40 
5 10 5 45 


,8 8 51 29 
8 16 54 16 S 
9 25 37 18 Jj 
10 3 40 5 S 


S 1725 
J 1726 
S 1727 
S 1728 


2 15 3 78 13 32 29 
21 12 35 47 9 1 54 41 
10 21 24 23^8 21 10 34 
,28 18 57 3J9 9 52 46 


3 19 53 50 
2 25 30 56 
1 5 19 1 
10 50 7 


10 11 42 52 S 
1 20 25 54 $ 
I 28 28 41 Ij 
7 11 42 S 


S 1729 13 3 45 40 8 28 48 39 
<J 1730 7 12 34 16j8< 18 4 31 
i 1731 26 10 6 56p 6 26 42 
^ 1732 14 18 55 33J8 25 42 34 


10 20 44 12 
9 32 17 
8 6 9 23 
6 15 57 28 


15 14 29 S 
23 17 16 > 
3. 2 17 S 
3 10 3 4 ^ 



330 



Astronomical Tables. 



s ^ 




















S 


s 


Moan Ne\\ 


Moon 




Sun's mean 


Moon's mean 


Sun's moan Dh. S 


s S, 




in Mai 


eh. 






Anoi 


naly. 




Anomaly. 


irom tlic Nodi;. S 


S 






















? 


k. ^"" 

s ^ 


D. 


H. 


M 


s. 


S 





' 


a 


s 


/ '/ 


s U ' " S 


S 1733 


4 


3 


44 


9 


8 


14 


58 


26 


4 25 


45 33 


3 18 551S 


J; 1734 


23 


1 


16 


49 


J 


3 


20 


38 


4 1 


22 3f- 


4 26 48 53 j> 


S 1735 


12 


10 


3 


'2, 


8 


22 


36 


30 


2 11 


10 44 


5 4 5 1 40 S 


!j 1736 





18 


54 


2 


8 


11 


52 


22 


20 


58 49 


5 12 54 27 S 


S 1737 


19 


16 


26 


42 


9 





14 


34 


11 26 


35 55 


621 37 29 s 


S 1738 


9 


1 


15 


IB 


8 


19 


oO 


26 


10 6 


24 ( 


6 iJ'j 40 16 v, 


> 1739 


27 


22 


47 


5 cS 


9 


7 


52 


38 


9 12 


1 6 


3 8 23 18 S 


S 1740 


16 


7 


36 


31 


8 


27 


8 


30 


7 21 


49 11 


8 16 26 5 $ 


<> 1741 


5 


16 


25 


1 i 


8 


16 


24 


22 


6 1 


37 Ifc 


8 24 28 52 S 


S 1742 




24 


13 


57 


52 


9 


4 


46 


34 


5 7 


14 22 


10 3 1 1 54 vj 


S 1743 


13 


22 


46 


27 


] 


24 


2 


27 


3 17 


2 27 


10 1 14 41 Ij 


S 1744 


2 


7 


35 


4 


3 


13 


18 


20 


1 26 


50 32 


10 19 17 2g S 


S 1745 


21 


5 


7 


44 


9 


I 


40 


32 


1 2 


27 38 


11 28 80 t 


Jj 1746 


10 


13 


56 


20 


8 


20 


56 


24 


11 12 


15 4:- 


6 3 17 S 


3 1747 


29 


11 


29 







9 


18 


36 


10 17 


52 49 


1 14 46 19 Jj 


% 1748 


17 


20 


17 


36 


3 


28 


34 


28 


8 27 


40 54 


1 22 49 5 


S 1749 


7 


5 


6 


13 


8 


ir 


50 


20 


7 7 


28 59 


2 51 52 S 


S 1750 


26 




38 


5o 


9 


6 


12 


32 


6 13 


6 5 


3 9 34 53 Jj 


S 1751 


15 


11 


27 , 


29 


8 


2;> 


28 


24 


4 22 


54 1C 


3 17 37 40 S 


; ? 1752 


3 


20 


16 


6 


8 


14 


44 


16 


3 2 


42 15 


3 35 40 27 Jj 


Ij 1753 


22 


17 


48 


45 


9 


3 


6 


28 


2 8 


19 2ll 5 4 23 28 Jj 


S 1754 


12 


2 


37 


2 2 


8 


22 


22 


20 


18 


7 2( 


5 12 26 15 S 


! 1755 


1 


11 


35 


59 


8 


11 


38 


12 


10 27 


55 31 


5 20 29 2 !j 


S 1756 


19 


8 


58 


38 


9 








24 


10 3 


32 37 


6 29 12 3 S 


S 1757 


8 


17 


47 


15 


8 


19 


16 


16 


8 13 


20 42 


7 7 14 50 ^ 


5 1758 


27 


15 


19 


54 


9 


7 


38 


28 


7 28 


57 48 


8 15 57 52 


'S 1759 


17 





8 


31 


8 


26 


54 


20 


5 28 


45 54 


8 24 39 S 


i^ 1760 


5 


8 


57 


8 


j 


16 


10 


12 


4 8 


34 6 


9 2 3 26 S 


'S 1761 


24 


6 


29 


47 


9 


4 


<j2 


24 


3 14 


11 6 


10 10 46 27 S 


^ 1762. 


13 


15 


18 


24 


8 


23 


48 


16 


1 23 


59 11 


10 18 49 14 {j 


V1763 


3 





7 


1 


8 


13 


4 


8 


3 


47 16 


10 26 52 1 S 


1764 
S 1765 


20 
10 


21 
6 


39 

28 


4C 
17 


9 
8 


1 

20 


26 
42 


20 
13 


11 9 
9 19 


24 21 
12 26 


5 35 2 <| 

13 37 49 S 


5 1766 


29 


4 





56 


g 


9 


4 


20 


8 24 


49 32 


1 22 20 51 s 



Astronomical Tables. 



331 



s s 




T 


ABLE 


I, concluded. Old Style. S 




Mean New Moon 


Sun's mean 


Moon's mean 


Sun's menn Dist. S 


S 8, 


in March. 


Anomaly. 


Anomaly. 


from the Node. *> 


P 






















s s 


* ? 


57" 


H. 


M. 


i>. 


s 





/ 


'/ 


S ' " 


s 


/ n ^ 


S 1767 


18 


12 


49 


33 


8 


28 


20 


17 


7 4 37 37 


2 


23 38 s 


^ 1768 


6 


21 


38 


10 


3 


17 


36 


9 


5 14 25 42 


2 8 


26 25 > 


S 1769 


5 


19 


10 


40 


9 


5 


58 


21 


4 20 2 48 


3 17 


9 27 > 


^ 1770 


15 


3 


59 


26 


8 


25 


14 


13 


2 29 50 53 


3 25 


12 14S 


S 1771 


4 


12 


48 


2 


8 


14 


30 


5 


1 9 38 58 


4 3 


15 1 


S 1772 


22 


10 


20 


43 


9 


2 


52 


17 


15 16 4 


5 11 


58 3 S 


!j 1773 


11 


19 


9 


19 


8 


22 


8 


9 


10 25 4 9 


5 20 


50 s 


S 1774 


1 


s 


57 


55 


8 


11 


24 


1 


9 4 52 14 


5 28 


3 37 


S 1775 


20 


1 


30 


25 


8 


29 


46 


13 


8 10 29 20 


7 6 


49 38 s 


S 1776 


8 


10 


19 


12 


8 


19 


2 


5 


6 20 17 25 


7 14 


49 25 S 


S 1777 


27 


7 


51 


51 


y 


7 


24 


17 


5 25 54 31 


8 23 


32 26 S 


^ 1778 


16 


16 


40 


28 


8 


26 


40 


9 


4 5 42 36 


9 1 


35 13 <j 


S 1779 


6 


1 


29 


4 


a 


15 


56 


1 


2 15 30 41 


9 9 


38 S 


!j 1780 


23 


23 


1 


44 


9 


4 


IB 


IS 


1 21 7 47 


10 18 


21 1 <J 


S 1781 


13 


7 


50 


21 


8 


23 


34 


5 


55 52 


10 26 


23 48 S 


^ 1782 


2 


16 


38 


57 


8 


12 


49 


58 


10 10 43 57 


11 4 


26 35 S 


Jj 1783 


21 


14 


11 


37 


9 


1 


12 


10 


9 161 3 


1.3 


9 36 \ 


S 1784 


9 


23 





13 


a 


20 


28 


3 


7 26 9 8 


21 


12 23 S 


1785 


28 


20 


32 


53 


9 


8 


50 


15 


7 1 46 14 


1 29 


55 25 Sj 


S 1786 


18 


5 


21 


30 


8 


28 


6 


7 


5 11 34 19 


2 7 


58 12 S 


S 1787 


7 


14 


10 


6 


8 


17 


21 


59 


3 21 22 24 


2 16 


59 * 


S 1788 


25 


11 


42 


46 


9 


5 


44 


11 


2 26 59 30 


3 24 


44 1 5 


^ 1789 


14 


20 


31 


23 


8 


25 





3 


I 6 47 35 


4 2 


46 48 S 


S 1790 


4 


5 


19 


59 


8 


14 


15 


55 


11 16 35 40 


4 10 


49 35 ^ 


S 1791 


23 


2 


52 


39 


9 


2 


38 


7 


10 22 12 46 


5 19 


32 37 S 


% 1792 


11 


11 


41 


15 


8 


21 


53 


59 


9 2 52 


5 27 


35 24 S 


S 1793 


30 


9 


13 


55 


9 


10 


16 


11 


8 7 37 58 


7 6 


18 26 ^ 


S 1794 


19 


18 


2 


32 


8 


29 


32 


3 


6 17 26 4 


7 14 


21 13 S 


S 1795 


9 


2 


51 


8 


8 


18 


47 


55 


4 27 14 9 


7 22 


24 s 


S 179G 


27 





23 


48 


9 


7 


10 


7 


4 2 51 14 


9 1 


7 1 S 


S 1797 


16 


9 


12 


24 


8 


26 


25 


59 


2 12 39 19 


9 9 


9 48 S 


I; 1798 


5 


18 


1 


1 


3 


15 


41 


51 


22 27 25 


9 17 


12 35 !{ 


S 1799 


24 


15 


23 


41 


J 


4 


4 


3 


11 28 4 31 


10 25 


- - n-f L 

DJ 37 S 


I} 1800 


13 





22 


178 


23 


19 


55 10 7 52 36 


11 3 


58 22 ^ 



33: 



Astronomical Tables. 



J TABLE 


II. 


Mean 


New 


Moon 


, &c. in March, New Style, from : S 


S 






A. D 


. 1752 


to A 


. D. 1800. 


> 


S 


1 

Mean New Moon 


Sun's mean 


Moon's mean 


S 

Sun's mean Dist. ? 


C t-tl 


in March. 


Anomaly. 


Anomaly. 




ii-om the Nodi-. ^ 


s o 






















S 


s 

s ? 


D. 


H 


M. 


s. 


s ' " 


S ' 


// 


s ' ^Jj 


S 1752 


14 


20 


16 


6 


8 


14 


44 


16 


3 2 42 


15 


3 25 40 27 S 


S 1753 


4 


5 


4 


42 


8 


4 





8 


1 12 30 


20 


4 3 43 14 ^ 


S 1754 


23 


2 


37 


22 


S 


22 


22 


20 


18 7 


26 


5 12 26 15 S 


V 
























S 1755 


12 


11 


25 


59 


8 


11 


38 


12 


10 27 55 


31 


5 20 29 2 Sj 


S 1756 


30 


8 


58 


38 


9 








24 


10 3 32 


37 


6 29 12 3 S 


S 1757 


19 


17 


47 


15 


8 


19 


16 


16 


8 13 20 


42 


7 7 14 50 S 


^ 1758 


9 


2 


35 


51 


8 


8 


32 


8 


6 23 8 


47 


7 15 17 38 


S 1759 


28 





8 


31 


8 


26 


54 


20 


5 28 45 


54 


8 24 39 : 


^ 1760 


16 


8 


57 


8 


8 


i5 


10 


12 


4 8 34 





9 2 3 6 s 


S 1761 


5 


17 


45 


44 


S 


5 


26 


4 


2 18 22 


5 


9 10 6 13 S 


S 1762 


24 


15 


18 


24 


8 


23 


48 


16 


1 23 59 


1 1 


10 18 49 14 S 


J> 1763 


14 





7 


i 


8 


13 


4 


8 


3 47 


16 


10 26 52 1 ^ 


S 1764 


2 


8 


55 


36 


8 


2 


20 





10 13 35 


21 


11 4 54 48 S 


> 1765 


21 


6 


28 


17 


8 


20 


42 


13 


9 19 12 


2G 


13 37 49 Jj 


S 1766 


10 


15 


16 


53 


a 


9 


58 


5 


7 29 


3 i 


21 40 37 S 


1767 


29 


12 


49 


33 


8 


28 


20 


17 


7 4 37 


J7 


2 23 38 S 


> 1768 


17 


21 


38 


9 


8 


17 


36 


9" 


5 14 25 


42 


2 8 26 25 lj 


S 1769 


7 


6 


26 


46 


8 


6 


52 


1 


3 24 13 


47 


2 16 29 13 S 


J 1770 


26 


3 


59 


86 


8 


25 


14 


1 3 


2 29 50 


53 


3 25 12 14 Jj 


S 1771 


15 


12 


48 


2 


8 


14 


so 


5 


1 9 38 


58 


4 315 IS 


S 177^ 


3 


21 


36 


39 


a 


3 


45 


57 


11 19 27 


S 


411 17 48 S 


Jj 1773 


22 


19 


9 


19 


8 


22 


8 


Q 


10 25 4 


9 


5 20 50 


S 17T4 


12 


3 


5? 


55 


8 


11 


24 


1 


9 4 52 


14 


5 28 3 37 S 


^ 1775 


1 


12 


46 


3 1 


8 





39 


53 


7 14 40 


19 


6 6 6 24 > 


S 1776 


19 


10 


19 


12 


8 


19 


2 


5 


6 20 17 


25 


7 14 49 25 S 
( 


S 1777 


8 


19 


7 


48 


8 


8 


17 


57 


5 Q 5 


30 


7 22 52 12 s 


Jj 1778 


27 


16 


40 


28 


8 


26 


40 


9 


4 5 42 


.36 


9 1 35 13 S 


S 1779 


17 


1 


29 


4 


8 


15 


56 


1 


2 15 30 


41 


9 9 38 J 


^ 1780 


5 


10 


17 


40 


3 


5 


11 


53 


25 18 


46 


9 17 40 47 S 


S 1781 


24 


7 


50 


21 


8 


23 


34 


5 


55 


52 


10 26 23 48 J 
t 


5 1782 


13 


16 


38' 


57 


8 


12 


49 


58 


10 10 43 


57 


il 4 26 35 ^ 


S 1783 


3 


1 


27 


33 


g 


2 


5 


50 


8 20 32 


2 


11 12 29 22 S 


S 1784 


20 


23 





33 


8 


20 


28 


3 


9 26 9 


8 


21 12 23 


S 1785 


10 


7 


48 


50 


8 


9 


43 


55 


6 5 57 


13 


29 15 .10 S 


S 1786 


29 


5 


21 


30 


8 


28 


6 


7 


5 11 34 


19 


2 7 58 12 Ij 



Astronomical Tables. 



333 



S ' TABLE II, concluded. New Style. \ 


S ^ 

^ 

v 1787 
S 1788 
S 1789 
> 1790 
S 1791 


Mean New Moon 
in March. 


Sun's mean 
Anomaly. 


Moon's mean 
Anomaly. 


> 

Sun's mean Dis. /* 
from the Xode. ? 


D. H. M. S. 


s ' " 


s ' " 


sO' " S 


18 14 10 6 
6 22 58 42 
25 20 31 23 
15 5 19 59 
4 14 8 35 


8 17 21 59 
8 6 37 51 
8 25 3 
8 14 15 55 
8 3 31 47 


3 21 22 24 
2 1 10 29 
1 6 47 35 
11 16 35 40 
9 26 23 45 


2 16 9 59 c 
2 24 3 46 S 
4 2 46 48 S 
4 10 49 35 J 
4 18 52 22 5 


J 1792 
J 1793 
S 1794 
S 1795 
!j 1796 
S 1797 
J 1798 
J 1799 
S 180C 


22 11 41 15 
11 20 29 51 
30 18 2 32 
20 2 51 8 
8 11 39 44 


8 21 53 59 
8 11 9 51 
8 29 32 3 
8 18 47 55 
8 8 3 47 


9 2 52 
7 11 48 57 
6 17 26 4 
4 27 14 9 
3 7 2 14 


5 27 35 24 
6 5 31 11 > 
7 14 21 13 S 

7 22 24 OS 
8 26 47 S 
y 9 ~9~48 S 
9 17 12 35 S 
9 25 15 22 J 
11 3 58 25 L 


27 9 12 2i 
16 18 1 1 

6 2 49 57 
25 22 17 


8 26 25 o9 
8 15 41 51 
8 4 57 4o 
8 23 19 55 


2 12 39 19 
22 27 25 
11 2 15 30 
10 7 52 36 



*.' 



ABLE III. Mean Anomalies, and Sun's mean Distance S 
from the Node, for 1 3-| mean Lunations. <J 



No. 


Mean 
Lunations. 


Sun's mean 
Anomaly. 


Moon's mean 
Anomaly. 


Sun's mean Dis. S 
from the Node. > 




D. H. M. S- 


S ' " 


s ' " 


S ' " S 


5 


29 12 44 3 
59 1 28 6 
88 14 12 9 
118 2 56 12 
147 15 40 15 


29 6 19 
1 28 12 39 
2 27 18 58 
3 26 25 17 
4 25 31 37 


25 49 
1 21 38 1 
2 17 27 1 
3 13 16 2 
4952 


1 40 14 
2 1 20 28 ^ 
3 2 42 S 
4 2 40 56 S 
5 3 21 10 


6 
7 
8 
9 
10 


177 4 14 18 
206 17 8 21 
-'36 5 52 24 
265 18 36 27 
295 7 20 30 


5 24 37 56 
6 23 4^ 15 
7 22 50 35 
8 21 56 54 
9 21 3 14 


5 4 54 3 
6 43 3 
6 26 32 3 
7 22 21 4 
8 18 10 4 


6 4 1 24 S 
7 4 41 33 S 
8 5 21 52 > 
9 6 2 6 
10 6 42 20 ? 


11 

13 


324 20 4 33 
354 8 48 30 
383 21 32 40 


10 20 9 33 
11 19 15 52 
18 22 12 


9 13 59 5 
10 9 48 5 
11 5 37 6 


11 7 22 34 
82 47 s 
1 8 43 IS 


| 


14 18 22 2 


14 33 10 


6 12 54 30 


15 20 7 t 



334 



Astronomical Tables, 



STABLE IV. The Days of the Year, reckoned from\ 

the Beginning of March. 



r; 


1 


> 


I 


r; 


^ 


g 


rt 

ft 







f 

n 


O 



r& 


f 


a S 


S- 


1 


r 1 




3 

n> 


^ 


03 
en 

r-t- 


3 

cr 


o 
cr 


cr 


5 

cr 

2 


1 


11 


- 


1 


* 

32 


52 


93 


23 


154 


185 


215 


246 






s 

338 <J 


276 


307 


s * 


2 


33 


53 


94 


24 


155 


186 


216 


247 


277 


308 


339 * 


s 3 


3 


34 


54 


95 


25 


156 


187 


217 


248 


278 


309 


340 S 


S 4 


4 


35 


55 


96 


26 


157 


188 


218 


249 


279310 


341 % 


S 5 

s, 


5 


36 


56 


97 


27 


158 


189 


219 


250 


280311 


342 S 


S 6 


6 


37 


67 


98 


28 


159 


190 


220 


251 


281312 


343 Jj 


s s r 


7 


38 


68 


99 


29 


160 


191 


221 


252 


282:313 


344 S 


S 8 


8 


39 


69 


100 


30 


161 


192 


222 


253 


283 


314 


345 it 


S 9 


9 


40 


70 


101 


31 


162 


193 


223 


254 


284 


315 


346 !j 


SlO 


10 


41 


71 


102 


32 


163 


194 


224 


255 


285 


316 


347 S 


L 


11 


42 


72 


103 


133 


164 


195 


225 


256 


286 


317 


348 S 


*> 12 


[2 


43 


73 


104 


134 


165 


196 


226 


257 


287318 


349 S 


S 13 


13 


44 


74 105 


135 


166 


197 


227 


258 


288319 


350 \ 


S ^4 


14 


45 


75 


106 


136 


167 


198 


228 


259 


289320 


351 S 


|l5 


15 


46 


76J107 


137 


168 


199 


229 


260 


290321 


352 % 


5 16 


16 


47 


77 ! 10S 


138 


169 


200 


230 


261 


291 


322 


^3$ 


S.17 


17 


48 


78 109 


139 


170 


201 


231 


262 


292 


323 


354 J; 


S 13 


18 


49 


79 


110 


140 


171 


202 


232 


263 


293 


324 


355 S 


S 19 


19 


50 


80 111 


141 


172 


203 


233 


264 


294 


325 


356 


^20 


20 


51 


81 112 


142 


173 


204 


234 


265 


295 


326 


357 ^ 

r 


\3i 


" 

21 


52 


82 11 


143 174 


205 


235 


266 


296 


327 


T 

358 


S;*a 


22 


53 


83 


114 


144 


175 


206 


236 


267 297 


328 


359 S 


7 


23 


54 


8-1 


11 


145 


176 


207 


237 


268 


298 


329 


360s 


S24 


2455 


8^ 


lie 


146 


177 


208 


238 


269 


299 


330 


361 <J 




2556 


8 


> 11 


147 


m 


209 


239 


270 


300 


331 


362 S 


S 


2C 


.57 


87:118 


148 


m 


>21C 


240 


271 


301 332 


363 ^ 


S27 


'27 


' 5 


88 119 


14? 


> 18C 


)211 


241 


272 


302 


333 


364 S 


S2 


$26 


> 5 


1 89 12C 


15C 


) 181 


212 


242 


273 


303 


334 


365 s 


S <!><: 


(2< 


)6C 


) 90 121 


151 


IBS 


5213 


243 


274 


304 


335 


366 


|SC 


)3( 


)61 


911122 


15$ 


i8i 


J214 


244 


275 


305 


336 


^ 

t 




31 


L 


95 


> 


15^ 


18-1 




245 


1306 


i 


s s 


S_ ' -<^ 



Astronomical Tables. 



TABLE V. Mean Lunations from 1 to 100000. 



Lunat. 


Days. Decimal Parts. 


Days. 


Hou. 


M. 


S. 


Th. 


| 


1 


29.520590851080 


= 29 


12 


44 


3 


2 




2 


59.061181702160 


59 


1 


28 


6 


5 


57 S' 


3 


88.591772553240 


88 


14 


12 


9 


8 


55$ , 


4 


118.122363404320 


118 


2 


56 


12 


11 


53 S 


5 


147.652954255401 


147 


15 


40 


15 


14 


52.5! 


6 


177.183545106481 


177 


4 


24 


18 


17 


50 S 


7 


206.714135957561 


206 


17 


8 


21 


20 


48? 


8 


236.244726808641 


236 


5 


52 


24 


23 


47 S; 


9 


265.77531765972; 


265 


18 


36 


27 


26 


4S] 


10 


295.30590851080 


295 


7 


20 


30 


29 


43 S 


20 


590.61181702160 


590 


14 


41 





59 


el 


30 


885.91772553240 


885 


22 


1 


31 


29 


10 S 


40 


1181.22363404320 


1181 


5 


22 


1 


58 


53 v 


50 


-1476.52954255401 


1476 


12 


42 


32 


28 


36 S : 


60 


1771.83545106481 


1771 


20 


3 


2 


58 


19? 


70 


2067.14135957561 


2067 


3 


23 


33 


28 


2 S 


80 


2362.44726808641 


2362 


10 


44 


3 


57 


46 S 


90 


2657.75317659722 


2657 


18 


4 


34 


27 


29 S 


100 


2953.0590851080 


2953 


1 


25 


4 


57 


12 J 


200 


5906.1181702160 


5906 


2 


50 


9 


54 


24 S 


300 


8859.1772553240 


8859 


4 


15 


14 


51 


36 


400 


11812.2363404320 


11812 


5 


40 


19 


48 


48 > 


500 


14765.2954255401 


14765 


7 


5 


24 


46 


OS 


600 


17718.3545106481 


17718 


8 


30 


29 


43 


12 ** 


700 


20671.4135957561 


20671 


9 


55 


34 


40 


24 S 1 


800 


23624.4726808641 


23624 


11 


20 


39 


3,7 


36 !* : 


900 


26577.5317659722 


26577 


12 


45 


44 


34 


48 S. 


1000 


29530.590851080 


29530 


14 


10 


49 


32 


o i 


2000 


59061. 18ir02160 


59061 


4 


21 


39 


4 


OS 


3000 


88591.772553140 


88591 


18 


32 


28 


36 


t 


4000 


118122,363404320 


118122 


8 


43 


18 


8 


OS 


5000 


147652.954255401 


147652 


22 


54 


7 


40 





6000 


177183.545106481 


177183 


13 


4 


57 


12 


OS 


7000 


206714.135957561 


206714 


3 


15 


46 


44 


t 


8000 


236244.726801641 


236244 


17 


26 


36 


16 


0?i 


9000 


265775.317659722 


265775 


7 


37 


25 


48 


v i 


10000 


295305.90851080 


295305 


21 


48 


15 


20 


os ; 


20000 


590611.81702160 


590611 


19 


36 


30 


40 


of 


30000 


885917.72553240 


855917 


17 


24 


46 








40000 


1188223.63404320 


1188223 


15 


13 


1 


20 


l\ 


50000 


1476529.54255401 


1476529 


13 


1 


16 


40 




60000 


1771835.45106481 


1771835 


10 


49 


32 





u 


70000 


2067141.35957561 


2067141 


8 


37 


47 


20 


OS 


80000 


2362447.26808641 


2362447 


6 


25 


2 


40 


i\ 


90000 


2657-753.17659722 


2657753 


4 


14 


18 







100000 


2953959.0851080 


2953959 


3 


2 


33 


20 


s 



336 



Astronomical Tables. 



~C*. ^^* ^ * ^^^^^V^ ( ^^^y\A<^,X'Av^'^'*y\^s^^.^>^/',A^Vy s ,^./',X' < y",>\A,y\/^^/> r 

Jj TABLE VI. The first mean New Moon, with the mean Anomalies ' 
S of the Sun and Moon$ and the Sun's mean Distance from the As- \ 
Jj pending Node, next after complete Centuries of Julian Years. 


S Luna- 
^ tions. 


-< ' ( 

re C 
80 fr: 


First 

New Moon 


-Min's mean 
Anomaly 


Moon's mean 
Anomaly 


Sun from < 
Node. < 


D. H. M. S. 


s ' 


s 


so'; 


S 1237 
S 2474 
!; 3711 
S 4948 


100 
200 
300 
400 


4 8 1O 52 
8 16 21 44 
13 32 37 
17 8 43 29 


3 21 
6 42 
10 3 
13 24 


8 15 22 
5 44 
1 16 6 
10 1 28 


4 19 27 , 
9 8 55 
1 28 22 
6 17 49 


S 6185 
S 7422 
^ 8658 
S 9895 


500 
600 
700 
800 


21 16 54 21 
26 1 5 14 
20 32 3 
5 4 42 55 


16 46 
20 7 
11 24 22 
11 27 34 


6 16 50 
3 2 12 
10 21 45 

777 


11 7 16 
3 26 44 
7 15 31 
4 58 


11132 
S 12369 
Jj 13606 
S 14843 


900 
1000 
1100 
1200 


9 12 53 47 
13 21 4 40 
18 5 15 32 

22 13 26 24 


014 
O 4 25 
7 46 
0117 


3 22 29 
7 51 
8 23 13 
5 8 35 


4 24 25 
9 13 53 
2 3 20 
6 22 47 


S 16080 
S 17316 
Ij 18553 
S 19790 


1300 
140O 
1500 
160O 


26 21 37 16 
1 17 4 6 
6 1 14 58 
10 9 25 50 


14 28 
11 18 43 
11 22 4 
11 25 25 


1 23 57 
9 13 30 
5 28 52 
2 14 14 


11 12 15 
312 
7 20 29 
9 56 


> 21027 
S 22264 
!j 23501 
S 24738 


170O 
1800 
1900 
2000 


14 17 36 42 
19 1 47 35 
23 9 58 27 
27 18 9 19 


11 28 46 
028 
O 5 29 
O 8 50 


10 29 36 
7 14 58 
4 O 20 
15 42 


4 29 23 
9 18 51 
2 8 18 
6 27 45 


S 25974 
Ij27211 
^ 28448 
S 29685 


2100 
2200 
2300 
2400 


2 13 36 8 
6 21 47 1 
11 5 57 53 

15 14 8 45 


11 13 5 
11 16 26 

11 19 47 
11 23 8 


8 5 15 

4 20 37 
1 5 59 
9 21 21 


10 16 32 
360 
7 25 27 
14 54 


S 30922 
\ 32159 
S 33396 
S 34632 


2500 
2600 
2700 
2800 


19 22 19 38 
24 6 30 30 
28 14 41 22 
3 10 8 11 


11 26 29 
11 29 50 
3 11 
11 7 76 


6 6 43 
2 22 4 
11 7 26 

6 26 59 


5 4 22 
9 23 49 
2 13 16 
623 


S 35869 
37106 
S 38343 
S 39580 


2900 
3000 
3100 
3200 


7 18 19 3 
12 2 29 56 
16 10 40 48 
20 18 51 40 


11 1O 47 
11 14 8 
11 17 30 
11 20 51 


3 12 21 
11 27 43 
8 13 5 
4 28 27 


10 21 30 
3 10 58 
8 25 
19 52 



Astronomical Tables. 



337 



s 

J TABLE VI. concluded. 

> s 


S Luna- 
^ tions. 
S 

^ 40S 17 
S 42054 
I} 43290 
S 44527 


l *i c ~ > 

rs c^ 

P 1' 


IMl'St 

New Moon. 


Sun's mean 
Anomaly. 


.Moon's mean 
Anomaly. 


bun's mean ? 
Dis.fromNode ^ 


D. H. M. S. 


s ' 


s ' 


s ' \ 


3300 
3400 
3500 
3600 


25 3 2 33 
29 11 13 25 
4 6 40 14 
8 14 51 6 


\( 24 12 
11 27 33 
1 1 48 
1 5 9 


1 13 49 
9 29 11 
5 18 44 

2 4 6 


5 9 20 > 
9 28 47 S 
1 17 34> 
67 I? 


S 45701 
J 47001 
S 48238 
S 49475 


3700 
3800 
3900 
4000 


12 23 1 59 
17 7 12 51 
21 15 23 43 
25 23 34 35 


1 8 3(. 
1 11 51 
1 J5 12 

1 18 33 


10 19 28 
7 4 50 
3 20 12 
5 34 


10 26 29 s 
3 15, 56 S 
8 5' 23? 
24 50 J 


Ij 50711 
S 51948 
S 53185 
S 54422 
S 5*5659 
I* 56896 
5 58133 
\ 59369 


4100 
4200 
4300 
4400 


19 1 27 
5 3 12 17 
6 11 23 9 
13 19 34 1 


10 22 48 
10 26 9 
10 29 31 
11 2 52 


7 25 7 
4 10 29 
25 51 
9 11 13 


4 13 37 S 

9 3 5<J 

1 22 32 
6 \\ 59 ^ 


4oOO 
4600 
4700 
4800 


13 3 44 54 
22 11 55 46 
26 20 6 38 
1 15 33 27 


11 6 13 
11 9 34 
11 12 55 
[0 17 


5 26 35 
2 1 1 57 

10 27 19 
6 16 52 


11 1 27s 
3 20 54 S 
8 10 21 ^ 
11 29 8S 


^ 606^)6 
S 61843 
63080 
S 64317 


4900 
5000 
5100 
:>200 


5 23 44 20 
10 7 55 12 
\4 16 6 4 
19 16 56 


10 20 31 
.10 23 52 
10 27 13 
\\ 34 


3 2 U 
11 17 30 

8 2 5H 
4 18 20 


4 18 36 S 
9 8 3 Ij 
1 27 30 S 
6 16 57? 


J? 66791 
? 68028 
!j 69265 


5 400 
5oOO 


23 8 27 4P 
27 16 38 41 
2 12 5 30 
6 20 16 22 


U 3 5a 
11 7 16 
10 11 31 
10 14 52 


1 3 42 
9 19 4 
5 8 37 
1 23 59 


H 6 25 ? 
2 25 52 S 
7 14 39 J 
04 6 S 


? rirso 

!j 72976 

S 74212 


5700 

5803 
5900 
6000 


11 4 27 15 
15 12 38 7 
19 20 48 59 
24 4 59 52 


10 18 U 
10 21 35 
10 24 56 
10 28 17, 


i 9 2 i 
6 24 43 
3 10 5 
11 25 27 


4 23 34 S 
913 1 
2 2 28 S 
6 21 56 S 



V 



If Dr. Pound's mean Lunation (which we have kept by in 
J> making these tables) be added 74212 times to itself, the sum 
^ will amount to 6000 Julian years 24 days 4 hours 59 minutes 
S 5 1 seconds 40 thirds ; agreeing with the first part of the last S 
!ine of this table, within half a second. 



UNIVERSITY 1 



OF 



338 



Astronomical Tables. 



TABLE V 



II. The annual, tr first Equation of the mean S 
to the true Syzygij. ^ 



Argument. Sun's mean Anomaly. 



Jj Subtract. ^ 


5i 

s 



Sign. 


1 
Sign. 


2 
Signs. 


o 

Signs. 


4 
Signs. 


5 

Signs. 


? ' i* 


H.M.S. 


H.M.S. 


H.M.S. 


H.M.S. 


H.M.S. 


H. M. S. 


S o 





2 3 12 


3 35 


4 10 53 


3 39 30 


2 7 45 


30 i; 


\ * 

|i 


4 18 
8 35 
) 12 51 
17 8 
21 24 


3 6 55 
3 10 36 
2 14 14 
3 17 52 
2 21 27 


3 37 10 
3 39 18 
3 41 23 
3 43 26 

3 45 25 


i 10 57 

4 10 55 
4 10 49 
4 10 39 
4 10 24 


3 37 19 
3 35 6 
3 32 50 
3 30 30 

3 28 5 


2 355 
2 1 
I 56 5 
I 52 6 
1 48 4 


29 
28 S 

27 S 
26? 
25 S 


25 39 
28 55 
34 11 
38 26 

42 39 


2 25 9 
2 28 29 
2 31 57 
2 35 22 
2 38 44 


3 47 19 
3 49 7 
3 50 50 
3 52 29 
3 54 4 


4 10 4 
4 9 39 
4 9 10 
4 8 37 

4 7 59 


3 25 35 
3 23 C 
3 20 20 
3 17 35 
3 14 49 


I 41 1 
I 39 56 
1 35 49 
1 31 41 
1 27 31 


24 S 
23 S 

?,\ 

20^ 


1 12 

'S 15 


46 52 
51 4 
55 17 
59 27 
I 3 36 


2 42 3 
2 45 18 
2 48 30 
2 51 40 
2 54 48 


3 55 35 

3 57 2 
3 58 27 
3 59 49 
3 1 7 


4 7 16 
4 6 29 
i 5 37 
4 4 41 

4 3 40 


3 11 59 
396 
3 6 10 
3 3 10 
307 


1 23 19 
1 19 5 
1 14 49 
I 10 33 
i 6 15 


19 S 
18 1 

17 

w ; 


S 18 

S 19 

S20 

S22 
523 
S 24 


I 7 45 
i 11 53 
1 16 
1 20 6 
1 24 10 


2 57 53 
3 54 
3 3 51 
3 6 45 
3 9 36 


4 2 18 

4 3 23 
4 4 22 
4 5 18 
4 6 10 


4 2 35 
4 1 26 
t 12 
3 58 52 
3 57 27 


2 57 
2 53 49 
2 50 36 
2 47 18 
2 43 57 


1 1 56 
57 36 
53 15 
48 52 

44 28 


\3\ 
12 S 

!os 


28 12 
32 12 
36 10 
40 6 
44 1 


3 12 24 
3 15 9 
3 17 51 
3 20 30 
3 23 5 


4 6 58 
4 7 41 
4 8 21 
4 8 57 
4 9 29 


3 55 J>9 
3 54 26 
3 52 49 
3 51 9 
3 49 26 


2 40 35 
2 37 6 
2 33 35 
2 30 2 
2 26 26 


40 2 
35 36 
31 10 
26 44 
22 17 


9 ? 

i 

6S 


526 
S27 
^28 
S 29 
!j 30 


47 54 
51 46 
55 37 
t 59 26 
2 3 12 


3 25 36 
3 28 3 
3 30 26 
3 32 45 
3 35 


4 9 55 
4 10 16 
4 10 33 
4 10 45 
4 10 53 


3 47 38 
3 45 44 
3 43 45 
3 41 40 
3 39 30 


2 22 47 
2 19 5 
2 15 20 
2 11 35 
2 7 45 


17 50 
13 23 
8 56 
4 29 
000 


4 s 

2 S 


*!? 

S 05 


11 
Si^ns. 


10 
Signs. 


9 

Signs. 


8 

Signs. 


7 
Signs. 


6 
Signs. 




Add C 



Astronomical Tables. 



339 



tA9 .IWi 

S TABLE VIIL Equation of the Moon's mean Anomaly. S 


S Argument. Sun's mean Anomaly. J 


S Subtract S 


s c 

S rt> 

_ 

S 

1 

Li 

h 

1 



Sign. 


1 
Sign. 


2 
Signs. 


3 
Signs. 


4 
Signs. 


5 

Signs. 


< 

G s 

rt S 

'J'-i () 


' " 


' " 


' " 


' " 


' " 


' " 


000 


46 45 


1 21 32 


1 35 1 


1 23 4 


48 It) 


SOS 


1 37 
3 IS 
4 52 
6 28 
086 


48 10 
49 34 
50 53 
52 19 
53 40 


I 22 21 
1 23 10 
I 23 57 
1 24 41 
1 25 24 


1 35 2 
I 35 1 
1 35 
1 34 57 
1 34 50 


I 22 14 
1 21 24 
1 20 32 
1 19 38 
I 18 42 


46 51 
45 23 
43 54 
42 24 
40 5B 


29 ; 

28? 
27 S 
26? 

S 

23 J; 

22 S 
21? 
20 Jj 


9 42 
11 20 
12 56 
14 33 
16 10 


55 
56 21 
57 38 
58 56 
1 13 


1 26 6 
I 26 48 
1 27 28 
1 28 6 

I 28 43 


1 34 43 
1 34 33 
I 34 22 
1 34 9 
I 33 53 


1 17 45 
1 16 48 
1 15 47 
1 14 44 
I 13 41 


39 21 
37 49 
36 15 
34 40 
33 5 


S 13 

S 14 


17 47 
19 23 
20 59 
22 35 
24 10 


1 1 29 
I 2 43 
1 3 56 
1 5 8 
1 6 18 


1 29 17 
1 29 51 
1 30 22 
1 30 50 
1 31 19 


I 33 37 
I 33 20 
1 33 
1 32 38 
1 32 14 


1 12 37 
1 11 33 
1 10 26 
1 9 17 
1 8 S 


31 31 

29 54 
28 18 
26 40 
25 3 


1 Q T 

!i 
'I 


S 16 
S17 

J;i8 

S 19 
Ij 20 


25 45 
27 19 
28 52 
30 25 
31 57 


I 7 27 
1 8 36 
I 9 42 
1 10 49 
1 11 54 


1 31 45 
I 32 12 
1 32 34 
1 32 57 
I 33 17 

I 33 36 
I 33 52 
1 34 6 
1 34 18 
1 34 30 


1 3 1 50 
I 31 23 
I 30 55 
1 30 25 

1 29 54 


1 6 58 
1 5 46 
I 4 32 
1 3 19 
1 2 1 


23 23 
21 45 
20 7 
18 28 
16 48 


\t\ 

i; 
% 

8 "S 

7 S 

\\ 

3 S 
2 S 

1 


pi 

!? 


33 29 
35 2 
36 32 
38 1 
39 29 


1 12 58 
1 14 1 
1 15 1 
1 16 
1 16 59 


I 29 20 
1 28 45 
1 28 9 
1 27 30 
1 26 50 


1 45 
59 26 
58 7 
56 45 
55 23 


15 8 
13 28 
1 1 48 
10 7 
8 20 


26 
S27 
^-28 
^ 29 
S 30 

^ CT3 

? 


40 59 
42 26 
43 54 
45 19 
47 45 


1 17 57 
1 18 52 
1 19 47 
1 20 40 
1 21 32 


I 34 40 
I 34 48 
1 34 54 
1 34 58 
1 35 1 


1 26 27 
I 25 5 
I 24 39 
1 23 52 
I 23 4 


54 1 
52 57 
51 12 
49 45 
48 19 


6 44 

053 
3 21 
1 40 
000 

6 
Signs. 


11 
Signs. 


10 
Signs. 


9 
Signs. 


8 
Signs. 


7 
Signs. 


j\ 


s Add J 



340 



Astronomical Tables. 



TABLE IX. The second Equation of the mean to the true S 
Argument. Moon's equated Anomuiy. c 



If 



Sign. 


1 
Sign. 


2 
Signs. 


3 
Signs. 


4 
Signs. 


5 
Signs. 


cS 


\ ' 


H.M.S 


H.M.S 


H.M.S 


H.M.S 


H.M.S 


H.M.S 


1 


\: 


000 


5 12 48 


8 47 8 


9 46 44 


8 8 59 


4 34 33 


30 Ij 


I 1 - 
\ l - 


10 58 
21 56 
32 54 
42 52 
54 50 


5 21 56 
5 30 57 
5 39 51 
5 48 37 
5 57 17 


8 51 45 
8 56 10 
9 25 
9 4 31 
9 8 25 


9 45 3 
9 45 12 
9 44 11 

9 42 59 
9 41 36 


8 3 12 
7 57 23 
7 51 33 
7 45 46 
7 39 46 


4 26 1 
4 17 25 
4 8 47 
407 
3 1 23 


28 S 

27 s 

23 S 


! 

*i 


1 5 48 
1 16 46 
1 27 44 
I 38 40 
1 49 33 


6 5 51 

6 14 19 
6 22 41 
6 30 57 
6 39 4 


9 12 9 
9 15 43 
9 19 5 
9 22 14 
9 25 12 


9 40 S 
9 38 19 
9 36 24 
9 34 18 
9 32 1 


7 33 36 
7 27 22 
7 21 2 
7 14 30 

7 7 50 


3 42 32 

o no o o 
O OO OO 

3 24 42 
3 15 44 
3 6 45 


III 

20 ^ 


s 12 

S 13 


2 23 
2 11 10 
2 21 54 
2 32 34 

2 43 9 


6 47 
6 54 46 
7 2 24 
7 9 52 
7 17 9 


9 27 58 
9 30 32 
9 32 58 
9 35 12 
9 37 14 


9 29 33 
9 26 54 
9 24 4 
9 21 3 
9 17 51 


7 1 2 
6 54 8 
6 47 9 
6 40 6 
6 32 56 


2 57 45 
2 48 39 
2 39 34 
2 30 28 
2 21 19 


ill 


\\7 

V 8 

Sl9 
S 20 


2 53 38 
343 

3 14 24 
3 24 42 
3 34 58 


7 24 10 
7 31 18 
7 58 9 
7 44 51 
7 51 24 


9 39 8 
9 40 51 
9 42 21 
9 43 42 
9 44 53 


9 14 28 
9 10 54 
979 
9 3 13 
8 59 6 


6 25 40 
6 18 18 
6 10 49 
6 3 16 
5 55 38 


2 12 8 
2 2 53 
53 36 
44 16 
34 54 


:sj 

"\ 

10 


Ij 22 

S 23 
5 24 


3 45 11 
3 55 21 
i 5 26 
4 25 26 
4 25 20 


7 57 45 
8 3 56 
8 9 57 
8 15 46 
8 21 24 


9 45 52 
9 46 38 
9 47 13 
9 47 36 
9 47 49 


8 54 5C 
8 50 24 
8 45 48 
8 41 2 
8 36 6 


5 47 54 
5 40 4 
5 32 9 
5 24 9 
5 16 5 


25 31 
16 7 
6 41 
57 13 
47 44 


; 
*l 


\ll 

S 30 


4 35 6 

4 44 42 
4 54 11 
5 3 33 
5 12 48 


8 26 53 
8 32 11 
8 37 19 
8 42 18 
8 47 8 


9 47 54 
9 47 46 
9 47 33 
9 47 14 
9 46 44 


8 31 
8 25 44 
8 20 18 
8 14 33 
8 8 59 


5 7 56 
4 59 42 
4 51 15 

4 43 2 
4 34 33 


38 13 
28 41 
19 8 
9 34 
000 


4 <! 
3 
2 S 
1 ^ 
J 




11 
Signs. 


10 
Signs. 


9 

Signs. 


8 

Signs. 


7 
Signs. 


6 

Signs. 


jfj 



ubtract 



Astronomical Tables. 



341 



*> TABLE X. The third Equati- 
Jj onofthe mran to the true Syzygv t 


TABLE XI. The fourth Equati-\ 
on of the mean to the true Syzygy. S 


S drgumtnt. Sun's Anomaly. 
S Moon's Anomaly. 


Argument. Sun's mean Distance ^ 
from the Node. S 


if 

s ? 


Signs. 


Signs. 


Signs. 


n> 


Add \ 


Sub. 
6 Adi 1 


1 Suo 

7 Add 


2 Suo 

8 Ado 


it 
crc 


j|s*. 


$** 


8} Si & 


1 1 


M. S. 


M. S. 


M. S 


M. S. 


M. S. 


M. S. 


S 





2 22 


4 12 


30 








1 22 


1 22 


30 <| 


Ij 


5 
10 
15 

20 

25 


2 26 
2 30 
2 34 
2 38 

2 42 


4 15 
4 18 
4 21 

4 24 
4 27 


29 

28 
27 
26 

25 


1 

^ 


4 
7 
10 
13 
16 


1 23 
1 24 
1 25 

1 26 
1 27 


1 21 
1 20 
1 18 
1 16 
1 14 


29 S 
28 ? 
27 s 
26 
25 I 


S 6 
S 7 

S 9 
SlO 


30 
35 
40 
45 
50 


2 46 
2 50 
2 54 
2 58 
3 2 


4 30 
4 32 
4 34 
4 36 
4 38 


24 
23 
22 
21 
20 


6 
7 
8 
g 

10 

11 

12 
13 
14 
15 


20 
23 
26 
29 
32 


1 28 
1 29 
1 30 
1 31 
1 32 


1 12 
1 10 
1 8 
1 6 

1 


24 !; 

23 S 
22 > 
21 J 
20 S 


1 


55 
1 
1 5 
1 1C 
1 15 

1 20 
1 25 
1 30 
1 35 
1 4C 

1 45 
1 49 
1 52 
1 56 
2 


3 6 

3 10 
3 14 

3 Id 
3 22 


4 40 
4 42 
4 44 
4 46 
4 48 


19 
18 
17 
16 
15 


35 
38 
41 
44 
47 


1 33 
1 33 
1 34 
1 34 

1 34 


1 
57 
54 
51 
49 


19 J 
18 \ 
17 ? 
16 S 
15 ^ 

14 s 
13 S 
12 s 
11 S 
10 J 


11 

S 19 


3 26 
3 30 
3 34 
3 38 

3 42 

3 45 
3 48 
3 51 

3 54 
3 57 


4 50 
4 51 

4 52 
4 53 
4 54 


14 
13 
12 
11 
10 

9 
8 
7 
6 
5 


16 
17 

18 
19 

20 


50 
52 
54 
57 
1 C 


1 34 
1 34 
1 34 
1 33 
1 33 


45 
41 
37 
34 
31 


S 22 
? 23 

S24 


4 55 
4 56 
4 57 
4 57 
4 57 

4 58 
4 58 
4 58 
4 58 
4 58 


21 

22 
23 
24 
25 


1 2 
1 5 
1 8 
1 10 

1 12 


1 32 
1 31 
1 30 

1 28 


28 
25 
22 
19 
16 


9 S 
8 S 

7 % 
5 \ 


$26 
S27 
S2& 
S29 
30 


2 4 
2 9 
2 13 
2 18 

2 2? 

Signs. 


4 
4 3 
4 6 
4 9 

4 12 


4 
3 
2 
1 



26 

27 
28 

29 
SO 


1 14 
1 16 
1 18 

1 20 
122 


1 27 
1 26 
1 25 
1 24 
1 22 


13 
10 
6 
3 



n 

s 


$s 

\l 


Signs. 


Signs. 


I 


r- 
1 
I 


5? 
115 ^ 


4") 

105^ 


1 's 

w 


5 SUD 
|ll Add 


4 Suo 
10 Adc 


3 Sub. 
9 Add 


Subtract. 



342 



Astronomical Tables. 



TABLE XII. The Sun's mean Longitude^ Motion^ and S 
Anomaly ; Old Style. \ 



J cr 
S o 


Sun's mean 


Sun's mean 


o 


Sun's mean 


Sun's mean Jj 




Longitude. 


Anomaly. 


! 


Motion. 


Anomaly. S 

S 


P 2 nj 






"2. 






< 5*3 
S era 


s o f // 


S / 


rt> & 


so/// 


/ S 


^ 1 


9 7 53 10 


6 28 48 


19 


11 29 24 16 


29 4 <J 


J 201 


9 9 23 50 


6 26 57 


20 


0094 


29 48 S 


S 301 


9 10 9 10 


6 26 1 


40 


18 8 


29 37 $ 


!; 401 


9 10 54 30 


6 25 5 


60 


27 12 


29 26 S 


S 501 


9 11 39 50 


6 24 9 


80 


36 16 


1 29 15 s 


5 1001 


9 15 26 30 


6 19 32 


100 


45 20 


1 29 4 S 


S 1101 


9 16 11 50 


6 18 36 


200 


1 20 40 


1 28 8s 


? 1201 


9 16 57 10 


6 17 40 


300 


2 16 


1 27 12 S 


S 1301 


9 17 42 30 


6 16 44 


400 


3 1 20 


1 26 16 ? 


Jj 1401 


9 18 27 50 


6 15 49 


500 


3 46 40 


1 25 21 S 


S 1501 


9 19 13 10 


6 14 53 


600 


4 32 


1 24 25 S 


J 1601 


9 19 58 30 


6 13 57 


700 


5 17 20 


11 23 295 


S 1701 


9 20 43 50 


6 13 1 


800 


6 2 40 


11 22 33 S 


Jj 1801 


9 21 29 10 


6 12 6 


900 


6 48 


11 21 37^ 


L 






1000 


7 33 20 


11 20 1 1 < 


2 o 

V H 


Sun's mean 
Motion. 


Sun's mean 
Anomaly. 


2000 
3000 
400O 


15 6 40 
22 4*0 
1 13 20 


11 11 22j| 
11 2 3 ^ 

10 22 44 \ 


lu 


S / // 


S / 


*i \J\J\s 

5000 


1 7 46 40 

11 f or\ r\ 


10, 13 25 

i r\ A tz. 


? J 


11 29 45 40 


11 29 45 


6000 


15 20 


1U 4 O $ 


5 2 


11 29 31 20 


11 29 29 






j 


3 


11 29 17 


11 29 14 


^ 


Sun's mean 


Sun's mean j 


S 4 


1 49 


11 29 58 





Motion. 


Anomaly. { 


S 5 


1 1 9Q A 1 ? 9C 


11 9Q A 9 


53* 




1 




1 1 Zy Ht f y 


1 Zy 4.4 


01 


s 1 // 


S / (, 


S 6 


11 29 33 9 


11 29 27 






s 


S 7 


11 29 18 49 


11 29 11 


Jan. 


0000 


0^ 


S 8 


3 38 


11 29 5 


Feb. 


1 33 18 


1 33 J 


S 9 


11 29 49 18 


11 29 40 


Mar 


1 28 9 1 


1 28 9V 


S 10 


11 29 34 58 


11 29 24 


Apr. 


2 28 42 30 


2 28 42 \ 


S 11 


11 29 20 38 


11 29 9 


May 


3 28 16 40 


3 28 17 v 


^ 12 


00 5 26 


11 29 53 


June 


4 28 49 58 


4 28 50 ^ 


S 13 


11 29 51 7 


11 29 37 


July 


5 28 24 


5 28 24 j 


J> 14 


1.1 29 36 47 


1 1 29 22 


Aug 


6 29 57 2 


6 28 57 v 


S 15 


11 29 22 27 


11 29 7 


Sept 


7 29 30 44 


7 29 30 ^ 


S 16 


7 15 


11 29 5C 


Oct. 


8 2'9 4 54 


8 29 4 ! 


S 17 


11 29 52 55 


11 29 35 


Nov 


9 29 38 12 


9 29 37 S 


<5 18 


11 29 38 35 


11 29 2C 


Dec 


10 29 12 22 


10 29 11 ^ 



Astronomical 1 \iblzs. 



343 



"S TABLE XII. concluded. \ 


4. f 


S 


Sun's mean 


Sun's mean 


Sun's mean 


Sun's mean 


Sun's mean s 


s 


Motion and 


Motion and 


Dist. from 


Motion and 


Dist. from S 


s s t 


, Anomaly. 


Anomaly. 


Node. 


Anomaly. 


Node. 


I 




J- 

IVI 


' ' 


' ' 


' H 


' ' 


t o ' " 




s 


SO'' 


, iVJ 










s 


t 




v ^ 










/ /// s 


s~ 


59 8 








. 




s 








^ 


S 2 


1 58 17 




2 28 


2 36J31 


i 162: 


1 20 30 s 


s s s 


2 57 25 


2 


4 56 


5 2 


3 '2 


1 18 51 


1 23 6 


S 4 


3 56 33 


3 


7 24 


7 48 


33 


[1 21 19 


1 25 42 s 


S 5 


4 55 42 


4 


0951 


10 23 


34 


1 23 47 


1 28 18 S 


S 6 


5 54 50 


5 


12 19 


12 50 


35 


1 26 15 


1 30 54 S 


s s ^ 


6 53 58 


6 


14 47 


15 35 


36 


1 28 42 


1 33 29 


S 8 


7 53 7 


7 


17 15 


18 11 


37 


1 31 10 


1 36 5s 


S 9 


8 52 15 


8 


19 43 


20 47 


38 


1 33 38 


1 3.8 40 


S 10 


9 51 23 


9 


22 11 


23 23 


39 


I 36 6 


1 41 16s 


S * J 


10 50 32 


10 


24 38 


25 58 


40 


1 38 34 


1 43 52 


S 12 


11 49 40 


11 


27 6 


28 34 


41 


1 41 2 


1 46 28 S 


S 13 


12 48 48 


12 


29 34 


31 10 


47! 


I 43 30 


1 49 4 


S 14 


13 47 57 


13 


32 2 


33 45 


43 


1 45 57 


1 51 39 s 


S 15 


14 47 5 


14 


34 36 


36 21 


44 


1 48 25 


I 54 15 J; 


S 16 


15 46 IS 


15 


36 58 


38 57 


45 


I 50 53 


1 55 51 S 


S ^ 


16 45 22 


16 


39 26 


41 33 


fc 6 


53 21 


1 59 27 J 


S 18 


17 44 30 


17 


41 53 


44 8 


17 


1 55 49 


2 2 3 S 


lj 19 


18 43 38 


18 


44 21 


46 44 


18 


1 58 17 


2 4 39 S 


S 20 


19 42 47 


19 


46 49 


49 20 


49 


2 44 


3 7 13? 


S 21 


20 41 55 


20 


49 17 


351 56 


50 


2 3 12 


3 9 50 S 


S 22 


21 41 3 


21 


51 45 


3 54 32 


51 


2 5 40 


2 12 25 


S 90 


22 40 12 


22 


54 13 


3 57 8 52 


288 


215 2 S 


S 24 


23 39 20 


23 


56 40 


3 59 43 


53 


2 10 36 


2 17 38s 


. 25 


24 38 28 


24 


59 8 


1 219 


>4 


2 13 4 


2 20 14 S 


S26 


25 37 37 


25 


1 36 


4 55 


55 


2 15 32 


2 22 . 50 s 


$27 


26 36 45 


26 


4 4 


7 31 


56 


2 17 59 l 


2 25 26 S 


S 28 


27 35 53 


27 


6 32 


10 7 


37 


2 20 27 


2 28 8s 


29 


28 35 2 


28 


9 


12 43 


58 


I 22 55 


2 30 32 > 


S 30 


29 34 10 


29 


11 28 


15 19 


39 


I 25 23 < 


2 33 14 s 


s 31 


1 30 33 18 


30 


13 55 


I 17 55 


SO 


2 27 51 


2 35 50 S 


S In leap-years, after February, add one day, and one day's motion. S 


S S 



Xx 



Astronomical '1 \ibles. 



-*? f 



A 



T 



ABLE XI If. Equation of the Surf* Centre, or the Dif- 
ference between hi a wean and true Place. 



Sun's mean Anomaly. 



Subtract. 



S | 

<5 



Sign. 


1 
Sign. 


2 
Signs. 


3 

Signs. 


4 
Signs. 


5 

Signs. 


OS 

CD > 

^ S 
rf S 

-\ 

SOS 


Q f n 


' " 


o ' " 


' " 


' " 


' ' 





56 47 


1 39 6 


i 55 37 


1 41 12 


58 53 


S 1 

s 

S 3 

S 5 

1 

s 1 

y 


1 59 
3 57 
5 56 
7 54 

9 52 


58 30 
1 12 
1 1 53 
1 3 33 
1 5 12 


1 40 7 
1 41 6 
1 42 3 
1 42 59 

1 43 52 


I 55 39 
1 55 38 
1 55 36 
1 55 31 
1 55 24 


1 40 12 
1 39 10 
1 38 6 
1 37 
I 35 52 


57 7 
55 19 
53 30 
51 40 

49 49 


29 S 
28 ^ 
27 S 
26^ 
25 S 

24 S 
23 S 
22 S 
31 S 
20 ? 


1 1 50 
13 48 
15 46 
17 43 
19 40 


1 6 50 
1 8 27 
1 10 2 
1 11 36 
1 13 9 


-1 44 44 
I 45 34 
I 46 22 
1 47 8 
I 47 53 


1 55 15 
1 55 3 

I 54 50 
I 54 35 
1 54 17 


1 34 43 
1 33 32 
1 32 19 
1 31 4 
1 29 47 


47 57 
46 5 
44 11 
42 16 
40 21 


" 


S 15 

Ma 

$ 19 

^ 20 


21 37 
23 33 

25 29 
27 25 
29 20 


1 14 41 
1 16 11 

1 17 40 
1 19 8 
1 20 34 


1 48 35 
1 49 15 
1 49 54 
1 50 30 
1 51 5 


\ 53 57 
1 53 36 
1 53 12 
I 52 46 
1 52 18 


I 28 29 
1 27 9 
1 25 48 
1 24 25 
1 23 


38 25 
36 28 
34 30 
32 32 
30 33 


'9 S* 
18 S 

17? 


31 15 

33 9 
35 2 
36 55 
38 47 


1 21 59 
1 23 22 
1 24 44 
1 26 5 
1 27 24 


1 51 37 
I 52 8 
1 52 36 
1 53 8 
1 53 27 


1 51 48 
I 51 15 
1 50 41 
1 50 3 
1 49 26 


1 21 34 
1 20 6 
1 18 36 
1 17 5 
1 15 33 


28 53 
26 33 
24 33 
22 32 
20 30 


''s 

10 S 


S 21 
S 22 

S 24 
S 2o 


40 3 1 J 
42 30 
44 20 
46 9 

47 57 


1 28 41 
1 29 57 
1 31 11 
1 32 25 
1 33 35 


1 53 50 

I 54 10 
1 54 28- 
1 54 44 
1 54 58 


1 48 46 
1 48 3 
1 47 19 
I 46 32 
1 45 44 


I 13 59 

1 12 24 
1 10 47 
1 9 9 
1 7 29 


18 28 
16 26 
14 24 
12 21 
10 18 


M 

8 S 
6 S 

1j 


S26 
S27 
S 28 

J30 


49 45 
51 32 
53 18 
55 3 
56 47 


1 34 45 
1 35 53 
1 36 59 
1 38 S 
1 39 6 


1 55 10 
1 55 20 
1 55 28 
I 55 34 
1 55 37 


I 44 53 
1 44 1 
i 43 7 
1 42 10 
1 41 12 


I 5 49 
1 4 7 
1 2 24 
1 39 
58 53 


) 8 14 
0611 
047 
024 
000 


i C 

T fi> 

i CTQ 


11 
Signs, 


10 
Signs. 


9 
Signs. 


8 
Signs. 


7 
Signs. 


6 
Signs. 


? s 


S Add. J 



Astronomical 1 ables. 



345 



> TABLE XIV. The Sun's 


TABLE XV. Equation of the Sun's S 


<J Declination. 


mean Distance from the Node. ^ 


Argument, Sun's true Place 


Argument, Sun's mean Anomaly. 




Signs 


signs. 


Signs. 




Subtract. 


, 

s o 


A*. 


i j\r. 


2 A: 


U 

CD 
(9 







1 


2 


3 


i 
4 


5 





So 


6 S. 


7 S. 


8 S. 


d 

n 


<? 


Sig 


Sis 


Sig 


Sig. 


SL> 


I . 


R J 

* 


C/5 

r 


' 


' 


' 






' 


' 


' 


' 


o ' 


' 




\ 





1 1 30 


20 11 


30 








1 2 


1 47 


2 5 


I 50 


1 4 


30 S 




24 


11 51 


20 24 


29 


1 


2 


1 4 


48 


2 5 


1 48 


1 2" 


J 

O Q 

S 


S 2 


48 


12 11 


20 36 


28 


2 


4 


6 


1 49 


2 5 


1 47 


1 


28 S 


S 3 


1 12 


12 32 


20 48 


27 


3 


6 


8 


1 50 


2 5 


1 46 


58 


27 ^ 


S 4 


1 36 


12 53 


20 59 


26 


4 


9 


10 


1 51 


2 5 


1 45 


56 


26 ^ 


S 5 


1 59 


13 13 


21 10 


25 


5 


11 


12 


1 52 


2 5 


1 44 


54 


25!; 


s 












* 












s 


i 6 


2 23 


13 33 


21 21 


24 


6 


13 


14 


1 53 


2 5 


1 43 


52 


24 $ 


\ r 


2 47 


13 53 


21 31 


23 


7 


15 


16 


1 54 


2 4 


1 41 


J 50 


23 S 


S 8 


3 11 


14 12 


21 41 


22 


8 


17 


17 


1 55 


2 4 


40 


) 48 


20 


^ 9 


3 34 


14 31 


21 50 


21 1 


9 


19 


18 


I 56 


2 4 


1 39. 


46 


21 * 


S 10 


3 58 


14 50 


21 59 


20 


10 


21 


19 


1 57 


2 4 


1 37 


44 


20 < 


f H 


4 22 


15 9 


22 8 


19 


11 


23 


21 


1 58 


2 3 


I 36 


42 


19 i 


S l2 


4 45 


15 28 


22 16 


18 


12 


25 


22 


1 58 


2 3 


1 34 


40 


^ 


<13 


5 9 


15 46 


22 24 


17 


. 3 


28 


24 


1 59 


2 3 


1 33| 


37 




s 14 


5 32 


16 4 


22 31 


16 


14 


30 


26 


2 


2 2 


1 31 


35 


16 Jj 


i 15 


5 35 


16 22 


22 38 


15 


15 


32 


27 


2 


2 2 


30 


3 33 


15 S 


S 16 


6 18 


16 39 


22 45 


14 


1 6 


3 34 


28 


2 


2 1 


28 


) 31 


14 ^ 


S *" 


6 41 


16 57 


22 51 


13 


17 


36 


30 


2 1 


2 1 


1 27 


29 


13 S 


S 18 


7 4 


17 14 


22 56 


12 


18 


38 


31 


2 2 


2 


1 25 


27 


12 ^ 


i i? 


7 27 


17 30 


23 2 


11 


19 


40 


34 


2 2 


2 


1 24 


24 


1 1 S 


S20 


7 50 


17 46 


23 6 


10 


20 


42 


35 


2 3 


59 


1 23 


22 


10 S 

s 


S 21 


8 15 


18 2 


23 11 


9 


21 


44 


1 36 


2 3 


I 59 


I 21 






!} 22 


8 35 


18 18 


23 14 


8 


22 


4C 


1 37 


2 4 


1 58 


i \\> 


) Ifc 


8 S 




9 57 


18 33 


23 18 


7 


! 23 


48 


I 39 


2 4 


1 57 


17 


) 16 


7 Jj 


w 2A 


9 20 


18 48 


23 21 


6 


124 


50 


40 


2 4 


1 5 


li 


l;i 


6 S 


JJ25 


9 42 


19 3 


23 21 


5 


25 


52 


41 


2 4 


i 5i 


i. 


,) 11 


5 S 


S 26 


10 4 


19 17 


23 25 


4 


126 


54 


43 


2 : 


1 M 


1 1 


.) 1 


4 S 


Jj 27 


10 25 


19 31 


23 27 


3 


27 


5f 


44 


2 5 


1 5T 


c 


7 


3. S 


L 28 


10 47 


19 45 


23 28 


2 


128 


58 


45 


2 L 


i 5^: 


1 r 




< 


S 29 


11 fc 


19 58 


23 29 


1 


29 


1 ( 


46 


2 I 


1 5- 


L *t 




1 S 


s _ 


11 30 


20 11 


23 29 





30 


I 2 


47 


2 5 


1 51 


1 : 


m 


15 

|l 


Signs 


Signs 


Signs 


O 

J3 


C 


11 


10 
Sig 


9 
Sig 


8 
. Sig 


ol - l *'\ J ? , 


11 S 


10 S 


9 S 


t ft 
i " 


5 N 


4 A* 


3 A* 




o 

ai 


Add. 



346 



Astronomical Tables. 



STABLE XVI. 

vj The Moon't, 
S Latitude in 

\ 


TABLE XVII. The Moon's horizontal Pa- S 
rallax, with the Semidiawcters and true Ho- ^ 
rary Motion of the &un and Moon, and eve- S 
ry tiixth Degree of their mean Anomalies, \ 
the Quantities for the intermediate Degrees S 
()>'.inp easily /iro/iortioned by Sight. \ 

- ,_m t 


S Argument, Moon's 
S equated Distance 
from the Node. 


CD H 
"^ f 


MoCJn's 
horizor.t. 
Parallax. 


j3| 


m 

~' & """ 


o 2 9 


;S ffi v ' 
3 *< 


? r| 


S Sign 

<J North Ascending 


5 -' 


6 Signs' 
S South Descending 


s 


' " 


f / 


/ ft 


/ n 


/ // 


s ^ 


S 

4 


o '; " 






6 
12 

18 

24 


54 29 

54 31 
54 34 
54 40 
54 47 

54 56 
55 6 
55 17 
55 29 
55 42 

55 56 
56 12 
56 29 
56 48 
57 8 


15 50 
15 50 
15 50 
15 51 
15 51 


14 54 
14 56 
14 56 
14 57 
14 58 


30 10 
30 12 
30 15 
30 19 
30 26 


2 23 
2 23 
2 23 
2 23 
2 23 


12 

24 S 

18 S 
12 S 

6 |j 

11 ! 

24 S 

* 


n 
n 

S 6 

<! 7 
S 8 

S 10 

> 11 

S 12 
S 13 

vii 

IS 

s 18 


'J 
5 15 
10 30 
15 45 
20 59 
26 13 
31 26 
36 39 
41 51 
47 22 
52 13 
57 23 
1 2 31 
I 7 38 
1 12 44 
1 17 49 
1 22 52 
1 27 53 
i 32 52 
1 37 49 


30 
29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 
11 


1 C 

6 
12 
18 
24 

2 
6 
12 
18 

24 


15 52 
15 53 
15 54 
15 55 
15 56 


14 59 
15 1 
15 4 
15 8 
15 12 


30 34 
30 44 
30 55 
31 9 

31 2.; 


2 24 

2 24 
2 24 
2 24 
2 25 


15 58 
.15 59 
16 1 
16 2 
16 4 


15 17 
15 22 
15 26 
15 30 
15 36 

15 41 
15 46 
15 52 
15 58 
16 3 


Jl 40 
31 56 
32 17 
32 39 
33 11 


,2 25 
2 26 
2 27 
2 27 
2 2f, 


10 e 

24 S 

18 S 
12S 


3 Q 
6 
12 
18 
24 


57 30 
57 1 52 
53 12 
58 31 
58 49 


16 6 
16 8 
16 10 
16 11 
16 13 


33 23 
33 47 
34 11 
34 34 
34 58 


2 28 
2 2& 
2 29 
2 29 
2 30 

2 30 
2 31 
2 31 
2 32 
2 32 


9 I> 

24 S 

12 S 

80$ 
24 S 
18 <J 
12 S 

s 


S. 5 Signs 

S North- Descending. 


4 
6 
12 
18 

24 


59 6 
59 21 
59 35 
59 48 
60 


16 14 
15 15 
16 17 
16 19 

16 20 


16 9 
16 14 
16 10 
16 24 
16 28 


35 22 
35 45 
36 
36 20 
36 40 

37 
37 10 
37 19 

37 28 
37 36 


S 1 1 Signs 

^ South Ascending. 


^ This Table shews 
S the Moon's Lati- 
S tude a little be- 
S yond the utmost 
Jj Limits of Eclip- 
^ses. 

S 


5 
6 
12 
18 
24 


60 11 
60 21 
60 30 
60 38 

60 45 


16 21 
16 21 
16 22 
16 22 
16 23 


16 31 

16 32 
16 37 
16 38 
16 39 


2 32 
2 33 
2 33 
2 33 
2 33 


r oj 

24 S 
12 J 


6 


60 45 


16 23 


16 39 


37 40 


2 33 


60^ 



Precepts relative to the preceding Tables. 347 



To calculate the true Time of New or Full Moon. 

PRECEPT I. If the required time be within the 
limits of the 18th century, write out the mean time 
of new Moon in March, for the proposed year, 
from Table I, in the old style, or from Table II, 
in the new ; together with the mean anomalies 
of the Sun and Moon, and the Sun's mean dis- 
tance from the Moon's ascending node. If you 
want the time of full Moon in March, add the 
half lunation at the foot of Table III, with its 
anomalies, &c. to the former numbers, if the* 
new Moon fall before the 15th of March; but 
if it fall after, subtract the half lunation, with 
the anomalies, &c. belonging to it, from the for- 
mer numbers, and write down the respective sums 
or remainders. 

II. In these additions or subtractions, observe, 
that 60 seconds make a minute, 60 minutes make a 
degree, 30 degrees make a sign, and 12 signs 
make a circle. When you exceed 12 signs in ad- 
dition, reject 12, and set down the remainder. 
When the number of signs to be subtracted is 
greater than the number you subtract from, add 12 
signs to the lesser number, and then you will have 
a remainder to set down. In the tables, signs 
are marked thus s , degrees thus , minutes thus ', 
and seconds thus ". 

III. When the required new or full Moon is 
in any given month after March, write out as many 
lunations, with their anomalies, and the Sun's dis- 
tance from the node, from Table III. as the given 
month is after March; setting them in order below 
the numbers taken out for March. 

IV. Add all these together, and they will give 
the mean time of the required new or full Moon, 
with the mean anomalies and Sun's mean distance 
from the ascending node, which are the^arguments 
for finding the proper equations. 



Precepts relating to the preceding Tables. 

V. With the number of days added together, 
enter Table IV, under the given month, and against 
that number you have the day of mean new or 
full Moon in the left-hand column, which set 
before the hours, minutes, and seconds, already 
found. 

But (as it will sometimes happen) if the said 
number of days fall short of any in the column 
under the given month, add one lunation and its 
anomalies, &c. (from Table III, to the foresaid 
sums, and then you will have a new sum of days 
wherewith to enter Table IV, under the given 
month, where you are sure to find it the second 
time if the first fall short. 

VI. With the signs and degrees of the Sim's 
anomaly, enter Table VII, and therewith take out 
the annual or first equation for reducing the mean 
syzygy to the true ; taking care to make propor- 
tions in the table for the odd minutes and seconds 
of anomaly, as the table gives the equation only to 
whole degrees. 

Observe in this and every other case of finding 
equations, that if the signs be at the head of the 
table, their degrees are at the left hand, and are 
reckoned downward ; but if the signs be at the 
foot of the table, their degrees are at the right 
hand, and are counted upward; the equation being 
in the body of the table, under cr over the signs, 
in a collateral line with the degrees. The titles 
Add or Subtract at the head or foot of the tables 
where the signs are found, shew \\Uether the 
equation is to be added to the mean time of new 
or full Moon, or to be subtracted from it. In 
this table, the equation is to be subtracted if the 
signs of the Suns anomaly be found at the head of 
the table ; but it is to be added, if the signs be at 
the foot. 

VII. With the signs and degrees of the Sun's 
mean anomaly, enter Table VIII, and take out 



Precepts relating t.o the preceding Dalies. 34!' 

the equation of the M on's mean anomaly ; subtract 
this equation from her mean anomaly, if the signs 
of the Sun's anomaly be at the head of the table, 
but add it if they be at the foot ; the result will be 
the Moon's equated anomaly, with which enter 
Table IX, and take out the second equation for re- 
ducing the mean to the true time of new or full 
Moon ; adding this equation, if the signs of the 
Moon's anomaly be at the head of the table, but 
subtracting it if they be at the foot, and the result 
will give you the mean time of the required new or 
full Moon twice equated, which will be sufficiently 
near for common almanacks. But when you want 
to calculate an eclipse, the following equations must 
be used : thus, 

VIII, Subtract the Moon's equated anomaly 
from the Sun's mean anomaly, and with the re- 
mainder in signs and degrees, enter Table X, and 
take out the third equation, applying it to the former 
equated time, as the titles Addvr Subtract do direct. 

IX. With the Sun's mean Distance from the as- 
cending node enter Table XI, and take out the 
equation answering to that argument, adding it to, 
or subtracting it from, the former equated time, as 
the titles direct, and the result will give the time 
of new or full Moon, agreeing with well-regulated 
clocks or watches, very near the truth. But, to 
make it agree with the solar, or apparent time, ap- 
ply the equation of natural days, found in the table 
(from page 193 to page 205) as it is leap-year, or 
the first, second, or third after. 

The method of calculating the time of any new 
or full Moon without the limits of the 18th century, 
will be shewn further on. And a few examples, 
compared with the precepts, will make the whole 
work plain, 

A". B. The tables begin the day at noon, and 
reckon forward from thence to the noon following. 
Thus, March the 31st, at 22h. 30min. 25sec. of 
tabular time, is April 1st (in common reckoning) at 
5scc. after 10 o'clock in the morning. 



350 



Precepts and Examples* 

^r-rvr-r-r^ 

II \ i-f-M 




relative to the preceding Tables* 



s 

p-l 



w I 




-*- ' ^ ^ w " *~ w w su 'ri /-> 

fl'lfijljllll 

c ^^^s~^l 

o ^ oj t3 ai -f *S 



S 5 S 
3sj-*Si5 



To calculate the Time of New and Full Moon in a 
given Tear and Month of any particular Century^ 
between the Christian Mr a and the l&tb Century. 

PRECEPT!. Find a year of the same number in 
the 1 8th century with that of the year in the century 
proposed, and take out the mean time of new Moon 
in March, old style, for that year, with the mean 
anomalies and Sun's mean distance from the node at 
that time, as already taught. 

II. Take as many complete centuries of years from 
Table VI. as, when subtracted from the abovesaid 
year in the t Sthcentury, will answer tothe given year; 
and take out the first mean new Moon and its anoma- 
lies, &c f belonging to the said centuries, and set them 

Yy 



352 Precepts and Examples 

below those taken out for March in the 1 8th century. 

III. Subtract the numbers belonging to these cen- 
turies, from those of the 18th century, and the re- 
mainders will be the mean time and anomalies, &c. 
of new Moon in March, in the given year of the cen- 
tury proposed. Then, work in all respects for the 
true time of new or full Moon, as shewn in the above 
precepts and examples. 

IV. If the days annexed to these centuries exceed 
the numberof days from the beginning of March taken 
out in the 18th century, addalunation and its anoma- 
lies &c.;from Table, III to the time and anomalies of 
new Moon, in March, and then proceed in all respects 
as above. This circumstance happens in example V. 







relative to the preceding Tables. 

To calculate the true Time of New or Full Moon in any given 
Year and Month before the C/iristian ./Era. 

PRECEPT I. Find a year in the 18th century, 
which being added to the given number of years be- 
fore Christ, diminished by one, shall make a num- 
ber of complete centuries. 

II. Find this number of centuries in Table VI, 
and subtract the time and anomalies belonging to it 
from those of the mean new Moon in March, the 
above-found year of the i8th century ; and the re- 
mainder will denote the time and anomalies, &c. of 
the mean new Moon in March, the given year before 
Christ. Then, for the true time of that new Moon, 
in any month of that year, proceed in the manner 
taught above 



& $ 


^ 


>r> 


>O CM 


b- ^^ S a . 




- \l 

1 i 1 
* 11 





b- b- 

CM CM 
r-f* b- 


C 
CM 
O> CO 


O /* j X W .Q 

- ^ ^ 3 s - 

70 J^l ^f 1 

Q r; G "^ ^ C ^ 




.-: s s A 


0! 






^ ^ > ^--5 




5* ro 2 ' + 


^ 


C-l O 


CM ~- 




^ <- 




^ cl S 










CM "cS S "^ .^ 




!. S o 














3 o s 5 

C*> C ^C 


V. 


2! $ 


1!0 b- 

CM 


CO I 

-* 1 


'* 6 ^ : < 




c Si." 

" " S 5 


o 


^ *^ 


co b- 

CM 


o 


'O ^ S O ^ 

*~* J V f < 




^ So 




T? ' 


CM CM 


'O 


>o SJD S - B cr 




^ n't C t w . 


ao 








<<< S r- "~^J 




8 v5 -^ S ^ 










**^ ^ ^2 c 




"CO rj S . 

IS s 1 


- 


-> O 

( 
O N- 


o cc 

CO 4 O 
CO CO 


o ci 


^ M s 

- it o s 




P^- 'r* *-^ C ^3 


^ 


IQ '' 


""* 


CN "i- 


r-T-i Q,^ C , - "^^ 




!f^ - s < 




tM CTi 


CO b- 


O >--; 


^, -a S ^ c ^ 




A* . s !; - 


;; 


r< 


^J 




^ C - L C/2 S 




ref -S S C 




00 


7> CM 


?. '- 


o r ^ ^ 




**N ^ S C 


a 


^~ 






? ' ^ 




C> '^J *; 










*~*S* *r*~f~ 


-^ v ^ r *-^'^v 


^ S 


-.C 


^ c v ^ 


o cr- 

CO 


-^ i^ 


co 00 "O CO ;T- 


' j 's 


Tjl V (-> 


' 


J 






O 


CO s 


* co t 
K o /. C 




CO b- 

co *o 


co 51 


1>- . 


-^ CM 


4- W S 


C/3 S 5 












*1 






b~ X.O 


-^t 


" 1 


-CM "^ _1_ 1 ^ 


- S 


S c; C * 


"* 


' 


^H 


1 




s 


ij ?* :? 4J 




. r~ 


00 


30 


oo i X) oo 


'/} ^ 


A *> ^ 


d 


.- * ^ < 


CO 


.1 




" S 




O -tj -tJ 

BO 

to "2 

t-^ ^: ^ ^3 -C ^T 

g ^ ? CJ o o . 
S & j f ' 

i i|ll! s 

>> g .8 ^ .3"S ; 

K ". CM ; < r^ p 



354 



Precepts and Examples 



These tables are calculated for the meridian of 
London ; but they will serve for any other place, by 
subtracting four minutes from the tabular time, for 
every degree that the meridian of the given place is 
westward of London, or adding four minutes for 
'every degree that the meridian of the given place is 
eastward : as in 



s 




relative to the preceding Tables. 



S55 




Tc calculate the true Time of New or Full Moon> in 
any given Tear and Month after the 1 8th Century. 

PRECEPT I. Find a year of the same number in 
the 1 8th century with that of the year proposed, and 
take out the mean time and anomalies &c. of new 
Moon in March^ old style, for that year, in Table I. 

II. Take so many years from Table VI, as, when 
added to the above-mentioned year in the 18th cen- 
tury, will answer to the given year in which the new 
or full Moon is required: and take out the first new 
Moon,with its anomalies, for these completecenturies. 



356 



Precepts and Examples 



III. Add all these together, and then work in all respects 
as shewn above, only remember to subtract a lunation and 
its anomalies, when the above-mentioned addition carries the 
new Moon beyond the 31st of March ; as in the following 
example : 



w 

i-3 

O< 





S 







P; 



In keeping by the old style, we are always sure to be 
right, by adding or subtracting whole hundreds of years 
to or from any given year in the 18th century. But in 
the new style we may be very apt to make mistakes, on 
account of the leap-years not coming in regularly every 
fourth year: And therefore, when we go without the 



relative to the preceding Tables. 

limits of the 1 8th century, we had best keep to the 
old style, and at the end of the calculation reduce 
the time to the new. Thus, in the 22d century, 
there will be 14 days difference between the styles; 
and therefore, the true time of new Moon in this 
last example being reduced to the new style, will be 
the 22d of July, at 22 minutes 53 seconds past VI 
in the evening. 

To calculate the true Place of the Sun for any given 
Moment of Time. 

PRECEPT I. In Table XII, find the next lesser 
year in number to that in which the Sun's place is 
sought, and write out his mean longitude and ano- 
maly answering thereto: to which add his mean mo- 
tion and anomaly for the complete residue of years, 
months, days, hours, minutes, and seconds, down 
to the given time, and this will be the Sun's mean 
place and anomaly at that time, in the old style; 
provided the saidtime bein any year after the Chris- 
tian ^ra. See the first following example. 

II. Enter Table XIII with the Sun's mean ano- 
maly, and making proportions for the odd minutes 
and seconds thereof, take cut the equation of the 
Sun's centre: which, being applied to his mean 
place, as the title Add or Subtract directs, will give 
his true place or longitude from the vernal equinox 
at the time for which it was required. 

III. To calculate the Sun's place for any time in 
a given year before the Christian sera, take out his 
mean longitude and anomaly for the first year there- 
of, and from these numbers, subtract the mean mo- 
tions and anomalies for the complete hundreds or 
thousands next above the given year; and to the 
remainders add those for the residue of years, 
months, &c. and then work in all respects as above. 
See the second example following. 



358 



Examples from the preceding Tables. 



w 



II 



ir > S 

CM 

2 -S 

a 

I I 

o ^ 

^ xn 

?2 co 

* j 

o -t^ 



.s 






i 


OOOOwico^- 


c3 >- 


o 




^^0,^^^, 


^ I 


c 




< C9 * ^J 1 *O 


C-* ,_ 


<c 






^ < 


c/3 


^ 


^0 C^ <7i 00 O 

' cr< CN c^ CN 


~* c 









CD 


-jn 




^ 


-S 


6 




O<MO-'nco^- 


-< 


"5 






CO CO 


'S: 


^ 


CO h. h- 0^ T? 


r? in 






^ GQ " "* "* 


* 


>-! 


O 


O O cr> co O 


O ' 


tf 




(M CN C< C* 


1 


"C 








5 




o o - 


o 



:i 
*\ 






O 



ii-5.1 




Examples from the preceding Tables. 



359 



1-1 s 



8? > a 



*a 



.* 

sT^ S ^ 

R 

, t! 



^ 







ooococ^^o 

" C< 


00 - 


~ 








"~& 


5 



s 


- 


00 iO 


CON-VJCO^OO^C^ 

C< CO *O ^ CO 


4 


< 












* 


00 CO 


n "^ ^ Oi o^ o^ c^ 


00 


^ 




C* 


~- * C*^ C^ C^ C$ s ? 


c^ \^ 


c 








C3 










3 


7^ 


00 


o o 


00 >- "- -^ 00 




. 







oo^^^w^oo 


* 


a 






CO (N O <-* s * CN 




gj 

r/: 


- 


CO O 
O r? 


OOOOvc^OOiC^ 
^ CO T? CO 


CO CO 


-5 


O 


*> ^* 


O O O O Ov C" 


o 


in 






c* c* 




tt 


N 


cn - 


00 O O O 50 







w 



o 



|| 

C ^ 




Zz 



36t> Concerning Eclipses of the Sun and Moon. 

So that in the meridian of London, the Sun was 
then just entering the sign =& Libra, and conse- 
quently was upon the point of the autumnal equi- 
nox. 

If to the above time of the autumnal equinox at 
London, we add 2 hours 2 5 minures 4 seconds for 
the longitude of Babylon, we shall have for the 
time of the same equinox, at that place, OctoberZSd, 
at 19 hours 22 minutes 41 seconds; which, in 
the common way of reckoning, is October 24th, at 
22 minutes 41 seconds past VII in the morning.* 

And it appears by example VI, that in the same 
year, the true time of full Moon at Babylon was 
October 23d, at 42 minutes 46 seconds after VI in 
the morning ; so that the autumnal equinox was 
on the day next after the day of full Moon. The 
Dominical letter for that year was G, and conse- 
quently the 24th of October was on a Wednesday. 

* The reason why this calculation makes the autumnal 
equinox, in the year of the Julian period 706, to be two days 
sooner than the time of the same equinox mentioned in page 
183, is, that in that page the mean time only is taken into 
the account, as if there was no equation of the Sun's motion. 

The equation at the autumnal equinox then, did not ex- 
ceed an hour and a quarter, when reduced to time But, in 
the year of Christ 1756, (which was 5763 years after,) the 
equation at the autumnal equinox amounted to 1 cLy 22 
hours 24 minutes, by which quantity the true time fell later 
than the mean. So that if we consider the true time of 
this last-mentioned equinox, only as mean time, the mean 
motion of the Sun carried thence back to the autumnal 
equinox in the year of the Julian period 706 will fix it to 
the 25th of October in that year. 



Concerning Eclipses of the Sun and Moon. 361 



To find the Sun's Distance from the Moon's ascend- 
ing Node, at the 1 me oj any given New or Full 
Moon ; and consequently, to know whether there 
is an Eclifse at that Time or not. 

The Sun's distance from the Moon's ascending- 
node is the argument for finding the Moon's fourth 
equation in the syzygies, and therefore it is taken 
into all the foregoing examples in finding the 
times of these phenomena. 1 hus, at the time of 
mean new Moon in April 1764, the Sun's mean 
distance from the ascending node is s 5 35' 2", 
See Example I. p. 350. 

The descending node is opposite to the ascend- 
ing one, and they are, therefore, just six signs dis- 
tant from each other. 

When the Sun is within 1 7 degrees of either of 
the nodes at the time of new Moon, he will be 
eclipsed at that time : and when he is within 1 2 
degrees of either of the nodes at the time of full 
Moon, the Moon will be then eclipsed. Thus we 
find, that there will be an eclipse of the Sun at the 
time of new Moon in April 1764. 

But the true time of that new Moon comes out 
by the equations to be 50 minutes 46 seconds later 
than the mean time thereof, by comparing these 
times in the above -example : and therefore, we 
must add the Sun's motion from the node during 
that interval to the.above mean distance s 5 35' 2", 
which motion is found in Table XII, for 50 mL- 
nutes 46 seconds, to be 2 12". And to this we 
must apply the equation of the Sun's mean distance 
from the node, in Table XV, found by the Sun's 
anomaly, which, at the mean time of new Moon 
in example I, is 9^ 1 26' 19" ; and then we shall 
have the Sun's true distance from the node, at the 
true time of new Moon, as follows : 



-362 Elements for Solar Eclipses. 

At the mean time of new Moon in 



Sun from Node, 
s o / // 



O 5 35 2 

Sun's motion from the 7 50 minutes 2 1O 

node for 3 46 seconds 2 

* Sun's mean distance from node at? 

yr > O 5 37 14 

true new Moon 3 
Equation of mean distance from? 950 
node, add 3 

Sun's true distance from the as- 



( O 7 42 14 
cending node j 

which, being far within the above limit of 1 7 de- 
grees, shews that the Sun must then be eclipsed. 

And now we shall shew how to project this, or 
any other eclipse, either of the Sun or Moon. 

To project' an Eclipse of the Sun. 

In order to this, we must find the ten following 
elements by means of the tables. 

1. The true time of conjunction of the Sun and 
Moon ; and at that time, 2. The semidiameter of 
the Earth's disc, as seen from the Moon, which is 
equal to the Moon's horizontal parallax. 3. The 
Sun's distance from the solstitial colure to which 
he is then nearest. 4. The Sun's declination. 
5. The angle of the Moon's visible path with the 
ecliptic. 6. The Moon's latitude. 7. The Moon's 
true horary motion from the Sun. 8. The Sun's 
semidiameter. 9. The Moon's. 10. The semidia- 
meter of the penumbra. 

We shall now proceed to find these elements 
for the Sun's eclipse in April 1 764. 

To find the true time of new Moon. This, by 
example I, p. 350, is found to be on the first day 
of the said month, at 3O minutes 25 seconds after 
X in the morning. 




Elements for Solar Eclipses. '363 

2. To find the Moon's horizontal parallax, or sc- 
midtameter of the Earth's disc, LS sun frc?n the 
Moon. Enter Table XVII, with tie signs and de- 
grees of the Moon's anomaly, (making proportions, 
because the anomaly is in the table only to every 
6th degree,) and thereby take out the Moon's hori- 
zontal parallax; which, for the above tiire, answer- 
ing to the anomaly 1 1 s 9 24' 21 , is 54' 43". 

3. To find the Sun's distance -jrom the nearest sol- 
stice, 'viz. the beginning of Cancer, iihich is 3 s cr 
90 from the beginning of Aries. It appears by the 
example on page 358 (where the Sun's place is 
calculated to the above time of new Moon) that 
the Sun's longitude from the beginning of Aries 
is thenO 5 12 10' 7'', that is, the Sun's place at that 
time is r Aries, 12 1O' 7". 

s o / n 

Therefore from 3 O O 

Subtract the Sun's longitude or place O 12 1O 7 

Remains the Sun's distance from ? _ -, ^ . a ro 

i_ i c <" 1 / 4*-/ o o 

the solstice <& 3 

Or 77 49' 53": each sign containing 30 degrees. 

4. To find the Sun's delcination. Enter Table 
XIV, with the signs and degrees of the Sun's true 
place, viz. O s i 2, and making proportion for the 
1O' 7", takeout the Sun's declination answering to 
his true place, and it will be found to be 4 49' 
north. 

5. To find the Moon's latitude. This depends on 
her distance from her ascending node, which is 
the same as the Sun's distance from it at the time 
of new Moon : and with this the Moon's latitude 
is found in Table XVI. 

Now we have already found, that the Sun's 
equated distance from the ascending node, at the 
time of new Moon in April 1764, is s 7 42' 14". 
See the preceding page. 

Therefore, enter Table XVI, with O sign at the 
top. and 7 and 8 degrees at the left hand, and take 



The Delineation of Solar Eclipses. 

out 36' and 39' , the latitude for 7; and 41' 51", 
the latitude for 8 : : and by making pr portion be- 
tween these latitudes for the 42' 14" by which the 
Moon's distance from the node exceeds 7 degrees ; 
her true latitude will be found to be 40 18" north- 
ascending. 

6. 'Lofind the Moon's true horary motion from the 
Sun. With the Moon's anomaly, viz. il s 9 24' 
21", enter Table XVII, and take out the Moon's 
horary motion ; which, by making proportion in 
that table, will be found to be 30' 22". Then, with 
the Sun's anomaly, 9 s 1 26' 16", take out his 
horary motion 2 ,28' from the same table: and 
subtracting the latter from the former, there will 
remain 27 54" for the Moon's true horary motion 
from the Sun. 

7. To find the angle of the Moon's visible path 
with the ecliptic. This, in the projection of eclip- 
ses, may be always rated at 5 35 , without any 
sensible error. 

8,9. To find the semi diameters of the Sun and 
Moon. These are found in the same table, and by 
the same arguments, as their horary motions. 
In the present case, the Sun's anomaly gives his 
semidiameter 16' 6", ar.d the Moon's anomaly 
gives her semidiameter 14' 57". 

1O. To find the semidiameter of the -penumbra. 
Add the Moon's semidiameter to the Sun's, and 
their sum will be the semidiameter of the penum- 
bra, viz. 31' 3' . 

Now collect these elements, that they may be 
found the more readily when they are wanted in 
the construction of this eclipse. 

1 . True time of new Moon in ~) (1 1t , K , 

/I / t^-r-A ( * *" ^ ^ 

April 1764 3 

6 /"'" 

2. Semidiameter of the Earth's disc, O 54 43 

3. Sun's dist. from the nearest solst. 77 49 53 

4. Sun's declination, north 4 49 O 

5. Moon's latitude, north-ascending 40 18 






The Delineation of Solar Eclipses, 



6. Moon's horary motion from the Sun O 27 54 

7. Angle of the Moon's visible? 

path with the ecliptic 3 

8. Sun's semidiameter 16 6 

9. Moon's semidiameter 14 51 
10. Semidiameter of the penumbra 31 3 



To project an Eclipse of the Sun geometrically. 

Make a scale of any convenient length, as AC, Plate xn, 
and divide it into as many equal parts as the Earth's Fl - L 
semi-disc contains minutes of a degree ; which, at 
the time of the eclipse in April 1764, is 54 43 '. 
Then, with the whole length of the scale as a ra- 
dius, describe the semicircle ^fM^upon the centre 
C; which semicircle shall represent the northern 
half of the Earth's enlightened disc, as seen from 
the Sun. 

Upon the centre C raise the straight line CH, 
perpendicular to the diameter ACE; so ACE shall 
be a part of the ecliptic, and CH its axis. 

Being provided with a good sector, open it to 
the radius CA in the line of chords ; and taking 
from thence the chord of 23^- degrees in your com- 
passes, set it off both ways from //, tog and to b, 
in the periphery of the semi-disc ; and draw the 
straight line gVk 9 in which the north pole of the 
disc will be always found. 

When the Sun is in Aries, Taurus, Gemini, Can- 
cer, Leo, and Virgo, the north pole of the Earth 
is enlightened by the Sun : but while the Sun is in 
the other six signs, the south pole is enlightened, 
and the north pole is in the dark. 

And when the Sun is in Capricorn, Aquarius,Pis- 
ces, Aries, Taurus, and Gemini, the northern half of 
the Earth's axis C XII P lies to the right hand of the 
axis of the ecliptic, as seen from the Sun ; and to 
the left hand, while the Sun is in the other six signs. 

v 



368 The Delineation of Solar Eclipses, 

Open the sector till the radius (or distance of the 
two 90' s) of the signs be equal to the length of Vb? 
and take the sine of the Sun's distance from the 
solstice (77 49' 53') as nearly as you can guess, 
in your compasses, from the line of sines, and set 
off that distance from V to P in the line gVh 9 be- 
cause the Earth's axis lies to the right hand of the 
axis of the ecliptic in this case, the Sun being in 
Aries ; and draw the straight line C XII P for the 
Earth's axis, of which P is the north pole. If the 
Earth's axis had lain to the left hand from the axis 
of the ecliptic, the distance 7P would have been 
set off from V toward g. 

To draw the parallel of latitude of any given place, 
as suppose London, or the path of that place on the 
Earth's enlightened disc as seen from the ^un, from 
Sun-rise till Sun-set, take the fallowing method. 

Subtract the latitude of London, 51i from 90 
and the remainder 38 \ will be the co-latitude, which 
take in your compasses from the line of chords, 
making CA or CB the radius, and set it from h 
(where the Earth's axis meets :he periphery of the 
disc) to VI and VI, and draw the occult or dotted 
line VI K VI. Then, from the points where this 
line meets the Earth's disc, set off the chord of 
the Sun's declination 4 49' to D and F, and to E 
and G, and connect these points by the two occult 
lines F XII G and OLE. 

Bisect LK XII in K, and through the point K 
draw the black line VI K VI. Then making CB 
the radius of a line of sines on the sector, take the 
co-latitude of London 38 1" from the sines in your 
compasses, and set it both ways from K, to VI and 
VI. These hours will be just in the edge of the 
disc at the equinoxes, but at no other time in tfte 
whole year. 

With the extent X" VI,taken into your compasses, 
set one foot in K (in the black line below the occult 
one) as a centre, and with the other foot describe the 
semicircle VI, 7, 8, 9, 1O, &c. and divide it into 12 



The Delineation of Solar Eclipses. 367 

equal parts. Then from these points of division, 
draw the occult lines 7 p, 8, o n, &c. parallel to the 
Earth's axis C XII P. 

With the small extent ^XII as a radius, describe 
the quadrantal arc XII yj and divide it into six equal 
parts, as XII a, ab, be, cd, de, and ef\ and through 
the division- points, a, b, c, d, e, draw the occult 
lines VII e V, VIII d IV, IX c III, X b II, and 
XI a I, all parallel to VI K VI, and meeting the for- 
mer occult lines 7/>, 8 o, &c. f in thepoints VII, VIII, 
IX, X, XI, V. IV, III, II, and I: which points shall 
mark the several situations of London on the Earth's 
disc, at these hours respectively, as seen from the 
Sun ; and the elliptic curve VI VII VIII, &c. be- 
ing drawn through these points shall represent the 
parallel of latitude, or path of London on the disc, 
as seen from the Sun, from its rising to its setting. 

A*. B. If the Sun's declination had been south, 
the diurnal path of London would have been on the 
upper side of the line VI JTVI, and would have 
touched the line DLE in L.- It is requisite to di- 
vide the horary spaces into quarters (as some are in 
the figure) and, if possible, into minutes also* 

Make CB, the radius of a line of chord on the 
sector, and taking therefrom the chord of 5 35', 
the angle of the Moon's visible path with the eclip- 
tic, set it off from H to Mon the left hand of CH> 
the axis of the ecliptic, because the Moon's latitude 
is north-ascending. Then draw CM for the axis of 
the Moon's orbit, and bisect the angle MCffby the 
right line Cz.- Jf the Moon's latitude had been north- 
descending, the axis of her orbit would have been 
on the right hand from the axis of the ecliptic. 
A". B. The axis of the Moon's orbit lies the same 
way when her latitude is south-ascending, as when 
it is north-ascending ; and the same way when south- 
descending, as when north-descending. 

Take the Moon's latitude 40' 18" from the scale 
CA in your compasses, and set it from i to x in the 

3 A 



The Delineation of Solar Eclipses. 

bisecting line Cz, making ix parallel to Cy : and 
through x, at right-angles to the axis of the Moon's 
orbit CM, draw the straight line N-wxy S, for the 
path of the penumbra's centre over the Earth's disc. 
The point w in the axis of the Moon's orbit, is that 
where the penumbra's centre approaches nearest to 
the centre of the Earth's disc, and consequently is 
the middle of ihe general eclipse: the point x is that 
where the conjunction of the Sun and Moon falls, 
according to equal time by the tables ; and the p6int 
y is the ecliptical conjunction of the Sun and Moon. 

Take the Moon's true horary motion from the 
Sun, 27' 54", in your compasses, from the scale 
CA (every division of which is a minute of a de- 
gree), and with that extent make marks along the 
path of the penumbra's centre; and divide each space 
from mark to mark into sixty equal parts or horary 
minutes, by dots ; and set the hours to every 60th 
minute in such a manner, that the dot signifying the 
instant of new Moon by the tables, may fall, into the 
point x, half way between the axis of the Moon's 
orbit, and the axis of the ecliptic ; and then the rest 
of the dots will shew the points of the Earth's disc, 
where the penumbra's centre is at the instants de- 
noted by them, in its transit over the Earth. 

Apply one side of a square to the line of the pe- 
, numbra's path, and move the square backward and 
forward, until the other side of it cuts the same 
hour and minute (as at m and n) both in the path of 
London, and in the path of the penumbra's centre : 
and the particular minute or instant which the square 
cuts at the same time in both paths, shall be the in- 
stant of the visible conjunction of the Sun and Moon, 
or greatest obscuration of the Sun, at the place for 
which the construction is made, namely, London, 
in the present example ; and this instant is at 47! 
minutes past X o'clock in the morning ; which is 
17 minutes 5 seconds later than the tabular time of 
true conjunction. 



The Delineation of Solar Eclipses. 369 

Take the Sun's semidiameter, 16' 6", in your 
compasses, from the scale CA, and setting one foot 
in the path of London at ;;z, namely at 47-| minutes 
past X, with the other foot describe the circle U\\ 
which shall represent the Sun's disc as seen from 
London at the greatest obscuration. Then take the 
Moon's semidiameter, 14' 57", in your compasses, 
from the same scale ; and setting one foot in the 
path of the penumbra's centre at m, 47- minutes 
after X ; with the other foot describe the circle TY 
for the Moon's disc, as seen from London, at the 
time when the eclipse is at the greatest ; and the 
portion of the Sun's disc which is hid or cut off by 
the Moon's, will shew the quantity of the eclipse at 
that time ; which quantity may be measured on a 
line equal to the Sun's diameter, and divided into 
12 equal parts for digits. 

Lastly, take the semidiameter of the penumbra 
31' 3 ;/ , from the scale CA in your compasses; and 
setting one foot in the line of the penumbra's central 
path, on the left hand from the axis of the ecliptic, 
direct the other foot toward the path tf London ; and 
carry that extent backward and forward till both the 
points of the compasses fall into the same instant in 
both the paths ; and that instant will denote the time 
when the eclipse begins at London. Then, do the 
like on the right hand of the axis of the ecliptic ; and 
where the points of the compasses fall into the same 
instant in both the paths, that instant will be the 
time when the eclipse ends at London. 

These trials give 20 minutes after IX in the morn- 
ing for the beginning of the eclipse at London, at the 
points A* and 0; 47 minutes after X, at the points 
7/2 and /?, for the time of greatest obscuration; and 18 
minutes after XII, at R and S, for the time when 
the eclipse ends ; according to mean or equal time. 

From these times we must subtract the equation 
of natural days, viz. 3 minutes 48 seconds, in leap- 
year April 1, and we shall have the apparent times ; 



3 70 The Delineation of Solar Eclipses. 

namely, IX hours 16 minutes 12 seconds for the 
beginning of the eclipse, X hours 43 minutes 42 
seconds for the time of greatest obscuration, and 
XII hours 14 minutes 12 seconds for the time when 
the eclipse ends. But the best way is to apply this 
equation to the true equal time of new Moon, before 
the projection be begun ; as is done in example I. 
For the motion or position of places on the Earth's 
disc answers to apparent or solar time. 

In this construction, it is supposed that the angle 
under which the Moon's disc is seen, during the 
whole time of the eclipse, continues invariably the 
same and that the Moon's motion is uniform and 
rectilinear during that time. But these suppositions 
do not exactly agree with the truth ; and therefore, 
supposing die elements given by the tables to be ac- 
curate, yet the times and phases of the eclipse, de- 
duced from its construction, will not answer exactly 
to what passes in the heavens ; but may be at least 
two or three minutes wrong, though done with the 
greatest care.- Moreover, the paths of all places of 
considerable latitudes are nearer the centre of the 
Earth's disc, as seen from the Sun, than those con- 
structions make diem ; because the disc is projected 
as if the Earth were a perfect sphere, although it is 
known to be a spheroid. Consequently, the Moon's 
shadow will go farther northward in all places of 
northern latitude, and farther southward 'in all places 
of southern latitude, than it is shewn to do in these 
projections. According to Mayer^s tables, this 
eclipse will be about a quarter of an hour sooner 
than either these tables, or Mr. Flamstead's, or Dr. 
Halley^, make it : and Mayer's tables do not make 
it annular at London, 






The Delineation of Lunar Eclipses. 

The projection qfLiyar Eclipses. 

When the Moon is within 12 degrees of either oi 
her nodes, at the time when she is full, she will be 
eclipsed, otherwise not. 

We find by example II. page 351, that at the 
time of mean full Moon in May, 1762, the Sun's 
distance from the ascending node was only 4 49' 
35'', and the Moon being then opposite to the Sim, 
must have been just as near her descending node, 
and was therefore eclipsed. 

The elements for constructing an eclipse of the 
Moon are eight in number, as follows : 

1. The true time of full Moon : and at that time. 
2. The Moon's horizontal parallax. 3. The Sun's 
semidiameter. 4. The Moon's. 5. The semidia- 
meter of the Earth's shadow at the Moon. 6. The 
Moon's latitude. 7. The angle of the Moon's visi- 
ble path with the ecliptic. 8. The Moon's true 
horary motion from the Sun. Therefore, 

1. To find the true time of full Moon. Work a f 
already taught in the precepts. Thus we have tlte 
true time of full Moon in May, 1762, (see exam- 
ple II. page 351,) on the 8th day, at 50 minutes 50 
seconds past III o'clock in the morning. 

2. To find the Moon's horizontal parallax. Enter 
Table XVII. with the Moon's mean anomaly (at 
the above full) 9 8 2 42' 42", and thereby take out 
her horizontal parallax ; which by making the re- 
quisite proportion, will be found to be 57' 20". 

3. 4. To find the semidiameter s of the Sun and 
Moon. Enter Table XVII, with their respective 
anomalies, the Sun's being 10 s 7 27' 45" (by the 
above example), and the Moon's 9 s 2 42' 42" ; and 
thereby take out their respective semidiameters : the 
Sun's 15' 56", and the Moon's 15' 39". 

5. To find the semidiameter of tJie Earth'' s sha- 
dow at the Moon. Add the Sun's horizontal paraU 



372 The Delineation of Lunar Eclipses. 

lax, which is always 10", to the Moon's, which in/ 
the present case is 57' 20", the sum will be 57' 30", 
from which subtract the Sun's semidiamcter 15' 56", 
and there will remain 41' 34" for the semidiameter 
of that part of the Earth's shadow which the Moon 
then passes through. 

6. To find the Momti latitude. Find the Sun's 
true distance from the ascending node (as already 
taught in page 361) at the true time of full Moon ; 
and this distance, increased by six signs, will be the 
Moon's true distance from the same node ; and con- 
sequently the argument for finding her true latitude* 
as shewn in page 363. 

Thus, in example II. the Sun's mean distance 
from the ascending node was s 4 49' 35", at the 
time of mean full Moon : but it appears by the ex- 
ample, that the true time thereof was 6 hours 33 
minutes 38 seconds sooner than the mean time, and 
therefore we must subtract the Sun's motion from 
the node (found in Table XII, page 342) during 
this interval, from the above mean distance s 4 49' 
35", in order to have his mean distance from it at 
the true time of full Moon. Then to this apply the 
equation of his mean distance from the node found 
in Table XV. by his mean anomaly 10 s 7 27' 45"; 
and lastly, add six signs : so shall the Moon's true 
distance from the ascending node be found as 
follows : 

s O / // 

Sun from node at mean full Moon 4 49 35 



C 6 hours 15 35 

His motion from it in < 33 minutes 1 26 

r 38 seconds 



Sum, subtract from the uppermost line 17 3 
Remains his mean distance at true ? 



full Moon 3 



4 32 32 



The Delineation of Lunar Eclipses. 373 

s O f H 

Equation of his mean distance, add 1 38 

' i i -ii 

Sun's true distance from the node 6 10 32 
To which add 6000 

And the sum will be 6 6 10 32 

which is the Moon's true distance from her as- 
cending node at the true time of her being full ; and 
consequently the argument for finding her true lati- 
tude at that time. Therefore, with this argument, 
enter Table XVI. making proportion between the 
latitudes belonging to the 6th and 7th degree of the 
argument at the left hand (the signs being at the 
top) for the 10' 32", and it will give 32' 21" for the 
Moon's true latitude, which appears by the table to 
be south-descending. 

7. To find the angle of the Moon's visible path 
-with the ecliptic. This may 'be stated at 5 35', 
without any error of consequence in the projection 
of the eclipse. 

8. To find the Moon's true horary motion from 
the Sun. With their respective anomalies take out 
their horary motions from Table XVII. in page 346; 
and the Sun's horary motion subtracted from the 
Moon's, leaves remaining the Moon's true horary 
xnotion from the Sun : in the present case 30' 52". 

Now collect these elements together for use. 



D. H. M. S. 

1. True time of full Moon in 
May, 1762 



8 3 50 50 



2. Moon's horizontal parallax- 57 20 

3. Sun's semidiameter 15 56 

4. Moon's semidiameter * 15 39 

5. Semidiameter of the Earth's shadow") A .,, * * 
at the Moon T 41 4 



374 The Delineation of Lunar Eclipses. 

O I If 

6. Moon's true latitude, south-descending 32 21 

7. Angle of her visible path with the ") *" - Q t 
ecliptic J 

8. Her true horary motion from the Sun 30 52 

Plate XIL These elements being found for the construction 
of the Moon's eclipse in May 1762, proceed as 
follows : 

Fig. II. Make a scale of any convenient length, as W Jf, 
and divide it into 60 equal parts, each part standing 
for a minute of a degree. 

Draw the right line ACE (Fig. 3.) for part of 
the ecliptic, and CD perpendicular to it for the 
southern part of its axis ; the Moon having south 
latitude. 

Add the semidiameters of the Moon and Earth's 
shadow together, which, in this ellipse, will make 
57' 13" ; and take this from the scale in your com- 
passes, and setting one foot in the point C, as a cen- 
tre, with the other foot describe the semicircle 
AD B ; in one point of which the Moon's centre 
will be at the beginning of the eclipse, and in an- 
other at the end of it. 

Take the semidiameter of the Earth's shadow, 
41' 34", in your compasses from the scale, and set- 
ting one foot in the centre C, with the other foot de- 
scribe the semicircle KLM for the southern half 
of the Earth's shadow, because the Moon's latitude 
is south in this eclipse. 

Make C D the radius of a line of chords on the 
sector, and set oft' the angle of the Moon's visi- 
ble path with the ecliptic, 5 35', from D to E, and 
draw the right line C FE for the southern half of 
the axis of the Moon's orbit, lying to the right hand 
from the axis of the ecliptic CZ), because the Moon's 
latitude is south- descending. It would have been 
the same way (on the other side of the ecliptic) if 
her latitude had been north- descending; but contrary 



The Delineation of Lunar Eclipses. 375 

m both cases, if her latitude had been either north- 
ascending or south-ascending. 

Bisect the angle D C E by the right line C g, in 
which line the true equal time of opposition of the 
Sun and Moon falls, as given by the tables. 

Take the Moon's latitude, 32' 21", from the scale 
with your compasses, and set it from C Y to G, in the 
line C G g ; and through the point G, at right an- 
gles to CF E, draw the right line P H G F JV for 
the path of the Moon's centre. Then F shall be 
the point in the Earth's shadow, where the Moon's 
centre is at the middle of the eclipse ; G, the point 
where her centre is at the tabular time of her be- 
ing full ; and H, the point where her centre is at the 
instant of her ecliptical opposition. 

Take the Moon's horary motion from the Sun, 30' 
52", in your compasses from the scale ; and with 
that extent make marks along the line of the Moon's 
path, P G N: Then divide each space from mark 
to mark, into 60 equal parts, or horary minutes, and 
set the hours to the proper dots in such a manner, 
that the dot signifying the instant of full Moon, (viz. 
50 minutes 50 seconds after III in the morning) 
may be in the point G, where the line of the Moon's 
path cuts the line that bisects the angle D C E. 

Take the Moon's semidiameter, 15' 39", ia 
your compasses from the scale, and with that ex- 
tent, as a radius, upon the points JV, F, and P, as 
centres, describe the circle Q for the Moon at the 
beginning of the eclipse, when she touches the 
Earth's shadow at F ' ; the circle R for the Moon at 
the middle of the eclipse ; and the circle S for the 
Moon at the end of the eclipse, just leaving the 
Earth's shadow at 17. 

The point N denotes the instant when the eclipse- 
begins, namely, at 15 minutes 10 seconds after II 
in the morning ; the point F the middle of the 
eclipse, at 47 minutes 45 seconds past III ; and 
the point P the end of the eclipse, at 18 minutes 
after V. At the greatest obscuration the Moon is. 
10 digits eclipsed. 3 B 






376 An ancient Edipse'of the Moon described. 



Concerning an ancient Eclipse of the Moon. 

It is recorded by Ptolemy, from Hipparclws, 
that on the 22d of September, the year 201 before 
the first year of Christ, the Moon rose so much 
eclipsed at Alexandria, that the eclipse must have 
begun about half an hour before she rose. 

Mr. Carey puts down the eclipse in his Chrono- 
logy as follows, among several other ancient ones,, 
recorded by different authors : 



Jul. Per. 



451 



Sept. 22. 



Eel. />-. Gz/#i." 2 An. 54. Hor. 7. 

P. M. Alexandr. Dig. eccl. 10. 

[Ptolem. I. 4. c. 11.] 



Nadonassar. 

547. 
Mesor. 16. 



That is, in the 45 L3th year of the Julian period, 
which was the 547th year from Nabonassar, and 
the 54th year of the second Calif ic period, on the 
16th day of the month Mesori, (which answers to 
the 22d of September J the Moon was 10 digits 
eclipsed at Alexandria, at 7 o'clock in the evening. 

Now, as our Saviour was born (according to the 
Dionysianor vulgar sera of his birth) in the 4713th 
year of the Julian period, it is plain that the 4513th 
year of that period was the 200th year before the 
year of Christ's birth ; and consequently 201 years 
before the year of Christ 1. 

And in the year 201, on the 22d of September, 
it appears by example V. (page 354) that the Moon 
was full at 26 minutes 28 seconds past VII in the 
evening, in the meridian of Alexandria. 

At that time, the Sun's place was Virgo 26 14', 
according to our tables ; so that the Sun was then 
within 4 degrees of the autumnal equinox ; and ac- 
cording to calculation he must have set at Alexan- 
dria about 5 minutes after VI, and about one de- 
gree north of the west. 

The Moon being full at that time, would have risen 
just at Sun- set, about one degree south of the east, 




An ancient Eclipse of the Moon described. 377 

jf she had been in either of her nodes, and her visi- 
ble place not depressed by parallax. 

But her parallactic depression (as appears from 
her anomaly, viz. 10 9 6 nearly) must have been 
55' 17" ; which exceeded her whole diameter by 
24' 53" ; but then, she must have been elevated 33' 
45" by refraction; which, subtracted from her 
parallax, leaves 21' 32" for her visible or apparent 
depression. 

And her true latitude was 30 north-descending, 
which being contrary to her apparent depression, 
and greater than the same by 8' 58", her true time 
of rising must have been just about VI o'clock. 
Now, as the Moon rose about one degree south of 
the east at Alexandria, where the visible horizon is 
land, and not sea, we can hardly imagine her to have 
been less than 15 or 20 minutes of time above the 
true horizon before she was visible. 

It appears by Fig. 4, which is a delineation of this 
eclipse reduced to the time at Alexandria, that the 
eclipse began at 53 minutes after V in the evening ^ 
and consequently 7 minutes before the Moon was in 
the true horizon ; to which if we add 20 minutes, 
for the interval between her true rising and her be- 
ing visible, we shall have 27 minutes for the time 
that the eclipse was begun before the Moon was vi- 
sibly risen. The middle of this eclipse was at 30 
minutes past VII, when its quantity was almost 10 
digits, and its ending was at 6 minutes past IX in 
the evening. So that our tables come as near to 
the recorded time of this eclipse as can be expect- 
ed, after an elapse of 1960 years. 



37$ Of thefxed Stars. 

CHAP. XVJIL 

Of thefxed Stars. 

toSlta C rs354 T^HE Stars are said to be fixed, because 
appear " ' J_ they have been generally observed to 
bigger keep a t the same distances from each other, their 
viewed apparent diurnal revolution being caused solely by 
by the the Earth's turning on its axis. They appear of a 
than when sensible magnitude to the bare eye, because the 
seen retina is affected not only by the rays of light 
through w hj c h are emitted directly from them, but by 

a tele- J . . , r .. J 

scope. many thousands more, which falling upon our 

eye-lids, and upon the aerial particles about us, 

are reflected into our eyes so strongly, as to excite 

vibrations not only in those points of the retina 

where the real images of the stars are formed, but 

also in other points at some distance round about. 

This makes us imagine the stars to be much bigger 

than they would appear, if we saw them only by the 

few rays coming directly from them, so as to enter 

our eyes without being intermixed with others. Any 

one may be sensible of this, by looking at a star of 

the first magnitude through a long narrow tube ; 

which, though it takes in as much of the sky as 

would hold a thousand such stars, it scarce renders 

that one visible. 

The more a telescope magnifies, the less is the 
'aperture through which the star is seen ; and con- 
A proof sequently the fewer rays it admits into the eye. Now 
that they since the stars appear less in a telescope which mag- 
their own nifies 200 times, than they do to the bare eye, inso- 
much that they seem to be only indivisible points, 
it proves at once that the stars are at immense dis- 
tances from us, and that they shine by their own 
proper light. If they shone by borrowed light, 
the}- would be as invisible without telescopes as the 
satellites of Jupiter are ; for these satellites appear 



Of the fixed Stars. 379 

bigger when viewed with a good telescope than the 
largest fixed stars do. 

355. The number of stars discoverable in ei- 
ther hemisphere, by the naked eye, is not above a 
thousand. This at first may appear incredible, be- 
cause they seem to be without number : but the de- Their 
ception arises from our looking confusedly wp n m^hTess 
them, without reducing them into any order. For than is 
look but stedfastly upon a pretty large portion of the f^-jf^ 
sky, and count the number of stars in it, and you 
will be surprised to find them so few. And, if one 
considers how seldom the Moon meets with any 
stars in her way, although there are as many about 
her path as in other parts of the heavens, he will 
soon be convinced that the stars are much thinner 
sown than he was aware of. The British catalogue, 
which, besides the stars visible to the bare eye, in- 
cludes a great number which cannot be seen with- 
out the assistance of a telescope, contains no more 
than 3000 in both hemispheres. 

356. As we have incomparably more light from The ab- 
the Moon than from all the stars together, it is the *^> ling- 
greatest absurdity to imagine that the stars were the stars 
made for no other purpose than to cast a faint light ^ onlv 
upon the Earth : especially since many more require to shine " 
the assistance of a good telescope to find them out, "P us 
than are visible without that instrument. Our Sun night, 
is surrounded by a system of planets and comets ; 
all of which would be invisible from the nearest 
fixed star. And from what we already know of the 
immense distance of the stars, the nearest may be 
computed at 32,000,000,000,000 of miles from us, 
which is further than a cannon-ball would fly in 
7,000,000 of years. Hence it is easy to prove, 
that the Sun, seen from such a distance, would ap- 
pear no bigger than a star of the first magnitude. 
From all this it is highly probable that each star is a 
Sun to a system of worlds moving round it, though 
unseen by us ; especially as the doctrine of plurali- 
ty of worlds is rational, and greatly manifests the 
Power, Wisdom, and Goodness of the Great Cre- 
ator. 



380 Of the fixed Stars. 

Their dif- 357. The stars, on account of their apparently 
maTi var i us magnitudes, have been distributed into se- 
tudes : veral classes or orders. Those which appear larg- 
est, are called st'ars of the first magnitude ; the 
next to them in lustre, stars of the second magni- 
tude ; and so on to the sixth ; which are the small- 
est that are visible to the bare eye. This distribu- 
tion having been made long before the invention of 
telescopes, the stars which cannot be seen without 
the assistance of these instruments, are distinguish- 
ed by the name of telescopic stars. 

And dlvi- 358. The ancients divided the starry sphere into 
coMtetta- P art i cu l ar constellations, or systems of stars, ac- 
tions, cording as they lay near one another, so as to occu- 
py those spaces with the figures of different sorts of 
animals or things would take up, if they were there 
delineated. And those stars which could not be 
brought into any particular constellation, were called 
unformed stars. 

The use ^59. This division of the stars into different con- 
of this di- stellations or asterisms, serves to distinguish them 
vision. f r om one another, so that any particular star may 
be readily found in the heavens by means of a ce- 
lestial globe ; on which the constellations are so de- 
lineated as to put the most remarkable stars into 
such parts of the figures as are most easily distin- 
guished. The number of the ancient constella- 
tions is 48, and upon our present globes about 70. 
On Senex's globes, Bayer's letters are inserted ; 
the first in the Greek alphabet being put to the big- 
gest star in each constellation, the second to the 
, next % and so on : by which means, every star is as 
easily found as if a name were given to it. Thus, 
if the star v in the constellation of the Ram be 
mentioned, every astronomer knows as well what 
star is meant, as if it were pointed out to him in the 
heavens. 

The zodi- 360. There is also a division of the heavens into 

ac " three parts, 1. The zodiac (*r/**c f ) from fWicv 

zodion an animal, because most of the constellations 

in it, which are twelve in number, are the figures of 



Of the fixed Stars. 381 

animals : as Aries the Ram, Taurus the Bull, Ge- 
mini the twins, Cancer the Crab, Leo the Lion, 
Virgo the Virgin, Libra the Balance, Scorpia the 
Scorpion, Sagittarius the Archer, Capricornus the 
Goat, Aquarius the Water-bearer, and Pisces the 
Fishes. The zodiac goes quite round the heavens : 
it is about 16 degrees broad, so that it takes in the 
orbits of all the planets, and likewise the orbit of the 
Moon. Along the middle of this zone or belt is the 
ecliptic, or circle which the Earth describes annually 
as seen from the Sun ; and which the Sun appears 
to describe as seen from the Earth. 2. All that re- 
gion of the heavens, which is on the north side of 
the zodiac, containing 21 constellations. And, 3d, 
That on the south side, containing 15. 

361. The ancients divided the zodiac into the The man- 
above 12 constellations or signs in the folio wing "UJf^J" 
manner. They took a vessel with a small hole in by the an- 
the bottom, and having filled it with water, suffered 
the same to distil drop by drop into another vessel 
set beneath to receive it ; beginning at the moment 
when some star rose, and continuing until it rose the 
next following night. The water falling down into 
the receiver, they divided into twelve equal parts ; 
and having two other small vessels in readiness, each 
of them fit to contain one part, they again poured all 
the water into the upper vessel, and, observing the 
rising of some star in the zodiac, they at the same 
time suffered the water to drop into one of the small 
vessels ; and as soon as it was full, they shifted it, 
and set an empty one in its place. When each ves- 
sel was full, they took notice what star of the zodiac 
rose ; and though this could not be done in one 
night, yet in many they observed the rising of twelve 
stars or points, by which they divide the zodiac into 
twelve parts. 



382 



Of the fixed Stars. 



362. The names of the constellations and the number of 
stars observed in each of them by different astronomers, are 
as follows : 



The ancient Constellations. Ptolemy. Tycho. Hevcl Flamst. 

Ursa minor The Little Bear 712 24 


Ursa major 


The Great Bear 


35 


29 


73 


87 


Draco 


The Dragon 


31 


32 


40 


80 


Cepheus 


Cepheus 


13 


4 


51 


35 


Bootes, Arctofihilax 




23 


18 


52 


54 


Corona Borealis 


The Northern Crown 


8 


8 


8 


21 


Hercules, En-gonaszn 


Hercules kneeling 


29 


28 


45 


113 


Lyra 


The Harp 


10 


11 


17 


21 


Cygnus, Gallina 


The Swan 


19 


18 


47 


81 


Cassiopea 


The Lady in her Chair 


13 


26 


47 


55 


Perseus 


Perseus 


29 


29 


46 


59 


Auriga 


The Waggoner 


14 


9 


40 


66 


Serpentarius, Ofthiuchus 


Serpentarius 


29 


15 


40 


74 


Serpens 


The Serpent 


18 


13 


22 


64 


Sagitta 


The Arrow 


5 


5 


5 


IS 


Aquila, Vultur 


The Eagle > 


I 


\ 12 


23) 




Antinous 


Antinous $ 


i 


I 3 


19$ 




Delphinus 


The Dolphin 


10 


10 


14 


18 


Equulus, Equi sectio 


The Horse's Head 


4 


4 


6 


10 


Pegasus, Equus 


The Flying Horse 


20 


19 


38 


89 


Andromeda 


Andromeda 


23 


23 


47 


66 


Triangulum 


The Triangle 


4 


4 


12 


16 


Aries 


The Ram 


18 


21 


27 


66 


Taurus 


The Bull 


44 


43 


51 


141 


Gemini 


The Twins 


25 


25 


38 


85 


Cancer 


The Crab 


23 


15 


29 


83 


Leo 


The Lion > 




f 30 


49 


95 


Coma Berenices 


Berenice's Hair 5 


35 


14 


21 


43 


Virgo 


The Virgin 


32 


33 


50 


110 


Libra, Chela 


The Scales 


17 


10 


20 


51 


Sc6rpius 


The Scorpion 


24 


10 


20 


44 


Sagittarius 


The Archer 


31 


14 


22 


69 


Capricornus 


The Goat 


28 


28 


29 


51 


Aquarius 


The Water-Bearer 


45 


41 


47 


108 


Pisces 


The Fishes 


38 


36 


39 


113 


Cetus 


The Whale 


22 


21 


45 


97 


Orion 


Orion 


38 


42 


62 


78 


Eridanus, Fluvius 


Eridanus, the River 


34 


10 


27 


84 


Lepus 


The Hare 


12 


13 


16 


J9 


Canis major 


The Great Dog 


29 


13 


' 21 


31 


Canis minor 


The Little Dog 


2 


2 


13 


14 



Of the fixed Stars. 383 



The ancient Constellations. Ptolemy. Tycho. 


HtveLFlamst. 


Aro-o The Ship 45 3 


4 


64 


Hydra The Hydra 27 19 


31 


60 


Crater The Cup 7 3 


10 


Si 


Corvtis The Crow 7 4 




9 


Centaurus The Centaur S7 




35 


Lupus The Wolf 19 




24 


Ara The Altar 7 




9 


Corono Australia The Southern Crown 13 




12 


Piscis Australis The Southern Fish 18 




24 


The New Southern Constellations. 






Columba Naochi Noah's Dove 




LO 


llobur Carolinum The Royal Oak 




12 


Grus The Crane 




13 


Phoenix The Phenix 




13 


Indus The Indian 




12 


Pavo The Peacock 




14 


Apus, A-viz Indica The Bird of Paradise 




11 


Apis, Musca The Bee or Fly 




4 


Chamaeleon The Chameleon 




10 


Triangulum Australis The South Triangle 




5 


Piscis volans, Passer The Flying Fish 




8 


Dorado, Xiphias The Sword Fish 




6 


Toucan The American Goose 




9 


Hydrus The Water Snake 




10 


Hevelius's Constellations made out of the unformed 


Stars. 


Jfevelius. 


Flamst. 


Lynx The Lynx 


19 


44 


Leo minor The Little Lion 




53 


Asteron Sc Chara The Greyhounds 


23 


25 


Cerberus Cerberus 


4 




Vulpecula Sc Anser The Fox and Goose 


27 


35 


Scutum Sobieski Sobieski's Shield 


7 




Lacerta The Lizard 




16 


CameiOpardalus The Camelopard 


32 


58 


Monoceros The Unicorn 


19 


3 l 


Sextans The Sextant 


11 


41 



363. Ther,e is a remarkable track round the hea- 
vens, called the Milky Way, fr( m its peculiar white- 
ness, which is found, by means of the telescope, to 
be owing to a vast number of very small stars, that 

3 C 



384 Of Lucid Spots in the Heavens. 

are situate in that part of the heavens. This track 
appears single in some parts, in others double. 
Ltpd 364. There are several little whitish spots in the 

spots. heavens, which appear magnified, and more lumi- 
nous when seen through telescopes ; yet without any 
stars in them. One of these is in Andromeda's gir- 
dle, and was first observed A. D. 1612, by Simon 
Marius : it has some whitish rays near its middle, 
is liable to several changes, and is sometimes invisi- 
ble. Another is near the ecliptic, between the head 
and bow of Sagittarius : it is small, but very lu- 
minous. A third is on the back of the Centaur* 
which is too far south to be seen in Britain. A 
fourth, of a smaller size, is before Antinous's right 
foot, having a star in it which makes it appear more 
bright. A fifth is in the constellation of Hercules, 
between the stars and *, which spot, though but 
small, is visible to the bare eye, if the sky be clear, 
and the Moon absent. 

Cloudy 365. Cloudy stars are so called from their misty 
stars. appearance. They look like dim stars to the naked 
eye ; but through a telescope they appear broad illu- 
minated parts of the sky ; in some of which is one 
star, in others more. Five of these are mentioned 
by Ptolemy. \ . One at the extremity of the right 
hand of Perseus. 2. One in the middle of the 
Crab. 3. One, unformed, near the sting of the 
Scorpion. 4. The eye of Sagittarius. 5. One in 
the head of Orion. In the first of these appear more 
stars through the telescope than in any of the rest, 
although 21 have been counted in the head of Orion 9 
: and above forty in that of the Crab. Two are visi- 
ble in the eye of Sagittarius without a telescope, 
and several more with it. Flams tead observed a 
cloudy star in the bow of Sagittarius, containing 
many small stars : and the star d above Sagittarius' s 
right shoulder is encompassed with several more. 
Both Cassini and Flamstead discovered one between 
the Great and Little Dog, which is yery full of stars. 



Of new Periodical Stars. 

visible only by the telescope. The two whitish spots 
near the south pole, called the Magellanic clouds by 
sailors, which to the bare eye resemble part of the 
Milky Way, appear through telescopes to be amix- ni ^ c 
ture of small clouds and stars. But the most re- clouds, 
markable of all the cloudy stars is that in the middle 
of Orion's sword, where seven stars (of^which three 
are very close together) seem to shine through a 
cloud, very lucid near the middle, but faint and ill- 
defined about the edges. It looks like a gap in the 
sky, through which one may see (as it were) part of 
a much brighter region. Although most of these 
spaces are but a few minutes of a degree in breadth, 
yet, since they are among the fixed stars, they must 
be spaces larger than what is occupied by our solar 
system ; and in which there seems to be a perpetual 
uninterrupted day, among numberless worlds,which 
no human art ever can discover. 

366. Several stars are mentioned by ancient astro- Changes 
nomers, which are not now to be found ; and others J^ 
are now visible to the bare eye, which are not re- 
corded in the ancient catalogue. Hipparchus ob- 
served a new star about 120 years before CHRIST ; 
but he has not mentioned in what part of the hea- 
vens it was seen, although it occasioned his making 
a catalogue of the stars ; which is the most ancient 
that we have. 

The first new. star that we have any good account New 
of, was discovered by Cornelius Gemma on the 8th 
of Nove?/iber, A. D. 1572, in the chair of Cassio- 
pea. It surpassed Sirius in brightness and magni- 
tude ; and was seen for 16 months successively. At 
first it appeared bigger than Jupiter, to some eyes, 
by which it was seen at mid-day ; afterwards it de- 
cayed gradually both in magnitude and lustre, until 
March 1573, when it became invisible. 

On the 13th of August 1596, David Fabricius 
observed the Stella Mira, or wonderful star, in the 
neck of the Whale ; which has been since found to 
appear and disappear periodically seven times in six 



336 Of new Periodical S'ars. 

years, continuing in the greatest lustre for 15 days 
together ; and is never quite extinguished. 

In the year 160O, William Janserims discovered a 
changeable star in the neck of the Swan ; which, in 
time, became so small as to be thought to disappear 
entirely, till the years 1657, 1658, and 1 659, when 
it recovered its former lustre and magnitude, but 
soon decayed ; and is now of the smallest size. 

In the year 1 604, Kepler and many of his friends 
saw a new star near the heel of the right foot of Ser- 
pentarius, so bright and sparkling, that it exceeded 
any thing they had ever seen before ; and took notice 
that it was every moment changing into some of the 
colours of the rainbow, except when it was near the 
horizon, at which time it was generally white. It 
surpassed Jupiter in magnitude, which was near it 
all the month of October ^ but easily distinguished from 
Jupiterby the steady light of that planet. It disap- 
peared between October 16O5, and the February fol- 
lowing, and has not been seen since that time. 

In the year 167O, July 15, Hevelius discovered a 
new star, which in October was so decayed as to be 
scarce perceptible. In April following it regained its 
lustre, but wholly disappeared in August. In March 
1672, it was seen again, but very small ; and has not 
since been visible. 

In the year lt>86, a new star was discovered by 
Kirch, which returns periodically in 404 days. 

In the year 1672, Cassini saw a star in the neck 
of the B nil, which he thought was not visible in Ty- 
cbo's time ; nor when Bayer made his figures. 
Cannot be 367. Many stars, beside those above-mentioned, 
comets. have k een observed to change their magnitudes ; and 
as none of them could ever be perceived to have tails, 
it is plain they could not be comets ; especially as 
they had no parallax, even when largest and bright- 
est. It would seem that the periodical stars have vast 
clusters of dark spots, and very slow rotations on 
their axes j by which means, they must disappear 



Of Changes In the Heavens. 337 

when the side covered with spots is turned towards " 
us. And as for those which break out all of a sud- 
den with such lustre, it is by no means improbable 
that they are Suns whose fuel is almost spent, and 
again supplied by some of their comets falling upon 
them, and occasioningan uncommonblaze and splen- 
dour for some time : which indeed appears to be the 
greatest use of the cometary part of any system*. 

Some of the stars, particularly ^rr/^rz/j,havebeen Some star* 
observed to change their places above a minute of a thei 
degree with respect to others. But whether this be ce s- 
owing to any real morion in the stars themselves, must 
require the observations of many ages to determine. 
If our solar system change its place with regard to 
absolute space, this must in process of time occasion 
an apparent change in the distances of the stars from 
each other : and in such a case, the places of the near- 
est stars to us being more affected than those which 
are very remote, their relative positions must seem 
to alter, though the stars themselves were really im- 
moveable. On the other hand, if our own system 
be at rest, and any of the stars in real motion, this 
must vary their positions; and the more so, the nearer 
they are to us, or the swifter their motions are; or the 

* M. Maupertius, in his Dissertation on the figures of the 
Celestial Bodies (p. 91 93), is of opinion that some stars, by 
their prodigious quick rotations on their axes, may not only 
assume the figures of oblate spheroids, but that by the great 
centrifugal force arising from such rotations, they may be- 
come ot the figures of mill-stones ; or be reduced to fiat cir- 
cular planes, so thin as to be quite invisible when their edges 
are turned toward us ; as Saturn's ring is in such positions. 
But when any eccentric planets or comets go round any flat 
star, in orbits much inclined to its equator, the attraction 
of the planets or comets in their perihelions must alter the 
inclination of the axis of that star ; on which account it will 
appear more or less large and luminous, as its broad side is 
more or less turned toward us. And thus he imagines we 
may account for the apparent changes of magnitude and lus- 
tre in those stars, and likewise for their appearing and dis- 
appearing. 



383 Of Changes in the Heavens. 

more proper the direction of their motion is for our 
perception. 
The eclip- 353. r f [ le obliquity of the ecliptic to the equinoc- 

tic lessob- . . . r J , . 11- r 

lique now tial is round at present to be above the third part or a 
to the degree less than Ptolemy found it. Arid most of the 
thaiTfor- observers after him found it do decrease gradually 
down to Tycho's time. If it be objected, that we 
cannot depend on the observations of the ancients, 
because of the incorrectness of their instruments; we 
have to answer, that both Tycho and llamstead arc 
allowed to have been very good observers ; and yet 
we find that Flamstead makes this obliquity 24 mi- 
nutes of a degree less than Tycho did, about 10O 
years before him : and as Ptolemy was ] 324 years be- 
fore Tycho, so the gradual decrease answers nearly 
to the difference of time between these three astrono- 
mers. If we consider, that the Earth is not a per- 
fect sphere, but an oblate spheroid, having its axis 
shorter than its equatorial diameter; and thatthe Sun 
and Moon are constantly acting obliquely upon the 
greater quantity of matter about the equator,- pulling 
it as it were toward a nearer and nearer coincidence 
with the ecliptic ; it will not appear improbable that 
these actions should gradually diminish the angle be- 
tween those planes. Nor is it less probable that the 
mutual attraction of all the planets should have a ten- 
dency to bring their orbits to a coincidence ; but this 
change is too small to become sensible in many 
ages.* 

* M. de la Grange has demonstrated, in the most satisfac- 
tory manner, that no permanent change can take place in the 
magnitudes, figures, or inclinations, of the planetary orbits ; 
and that the periodical changes are confined within very 
narrow limits : the ecliptic therefore, will never coincide 
with the equator, nor change its inclination above 2 degrees. 
In short, the solar planetary system oscillates, as it were, 
round a medium state, from which it never swerves very 
far. See note subjoined to*p. 1 16. 



Of the Division of Time. 3SO 



CHAP. XXL 

Of the Division of Time. A perpetual Table of Nev, 
Moons. The Times of the Birth and Death of 
CHRIST. A Table of remarkable JEras or Events. 



369 TPHE parts of time are, seconds, minutes, 
JL hours 9 days, years, cycles, ages, and pe- 
riods. 

370. The original standard, or integral measure A year. 
of time, is a year ; which is determined by the re- 
volution of some celestial body in its orbit, viz. the 

Sun or Moon. 

371. The time measured by the Sun's revolution Tro ^ c * 
in the ecliptic, from any equinox or solstice to the >e 
same again, is called the solar or tropical year, 
which contains 365 days, 5 hours, 48 minutes, 57 
seconds ; and is the only proper or natural year, be- 
cause it always keeps the same seasons to the same 
"months. 

372. The quantity of time measured by the Sun's siderea 
revolution as from any fixed star to the same stary car - 
again, is called the sidereal year ; which contains 

365 days, 6 hours, 9 minutes, 14} seconds, and is 
20 minutes 171 seconds longer than the true solar 
year. 

373. The time measured by twelve revolutions of Lunar 
the Moon, from the Sun to the Sun again, is called ye 
the lunar year ; it contains 354? days, 8 hours, 48 
minutes, 36 seconds ; and is therefore 1O days, 21 
hours, O minutes, 21 seconds shorter than the solar 
year. This is the foundation of the epact. 

374. The civil year is that which is in common civil 
use among the different nations of the world ; of yea!% 
which, some reckon by the lunar, but most by the 
solar. The civil solar year contains 365 days, 02* 
three years running, which are called common years ; 
and then comes in what is called the bissextile or 



- : 90 Of the Division of Time. 

leap-year, which contains 366 days. This is also 
called the Julian year* on account of Julius C&sar, 
who appointed the intercalary day every fourth year, 
thinking thereby to make the civil and solar year 
keep pace together. And this day, being added to 
the 23d of February, which in the Roman calendar 
was the sixth of the Calends of March, that sixth day 
was twice reckoned, or the 23d and 24th were reck- 
oned as one day ; and was called Bis sextus dies, and 
thence came the name bissextile for that year. But 
in our common almanacks this day is added at the 
end of February. 

year" ^ 5 ' ^ ne civil lunar year is also common or in- 

tercalary. The common year.consists of 12 luna- 
tions, which contain 354 days ; at the end of which 
the year begins again. The intercalary, or embo- 
limic year, is that wherein a month was added to 
adjust the lunar year to the solar. This method was 
used by the Jews, who kept their account by the 
lunar motions. But by intercalating no more than a 
month of 30 days, which they called Ve-Adar, every 
third year, they fell 3| days short of the solar year in 
that time. 

Roman 376. The Romans also used the lunar embolimic 
year at first, as it was settled by Romulus their first 
king, who made it to consist only of ten months or 
lunations ; which fell 6 1 days short of the solar year, 
and so their year became quite vague and unfixed ; 
for which reason they were forced to have a table 
published by the high-priests, to inform them when 
the spring and other seasons began. But Julius Cte- 
sar, as already mentioned, 374, taking this trou- 
' bleso me affair into consideration, reformed the calen- 
dar, by making the year to consist of 365 days 6 
hours. 

The origi. 377. The year thus settled, is what was used in 

^rellrfal Britain till A. D. 1752 : but as it is somewhat more 

or new than 1 1 minutes longer than the solar tropical year, 

the times of the equinoxes go backward, and fall 

earlier by one day in about 130 years. In the time 



Of the Division of Time. 391 

of the Nicene council ( A. D. 325), which was 1439 
years ago, the vernal equinox fell on the 21st of 
"March: and if we divide 1444 by 130, it will quote 
11, which is the number of -days the equinox has 
fallen back since the council of Nice. This causing 
great disturbances, by unfixing the times of the cele- 
bration of Easter, and consequently of all the other 
moveable feasts, pope Gregory the XIII, in the year 
1582, ordered ten clays to be at once stricken out of 
that year; and the next day after the fourth of Octo- 
ber was called the fifteenth. By this means, the ver- 
nal equinox was restored to the 21st of March; and 
it was endeavoured, by the. omission of three inter- 
calary days in 400 years, to make the civil or politi- 
cal year keep pace with the solar for the time to come. 
This new form of the year is called the Gregorian 
account, or new style ; which is received in all coun- 
tries where the pope's authority is acknowledged, and 
ought to be in all places where truth is regarded. 

378. The principal division of the year is into Month* 
months, which are of two sorts, namely, astronomi- 
cal and civil. The astronomical month is the time 
in which the Moon runs through the zodiac, and is 
either periodical or si/nodical. The periodical month 
is the time spent by the Moon in making one com- 
plete revolution from any point of the zodiac to the 
same again ; which is 27 d 7 U 43 m . The synodical 
month, called a lunation, is the time contained be- 
tween the Moon's parting with the Sun at a conjunc- 
tion, and returning to him again ; which is 29 d 12 1 * 
44 m . The civil months are those which are framed 
for the uses of civil life ; and are different as to their 
names, number of days, and times of beginning, in 
several different countries. The first month of the 
Jewish Year fell, according to the Moon, in our Au- 
gust and September, old style ; the second in Sep- 
tember and October; and so on. The first month 
of the Egyptian year began on the 29th of our Au- 
gust. The first month- of the Arabic and Turkish 

3D 



392 Of the Division of Time. 

I/ear began the 16th ofJttly. The first month of 
the Grecian year fell, according to the Moon, in 
June and July, the second in July and August, and 
so on, as in the following table. 

379. A month is divided into four parts called 
-weeks, and a week into seven parts called days ; so 
that in a Julian year there are 13 such months, or 52 
weeks, and one day over. The Gentiles gave the 
names of the Sun, Moon, and planets, to the days 
of the week. To the first, the name of the Sun ; 
to the second, of the Moon ; to the third, of Mars ; 
to the fourth, of Mercury ; to the fifth, of Jupiter ; 
to the sixth, of Venus; and to the seventh, of Sa- 
turn . 



ST The Jewish 


year. 


Days'S 
c 


1 Tisri 


Aug. Sept. 


30 


2 Marchesvan 


Sept. Oct. 


29 s 


3 Casleau 


Oct. Nov. 


30 ^ 


4 Tebeth 


Nov Dec. 


29 ^ 


5 Shebat 


Dec. Jan. 


30 S 


6 Adar 


Jan. Feb. 


29 ? 


7NisanorAbib 


Feb Mar. 


30 s 


SJiar 


Mar. Apr. 


29 ^ 


9Sivan 


Apr. May 


30 ^ 


10 Tamuz 


May June 


29 \ 


11 Ab 


June July 


30 > 


12 Elul 


July Aug. 


29 \ 






s 


Days in the year 


354 <; 



S In the embolimic year after Adar they added a Ij 
!j month called Fe-Adar, of 30 days. 

Vflt ^S^ 



Of the Division of Time. 



393 



>N 


The Egyptian year. 


Days J; 


s 


* 




Thoth August 


29 


30 s 


S 2 


Paophi September 


28 


30 \ 


S S 3 


Athir October 


28 


30 ; 


! 4 


Chojac November 


27 


30 


> 5 


Tybi December 


27 


30 S 


5 6 


Mechir January 


26 


30 S 


S 7 


Phamenoth February 


25 


30 s 


8 


Parmuthi March 


27 


30 ^ 


S S 9 


Pachon April 


26 


30 


5 10 


Payni May 


26 


30 V 




Epiphi June 


25 


30 ? 


\ 12 


Mesori July 


25 


30 S 


S Epagomenx or days added 




^ 


<J Days in the year. 


\/\/\ 


365 

/\x",y,X^j 


5^^%^*sX\j 


The Arabic and Turkish year. 


~*r^- 


s-*r*r*r$ 

Days'5; 


s 






c 


\ 1 


Muharram July 


16 


30 S 


2 


Saphar August 


15 


29 s 


3 


Rabia I. September 


13 


30 ^ 


S 4 


Rabia II. October 


13 


29 ^ 


S 5 


Jornada I. November 


11 


30 \ 


s 6 


Jornada II. December 


11 


29 S 


s 7 


Rajab January 


9 


30 S 


S 8 


Shasban February 


8 


29 s 


s 9 


Ramadam March 


9 


30 \ 




Shawal April 


8 


29 


s n 


Dulhaadah May 


7 


30 \ 


\ 12 


Dulheggia June 


5 


29 ^ 


S Days in the year 


354 ^ 



S The Arabians add 1 1 days at the end of every s 
s year, which keep the same months to the same s 
\ seasons. > 



Of the Division of Time. 



s 


The ancient 


Grecian year. 


Day 3*1 


S 1 


Hecatombaeon 


June July 


30 S 


s 2 


Metagitnion 


July Aug. 


29 S 


S 3 


Boedromion 


Aug. Sept. 


30 s 


I 4 


Pyanepsion 


_ Sept. Oct. 


29 \ 


S S 5 


Maimacterion 


Oct. Nov. 


30 > 


5 6 


Posideon 


Nov. Dec. 


29 


S 7 


Gamelion 


Dec. Jan. 


30 


S 8 


Anthesterion 


Jan. Feb. 


29 s 


S S 9 


Elaphebolion 


Feb. Mar. 


30 5 


s 10 


Municheon 


Mar. Apr. 


29 !; 


^ 


Thargelion 
Schirrophorion 


- Apr. May 
May June 


30 
29 S 


Ij Days in the year 





354 



Days. 380. A day is either natural or artificial. The 

natural day contains 24 hours; the artificial, the 
time from Sun-rise to Sun-set. The natural day is 
either astronomical or civil. The astronomical day 
begins at noon, because the increase and decrease 
of days terminated by the horizon are very unequal 
among themselves; which inequality is likewise 
augmented by the inconstancy of the horizontal re- 
fractions, ^ 183; and therefore the astronomer takes 
the meridian for the limit of diurnal revolutions ; 
reckoning noon, that is, the instant when the Sun's 
centre is on the meridian, for the beginning of the 
day. The Uritish, French, Dutch, Germans, Span- 
iards, Portuguese, and Egyptians, begin the civil 
day at midnight : the ancient Greeks, Jews, Bohe- 
mians, Silesians, with the modern Italians and Chi- 
nese, begin it at Sun- setting : and the ancient Baby- 
lonians, Persians, Syrians, with the modern Greeks, 
at Sun-rising. 

Hour. 381. An hour is a certain determinate part of the 
day, and is either equal or unequal. An equal hour 
is the 24th part of a mean natural day, as shewn by 






Of the Division of Time. 395 

well-regulated clocks or watches ; but these hours 
are not quite equal as measured by the returns of 
the Sun to the meridian, because of the obliquity of 
the ecliptic, and Sun's unequal motion in it, \ 224 
245. Unequal hours are those by which the arti- 
ficial day is divided into twelve parts, and the night 
into as many. 

382. An hour is divided into 60 equal parts called Minutes, 
mnutes, a minute into 60 equal parts called seconds, sc p onds > 

. / T thirds, and 

and these again into 60 equal parts called thirds. SC rupies. 
The Jews, Chaldeans, and Arabians, divide the hour 
into 1080 equal parts called scruples; which num- 
ber contains 18 times 60, so that one minute con- 
tains 18 scruples. 

383. A cycle is a perpetual round, or circulation cycles of 
of the same parts of time of any sort. The cycle qf^ G Sun 
the Sun is a revolution of 28 years, in which time iS" t *ion. 
the days of the month return again to the same days 

of the week ; the Sun's place to the same signs and 
degrees of the ecliptic on the same months and days, 
so as not to differ one degree in 100 years ; and the . 
leap-years begin the same course over again with 
respect to the days of the week on which the days 
of the months fall. The cycle of the Moon, com- 
monly called the golden number, is a revolution of 
19 years; in which time, the conjunctions, oppo- 
sitions, and other aspects of the Moon, are within 
an hour and half of being the same as they were on 
the same days of the months 19 years before. The 
Indiction is a revolution of 15 years, used only by 
the Romans for indicating the times of certain pay- 
ments made by the subjects to the republic : it was 
established by Constantine, A. D. 312. 

384. The year of our SAVIOUR'S birth, according TO find 
to the vulgar sera, was the 9th year of the solar cycle ; the y ears 
the first year of the lunar cycle ; and the 312th year 

after his birth was the first year of the Roman indic- 
tion. Therefore to find the year of the solar cycle, 
add 9 to any given year of CHRIST, and divide the 
sum by 28, the quotient is the number of cycles 



.396 Of the Division of Time. 

elapsed since his birth, and the remainder is the cycle 
for the given year: if nothing remain, the cycle is 28. 
To find the lunar cycle, add I to the given year of 
CHRIST, and divide the sum by 19 ; the quotient is 
the number of cycles elapsed in the interval, and the 
remainder is the cycle for the given year : if nothing- 
remain, the cycle is 19. Lastly, subtract 312 from 
the given year of CHRIST, and divide the remainder 
by 15 ; and what remains after this division is the 
indictlon for the given year: if nothing remain, the 
indiction is 15. 

Thedefi- 385. Although the above deficiency in the lunar 
th^iunar c j c ^ e f an ^ our anc ^ half every 19 years be but 
cycle, and smallj yet in time it becomes so sensible as to make 
a w ^ e " atura l day m 3K) years. So that, although 
this cycle be of use, when the golden numbers are 
rightly placed against the days of the months in the 
calendar, as in our Common Prayer Books, for find- 
ing the days of the mean conjunctions or oppositions 
of the Sun and Moon, and consequently the time of 
Raster ; it will only serve for 310 years, old style. 
For as the new and full Moons anticipate a day in 
that time, the golden numbers ought to be placed 
one day earlier in the calendar for the next 310 
years to come. These numbers were rightly placed 
against the days of new Moon in the calendar, 
by the council of Nice, A. D. 325 ; but the antici- 
pation, which has been neglected ever since, is now 
grown almost into 5 days; and therefore all the golden 
numbers ought now to be placed 5 days higher in 
the calendar for the old style than they were at the 
time of the said council ; or six days lower for the 
new style ^ because at present it differs 1 1 days from 
the old. 

to 386. In the annexed table, the golden numbers 
*|nd the unc jer the months stand I'.irainst the days of new 

day of the .. r * i r i i ^ r > / 

new Moon Moon in tlie left-hand column, lor the new style ; 

by the adapted chiefly to the second year after leap-year, as 

number, being the nearest mean for all the four ; and will serve 

till the year 1900. Therefore, to find the day of new 



Of the Division of Time. 



S Q 


^ 


Ev 3 


Sj 


X 


;S ^ 


sT 


<>k 


? 


? 


^ 


b ^ 


S v^ 


a 


?** 


ft 


>j 


^ 


^ 


c> 




% 


J-V 


^ 


B s 


S co 






r* 


^ 











* 







s 


























s 




























s , 


9 




9 


17 


17 


6 








11 




19 s 


s 2 




17 






6 


14 


14 


3 


11 




19 


s 


* 


17 


6 


17 


6 






3 


11 




19 


8 


8 ^ 


\* 


6 




6 


14 


14 


3 






19 


8 




1GS 






14 






3 


11 


11 


19 


8 




16 


s 


s 
s 6 


14 


3 


14 


3 






19 






16 


5 


A 


s 7 


o 




3 


11 


11 


19 




8 


16 






13 s S 


S 8 




11 






19 


8 


8 


16 


5 


5 


13 


J 


j 


11 


19 


11 


19 












13 












19 


8 


8 


16 


16 


5 


13 




2 


10 S 


S 
























s 


s 






















s 


s n 


19 


8 










5 


13 


2 


2 


10 


s 


S 12 


8 


10 


8 


16 


16 


5 








10 




18 S 


S 13 










5 


13 


13 


2 


10 




18 


7s 


S S14 


16 


5 


16 


5 






2 


10 


18 


18 


'7 






5 




5 


13 


13 


2 








7 




15 S S 



























s 


S 
























s 






13 






2 


10 


10 


18 


7 




15 


s 


% *7 


13 


2 


13 


2 






18 


7 




15 


4 


4 Jj 


S 18 


2 




2 


10 


10 


18 






15 






12 ^ 


!j 19 




10 






18 


7 


7 


15 


4 


4 


12 


S 


s 


10 


18 


10 


18 






15 






12 


1 


1 s 


s 
























L 


511 


18 




18 


7 


7 


15 




4 


12 






9* 


S22 




7 




15 


15 


4 


4 


12 


1 


1 


9 


S 


S 23 


7 


i VJ 


7 








12 






9 


17 


17 S 


S24 






15 


4 


4 


12 




1 


9 






6 S 


^25 
S 


15 


4 






12 




1 


9 


17 


17 


6 


s 


S 
























S26 


4 


4 


12 




1 








6 




14s 


^27 


|12 




1 


1 


9 


9 


17 


6 




14 


S 


J>28 


12 


1 


12 




9 




17 


-6 


14 


14 


3 


3s 


S29 


1 




1 


9 




17 








3 




11 


S30 


u* 

9 


1 


c 





17 


6 


6 
14 


1 4 

1__ 

3 


4- 

In 


11 


s 
S 

s 

S 



398 Of the Division of Time. 

Moon in any month of a given year till that time, 
look for the golden number of that year under the 
desired month, and against it, you have the clay of 
new Moon, in the left-hand column. Thus, suppose 
it were required to find the day of new Moon in 
September 1757; the golden number for that year 
is 10, which I look for under September, and right 
against it in the left-hand column I find 13, which 
is the day of new Moon in that month. A". B. If 
all the golden numbers, except 17 and 6, were set 
one day lower in the table, it would serve from the 
beginning of the year 1900 till the end of the year 
2199. The first table after this chapter shews the 
golden number for 4000 years after the birth of 
CHRIST ; by looking for the even hundreds of any 
given year at the left hand, and for the rest to make 
up that year at the head of the table ; and where the 
columns meet, you have the golden number (which 
is the same both in old and new style} for the given 
year. Thus, suppose the golden number was want- 
ed for the year 1757; I look for 1700 at the left 
hand of the table, and for 57 at the top of it; then 
guiding my eye downward from 57 to over against 
1700, I find 10, which is the golden number for 
that year. 

A perpe- 387. But because the lunar cycle of 19 years some- 
of a the ble ti mes includes five leap-years, and at other times only 
time of four, this table will sometimes vary a day from the 
to the* trut ^ * n l ea p-y ears after February. And it is impos- 
nearest sible to have one more correct, unless we extend it 
hour for to four times 19 or 76 years ; in which there are 19 
leap-years without a remainder. But even then to 
have it of perpetual use, it must be adapted to the 
old style ; because in every centurial year not divi- 
sible by 4, the regular course of leap-years is inter- 
rupted in the new ; as will be the case in the year 
1800. Therefore, upon the regular old style plan, I 
have computed the following table of the mean times 
of all the new Moons to the nearest hour for 76 years; 




Of the Division of Time. 399 

beginning with the year of CHRIST 1724, and end- 
ing with the year 1800. 

This table may be made perpetual, by deducting 
6 hours from the time of new Moon in any given 
year and month from 1724 to 1800, in order to have 
the mean time of new Moon in any year and month 
76 years afterward; or deducting 12 hours for 152 
years, 18 hours for 228 years, and 24 hours for 
304 years : because in that time the changes of the 
Moon anticipate almost a complete natural day. And 
if the like number of hours be added for so many 
years past, we shall have the mean time of any new 
Moon already elapsed. Suppose, for example, the 
mean time of change was required for January, 
1802; deduct 76 years, and there remains 1726, 
against which, in the following table, under January, 
I find the time of new Moon was on the 21st day, 
at 1 1 in the evening ; from which take 6 hours, and 
there remains the 21st day, at 5 in the evening, for 
the mean time of change in January 1802. Or, if 
the time be required for May, A. D. 1701, add 76 
years, and it makes 1777, which I look for in the 
table, and against it, under May, I find the new 
Moon in that year falls on the 25th day, at 9 in the 
evening ; to which add 6 hours, and it gives the 26th 
day, at 3 in the morning, for the time of new Moon 
in May, A. D, 1701. By this addition for time 
past, or subtraction for time to come, the table will 
not vary 24 hours from the truth in less than 14592 
years. * And if, instead of 6 hours for every 76 
years, we add or subtract only 5 hours 52 minutes, 
it will not vary a day in 10 millions of years. 

Although this table is calculated for 76 years only, 
and according to the old style, yet by means of two 
easy equations it may be made to answer as exactly 
to the new style, for any time to come. Thus, be- 
cause the year 1724 in this table is the first year of 
the cycle for which it is made ; if from any year of 

3E 



400 Of the Division of Time. 

CHRIST after 1800 you subtract 1723, and divide 
the overplus by 76, the quotient will shew how 
* many entire cycles of 76 years are elapsed since the 
beginning of the cycles here provided for ; and the 
remainder will shew the year of the current cycle 
answering to the given year of CHRIST. Hence, if 
the remainder be 0, you must instead thereof put 
76, and lessen the quotient by unity. 

Then, look in the left-hand column of the table 
for the number in your remainder, ^nd against it 
you will find the times of all the mean new Moons in 
that year of the present cycle. And whereas in 76 
Julian years the Moon anticipates 5 hours 52 mi- 
nutes, if therefore these 5 hours 52 minutes be 
multiplied by the above-found quotient, that is, by 
the number of entire cycles past ; the product sub- 
tracted from the times in the table will leave the cor- 
rected times of the new Moons to the old style ; 
\vhich may be reduced to the new style thus : 

Divide the number of entire hundreds in the given 
year of CHRIST by 4, multiply this quotient by 3, 
to the product add the remainder, and from their 
sum subtract 2 : this last remainder denotes the 
number of days to be added to the times above cor- 
rected, in order to reduce them to the new style. 
The reason of this is, that every 400 years of the 
new style gains 3 days upon the old style : one of 
which it gains in each of the centurial years succeed- 
ing that which is exactly divisible by 4 without a re- 
mainder ; but then, whon you have found the days 
so gained, 2 must be subtracted from their number 
on account of the rectifications made in the calen- 
dar by the council of Nice, and since by pope Gre* 
gory. It must also be observed, that the additional 
days found as above- directed * do not take place in 
the centurial years which are not multiples of 4 till 
February 29th old style, for on that day begins the 
difference between the styles; till which day, there- 



Of the Division of Time* 401 

fore, those that were added in the preceding years 
must be used. The following example will make 
this accommodation plain* 

Required the mean time of new Moon in June, A, D 
1909 A*. S. 

From 1909 take 1723 

yearsj and there re- 
mains . . . . * 186 

Which divided by 76, 

gives the quotient 2 

and the remainder . . 34 
Then against 34 in the 

table is June 5 d 8 h O m afternoon* 

And 5 h 52 m multiplied by 

2 make to be subtn * 11 44 
Remains the mean time 

according to the old 

style, June * 5 d 8 k 16* 

Entire hundreds in 1909 

are 19, which divide 

by 4, quotes ....*. 4 
And leaves a remainder of 3 
Which quotient multipli- 
ed by 3 makes 12, and 

the remainder added 

makes 15 

From which subtract 2, 

and there remains ... 13 
Which number of days 

added to the above time, 

old style, gives June. . 18 d 8* 16 m morn. M S. 

So the mean time of new Moon in June 1909, 
nev> style, is the 18th day, at 16 minutes past 8 in 
the morning. 



402 Of the Division of Time. 

If 11 days be added to the time of any new 
Moon in this table, it will give the time of that new 
Moon according to the new style till the year 1800. 
And if 14 days 18 hours 22 minutes be added to 
the mean time of new Moon in either style, it will 
give the mean time of the next full Moon according 
to that style. 



Of the Division of Time. 



403 



s' 


/TABLE shewing the Times of all the mean Changes S 


s $ 


of the Moon, to the nearest Hour, through four ^ 


S 3 


Lunar Periods-) or 76 Years. IVJ Signifies Morn- ^ 


S o 


ing ; A Afternoon. Jj 


*5 










s s 


S rt 




January 


Februai^y 


March 


4/iril S 


S 


A.D. 








S 


s r 


















C 






D. H. 


D. H. 


D. H. 


D. H. s 


; 


1724 


14 5A 


13 5M 


13 6A 


12 7M J; 


s 










j 


2 


1725 


3 2M 


1 2A 


3 3M 


V, 


s s 3 


1726 


21 11 A 


20 11M 


21 12A 


20 1A^ 


S 4 


1727 


11 8M 


9 9A 


11 9M 


9 10 AS 


s 










s 


S 5 


1728 


30 6M 


28 7 A 


29 7M 


27 8A S 


* 6 


1729 


18 2A 


17 3M 


18 4A 


17 4M s 


^ 7 


1730 


7 11 A 


6 OA 


8 1M 


6 1 A jj 


<! 8 


1731 


26 9A 


25 10M 


26 10A 


15 llMs 


s 9 


1732 


16 5M 


14 6A 


15 7M 


23 sA jj 


S 10 


1733 


4 2A 


3 3M 


4 4A 


3 4Ms 


S 










s 


s ** 


1734 


23 OA 


22 1M 


23 1A 


22 2M 5; 


S 12 


1735 


12 9A 


11 9M 


12 10A 


11 11M s 


s 13 


1736 


2 5M 
31 6A 





1 7M 

30 8 A 


S 
29 9M Jj 


S14 


1737 


20 3M 


18 4A 


20 4M 


18 5A s 


S 










S 


S 15 


1738 


9 11M 


7 12A 


9 1 A 


8 1M S 


U 


1739 


28 9M 


26 10A 


28 1M 


S 
26 12 A 


s 17 


1740 


17 6A 


16 7M 


16 8A 


IS 9MS 


s 










S 


J18 


1741 


6 3M 


4 4A 


6 4M 


4 5A ^ 


\ 


1742 


24 12 A 


23 1A 


25 2M 


23 3A S 


S2O 


1743 


14 9M 


12 10A 


14 11M 


12 12 As 


S21 


1744 


3 6 A 


2 7M 


2 8A 


30 9A S 


S 22 


1745 


21 4A 


20 5M 


21 5A 


20 6M < 
X 


^23 


1746 


10 12A 


9 1A 


11 2M 


9 3A S 


S24 


1747 


29 10 A 


28 11M 


29 11A 


28 OA ^ 


Jj 25 


1748 


19 6M 


17 7A 


18 8M 


16 9AS 


? 










S 


S26 


1749 


7 3A 


6 4M 


7 5A 


6 6M 



404 



Of the Division of Time. 



s -^ 


><4 TABLE of the mean New Moon.?, Sec. 


s 












v "^ 




May 


June 


July 


August 


S & 


A. D. 










S 1 












S ^s 
















D. H 


D. H 


D. H 


D. H. 


\L 












\ i 


1724 


11 8A 


10 8M 


9 9A 


8 10M ^ 


* 2 


1725 


1 4M 


29 6M 


28 7 A 


27 8MS 


s 




30 5 A 








*! 


1726 


20 1M 


18 2A 


18 3M 


16 4A \ 

t 




1727 


9 11M 


7 12A 


7 OA 


6 IMS 


? 










S 


S 5 


1728 


27 8M 


25 9A 


25 10M 


23 HA!; 


S 


1729 


16 5A 


15 6M 


14 7A 


12 7M S 


S 7 


1730 


6 2M 


4 3A 


4 3M 


2 4A ![ 


Ja 


1731 


24 11 A 


23 OA 


23 1M 


21 2A S 


i 9 


1732 


13 8M 


11 9A 


11 10M 


91 1 A ^ 
1 1 Xl C 


,0 


1733 


2 5A 


1 6M 

so rA 


30 8M 


28 8 A S 


i* 


1734 


21 2A 


20 3M 


19 4A 


. 8 5 JV1 t 


^12 


1735 


10 11 A 


9 OA 


9 1M 


7 2AS 


J>13 


1736 


28 9A 


27 10M 


26 11 A 


25 OA ; 


5 14 


1/37 


18 5M 


16 6A 


16 7M 


14 8A ( 


* 


1738 


7 2A 


6 3A 


5 4A 


4 5MJ; 


16 


1739 


26 OA 


25 1M 


24 2A 


23 3M S 


sir 


1740 


14 9A 


13 10M 


12 11A 


1 OA 


7 


1741 


4 5M 


2 6A 


2 7M 

31 7A 


3O 8M S 


s 19 


1742 


23 3M 


21 4A 


21 5M 


19 6A > 


S 20 


1743 


12 OA 


11 1M 


10 2A 


9 3MS 


S 2l 


1744 


30 10M 


28 11 A 


28 OA 


26 12 A 


S 22 


1745 


19 6A 


8 7M 


17 8A 


16 8M S 


S 
S 23 


1746 


9 3M 


7 4A 


7 5M 


5 6AJ; 


S 24 


1747 


27 12A 


26 1 A 


26 2M 


24 3A s 


^ 25 


1748 


16 9M 


4 10A 


14 11M 


12 12A 


4 










2 9M S 


U 


1749 


5 6A 


4 7M 


3 8A 


SI 9A ^ 

.'V!! 



Of the Division of Time. 



405 



v 

\t 


A TABLE o/"Me mom New Moons, &c. S 


S ^ 




Sept. 


October 


Nov. 


Dec. 1 


S ^ 


A.D. 








S 


f 




D. H. 


D. H. 


D. H. 


D. H. S 


i 










^ 


724 


6 10 A 


6 11 M 


4 12 A 


4 1 AS 


s 










S 




725 


25 8 A 


25 9M 


23 10 A 


23 11MS 


s 










S 


i 3 


726 


15 5M 


14 5 A 


13 6M 


12 7 A 


^ 










9 4.M C 


S 4 


1727 


4 1 A 


4 2M 


2 3 A 


*J TT IVA ^ 


* 










31 5 A S 


S 5 


1728 


22 11M 


21 12 A 


20 1 A 


20 2M Ij 


c o 


1729 


11 8 A 


11 9M 


9 10 A 


9 1 1 M S 


\r 


1730 


2 5M 


30 7M 


28 8 A 


S 
28 9M > 






30 6 A 






^ 


S 8 


1731 


20 2M 


19 3 A 


18 4M 


17 5 A ^ 


S g 


1732 


8 11M 


7 12 A 


6 1 A 


6 2MS 


U 


1733 


27 9M 


26 10 A 


25 11M 


S 

24 11 A J 


S 


1734 


16 5 A 


16 6M 


14 7 A 


14 8M ^ 


S 12 


1735 


6 2M 


5 3A 


4 4M 


3 5 AS 


<! 13 


1736 


23 12 A 


23 1 A 


22 2M 


21 3 A Jj 


S 14 


1737 


13 8M 


12 9 A 


11 10M 


10 11A<J 


I 15 


1738 


2 5 A 


2 6M 

31 7A 


30 8M 


29 8 As 

s 


S 16 


1739 


21 3 A 


21 4M 


19 5 A 


19 6M S 


\\l 


1740 


9 12 A 


9 1 A 


8 2M 


7 3 A^ 




1741 


28 9 A 


28 10M 


26 11 A 


26 HMs 


I 19 


1742 


18 6M 


17 7 A 


16 8M 


15 9 A S 


S 20 


1743 


7 3 A 


7 4M 


5 5 A 


5 6M> 


c 










S 


S 21 


1744 


25 1 A 


25 2M 


23 3 A 


23 3M S 


;. 


1745 


14 9 A 


14 10M 


12 11 A 


12 OAJj 


I; 23 


1746 


4 6M 


3 7 A 


2 8M 


31 10MS 


S 24 


1747 


33 3M 


22 4 A 


21 5M 


20 6 A s 


S 25 


1748 


11 A 


11 1M 


9 2 A 


9 3M S 


^26 


1749 


30 10M 


29 11 A 


28 A 


27 12 A J; 



** 



406 



Of the Division of Time. 



S 


A TABLE of the mean New Moons continued. S 


* 

S f* 




January 


Feb. 


March 


Afir'd s 


S ^ 


A-D 










H 




D. H. 


D. H. 


D. H 


D K l 


S 27 


1 750 


26 1 A|25 2M 


26 3 A 


25 4M S 


^ 28 


1751 


15 10A 


14 11M 


15 11 A 


14 A Ij 


S 29 


1752 


5 6M 


3 7 A 


4 8M 


2 9 A Ij 


S30 


1753 


23 4M 


21 5 A 


23 6M 


21 7As 


S 31 


1754 


12 1 A 


11 2M 


12 3 A 


1 1 4M I* 


S 32 
V . 


1755 


1 10 A 
31 11M 




1 11 A 
31 OA 


29 12 A i 

s 




J.33 


175C- 


20 7 A 


19 8M 


19 9 A 


18 9MS 


^34 


1757 


9 4M 


7 5 A 


9 6M 


7 7AS 


^ 35 


1758 


28 2M 


26 3 A 


28 3M 


26 4A 


S 36 


1759 


17 10M 


15 11 A 


17 OA 


16 IMS 


j37 


1760 


6 7 A 


5 8M 


5 9 A 


4 10M S 


S 










s 


? 38 


1761 


24 5 A 


23 6M 


24 7 A 


23 8M ^ 


S 39 


1762 


14 2M 


12 3 A 


14 3M 


12 4 AS 


u 


1763 


3 11M 


1 12 A 


3 A 


2 1M S 


S41 


1764 


22 8M 


20 9 A 


21 10M 


19 11A^ 


^ 42 
t 


1765 


10 5 A 


9 6M 


10 6 A 


9 7M Jj 


S43 


1766 


29 2 A 


28 3 A 


29 4 A 


28 5M S 


S 44 


1767 


18 11 A 


17 12 A 


19 1M 


17 2A? 


^ 45 


1768 


8 8M 


6 9 A 


7 10M 


5 11A| 


U 


1769 


26 6M 


24 7 A 


26 7M 


24 8 AS 


S47 


1770 


15 2 A 


14 3M 


15 4A 


14 5M< 


^ 48 


1771 


4 11M 


3 OA 


5 1M 


3 2 AS 












S 


^ 49 


1772 


23 9 A 


22 10M 


22 10 A 


21 11M> 


S 5 C 


1773 


12 5M 


10 6 A 


12 7M 


8 AS 


& 


1774 


1 2 A 
31 3M 




1 4A 
31 5M 


.9 5 A ^ 




S 52 


1775 


20 OA 


19 1M 


20 2 A 


9 3M 


$53 


1776 


9 9 A 


8 10M 


8 10 A 


7 llM^ 



Of the Division of Time. 



407 



s % 


/I TABLE of the A"<?-zy Moons continued. S 


Is 




May 


June 


July 


August v 


s ? 


A.D 








j 


s 




D. H 


D. H 


D. H. 


D. H. S 


S o 










s s 


^ 


1750 


24 4 A 


23 5M 


22 6 A 


21 7MS 


S S 28 


1751 


13 12 A 


12 l A 


12 2M 


10 3 A^ 






o givi 






^ 


J 


1752 


^ *7 1>J 

31 10 A 


30 HM 


29 12 A 


28 A s 

s 


S30 


1753 


2 1 7M 


19 8M 


19 9M 


17 10AS 


?31 


1754 


10 4A 


9 5M 


8 6A 


7 7M !j 


I; 32 


1755 


29 1 A 


28 2M 


27 3 A 


25 3M% 


S 33 


1756 


17 10 A 


16 11M 


15 12 A 


14 1 A S 


S 










S 


$34 


1757 


7 7M 


5 8 A 


5 9M 


3 10 A ^ 


t 35 


1758 


26 4M 


24 5 A 


24 6M 


22 7 A<j 


S 36 


1759 


15 I A 


14 2M 


13 3 A 


12 2M S 


S 








1 12 A 


t 


S 37 


1760 


3 10 A 


2 11M 


1 ** \. 


30 1M 


S 








31 1 A 




^ 38 


1761 


22 9 A 


21 10M 


20 10 A 


19 HMjj 


S 39 


1762 


12 4M 


10 5 A 


10 6M 


8 7 AS 


S 40 


1763 


1 1 A 

31 2M 


29 3 A 


29 4M 


27 4 A J> 


\ 4} 


1764 


19 11M 


17 12 A 


17 1 A 


16 2M !; 




1765 


8 7A 


7 8M 


6 9A 


5 10M<! 


* 










s 


S 43 


1766 


27 5 A 


26 6M 


25 7 A 


24 8M S 


$44 


1767 


17 2M 


15 3 A 


15 4M 


13 5 A\ 


45 


1768 


5 11M 


3 12A 


3 1 A 


2 2M S 


c 










31 2 A ^ 


S 46 


1769 


24 8M 


22 9 A 


22 10M 


20 HAS 


s 47 


1770 


13 5 A 


12 4M 


11 7A 


10 SM 


^ 48 


1771 


3 2M 


1 3A 


1 4M 
30 5 A 


29 5M S 


S 49 


1772 


20 11 A 


19 A 


19 1M 


17 2 AS 


S50 


1773 


10 8M 


8 9 A 


8 9M 


6 10 A 5 


55. 


1774 


29 6M 


27 7 A 


27 8M 


25 8 AS 


S52 


1775 


18 3 A 


17 4M 


16 5 A 


15 6M ^ 


^53 


1776 


6 12A 


5 A 


5 1M 


3 2 A J; 



3F 



408 



Of the JDwision of Time. 



s * 
ss 

51 

S *p 


A TABLE of the mean New Moons continued. S 


A.D. 


Sefit. 


October 


Nov. 


Dec. S; 


D. H. 


D. H. 


D. H, 


D. H. S 

^ 










c 


S 27 


1750 


19 7 A 


19 8M 


17 9 A 


17 10M S 


<j 28 


1751 


9- 3M 


8 4 A 


7 5M 


6 6 A^ 


S 29 


1752 


27 1M 


26 2 A 


25 3M 


24 3 A ^ 


S 30 


1753 


16 10M 


15 11 A 


14 A 


14 1M S 


1 


1754 


5 7A 


5 8M 


3 9 A 


5 10M Jj 


S 32 


1755 


24 4 A 


24 5M 


22 6 A 


22 6M J[ 


S 33 


1756 


13 1M 


12 2 A 


11 3M 


10 4 A s 


*34 


1757 


2 10M 


1 11 A 
31 A 


30 1M 


29 1 A J! 


^35 


1758 


21 7M 


20 8 A 


19 9M 


18 10AS 


S36 


1759 


10 4 A 


10 5M 


8 6 A 


8 7M J; 


S 37 


1760 


28 2 A 


2a 3M 


26 4 A 


26 4MS 












S 


> 38 


1761 


17 11 A 


17 A 


16 1M 


15 2 A S 


S 39 


1762 


6 7M 


6 8 A 


5 9JM 


4 10 A 5 


40 


1763 


26 5M 


25 6 A 


24 7M 


23 7AS 


541 


1764 


14 '2 A 


14 3M 


12 4A 


12 5M > 


< 










1 1 AS 


S42 


1765 


3 10 A 


3 11M 


1 12 A 


1 z /&. ^ 

31 1M Ij 


S 43 


1766 


22 8 A 


22 9M 


20 10 A 


20 11MS 


!* 44 


1767 


12 6IM 


11 6 A 


10 7M 


9 8M S 


S 45 


1768 


30 3M 


29 4 A 


28 5M 


27 5 AS 


J>46 


1769 


19 1M 


18 12 A 


17 1 A 


17 2M S 


$47 


1770 


8 8A 


8 9M 


6 10 A 


6 11M ^ 


<U8 


1771 


27 6 A 


27 7M 


25 8 A 


25 9M Jj 


^ 49 


1772 


16 2M 


15 3 A 


14 4M 


13 5 AS 


S 50 


1773 


5 11M 


4 12 A 


3 1 A 


3 2M t 


$51 


1774 


24 9M 


23 10 A 


22 11M 


21 HAS 


* 


1775 


13 6A 


13 7M 


11 8 A 


11 9M s 


\ a 


1776 


32 2M 


1 3 A 

1 4M 


29 5 A 


29 5M ^ 






Of the Division of Time. 



409 



is 

58, 

ll 


^ TABLE 0/"fAe mean JVew Moons concluded. S 


A.D. 


January 


February 


March 


April <| 


D. H. 


D. H. 


D. H 


D. H. !j 


S 54 


1777 


27 6 A 


26 7M 


27 8 A 


26 9M S 


J 55 


1778 


17 3M 


15 4A 


17 5M 


15 6 A ^ 


S56 


1779 


6 OA 


5 1M 


6 2 A 


5 3M t 


J57 


1780 


25 10M 


23 11 A 


24 11M 


22 12 AS 


$58 


1781 


13 6A 


12 7M 


13 8 A 


12 9M > 


$ 

^ 


1782 


3 3M 


1 4A 


3 5M 


1 6 A? 


S60 


1783 


22 1M 


20 2 A 


22 2M 


20 3 A S 


s 












$61 


1784 


11 9M 


9 10 A 


10 11M 


8 12 AS 


$62 


1785 


29 7M 


27 8 A 


29 9M 


27 10 AS 


S 63 


1786 


18 4A 


17 5M 


18 5 A 


17 6M 


64 


1787 


7 12 A 


6 1 A 


8 2M 


6 3 A s 


5 65 


1788 


26 10 A 


25 11M 


25 12 A 


24 1 A 5 


S 66 


1789 


15 7M 


13 8A 


15 9M 


13 10 A ^ 


S67 


1790 


4 4 A 


3 5JV1 


4 5 A 


3 6M S 


S 68 


1791 


23 1 A 


22 2M 


23 3 A 


22 4M S 


5j 69 


1792 


12 10 A 


11 11M 


11 12 A 


10 1 A$ 


$70 


1793 


1 7M 

30 8 A 




1 9M 
30 10 A 


29 10M S 




j*l 


; ;794 


20 5M 


18 6A 


20 6M 


18 7A jj 


$ 72 


1795 


9 1 A 


8 2M 


9 3 A 


8 4M ^ 


S 73 


1796 


28 HM 


26 12 A 


27 A 


26 1M |j 


S74 


1797 


16 7 A 


15 8M 


16 9 A 


15 10M S 












S 


|75 


1798 


6 4M 


4 5 A 


6 6M 


4 7AS 


^76 


1799 


25 2M 


23 3 A 


25 4M 


23 5 AS 


s *j 


1800 


14 11M 


12 12 A 


13 A 


12 1M \ 



The year 1 800 begins a new cycle, 



410 



Of the Division of Tune, 



if 

S ^ 

S 54 


A TABLE of the mean New Moons concluded. S 


A.D 


May 


June 


July 


S 

August 


D. H. 


D. H 


D. H. 


D. H. S 


1777 


25 9 A 


24 10M 


23 1 1 A 


22 " A S 


S 55 


1778 


15 6M 


13 7A 


13 8M 


11 9 A^ 


S 56 


1779 


4 3 A 


3 4M 


2 5 A 


1 6MS 












30 6 A !j 


S 57 


1780 


22 A 


21 1M 


20 2 A 


19 3 A S 


i 58 


1781 


11 9 A 


10 10M 


9 11 A 


8 OM J[ 


S 59 


1782 


1 6M 

30 7 A 


29 8M 


28 9 A 


27 9M S 


i" 


1783 


20 3M 


18 4 A 


18 5M 


16 6 A S 




1784 


8 A 


7 1M 


6 2 A 


5 SMJ; 


62 


1785 


27 10M 


25 11 A 


25 A 


24 1M 


63 


1786 


16 6 A 


15 7M 


14 8 A 


13 9MS 


64 


1787 


6 3M 


4 4 A 


4 5M 


2 6 A!; 


65 


1788 


24 1M 


22 2 A 


22 3M 


20 4 AS 


66 


1789 


13 10M 


11 11 A 


11 OA 


10 IMS 


67 


1790 


2 6 A 


1 7M 
30 8 A 


30 9M 


S 

28 9 A jj 


^ 68 


1791 


21 4 A 


20 5M 


19 6 A 


18 7M5 


]> 69 


1792 


10 1M 


8 2 A 


8 3M 


6 4AS 


i> 70 


1793 


28 11 A 


27 A 


27 1M 


25 1 A Jj 


<! 71 


1794 


18 7M 


16 8 A 


16 9M 


14 10 A ^ 


^72 


1795 


7 4A 


6 5M 


5 6A 


4 7MS 


S 73 


1796 


25 1 A 


24 2M 


23 3 A 


22 4M 


S74 


1797 


14 10 A 


13 11M 


12 12 A 


11 1 AS 


S 75 


1798 


4 7M 


2 8A 


2 9M 
31 10A 


30 IOM S 


S 76 


1799 


23 5M 


21 6A 


21 6M 


19 8A> 


S 1 


1800 


11 1 A 


10 2M 


9 3 A 


8 4Mt 



Of the Division of Time. 



411 



f 3 


A TABLE of the mean New Moons concluded. S 


S ? 












s > 




Se fit ember 


October 


November 


Dec. $ 


j| 


A.D 








S 


?2 




D. H. 


D. H 


D. H. 


D. H. $ 




1777 


20 12A 


10 1 A 


19 2M 


18 3A S 


55 


1778 


10 9M 


9 10A 


8 11M 


7 12A J; 


s 










^ 


S56 


1779 


29 7M 


28 8 A 


27 9M 


26 9A S 


V 


1780 


17 3A 


17 4M 


15 5A 


S 
15 6M $ 


S 58 


1781 


6 12A 


6 1 A 


5 2M 


4 3A S 


u 


1782 


25 10A 


25 11M 


23 12 A 


S 

23 OA $ 


S60 


1783 


15 6M 


14 7A 


13 8M 


12 9A S 


S 61 

c 


1784 


3 3A 


3 4M 


1 5A 


1 6M $ 

30 6A $ 


?62 


1785 


22 1A 


22 2M 


20 3 A 


20 3M S 


$63 


1786 


11 9A 


11 10M 


9 HA 


9 OA $ 


S 64 


1787 


1 6M 
30 7A 


30 8M 


28 9A 


28 9M S 


$65 


1788 


19 4M 


18 5A 


17 6M 


16 7A$ 


S 66 


1789 


8 1 A 


8 2M 


6 3A 


6 4M S 


S 










S 


$ 67 


1790 


29 10M 


26 11 A 


25 OA 


24 12 A $ 


S68 


1791 


16 7A 


16 8M 


14 9A 


14 10M S 


$ 69 


1792 


5 4A 


4 5A 


3 6M 


2r A S 
'* ^ 


S70 


1793 


24 2M 


23 3 A 


22 4M 


21 4A S 


h- 


1794 


13 10M 


12 11 A 


11 OA 




S 72 


1795 


2 7A 


2 8M 
31 9A 


30 10M 


29 10AS 


$73 


1796 


20 4A 


20 5M 


18 6A 


18 7M > 


S 74 


1797 


1M 


9 2A 


8 3M 


7 4A^ 


S 










S 


$ 75 


1798 


28 11 A 


28 OA 


27 1M 


26 1A $ 


In 


1799 


18 8M 


17 9A 


16 10M 


15 HAS 


< 1|1800| 6 4A 


6 5M 


4 6A 


4 7M ^ 



412 Of the Division of Time. 



388. The cycle of Easter, also called the Dionysian 
'P er *od> is a revolution of 532 years, found by mul- 
tiplying the solar cycle 28 by the lunar cycle 19. If 
the new Moons did not anticipate upon this cycle, 
Easter-day would always be the Sunday next after 
the first full Moon which follows the 21st of March. 
But on account of the above anticipation, 422. 
to which no proper regard was had before the late 
alteration of the style, the ecclesiastic Easter has se- 
veral times been a week different from the true East- 
er within this last century : which inconvenience is 
now remedied by making the table which used to 
find Easter for ever, in the Common Prayer Book, 
of no longer use than the lunar difference from the 
new style will admit of. 

Number 389. The earliest Easter possible is the 22d of 
of direc- March, the latest the 25th of April. Within these 
limits are 35 days, and the number belonging to 
each of them is called the number of direction; be- 
cause thereby the time of Easter is found for any 
given year. To find the number of direction, ac- 
cording to the new style, enter Table V. following 
this chapter, with the complete hundreds of any 
given year at the top, and the years thereof (if any) 
below a hundred at the left hand ; and where the co- 
lumns meet is the Dominical letter for the given 
year. Then enter Table I. with the complete hun- 
dreds of the same year at the left hand, and the 
years below a hundred at the top; and where the 
columns meet is the golden number for the same 
year. Lastly, enter Table II. with the Dominical 
letter at the left hand, and golden number at the top ; 
and where the columns meet is the number of direc- 
tion for that year; which number added to the 21st 
day of March, shews on what day, either of March 
or April, Easter- Sunday falls in that year. Thus 
the Dominical letter new style for the year 1757 is B, 
(Table V.J and the golden number is 10, (Table I.) 
by which in Table II. the number of direction is 



Of the Division of Time. 4 13 

found to be 20; which reckoning from the 21st of TO find 

the trOe 
Easter. 



March, ends on the 10th of April, that is, Easter- tbe trfle 



Sunday, in the year 1757. N. B. There are always 
two Dominical letters to the leap-year, the first of 
which takes place to the 24th of February, the last 
for the following part of the year. 

390. The first seven letters of the alphabet are 
commonly placed in the annual almanacs, to shew 
on what days of the week the days of the months 
fall throughout the year. And because one of those 
seven letters must necessarily stand against Sunday, 
it is printed in a capital form, and called the Domi- Dominical 
nical letter : the other six being inserted in small Ietter * 
characters, to denote the other six days of the week. 
Now, since a common Julian year contains 365 
days, if this number be divided by 7 (the, number 
of days in a week) there will remain one day. If 
there had been no remainder, it is plain the year 
would constantly begin on the same day of the week. 
But since 1 remains, it is as plain that the year must 
begin and end on the same day of the week ; and 
therefore the next year will begin on the day follow- 
ing. Hence, when January begins on Sunday, A 
is the Dominical or Sunday letter for that year : 
then, because the next year begins on Monday, th 
Sunday will fall on the seventh day, to which is an- 
nexed the seventh letter G, which therefore will be 
the Dominical letter for all that year: and as the 
third year will begin on Tuesday, the Sunday wil 
fall on the sixth day ; therefore F will be the Sunday 
letter for that year. Whence it is evident, that the 
Sunday letters will go annually in a retrograde order 
thus, G, F, E, D, C, B, A. And in "the course 
of seven years, if they were all common ones, the 
same days of the week and Dominical letters would 
return to the same days of the months. But because 
there are 366 days in a leap-year, 4f this number be 
divided by 7, there will remain two days over and 
above the 52 weeks of which the year consists. 



41 4 Of the Division of Time. 

And therefore, if the leap-year begins on Sunday, 
it will end on Monday ; and the next year will be- 
gin on Tuesday, the first Sunday whereof must 
fall on the sixth of January, to which is annexed the 
letter F, and not G, as in common years. By 
this means, the leap-year returning every fourth 
year, the order of the Dominical letters is interrupt- 
ed ; and the series cannot return to its first state till 
after four times seven, or 28 years ; and then the 
same days of the months return in order to the same 
days of the week as before. 

To find 391. To find the Dominical letter for any year 
the . . either before or after the Christian (era. In Table 
cal "letter. ^- or IV. ^or o Id style, or V. for new style, look 
for the hundreds of years at the head of the table, 
and for the years below a hundred (to make up the 
given year) at the left hand; and where the columns 
meet, you have the Dominical letter for the year de- 
sired. Thus, suppose the Dominical letter be re- 
quired for the year of CHRIST 1758, new style, I 
look for 1700 at the head of Table V. and for 58 at 
the left hand of the same table ; and in the angle of 
meeting, I find A, nhich is the Dominical letter for 
that year. If it was wanting for the same year old 
style, it would be found by Table IV. to be D. 
But to find the Dominical letter for any given year 
before CHRIST, subtract one from that year, and 
then proceed in all respects as just now taught, to 
find it by Table III. Thus, suppose the Domini- 
cal letter be required fof the 585th year before the 
first year of C H R i s T, look for 500 at the head of Ta- 
ble III. and for 84 at the left hand ; in the meeting 
of these col umns you will find FE, which were the 
Dominical letters for that year, and shew that it was 
a leap-} ear ; because leap-year has always two Do- 
minical letters. 

TO find 392- To find the day of the month answering to 
the day amj day of the week, or the day of the week an- 
severing to any day of the month, for any year past 



Of the Divhwn of Time, 4L5 

jf to come. Having found the Dominical letter for 
the given year, enter Table VI, with the Dominical / 
letter at the head; and under it, all the days in that 
column are Sundays, in the divisions of the months; 
the next column to the right hand are Mondays; the 
next, Tuesdays ; and so on, to the last column un- 
der G; from which go back to the column under A, 
and thence proceed toward the right hand as before. 
Thus, in the year 1757, the Dominical letter new 
style is B, in Table V ; then, in Table VI, all the 
days under B are Sundays in that year, viz. the 2d, 
9th, 16th, 23d, and 3Oth of January and October ; 
the 6th, 13th, 2Oth, and 27th of February, March, 
and November; the 3d, lOth, and 17th of yf/>r/7and 
July, together with the 31st of July ; and so on, to 
the foot of the column. Then, of course, all the 
days under Care Mondays, namely, the 3d, 10th, 
&c. of January and October ; and so of all the rest 
in that column. If the day of the week answering 
to any day of the mon?h be required, it is easily had 
from the same table by the letter that stands at the 
top of the column in which the given day of the 
month is found. Thus, the letter that stands over 
the 28th of May .is A ; and in the year 58.5 before 
CHRIST, the Dominical letters were found to be 
F, E, 391 ; which being a leap-year, and E 
taking place from the 24th of February to the end 
of that year, shews, by the table, that the 25th of 
May was on a Sunday ; and therefore the 28th must 
have been on a Wednesday ; for when E stands for 
Sunday, F must stand for Monday, G for Tues- 
day, &c. Hence, as it is said that the famous eclipse 
of the Sun foretold by THALES, by which a peace 
"tfas brought about between the Medes and Lydians, 
happened on the 28th of May, in the 585th year 
before CHRIST, it fell on a Wednesday. 

393. From the multiplication of the solar cycle j u i ian 
of 28 years, into the lunar cycle of 19 years, and the period. 
Roman indiction of 1 5 years, arises the great Julian 
3G 



416 Of the Times of the Birth and Death of CHRIST, 

period, consisting of 7980 years, which had its be- 
ginning 764 years before Strauchius's supposed year 
uf the creation (for no later could all the three 
cycles begin together), and it is not yet completed : 
and therefore it includes all other cycles, periods, 
and seras. There is but one year in the whole pe- 
riod that has the same numbers for the three cycles 
of which it is made up : and therefore, if historians 
had remarked in their writings the cycles of each 
year, there had been no dispute about the time of 
any action recorded by them. 

TO find the 394. The Dionysian or vulgar sera of CHRIST'S 
period*.^ 15 birth was about the end of the year of the Julian pe- 
riod 4713 ; and consequently the first year of his 
age, according to that account, was the 4714th year 
of the said period* Therefore, if to the current 
year of CHRIST we add 4713, the sum will be the 
year of the Julian period. So the year 1 757 will be 
found to be the 6470th year of that period* Or, to 
find the year of the Julian period answering to any 
given year before the first year of CHRIST, subtract 
the number of that given year from 4714, and the 
remainder will be the Julian period. Thus, the 
year 585 before the first year of CHRIST (which 
was the 584th before his birth) was the 41 29th year 
of the said period. Lastly, to find the cycles of the 
Sun, Moon, and indiction, for any given year of this 
period, divide the given year by 28, 19, and 15; 
And the tne tnree remainders will be the cycles sought, and 
cycles of the quotients the numbers of cycles elapsed since 
that year. t h e beginning of the period. So in the above 47 14th 
year of the Julian period, the cycle of the Sun was 
10, the cycle of the Moon 2, and the cycle of indic- 
tion 4; the solar cycle having run through 168 
courses, the lunar 248, and the indiction 314. 
The true 395. The vulgar sera of CHRIST'S birth was 
CHRIST'S never settled till the year 527, when Dionysius Exi- 
birtb, guus, a Roman abbot, fixed it to the end of the 
4713th year of the Julian period, which was four 



Of the Times of the Birth and Death of CHRIST. 417 

years too late. For our SAVIOUR was born before 
the death of Herod, who sought to kill him as soon 
as he heard of his birth. And according to the tes- 
timony of Josephus (B. xvii. ch. 8.) there was an 
eclipse of the Moon at the time of Herod's last ill- 
ness ; which eclipse appears by our astronomical ta- 
bles to have been in the year of the Julian period 
47 1O, March 13th, at 3 hours past midnight, at Je- 
rusalem. Now as our SAVIOUR must have been 
born some months before Herod's death, since in the 
interval he was carried into Egypt, the latest time in 
which we can fix the true sera of his birth is about 
the end of the 4709th year of the Julian period. 

There is a remarkable prophecy delivered to us 
in the ninth chapter of the book of Daniel, which, 
from a certain epoch, fixes the time of restoring the 
state of the Jews, and of building the walls of Jeru- 
salem, the coming of the MESSIAH, his death, and 
the destruction of Jerusalem. But some parts of 
this prophecy (Ver. 25.) are so injudiciously pointed 
in our English translation of the Bible, that, if they 
be read according to those stops of pointing, they 
are quite unintelligible. But the learned Dr. Pri- 
deaux, by altering these stops, makes the sense very 
plain ; and as he seems to me to have explained the 
whole of it better than any other author I have read 
on the subject, I shall set down the whole of the 
prophecy according as he has pointed it, to shew in 
what manner he has divided it into four different 
parts. 

Ver. 24. Seventy weeks are determined upon thy 
People, and upon thy holy City, to finish the Trans- 
gression, and to make an end of Sins, and to make 
reconciliation for Iniquity, and to bring in everlast- 
ing Righteousness, and to seal up the Vision, and the 
Prophecy, and to anoint the most holy. Ver. 25, 
Know therefore and understand, that from the going 
forth of the Commandment to restore and to build Je- 
rusalem unto the MESSIAH the Prince shall be seven 



418 Of the Times of the Birth and Death of CHRIST. 

weeks and three-score and two weeks, the street shall 
be built again, and the wall even in troublous times. 
Ver. 2f>. And after three-score and two weeks shall 
MESSIAH be cut off, but not for himself, and the peo- 
ple of the Prince that shall come, shall destroy the 
City and Sanctuary, and the end thereof shall be 
with a Flood, and unto the end of the war desola- 
tions are determined. Ver. 27. And he shall con- 
firm the covenant with many for one week, and in 
the midst* of the week he shall cause the sacrifice 
and the oblation to cease, and for the overspreading 
of abominations he shall make it desolate even until 
the Consummation, and that determined shall be pour- 
ed upon the desolate. 

This commandment was given to Ezra by Artax- 
erxes Longimanus, in the seventh year of that king's 
reign (Ezra, ch. vii. ver. i 1 26). Ezra began the 
work, which was afterwards accomplished by Nehe- 
miah : in which they met with great opposition and 
trouble from the Samaritans and others, during the 
first seven weeks, or 49 years. 

From this accomplishment till the time when 
CHRIST'S messenger, John the Baptist, began to 
preach the Kingdom of the MESSIAH, 62 weeks, or 
434 years. 

From thence to the beginning of CHRIST'S pub* 
lie ministry, half a week, or 3y years. 

And from thence to the death of CHRIST, half a 
week, or 3y years; in which half-week he preached, 
and confirmed the covenant of the Gospel with many. 

In all, from the going forth of the commandment 
till the Death of CHRIST, 70 weeks, or 490 years* 

And, lastly, in a very striking manner, the pro- 
phecy foretels what should come to pass after the ex- 
piration of the seventy weeks ; namely, the Destruc- 
tion of the City and Sanctuary by the people of the 
Prince that was to come ; which were the Roman 

* The Doctor says, that this ought to be rendered the 
half part of the week) v&tthe midst. 



Of the Times of the Birth and Death of CHRIST. 41 9 

armies, under the command of Titus their prince, 
who came upon Jerusalem as a torrent, with their 
idolatrous images, which were an abomination to 
the Jews, and under which they marched against 
them, invaded their land, and besieged their holy 
city, and by a calamitous war, brought such utter 
destruction upon both, that the Jews have never 
been able to recover themselves, even to this day. 

Now, both by the undoubted canon of Ptolemy, 
and the famous tera of Nabonassar, the beginning 
of the seventh year of the reign of Artaxerxes Lon- 
gimanus, king of Persia, (who is called Ahasuerus 
in the book of Esther,} is pinned down to the 
4^56th year of the Julian period, in which year he 
gave Ezra the above-mentioned ample commission: 
from which, count 490 years to the death of 
CHRIST, and it will carry the same to the 4746th 
year of the Julian period. 

Our Saturday is the Jewish Sabbath : and it is 
plain from St. Mark, ch. xv. ver. 42, and St. Luke, 
ch. xxiii. ver. 54, that CHRIST was crucified on a 
Friday, seeing the crucifixion was on the day next 
before the Jewish Sabbath. And according to St. 
John, ch. xviii. ver. 28, on the day that the Passover 
was to be eaten, at least by many of the Jews. 

The Jews reckoned their months by the Moon, 
and their years by the apparent revolution of the 
Sun : and they ate the Passover on the 14th day of 
the month of Nisan, which was the first month of 
their year, reckoning from the first appearance of 
the new Moon, which at that time of the year might 
be on the evening of the day next after the change, 
if the sky was clear. So that their 1 4th day of the 
month answers to our fifteenth day of the Moon, 
on which she is full. Consequently, the Passover 
was always kept on the day of full Moon. 

And the full Moon at which it was kept, was that 
one which happened next after the vernal equinox. 
For Josef hus expressly $&y$^Antiq, B. iii. ch. 10.) 



420 Of the Times of the Birth and Death of CHRIST. 

c The Passover was kept on the 14th day of the 
"month of Nisan, according to the Moon, when the 
" Sun was in Aries." And the Sun always enters 
Aries at the instant of the vernal equinox ; which, 
in our Saviour's time, fell on the 22d day of March. 
The dispute among chronologers about the year 
of CHRIST'S death is limited to four or five years at 
most. But, as we have shewn that he was cruci- 
fied on the day of a Pascal full Moon, and on a 
Friday, all that we have to do, in order to ascer- 
tain the year of Kis death, is only to compute in 
which of those years there was a Passover full 
Moon on a Friday. For, the full Moons anticipate 
eleven days every year (12 lunar months being so 
much short of a solar year), and therefore, once 
in every three years at least, the Jews were oblig- 
ed to set their Passover a whole month for- 
warder than it fell by the course of the Moon, on 
the year next before, in order to keep it at the full 
Moon next after the equinox ; therefore there 
could not be two Passovers on the same nominal 
day of the week within the compass of a few 
neighbouring years. And I find by calculation, 
the only Passover full Moon that fell on a Friday, 
for several years before or after the disputed year 
of the crucifixion, was on the 3d day of April, in 
the 4746th year of the Julian period, which was 
the 4POth year after Ezra received the above-men- 
tioned commission from Ariaxerxes Longimanus, 
according to Ptolemy 9 s canon, and the year in which 
the MESSIAH was to be cut off, according to the 
prophecy, reckoning from the going forth of that 
commission or commandment : and this 490th year 
was the 33d year of our SAVIOUR'S age, reckoning 
from the vulgar asra of his birth ; but the 37th, 
reckoning from the true asra thereof. 

And, when we reflect on what the Jews told him, 
some time before his death (John viii. 57.) " thou. 
" art not yet fifty years old," we must confess that 
it should seem much likelier to have been said to a 



Of the Times of the Birth and Death of CHRIST. 42 i 

person near forty than to one but just turned of 
thirty. And we may easily suppose that St. Luke 
expressed himself only in round numbers, when 
he said that Christ was baptized about the SOtbyear 
of his age, when he began his public ministry; as our 
SAVIOUR himself did, when he said he should lie 
three days and three nights In the grave. 

The 4746th year of the Julian period, which we 
have astronomically proved to be the year of the 
crucifixion, was the 4th year of the 202d Olympiad; 
in which year, Phlegon, a heathen writer, tells us, 
there was the most extraordinary eclipse of the Su?t 
that ever was seen. But I find by calculation, that 
there could be no total eclipse of the Sun at Jerusa- 
lem^ in a natural way, in that year. So that what 
Phlegon here calls an eclipse of the Sun seems to 
have been the great darkness for three hours at the 
time of our SAVIOUR'S crucifixion, as mentioned 
by the Evangelists : a darkness altogether superna- 
tural, as the Moon was then in the side of the hea- 
vens opposite to the Sun ; and therefore could not 
possibly darken the Sun to any part of the Earth. 

396. As there are certain fixed points in the hea- 
vens from which astronomers begin their computa- 
tions, so there are certain points of time from which 
historians begin to reckon ; and these points, or 
roots of time, are called aras or epochs. The most 
remarkable aras are, those of the creation, theGra^ 
Olympiads, the building of Rome, the ara of Nabo* 
nassar, the death of Alexander, the birth of CHRIST, 
the Arabian Hegira, and the Persian Tesdegird : all 
which, together with several others of less note, 
have their beginnings in the fqllowing table fixed 
to the years of the Julian period, to the age of the 
world at those times, and to the years before and 
after the year of CHRIST'S birth. 



( 422 ) 



A Table of remarkable Mras and Events. 



1. The Creation of the World 

2. The Deluge, or Noah's Flood 

3. The Assyrian Monarchy founded by Nimrod 

4. The Birth of Abraham .... 

5. The Destruction of Sodo?n and Gomorrah 

6. The Beginning of the Kingdom of Athens by Cecrops 

7. Moses receives the Ten Commandments 

8. The Entrance of the Israelites into Canaan 

9. The Arganautic Expedition 
10. The Destruction of Troy 

\ 1. The Beginning of King David's Reign 

12. The Foundation of Solomon's Temple 

13. Lycurgus forms his excellent Laws 

14. Arbaces, the first King of the Medea 

15. Mandaucus, the second .... 

1 6. Sosarmus, the third ..... 

1 7. The Beginning of the Olympiads 

18. Attica, the fourth King of the Medes . 

19. The Catonian Efiocha of the Building of Rome 

20. The JEra of jYabonassar .... 

21. The Destruction of Samaria by Salmaneser 

22. The first Eclipse of the Moon on Record 

23. Cardicea, the fifth King of the Medes 

24. Phraortes, the sixth .... 

25. Cyaxares, the seventh .... 

26. The first Babylonish Captivity by Nebuchadnezzar 

27. The long War ended between the Medea and Lydiam 

28. The second Babylonish Captivity, and Birth of Cyrus 

29. The Destruction of Solomon's Temple 

30. Nebuchadnezzar struck with Madness 

31. Daniel's Vision of the four Monarchies 

32. Cyrus begins to reign in the Persian Empire 

33. The Battle of Marathon .... 

34. Artaxerxes Longimanus begins to reign 

5. The Beginning of Daniel's seventy Weeks of Years 
The Beginning of the Pelojionnesian War . 
Alexander's Victory at Arbela 

His Death 

The Captivity of 100,000 Jews by King Ptolemy 
. The Colossus of Rhodes thrown down by an Earthquake 
Antiochus defeated by Ptolemy Philofiater 
The famous ARCHIMEDES murdered at Syracuse 
Jason butchers the Inhabitants of Jerusalem 
Corinth plundered and burnt by Consul Mummius 
Julius Caesar invades Britain 
He corrects the Calendar 
Is killed in the Senate-House 



>3 

36 
37 
38 
39 
40 
41, 
42 
43 
44 
45 
46 
47 



Lilian 
Period. 


Y.ofthe 
World. 


Befott. 
Christ 


706 





4007 


2362 


1656 


2351 


2537 


1831 


2176 


2714 


2008 


1999 


2816 


2110 


i897 


3157 


2451 


1556 


3222 


2516 


1491 


3262 


2556 


1451 


3420 


2714 


1293 


3504 


2798 


1209 


3650 


2944 


1063 


3701 


2995 


1012 


3829 


3103 


884 


3838 


3132 


875 


3865 


3159 


848 


3915 


3209 


798 


3938 


3232 


775 


3945 


3239 


768 


3961 


3255 


752 


3967 


3261 


746 


3992 


3286 


721 


3993 


3287 


720 


3996 


3290 


717 


4058 


3352 


655 


4080 


3374 


633 


4107 


3401 


606 


4111 


3405 


602 


4114 


34C8 


599 


4125 


3419 


588 


4144 


3438 


569 


4158 


3452 


555 


4177 


3471 


536 
490 
464 


4223 

4249 


3517 
3543 


4256 


3550 


457 


4282 


3576 


431 


4383J3677 


330 


4390 


3684 


323 


4393 


3687 


320 


449 1 


3875 


222 


4496 


3790 


217 


4506 


3800 


207 


4543 


3837 


170 


4567 


3851 


146 


4659 


3953 


54 


4677 


3961 


46 


4671 


3965 


43 



A Table of remarkable Mr as ana Events. 423 



48. 
49. 
50. 
51. 

52. 

53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 

65. 
66, 



Herod made King of Judea ---<-. 
Anthony defeated at the Battle of Actium - 
Agrifijia builds the Pantheon at Rome 
The true ^.RA of CHRIST'S Birth 
The Death of Herod 



The Dyonisian or vulgar JRA of CHRIST'S Birth 
The true year of his Crucifixion .... 
The Destruction of Jerusalem - - - - - 
Adrian builds the Long Wall in Britain - - 
Constantius defeats the Picts in Britain - - 

The Council of Mice 

The Death of Constantine the Great - - - 
The Saxons invited into Britain . - * 
The Arabian Hegira --..-... 
The Death of Mohammed the pretended Prophet 
The Persian Yesdegird ----.-- 
The Sun, Moon, and all the Planets in Libra, 

Sefit. 14, as seen from the Earth 
The Art of Printing discovered - - - - 
The Reformation begun by Martin Luther - 



Julian 


Y.ofthe 


Before 


Period. 


World. 


Christ. 


4673 


3967 


40 


4683 


3977 


30 


4688 


3982 


25 


4709 


4003 


4 


4710 


4004 


3 






After 






Christ. 


4713 


4007 





4746 


4040 


33 


4783 


4077 


70 


4833 


4127 


120 


5019 


4313 


306 


5038 


4332 


325 


5050 


4344 


337 


5158 


4452 


445 


5335 


4629 


622 


5343 


4637 


630 


5344 


4638 


631 


5899 


5193 


1186 


6153 


5447 


1440 


6230 


5524 


1517 



In fixing the year of the creation to the 706th Age of 
year of the Julian Period, which was the 4007th the wor . ld 
year before the year of CHRIST'S birth, T have fol- U1 
lowed Mr. Bedford in his Scripture- Chronology, 
printed A. D. 1730, and Mr. Kennedy, in a work 
of the same kind, printed A. D. 1762. Mr. Bed- 
ford takes it only for granted thai the world was 
created at the time of the autumnal equinox ; but 
Mr. Kennedy affirms that the said equinox was at 
the noon of the fourth day of the creation -week, and 
that the moon was then 24 hours past her opposition 
to the Sun. If Moses had told us the same things, 
we should have had sufficient data for fixing the ara 
of the creation ; but as he has been silent on these 
points, we must consider the best accounts of chro- 
nologers as entirely hypothetical and uncertain. 

3K 



424 



Tables of Time. 



S TABLE I. Shewing the Golden Number (which is the same both 
IJ the Old and New Styles) from the Christian JEra to 4. D. 380. 

S ! , 

s Years less than an Hundred. 



1 



k W 







1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


5* 


S Hundreds 
S O f 


19 
38 


20 
39 


21 
40 


22 
41 


23 
42 


24 
43 


25 

14 


26 
4., 


27 


28 

47 


29 
8 


30 

49 


31 

50 


32 
51 


33 

52 


34 
53 


35 
54 


36 
55 


37 S 
56? 


s 

S Years. 


57 

76 


58 
77 


59 
78 


60 
79 


61 

80 


62 
81 


63 
82 


64 

t>3 


65 

84 


66 

85 


67 
86 


68 
87 


69 
88 


70 
89 


71 
90 


72 
91 


73 
92 


74 
93 


Si 


S 


95 


96 


97 


98 


99 




























$ 


5 c 


i900 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


^9$ 


$ loo 


2000 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5S 


> 200 


2100 


i 1 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 S 


S 300 


2200 


16 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 S 


Ij 400 


2300 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


Jj 500 


.400 


7 


8 


9 


10 


11 


12 


13 


14 


15 


If 


17 


18 


19 


1 


2 


3 


4 


5 




? 600 


4500 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


us 


> 700 


.;600 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 c 


? 800 


2700 


g 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


;16 


17 


18 


19 


1 


2S 


\ 


2800 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 \ 


? 1000 


2900 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 ^ 


S 1100 


3000 


18 


19 


1 


2 


3 


4 


5 


6 


7 


8' 


C 


10 


11 


12 


13 


14 


15 


16 


17 S 


Jj 1200 


3100 


4 


5 


6 


7 


8 


9 


10 


11 


2 


13 


14 


15 


16 


: 17 


18 


19 


1 


o 


3 ^ 


S 1300 


3200 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


r 


4 


5 


6 


7 


8S 


I| 1400 


3300 


14 


lo 


16 


17 


.18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 S 


Jj 1500 


3400 


19 


I 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 S 


S 1600 


3500 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4S 


J 1700 


3600 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


n 


4 


5 


6 


7 


8 


9 S 


S 1800 


3700 


15|16 


17 


18 


19 


1 


2 


-3 


4 


Cj 


6 


7 


8 


9 


10 


11 


12 


13 


14 - s 


Ri 



Tables of Time. 



425 




' Tables of Time. 



S TABLE III. Shelving the Dominical Letters, Ola ! S 
S Style, for 4200 Years before the Christian ;Era. 



5 Bcf. Christ 


Hundreds of Years Jj 


I 





100 


200 


300 


400 


500 


600 J 


Jj Years less 
S than an 
<J Hundred. 


70C 
1400 
2100 
280; 


800 
1500 
2200 
2901 


900 
1600 
2300 
300t 


1000 
1700 
2400 
3100 


1100 
1800 

2500 
3200 


1200 
1900 
2600 
3300 


1300 S 
2000 S 
2700 S 
3400 | 


S 


350L 


360C 


3700 


3800 


3900 


4000 


4100 ^ 


S 


28 


56 


84 


D C 


C B 


B A 


A G 


G I 


F E 


ED!; 


C 




















s 


h 


29 


57 


85 


E 


D 


C 


B 


A 


G 


F S 




30 


58 


86 


F 


E 


D 


C 


B 


A 


G S 


V c 


31 


59 


87 


G 


F 


E 


D 


C 


B 


A < 


i; 4 


32 


60 


88 


B A 


A G 


G F 


F E 


E D 


D C 


C BS 


s 


33 


61 


89 


C 


B 


A 


G 


F 


E 


D I 


S 6 


34 


62 


90 


D 


C 


B 


A 


G 


F 




h 7 


35 


63 


91 


E 


D 


C 


B 


A 


G 


F S 


f_! 


36 


64 


92 


G F 


F E 


E D 


D C 


C B 


B A 


A G? 


S 9 


37 


65 


93 


A 


G 


F 


E 


D 


C 


B 


5 10 


38 


6'" 


94 


B 


A 


G 


F 


E 


D 


C S 


in 


39 


o7 


95 


C 


B 


A 


G 


F 


E 


D c 


JM 


40 


68 


96 


E D 


D C 


C B 


B A 


A G 


G F 


FE^ 


(i 13 


11 


69 


97 


F 


E 


D 


C 


B 


A 


G S 


S 14 


42 


70 


98 


G 


F 


E 


D 


C 


B 


A 5 


Sis 


43 


71 


39 


A 


G 


F 


E 


D 


C 




56 


14 


72 




C B 


B A 


A G 


G F 


F E 


E D 


DC!; 


? 17 


4o 


73 




D 


C 


B 


A 


G 


F 


E ^ 


S 18 


46 


74 




E 


D 


C 


B 


A 


G 


F S 


S 19 


47 


75 




F 


E 


D 


C 


B 


A 


G \ 


S20 


48 






A G 


G F 


F E 


E D 


D C 


C B 


B AS 


te 


49 


7V 
















S 




B 


A 


G 


F 


E 


D 


c 


c 22 


50 


78 




C 


B 


A 


G 


F 


E 


T*l 


S23 


51 


70 




n 


C 


B 


A 


G 


F 


E 


?24 


... 


80 




F E 


E D 


D C 


C B 


B A 


A G 


GF!; 


^ 




















S 


s 2ft 


53 


81 




c; 


F 


E 


n 


C 


B 


A S S 


S26 


54 


82 




A 


G 


F 


E 


D 


C 


B J 


$27 


;5 


83 




B 


A 


G 


F 


E 


D 


.X* 



Tables of Time. 

S TABLE IV. Shewing the Dominical Letters^ Old\ 
S Style,' for 4200 Years after the Christian &ra. \ 



Alt. Christ 


Hundreds of Years. Jj 


S 




100 


200 


300 


400 


500 


600 


!j Years less 
S than an 
Ij Hundred. 


700 
1400 
2100 
2800 


800 
1500 

2200 
2900 


900 
1600 
2300 
3000 


1000 
1700 
2400 
3100 


1100 

'800 
2500 
3200 


1200 
1900 
2600 
3300 


1300 ? 
200O JJ 
2700 s 
3400 Jj 


s 


3500 


3600 


3700 


3800 


3900 


4000 


4100 s 


h 


28 
29 


56 


84 


D C 


E D 


F JL 


G F 


A G 


li A 


C B <J 


57 


85 


B 


C 


D 


E 


F 


G 


A s 


S 2 


30 


58 


',6 


A 


B 


C 


D 


E 


F 


G S 


5j j 


31 


59 


87 


G 


A 


B 


C 


D 


E 


F ^ 


S 4 


32 


60 


88 


F t 


G F 


A G 


B A 


C B 


D C 


EDS 


h 


."> O 

O ^ 


61 


89 


D 


E 


F 


G 


A 


B 


c 5 


* c 
s 


34 


62 


90 


C 


D 


E 


F 


G 


A 


B S 


S 7 


35 


63 


91 


B 


C 


D 


E 


F 


G 


A S 


S 8 


36 


64 


92 


AG 


B A 


C B 


D C 


E D 


F E 


G FS 


- 








F 


~ 




B 


C 




V 


37 


65 


93 


A 


D 


s 

Jhfl w 


S 10 


38 


66 


94 


E 


F 


G 


A 


B 


C 


D S 


?ll 


39 


67 


95 


D 


E 


F 


G 


A 


B 


c 5 


\- 


40 


68 


96 


C B 


D C 


E D 


F EG F 


A G 


BAS 


5 13 


41 


69 


97 


A 


B 


C 


D 


E 


F 


G S 


Ju 


42 


70 


98 


G 


A 


B 


C 


D 


E 


F * 


> 15 


43 


71 


99 


F 


G 


A 


B 


C 


D 


E J 


he 


44 


72 




ED 


F E 


G F 


A G 


B A 


C B 


DC!; 


s 




















c 




45 


73 




C 


D 


E 


F 


G 


A 


B $ 


S 18 


46 


74 




B 


C 


D 


E 


F 


G 


A S 


S 19 


47 


75 




A 


B 


C 


D 


E 


F 


G 


20 


48 


76 




G F 


A G 


B A 


C B 


D C 


E D 


F ES 


^ 




















s 


s 





__ 





'" 


i 








- 


1 




S21 


49 


77 




E 


F 


G 


A 


B 


C 


D S 


^ 22 


50 


78 




D 


E 


F 


G 


A 


B 


Q j 


S 23 


51 


79 




C 


D 


E 


F 


G 


A 


B S 


J 24 


52 


80 




B A 


C B 


D C 


E D 


F E 


G F 


A G 


s 




















^ 




53 


81 




G 


A 


B 


C 


D 


E 


F 


S 26 


54 


82 




F 


G 


A 


B 


C 


D 


E 5! 


$27 


55 


83 




E 


F 


G 


A 


B 


C 


D . 



428 



Tables of Time. 



S TABLE V. The Dominical Letter^ S 
S New Style, for 4000 Years after <J 
^ the Christian JEra. * S 



After Chr. 


Hundreds of Years. S 


S Years less 
5 than an 
S Hundred. 


100 
500 
900 
1300 
1700 
2100 
2500i 
2900 
3300 
3700 


200 
600 
1000 
1400 
1800 
2200 
2600 
3000 
3400 
3800 


300 
700 
1100 
1500 
1900 
2300 
2700 
3100 
3500 
3900 


400 S 

800 !; 

1200 S 
1600 5 
2000 S 

2400 !; 

2800 S 
3200 <J 
3600 J 
4000 

s 

B A!; 

s 


C 


E 


G 


i J 

1 1 

% 6 
> 11 

s sl! 

1:4 

S 14 
S 15 

S - 

j| 

j* 
S 22 
S 23 
S 14 

!> 26 
S 27 
5 28 


29 
30 
31 

32 



33 
34 
35 

36 

37 
38 
39 
40 


57 

58 
59 
60 


85 
86 
87 
88 

90 
91 

92 


B 
A 
G 
F E 


D 
C 
B 
A G 


F 
E 
D 
C B 


c 

1 ' 

DCS 


6 i 
62 

6 > 
64 


D 
C 
B 
A G 


F 
E 
D 
C JB 


A 
G 

F 
E D 


A ^ 

**\ 


60 
66 
67 
68 


93 
94 
95 
96 


F 
E 
.D 
C B 


A 
G 

F D 


C 
B 
A 
G T 


$ 

C \ 
B S 
A GS 


41 
42 

43 

44 


69 
70 

n 

72 


97 

98 
99 


A 
G 
F 
E D 


C 

B 
A 
G F 


E 
D 
C 

B A 


F > 
E s 
B J 
CBj 


45 
46 
47 

48 

49 
50 
j ; 
52 

55 
56 


73 

74 
75 
76 


M 


C 
B 
A 

G F 


E 
D 
C 
B A 


G 

F 
E 
D C 


A % 
G J 
F V 
E D> 

B 


77 
fj 

79 
80 

81 

83 

8-1 


E 
D 
C 
B A 


G 

F 
E 
D C 


B 
A 
G 

F F 


G 
F 
E 
D C 


B 
A 
G 
F E 


D 
C 
B 
A G 


H 

B A ? 



Tables of Time. 



429 



S the Months, for both Styles, by the J 
? Dominical Letters. s 


ij Week Days. 


A 

1 
8 
15 
22 
29 


B 

2 
9 
16 

23 
30 

6 
13 

20 
27 

3 
10 
17 
24 
31 

7 
14 
21 
28 


C 

n 

10 
17 
24 
31 


D 


E 

o 

12 

< 

26 

2 
9 
16 
23 
30 

6 
13 

20 

27 

3 
iO 

24 
31 

7 
14 
21 

28 





i!^ 

iU 

} 

15 1 

22 s 
29 S 

2 J 
16* 

1 

20 S 

1 


Ij January 31 
S October 3 1 


4 
11 
18 

25 

1 
8 
15 

22 
29 


6 
13 
20 

27 

3 

10 
17 

24 
31 

7 
14 
21 
28 

4 

li 
18 
25 

1 

8 
15 

22 
29 


S Feb. 28-29 
!j March 31 
S November 30 


5 
12 
19 
26 

2 
9 
16 

23 
30 


7 
14 

21 

28 

4 
11 

18 

25 

8 

15 

22 
29 

5 
12 
19 
26 


} 

S April 30 
^ July 3 1 

\ 


5 
12 
19 

26 

2 
9 
16 
23 

6 
13 

20 

27 

3 
10 

17 
24 
31 


S August 31 

s 


6 
13 
20 
27 


S 

\ September 30 
S December 31 


3 
10 
17 
24 
31 


4 
1 1 
IS 

25 


1 
8 
15 

22 
29 

5 
12 
19 
.6 


2 
9 
16 
23 
30 


4 
11 
18 

1 
8 
15 
22 

29 


5 
12 
19 
26 

2 
9 
16 
23 

30 


[ May 3 1 


7 
14 
21 

28 

4 
11 
18 
26 


S 
J> June 30 

S 


6 
13 

20 
27 


7 
14 
21 

28 



430 The ORRERY described. 



CHAP. XXII. 



A Description of the Astronomical Machinery serv- 
ing to explain and illustrate the foregoing Part 
of this Treatise. 



Frontin 39~ r I ^HE ORRERY. This machine shews the 

f he Title- JL motions of the Sun, Mercury, Venus, 

page. The Earth, and Moon ; and occasionally, the superior 

'RKERY. p} anets> Mars, Jupiter, and Saturn, may be put on; 

Jupiter's four satellites are moved round him in 

their proper times by a small winch ; and Saturn 

has his five satellites, and his ring, which keeps its 

parallelism round the Sun ; and by a lamp put in 

the Sun's place, the ring shews all the phases de- 

scribed in the 204th article. 

The Sun. In the centre, No. 1. represents the SUN, sup- 

ported by its axis inclining almost 8 degrees from 

the axis of the ecliptic ; and turning round in 25-j 

days on its axis, of which the north pole inclines 

toward the 8th degree of Pisces in the great ecliptic 

The eclip- (No. II.), whereon the months and days are en- 

tic. graven over the signs and degrees in \vhich the Sun 

appears, as seen from the Earth, on. the diffe 

days of the year. 

Mercury. The nearest planet (No. 2.) to the Sun is Mi 
cury, which goes round him in 87 days 23 hours, 
or 87ff diurnal rotations of the Earth ; but has no 
motion round its axis in the machine, because the 
time of its diurnal motion in the heavens is not 
known to ns. 

Venus. The next planet in order is Venus (No. 3.) which 
performs her annual course in 224 days 17 hours; 
and turns round her axis in 24 days 8 hours, or 
in 24| diurnal rotations of the Earth. Her axi 
inclines 75 degrees from the axis of the ecliptic 
and her north pole inclines toward the 20th de 
gree of Aquarius, according to the observations o 



sun 
rrent 

VIer. 



The ORRERY described* 431 

Bianchini. She shews all the phenomena described 
from the 30th to the 44th article in chap. 1. 

Next without the orbit of Venus is the Earth, TheEarth. 
(No. 4.) which turns round its axis, to any fixed 
point at a great distance, in 23 hours 56 minutes 
4 seconds, of mean solar time (\ 221, & seq.), but 
from the sun to the Sun again in 24 hours of the 
same time. No. 6. is a sidereal dial- plate under the 
Earth ; and No. 7. a solar dial- plate on the cover of 
the machine. The index of the former shews side- 
! real, and of the latter, solar time ; and hence, the for- 
\ mer index gains one entire revolution on the latter 
-} every year, as 365 solar or natural days contain 366 
sidereal days, or apparent revolutions of the stars. In 
the time that the Earth makes 36 5 diurnal rotations 
on its axis, it goes once round the Sun in the plane 
of the ecliptic ; and always keeps opposite to a mov- 
ing index (No. 10.), which shews the Sun's apparent 
daily change of place, and also the days of the months. 
The Earth is half covered vuth a black cap, to 
divide the apparently-enlightened half next the Sun 
from the other half) which when turned away from him. 
is in the dark. The edge of the cap represents the 
circle bounding light and darkness, and shews at what 
time the Sun rises and sets to all places throughout the 
year. The Earth's axis inclines 231 degrees from the 
j axis of the ecliptic, the north pole inclines toward the 
beginning of Cancer, and keeps its parallelism through- 
out its annual course, $ 48, 202; so that in summer 
the northern parts of the Earth inclines toward the 
Sun, and in winter declines from him : by which 
means the different lengths of days and nights, and 
the cause of the various seasons, are demonstrated 
to sight. 

There is a broad horizon, to the upper side of 
which is fixed a meridian- semicircle in the north and 
south points, graduated on both sides from the h >ri- 
zon to 90 in the zenith, or vertical point. The cage 

31 



432 The ORRERY described. 

of the horizon is graduated from the east and west to 
the south and north points, and within these divisions 
are the points of the compass. From the lower side 
of this thin horizon -plate, stand out four small wires, 
to which is fixed a twilight-circle 18 degrees from the 
graduated side of the horizon all round/ This hori- 
zon may be put upon the Earth (when the cap is taken 
away), and rectified to the latitude of anyplace: and 
then, by a small wire called the solar ray, which may 
be put on so as to proceed directly from the Sun's 
centre toward the Earth's, but to come no farther than 
almost to touch the horizon. The beginning of twi- 
light, time of sun-rising, with his amplitude, meridi- 
an-altitude, time of setting, amplitude then, and end 
of twilight, are shewn for every day of the year, at 
that place to which the horizon is rectified. 

TheMoon ^^ e Moon (No. 5.) goes round the Earth, from 
* between it and any fixed point at a great distance, in 
27 days 7 hours 43 minutes, or through all the signs 
and degrees of her orbit ; which is called her periodi- 
cal revolution : but she goes round from the Sun to 
the Sun again, or from change to change, in 29 days 
12 hours 45 minutes, which is her synodical revolu- 
tion ; and in that time she exhibits all the phases al- 
ready described, $ 255, 

When the above-mentioned horizon is rectified to 
the latitude of any given place, the times of the Moon's 
rising and setting, together with her amplitude, are 
shewn to that place as well as the Sun's, and all the 
various phenomena of the harvest-moon, 273, & 
seq. are made obvious to sight. 

The nodes. The Moon's orbit (No. 9.) is inclined to the 
ecliptic (No. 11.), one half being above, and the 
other below it. The nodes, or points at and 0, lie 
in the plane of the ecliptic, as described 317, 318, 
and shift backward through all its signs and degrees 
in 18f years, The degrees of the Moon's latitude, to 



The ORRERY described. 

the highest at N L (north latitude), and lowest at S 
L (south latitude), are engraven jpoth ways from her 
nodes at and ; and as the Moon rises and falls in 
her orbit according to its inclination, her latitude and 
distance from her nodes are shewn for every day ; 
having first rectified her orbit so as to set the nodes 
to their proper places in the ecliptic : and then, as 
they come about at different, and almost opposite, 
times of the year, 319, and point twice toward the 
Sun ; all the eclipses may be shewn for hundreds of 
years (without any new rectification) by turning the 
machinery backward for time past, or forward for 
time to come. At 17 degrees distance from each 
node, on both sides, is engraven a small sun ; and 
at 12 degrees distance, a small moon; which shew 
the limits of solar and lunar eclipses, 317: and 
when, at any change, the moon falls between either 
of these suns and the node, the Sun will be eclipsed 
on the day pointed to by the annual index (No. 10.), 
and as the Moon has then north or south latitude, 
one may easily judge whether *hat eclipse will be vi- 
sible in the northern or southern hemisphere ; espe- 
cially as the Earth's axis inclines toward the Sun or 
declines from him at that time. And when at any 
full, the Moon falls between either of the little moons 
and node, she will be eclipsed, and the annual index 
shews the day of that eclipse. There is a circle of 
29| equal parts (No. 8.) on the cover of the machine, 
on which an index shews the days of the Moon's age. 

A semi-ellipsis and semicircle are fixed to an el- Plate Ix, 
liptical ring, which being put like a cap upon the Flff ' X * 
Earth, and the forked part F upon the Moon, shews 
the tides as the Earth turns round within them, and 
they are led round it by the Moon. When the dif- 
ferent places come to the semi-ellipsis daEbB, they 
have tides of flood : and when they come to the se- 
micircle CED, they have tides of ebb, 304, 305 ; 



434 The ORRERY described. 

the index on the hour-circle (No. 7.) shewing the 
times of these phenomena. 

There is a jointed wire, of which one end being 
put into a hole in the upright stem that holds the 
Earth's cap, and the wire laid into a small forked 
piece which may be occasionally put upon Venus or 
Mercury, shews the direct and retrograde motions of 
these two planets, with their stationary times and 
places as seen from the Earth. 

The whole machinery is turned by a winch or 
handle (No. !.), and is so easily moved, that a clock 
might turn it without any danger of stopping. 

To give a plate of the wheel- work of this machine 
would answer no purpose, because many of the 
wheels lie so behind others, as to hide them from 
sight in any view whatsoever. 

Another 398. Another ORRERY. In this machine, which 
ORRERY. j s ^ le simplest I ever saw, for shewing the diurnal 
" te y L and annual motions of the Earth, together with the 
motion of the Moon and her nodes, A and B are 
two oblong square pkt.es held together by four up- 
right pillars; of which three appear atjT, g 9 andg* 2. 
Under the plate A is an endless screw on the axis of 
the handle 6, which works in a wheel fixed on the 
same axis with the double-grooved wheei E; and on 
the top of this axis is fixed the toothed wheel f, which 
turns the pinion k, on the top of whose axis is the 
pinion k 2, which turns another pinion b 2, and that 
turns a third, which being fixed on a 2, the axis of 
the Earth /, turns it round, and the earth with it : 
this last axis inclines in an angle of 23-| degrees. The 
supporter X 2, in which the axis of the earth turns, 
is fixed to the moveable plate C. 

In the fixed plate B, beyond H, is fixed the strong 
wire cf, on which hangs the sun 7\ so as it may turn 
round the wire. To this sun is fixed the wire or so- 
lar ray Z, which (as the earth Z/turns round its axis) 
points to all the places that the Sun passes vertically 
over, every day of the year. The earth is half co- 






The ORRERY described. 435 



f ered with a black cap a, as in the former Orrery, for 
dividing the day from the night ; and as the different 
places come out trom below the edge of the cap, or 
go in below it, they shew the times of sun-rising and 
setting every day of the year. This cap is fixed on 
the wire 6, which has a forked piece C turning round 
the wire d: and, as the earth goes round the sun, it 
carries the cap, wire, and solar ray round him ; so 
that the solar ray constantly points toward the earth's 
centre. 

On the axis of the pinion k is the pinion m, which 
turns a wheel on the cock or supporter 72, and on the 
axis of this wheel nearest n is a pinion (hid from 
view) under the plate C, which pinion turns a wheel 
that carries the moon /Around the earth U ; the moon's 
axis rising and falling in the socket W, which is fix- 
ed to the triangular piece above 2* ; and this piece is 
fixed to the top of the axis of the last- mentioned 
wheel. The socket TFis slit on the outermost side : 
and in this slit the two pins near Y, fixed in the moon's 
axis, move up and down ; one of them being above 
the inclined plane FJf, and the other below it. By 
this mechanism, the moon V moves round the earth 
T in the inclined orbit ^, parallel to the plane of the 
ring YX; of which the descending node is at Jf, and 
the ascending node opposite to it, but hid by the sup- 
porter X 2. 

The small wheel E turns the large wheels D and 
F 9 of equal diameters, by cat-gut strings crossing 
between them : and the axes of these two wheels are 
cranked at G and H 9 above the plate . The up- 
right stems of these cranks going through the plate 
C, carry it over and over the fixed plate JB, with a 
motion which carries the earth U round the sun T y 
keeping the earth's axis always parallel to itself, or 
still inclining toward the left hand of the plate ; and 
shewing the vicissitudes of seasons, as described in 
the tenth chapter. As the earth goes round the sun , 



436 The ORRERY described. 

the pinion k goes round the wheel i, for the axis of 
k never touches the fixed plate .Z?, but turns on a 
wire fixed into the plate C. 

On the top of the crank G is an index L, which 
goes round the circle m 2 in the time that the earth 
goes round the sun, and points to the days of the 
months ; which, together with the names of the sea- 
sons, are marked in this circle. 

This index has a small grooved wheel L fixed 
upon it, round which, and the plate Z, goes a cat- 
gut string crossing between them ; and by this means 
the moon's inclined plane YX, with its nodes, is 
* turned backward, for shewing the times and returns 
of eclipses, 310, 320. 

The following parts of this machine must be con- 
sidered as distinct from those already described. 

Toward the right hand, let S be the earth hung 
on the wire e, which is fixed into the plate B ; and 
let be the moon fixed on the axis AT, and turning 
round within the cap P, in which, and in the plate 
C, the crooked wire Q is fixed. On the axis M is 
also fixed the index K, which goes round a circle h 
2, divided into 29 equal parts, which are the days 
of the Moon's age : but to avoid confusion in the 
scheme, it is only marked with the numeral figures 
1234, for the quarters. As the crank H carries 
this moon round the earth S in the orbit , she shews 
all her phases by means of the cap P for the different 
days of her age, which are shewn by the index K; 
this index turning just as the moon does, demon- 
strates her turning round her axis, as she still keeps 
the same side toward the earth , 262. 

At the other end of the plate C T , a moon N goes 
round an earth R in the orbit p. But this moon's 
axis is stuck fast into the plate C at 2, so that nei- 
ther moon nor axis can turn round ; and as this moon 
goes round her earth, she shews herself all round to 
it ; which proves, that if the Moon was seen all round 



The CALCULATOR described. 437 

from the Earth in a lunation, she could not turn round 
her axis. 

N.- B. If there were only the two wheels D and 
.F, with a cat- gut string over them, but not crossing 
between them, the axis of the earth U would keep 
its parallelism round the Sun 7 1 , and shew all the sea- 
sons ; as I sometimes make these machines : and the 
moon would go round the earth S, shewing her 
phases as above ; as likewise would the moon Aground 
the earth R; but then neither could the diurnal mo- 
tion of the earth 7 on its axis be shewn, nor the mo- 
tion of the moon Ground the earth. 

399. In the year 1746 I contrived a very simple The CAL- 
machine, and described its performance in a small CULATOR ' 
Treatise^ upon the Phenomena of the Harvest- Moon, 
published in the year 1747. I improved it soon 
after, by adding another wheel, and called it The 
Calculator. It may be easily made by any gentleman 
who has a mechanical genius. 

The great flat ring supported by twelve pillars, and Plate 
on which the twelve signs with their respective de- . ", 
grees are laid down, is the ecliptic ; nearly in the lg * 
centre of it is the sun S t supported by the strong 
crooked wire /; and from the sun proceeds a wire W+ 
called the solar rat/, pointing toward the centre of 
the earth E, which is furnished with a moveable ho- 
rizon H t together with a brazen meridian, and quad- 
rant of altitude. R is a small ecliptic, whose plane 
coincides with that of the great one, and has the like 
signs and degrees marked upon it ; and is supported 
by two wires D and Z), which are put into the plane 
PP 9 but may be taken off at pleasure. As the earth 
goes round the sun, the signs of this small circle 
keep parallel to themselves, and to those of the great 
ecliptic. When it is taken off, and the solar ray W 
drawn farther out, so as almost to touch the horizon 
ff, or the quadrant of altitude, the horizon being rec* 



438 The CALCULATOR described. 

tified to any given latitude, and the earth turned round 
its axis by hand, the point of the wire IV shews the 
sun's declination in passing over the graduated brass 
meridian, and his height at any given time upon the 
quadrant of altitude, together with his azimuth, or 
point of bearing upon the horizon at that time ; and 
likewise his amplitude, and time of rising and setting 
by the hour-index, for any day of the year that the 
annual-index U points to in the circle of months be- 
low the sun. M is a solar-index or pointer support- 
ed by the wire L y which is fixed into the knob K: 
the use of this index is to shew the Sun's place in the 
ecliptic every day in the year ; for it goes over the 
signs and degrees as the index U goes over the 
months and days ; or rather, as they pass under the 
index U, in moving the cover- plate with the earth and 
its furniture round the sun ; for the index Z7is fixed 
tight on the immoveable axis in the centre of the ma- 
chine, ^is a knob or handle for moving the earth 
round the sun, and the moon round the earth. 

As the earth is carried round the sun, its axis con- 
stantly keeps the same oblique direction, or parallel 
to itself, 48, 202, shewing thereby the different 
lengths of days and nights at different times of the 
year, with all the various seasons. And, in one an- 
nual revolution of the earth, the moon M goes 12-| 
times round it from change to change, having an oc- 
casional provision for shewing her different phases. 
The lower end of the moon's axis bears by a small 
friction- wheel upon the inclined plane J*, which causes 
the moon to rise above and sink below the ecliptic R 
in every lunation ; crossing it in her nodes, which shift 
backward through all the signs and degrees of the 
said ecliptic, by the retrograde motion of the in- 
clined plane 7 1 , in 18 years and 225 days. On 
this plane the degrees and parts of the moon's 
north and south latitude are laid down from both 



The CALCULATOR described. 439 

the nodes, one of which, viz. the descending node, 
appears at 0, by DN above B ; the other node be- 
ing hid from sight on this plane by the plate PP ; 
and from both nodes, at proper distances, as in the 
other Orrery, the limits of eclipses are marked, and 
all the solar and lunar eclipses are shewn in the same 
manner, for any given year within the limits of 6000, 
either before or after the Christian asra. On the 
plate that covers the wheel- work, under the Sun S, 
and round the knob K, are astronomical tables, by 
which the machine may be rectified to the begin- 
ning of any given year within these limits, in three 
or tour minutes of time ; and when once set right, 
may i>e turned backward for 300 years past, or for- 
ward for as many to come, without requiring any 
new rectification. There is a method for its adding 
up the 29th of February every fourth year, and 
allowing only 28 days to that month for every other 
three ; but ail this being performed by a particular 
manner of cutting the teeth of the wheels, and 
dividing the month-circle, too long and intricate to 
be described here, I shall only shew how these 
motions may be performed near enough tor com- 
mon use, by wheels with grooves and cat-gut strings 
round them ; only here I must put the operator in 
mind, that the groove are to be made sharp-bottom- 
ed, (not round) to keep the strings from slipping. 

The moon's axis moves up and down in the 
socket jV, fixed into the bar 0, (which carries her 
round the earth) as she rises above or sinks below 
the ecliptic; and immediately below the inclined 
plane T is a flat circular plate (between Fand T] 
on which the different eccentricities of the Moon's 
orbit are laid down ; and likewise her mean anomaly 
and elliptic equation, by which her true place may 
be very nearly found at any time. Below this apo- 
gee-plate, which shews the anomaly, &c. is a 
circle F divided into 29 equal parts, which are the 

( 3K) 



.440 The CALCULATOR described. 



days of the Moon's age : and the forked end A of 
the index AB (Fig. II.) may be put into the apo- 
gee-part of this plate ; there being just such another 
index to put into the inclined plane T at the as- 
cending node : and then the curved points B of these 
indexes shew the direct motion of the apogee, and 
retrograde motion of the nodes through the ecliptic 
R, with their places in it at any given time. As the 
inoon M goes round the earth E^ she shews her 
place every day in the ecliptic 7t!, and the lower end 
of her axis shews her latitude and distance from her 
node on the inclined plane Y 1 , also her distance from 
her apogee and perigee, together with her mean 
anomaly, the then eccentricity of her orbit, and her 
elliptic equation, all on the apogee-plate, and the 
day of her age in the circle Y of 29| equal parts, 
for every day of the year, pointed out by the annual 
index Uin the circle of months. 

Having rectified the machine by the tables for 
the beginning of any year, move the earth and 
moon forward by the knob K, until the annual 
index comes to any given day of the month, then 
stop, and not only all the above phenomena may 
be shewn for that day, but also, by turning the 
earth round its axis, the declination, azimuth, 
amplitude, altitude of the Moon at any hour, and 
the times of her rising and setting, are shewn by 
the horizon, quadrant of altitude, and hour-index. 
And in moving the earth round the sun, the days 
of all the new and full moons and eclipses in any 
given year are shewn. The phenomena of the 
harvest-moon, and those of the tides, by such a cap 
as that in plate IX. Fig. 10. put upon the earth and 
moon, together with the solution of many problems 
not here related, are made conspicuous. 

The easiest, though not the best, way, thai I can 
instruct any mechanical person to malge the wheel-* 

fc-V 



772? CALCULATOR described. 441 

work of such a machine, is as follows: which is the 
way that I made it, before I thought of numbers 
exact enough to make it worth the trouble of cut- 
ting teeth in the wheels. 

Fig. 3d of Plate VIII. is a section of this ma- PLATE 
chine ; in which ABCD is a frame of wood held to- Fi VI I 1 I I f 
gether by four pillars at the corners ; two of which ^' 
appear at AC and BD. In the lower plate CD of 
this frame are three small friction-wheels, at equal 
distances from each other ; two of them appearing 
at e and e. As the frame is moved round, these 
wheels run upon the fixed bottom -plate , which 
supports the whole work. 

In the centre of this last-mentioned plate is fixed 
the upright axis GFFf, and on the same axis is 
fixed the wheel HHH> in which are four grooves^ 
/, X, k, jLj of clifierent diameters. In these grooves 
are cat-gut strings going also round the separate 
wheels M, JV, O, and P. 

The wheel Mis fixed on a solid spindle or axis, 
the lower pivot of which turns at R in the under 
plate of the moveable frame ABCD ; and on the 
upper end of this axis is fixed the plate oo (which 
is PP, under the earth, in Fig; 1.^, and to this 
plate is fixed at an angle of 23^ degrees inclination, 
the dial-plate below the earth T ; on the axis of 
which, the index q is turned round by the earth. 
This axisj together with the wheel M^ and plate oo, 
keep their parallelism in going round the sun S. 

On the axis of the wheel M is a moveable 
socket j on which the small wheel JV is fixed, and 
on the upper end of this socket is put on tight (but 
so as it may be occasionally turned by hand) the 
bar ZZ (viz. the bar in Fig. 1.) which carries 
the moon 772 round the earth 7", by the socket n^ 
fixed into the bar. As the moon goes round the 
earth, her axis rises and falls in the socket n ; be- 
cause, on the lower end of her axis, which is turned 
inward, there is a small friction- wheel $ running 



442 The CALCULATOR described. 

on the inclined plane X (which is Tin Fig. 1.), and 
so causes the moon alternately to rise above and 
sink below the little ecliptic VV (R in Fig. 1.) in 
every lunation. 

On the socket or hollow axis of the wheel A r , 
there is another socket, on which the wheel is 
fixed; and the moon's inclined plane X is put 
tightly on the upper end of this socket, not on a 
square, but on a round, that it may be occasionally 
set by hand without wrenching the wheel or axle. 

Lastly, on the hollow axis of the wheel O is an- 
other socket, on which is fixed the wheel P, and on 
the upper end of this socket is put on tightly the 
apogee-plate Y(that immediately below Tin Fig. 1.) 
All these axles turn in the upper plate of the move- 
, .able frame at Q / which plate is covered with the 
thin plate cc (screwed to it), whereon are the fore- 
mentioned tables and month- circle in Fig. 1. 

The middle part of the thick fixed wheel HHH 
is much broader than the rest of it, and comes out 
between the wheels M and O almost to the wheel 
JV. To adjust the diameters of the grooves of this 
fixed wheel to the grooves of the separate wheels 
M, A", 0, and P, so as they may perform their 
motion in their proper times, the following method 
must be observed. 

The groove of the wheel M, which keeps the 
parallelism of the earth's axis, must be precisely 
of the same diameter as the lower groove / of the 
fixed wheel HHH; but, when this groove is so 
well adjusted as to shew, that in ever so many an- 
nual, revolutions of the Earth, its axis keeps its 
parallelism, as may be observed by the solar ray 
7F(Fig. 1.) always coming precisely to the same 
degree oi the small ecliptic R at the end of every 
annual revolution, when the index AT points to the 
like degree in the great ecliptic ; then, with the 
edge ol a thin file, give the groove of the wheel M 
a small rub all round, and, by that means lessening 



The CALCULATOR described. 443 

the diameter of the groove perhaps about the 20th 
part of a hair's breadth, it will cause the earth to 
shew the precession of the equinoxes ; which, in 
many annual revolutions, will begin to be sensible, 
as the earth's axis deviates slowly from its paralle- 
lism, 246, toward the antecedent signs of the 
ecliptic. 

The diameter of the groove of the wheel TV, 
which carries the moon round the earth, must be 
to the diameter of the groove X, as a lunation is to 
a year, that is, as 29$ to 365|. 

'The diameter of the groove of the wheel 0, 
which turns the inclined plane X with the moon's 
nodes backward, must be to the diameter of the 
groove , as 20 to 18ff. And, 

Lastly, the diameter of the groove of the wheel 
P, which carries the moon's apogee forward, must 
be to the diameter of the groove .L, as 70 to 62. 

But after all this nice adjustment of the grooves 
to the proportional times of their respective wheels 
turning round, and which seems to promise very 
well in theory, there will still be found a necessity 
of a farther adjustment by hand ; because proper 
allowance must be made for the diameters of the 
cat- gut strings : and the grooves must be so adjust- 
ed by hand, as, that in the time the earth is moved 
once round the sun, the moon must perform 12 
sy nodical revolutions round the earth, and be almost 
11 days old in her 13th revolution. The inclined 
plane with its nodes must go once round backward t 
through all the signs and degrees of the small eclip- 
tic in 18 annual revolutions of the earth, and 225 
days over. And the apogee-plate must go once 
round forward, so as its index may go over all the 
signs and degrees of the small ecliptic in eight 
years (or so many annual revolutions of the earth) 
and 312 days over. 

N B. The string which goes round the grooves 
X and JV, for the moon's motion, must cross .be- 
tween these wheels; but all the rest, of the 



R1UM 



444 The COMETARIUM described. 

go in their respective grooves, IMk, O, and LP, 
without crossing. 

The 400. The COMETARIUM. This curious ma- 

COMETA- c hine shews the motion of a comet, or eccentric 
body moving round the Sun, describing equal areas 
in equal times, \ 152, and may be so contrived as 
to shew such a motion for any degree of eccen- 
tricity. It was invented by the late Dr. DESAGU- 

LIERS. 

The dark elliptical groove round the letters 
abcdefghiklm is the orbit of the comet Y: this 
comet is carried round in the groove, according to 
tne or( * er f l etters by the wire W fixed in the sun 
S, and slides on the wire as it approaches nearer 
to, or recedes farther from, the sun ; being nearest 
of all in the perihelion c, and farthest in the aphe- 
lion g. The areas aSb, bSc, cSd, &c. or contents 
of these several triangles, are all equal : and in every 
turn of the winch JV", the comet Y is carried over 
one of these areas : consequently, in as much time 
as it moves from f to g, or from g to /z, it moves 
from 772 to a, or from a to b ; and so of the rest, 
being quickest of all at tz, and slowest at g. Thus 
the comet's velocity in its orbit continually decreases 
from the perihelion a to the aphelion gv and increases 
in the same proportion from g to a. 
. The elliptical orbit is divided into 12 equal parts 
or signs, with their respective degrees, and so is 
the circle nopqrstn, which represents a great circle 
in the heavens, and to which the comet's motion is 
referred by a small knob on the point of the wire 
W. While the comet moves from f to g in its 
orbit, it appears to move only about 5 degrees in 
this circle, as is shewn by the small knob on the 
end of the wire W; but in the like time, as the 
comet moves from m to #, or from a to b y it appears 
to describe the large space tn or no in the heavens, 
either of which spaces contains 120 degrees, or four 
signs. Were the eccentricity of its orbit greater. 



The COMETARIUM described. 445 

die greater still would be the difference of its 
motion, and vice versa. 

ABCDEFGH1KLMA is a circular orbit for 
shewing the equal motion of a body round the sun 
S, describing equal areas ASB, BSC, &c. in equal 
times with those of the body Y in its elliptical orbit, 
above mentioned , but with this difference, that the 
circular motion describes the equal arcs AB, BC, 
&c. in the same equal times that the elliptical mo- 
tion describes the unequal arcs ab, be, &c. 

Now, suppose the two bodies Fand 1 to start 
from the points a and A at the same moment of 
time, and each having gone round its respective 
orbit, to arrive at these points again at the same 
instant, the body F will be forwarder in its orbit 
than the body 1 all the way from a to g, and from 
A to G ; but 1 will be forwarder than Y through 
all the other half of the orbit ; and the difference is t 
equal to the equation oi % the body Fin its orbit. 
At the points a, A, and g, 6r, that is in the perihe- 
lion and aphelion, they will be equal ; and then the 
equation vanishes. This shews why the equation 
of a body moving in an elliptic orbit, is added to 
the mean or supposed- circular motion, from the 
perihelion to the aphelion; and subtracted, from the 
aphelion to the perihelion, in bodies moving round 
the Sun, or from the perigee to the apogee, and 
from the apogee to the perigee, in the Moon's 
motion round the Earth, according to the precepts 
in the 353d article ; only we are to consider, that 
when motion is turned into time, it reverses the 
titles in the table of The Moorfs elliptic Equal ion. 

This motion is performed in the following man- plate /r 
ner by the machine. ABC is a wooden bar (in the Fig. v. 
box containing the wheel- work), above which are 
the wheels Z? ii $ E ; and below it the efl p j^iatf s 
FF and GO;, each plate being fixed on ;.n axis in 
one of its focuses, at E and K: and the wheel E is 
fixed oil the same axis with the plate FF, These 



446 , The COMETARIUM described. 

plates have grooves round their edges precisely of 
equal diameters to one another, and in these grooves 
is the cat-gut strings gg, gg, crossing between the 
plates at h. On H (the axis of the handle or winch 
JVin Fig. 4th) is an endless screw in Fig. 5, work- 
ing in the wheels D and E, whose numbers of teeth 
being equal, and should be equal to the number of 
lines aS, bS, cS, &c. in Fig. 4, they turn round 
their axes in equal times to one another, and to the 
motion of the elliptic plates. For the wheels D and 
E having an equal number of teeth, the plate FF 
being fixed on the same axis with the wheel E, 
and the plate FF turning the equally-large plate 
GG, by a cat- gut string round them both, they 
must all go round their axes in as many turns of 
the handle A* as either of the wheels has teeth. 

It is easy to see, that the end h of the elliptical 
plate FF being farther from its axis E than the 
opposite end i is, must describe a circle so much 
the larger in proportion; and must therefore move 
through so much more space in the same time; and 
for that reason the end // moves so much faster 
than the end i, although it goes no sooner round 
the centre E. But then, the quick- moving end h 
of the plate FF leads about the short end /z/f of 
the plate GG with the same velocity ; and the slow- 
moving end i of the plate FF coming half round, 
as to B, must then lead the long end k of the plate 
GG as slowly about. So that the elliptical plate 
FF and it axis E move uniformly and equally 
quick in every part of its revolution ; but the 
elliptical plate GG, together with its axis JT, must 
move very unequally in different parts of its revo- 
lution ; the difference being always inversely as the 
distance of any points of the circumference of GG 
from its axis at K: or in other words, to in- 
stance in two points ; if the distance Kk, be four, 
five, or six times as great as the distance A7z, the 
point h will move in that position four, five, or six 



The improved CELESTIAL GLOBE described. 447 

times as fast as the point k does ; when the plate 
GG has gone half round : and so on for any other 
eccentricity or difference of the distances Kk and 
Kh. The tooth i on the plate FF falls in between 
the two teeth at k on the* plate GG, by which means 
the revolution of the latter is so adjusted to that 
of the former, that they can never vary from one 
another. 

On the top of the axis of the equally-moving 
wheel D, in Fig. 5th, is the sun S in Fig. 4th; 
which sun, by the wire Z fixed to it, carries the 
ball 1 round the circle ABCD, &c. with an equa- 
ble motion according to the order of the letters ; 
and on the top of the axis JTof the unequally-mov- 
ing ellipsis GG, in Fig. 5th, is the sun S in Fig. 
4th, carrying the ball Funequally round in the ellip- 
tical groove abed, &c. JV". B This elliptical groove 
must be precisely equal and similar to the verge of 
the plate GG, which is also equal to that of FF. 

In this manner, machines may be made to shew 
the true motion of the Moon about the Earth, or of 
any planet about the Sun ; by making the elliptical 
plates of the same eccentricities, ia proportion to 
the radius, as the orbits of the planets are whose 
motions they represent ; and so,, their different equa- 
tions, in different parts of their orbits, may be made 
plain to the sight : and'ciearer ideas of these motions 
and equations will be acquired in half an hour, than 
could be gained from reading half a day about them. 

401. The IMPROVED CELESTIAL GLOBE. OnTheim- 
the north pole of the axis, above the hour-circle, 
is fixed an arch MKH tf 23* degrees; and at the 
end //is fixed an upright pin //G, which stands 
directly over the north pole of the ecliptic, and per- 
pendicular to that part of the surface of the globe. 
On this pin are two moveabie collets at Z) and H^ 
to which are fixed the quadrantal wires N and 0, Fi - In - 

3L 



448 The improved CELESTIAL GL QBE described. 

having two little balls on their ends for the sun and 
moon, as in the figure. The collet D is fixed to 
the circular plate F, on which the 29i days of the 
Moon's age are engraven, beginning just under the 
sun's wire A"; and as this ivire is moved round the 
globe, the plate F turns round with it. These wires 
are easily turned, if the screw G be slackened ; and 
when they are set to their proper places, the screw 
serves to fix them there ; so that when the globe is 
turned, the wires with the sun and moon may go 
round with it ; and these two little balls rise and set 
at the same times, and on the same points of the 
horizon, for.ithe day to which they are rectified, as 
the Sun and Moon do in the heavens. 

Because the Moon keeps not her course, in the 
ecliptic (as the Sun appears to cio) but has a decli- 
nation of 5*. degrees, on each side, from it in every 
lunation, 317, her ball may be screwed as many 
degrees to either side of the ecliptic as her latitude, 
or declination from the ecliptic, amounts to, at any 
given time ; and for this purpose S is a small piece 
of pasteboard, of which the curved edge at S is to 
be set upon the globe, at right angles to the ecliptic, 
and the dark line over S to stand upright upon it. 
From this line, on the convex edge, are drawn the 
5* degrees of the Moon's latitude on both sides of 
the ecliptic ; and when this piece is set upright on 
the globe, its graduated edge reaches to the moon 
on the wire 0, by which means she is easily adjust- 
ed to her latitude found by an ephemeris. 

The horizon is supported by two semicircular 
arches, because pillars would stop the progress of 
the balls, when they go below the horizon in an 
oblique sphere. 

TO rectify To rectify this globe. Elevate the pole to the 
u * latitude of the place; then bring the Sun's place 

in the ecliptic for the given clay to the brass meri- 
dian, and set the hour-index to XII at noon, that is, 



The PLANE T A R V GLOBE described. 

to the upper XII on the hour-circle, keeping the 
globe in that situation ; slacken the screw G, and 
set the sun directly over his place on the meridian ; 
which being done, set the moon's wire under the 
number that expresses her age for that day on the 
plate F 9 and she will then stand over her place in 
the ecliptic, and shew what constellation she is in. 
Lastly, fasten the screw G> and laying the curved 
edge of the pasteboard S over the ecliptic, below the 
moon, adjust the moon to her latitude over the gra- 
diuted edge of the pasteboard ; and the globe will 
be rectified. 

Having thus rectified the globe* turn it round, and its ua>, 
observe on what points of the horizon the sun and 
moon balls rise and set, for these agree with the 
points of the compass on which the Sun and Moon 
rise and set in the heavens on the given day : and 
the hour- index shews the times of their rising and 
setting ; and likewise the time of the Moon's pass^ 
ing over t he meridian. 

This simple apparatus shews all the varieties that 
can happen in the rising and setting of the Sun and 
Moon ; and makes the ibrementioned phenomena of 
the harvest- moon. (Chap, xvi.) plain to the eye. It 
is also very useful in reading lectures on the globes, 
because a large company can see this sun and moon 
go round, rising above and setting below the hori- 
zon at different times, according to the seasons of 
the year ; and making their appulses to different 
fixed stars. But in the usual way, where there is 
only the places of the Sun and Moon in the ecliptic 
to keep the eye upon, they are easily lost sight of, 
.unless they be covered with patches. 

402. THE PLANETARY GLOBES. In this ma- The 
chine, TMs a terrestrial globe fixed on its axis stand- * ETA * 
ing upright on the pedestal CZXE, on which is anptate 
hour-circle, having its index fixed on the axis, V ! IL 
which turns somewhat tightly in the pedestal, so Flff>I> 



1 lie PLANETARY GLOBE described, 

that the globe may not be liable to shake ; to prc* 
rent which, the pedestal is about two inches thick, 
and the axis goes quite through it, bearing on a 
shoulder. The globe is hung in a graduated brazen 
meridian much in the usual way ; and the thin plate 
JV, NE\ E, is a moveable horizon, graduated round 
the outer edge, for shewing the bearings and ampli- 
tudes of the Sun, Moon, and planets. The brazen 
meridian is grooved round the outer edge : and in 
this groove is a slender semicircle of brass, the ends 
of which are fixed to the horizon in its north and 
south points: this semicircle slides in the groove 
as the horizon is moved in rectifying it for different 
latitudes. To the middle of the semicircle is fixed 
a pin, which always keeps in the zenith of the hori- 
zon, and on this pin, the quadrant of altitude g turns; 
the lower end of which, in ail positions, touches the 
horizon as it is moved round the same. This quad- 
rant is divided into 90 degrees from the horizon to 
the zenith-pin on which it is turned, at PO. The 
great flat circle or plate AE is the ecliptic, on the 
outer edge of which the signs and degrees are laid 
down ; and every fifth degree is drawn through the 
rest of the surface of this plate toward its centre. 
On this plate are seven grooves, to which seven little 
balls are adjusted by sliding wires, so that they are 
easily moved in the grooves without danger of start- 
ing out of them. The ball next the terrestrial globe 
is the moon, the next without it is Mercury, the 
next Venus, the next the sun, then Mars, then Jupi- 
ter, and lastly Saturn ; and in order to know them, 
they are separately stampt with the following charac- 
ters; ,$, 9,0,,V,i2. This plate or eclip- 
tic is supported by four strong wires, having' their 
lower ends fixed into the pedestal, at 6 T , />, and E; 
the fourth being hid by the globe. The ecliptic is 
inclined 23* degrees to the pedestal, and is there- 



The PLANETARY GLOBE described. 45 1 

fore properly inclined to the axis of the globe which 
stands upright on the pedestal. 

To rectify this machine. Set the sun and all the 
planetary balls to the geocentric places in the eclip- 
tic for any given time, by an ephemcris ; then set 
the north point of the horizon to the latitude of your 
place on the brazen meridian, and the quadrant of 
altitude to the south point of the horizon ; which 
done, turn the globe with its furniture till the quad* 
rant of altitude comes right against the Sun, viz. to 
his place in the ecliptic ; and keeping it there, set 
the hour-index to the XII next the letter C; and 
the machine will be rectified, not only for the follow- 
ing problems, but for several others, which the art- 
ist may easily find out. 

* V 

PROBLEM I. 

To find the Amplitudes, Meridian* Altitudes ', and 
Tunes of rising^ culminating, and setting^ oftlie 
Sun, Moon y and Planets. 

\ 

Turn the globe round eastward, or according to its use, 
the order of the signs ; and when the eastern edge of 
the horizon comes right against the sun, moon, or 
any planet, the hour-index will shew the time of its 
rising ; and the inner edge of the ecliptic will cut its 
rising-amplitude in the horizon. Turn on, and when 
the quadrant of altitude comes right against the sun, 
moon, or any planet, the ecliptic will cut their meri- 
dian-altitudes on the quadrant, and the hour-index 
will shew the times of their coming to the meridian. 
Continue turning, and when the western edge of the 
horizon comes right against the sun, moon, or any 
planet, their setting-amplitudes will be cut on the 
horizon by the ecliptic ; and the times of their set- 
ting will be shewn by the index en the hour-circle. 



452 The PLANETARY GL o u E described. 



PROBLEM II. 

To find the Altitude and Azimuth of the Sun, 

and Planets, at any Time of their being above 
the Horizon. 

Turn the globe till the index comes to the given 
time in the hour-circle ; then keep the globe steady; 
and moving the quadrant of altitude to each planet 
respectively, the edge of the ecliptic will cut the 
planet's mean altitude on the quadrant, and the 
quadrant will cut the planet's azimuth, or point of 
bearing on the horizon. 



PROBLEM III. 

The Sun's Altitude being given at any Time either 
before or after Noon, to find the Hour of the Day, 
and the Variation of the Compass, in any known 
Latitude. 

With one hand hold the edge of the quadrant 
right against the sun ; and with the other hand, turn 
the globe westward, if it be in the forenoon, or east- 
ward if it be in the afternoon, until the sun's place 
at the inner edge of the ecliptic cuts the quadrant in 
the sun's observed altitude, and then the hour-index 
will point out the time of the day, and the quadrant 
will cut the true azimuth or bearing of the sun for 
that time : the difference between which, and the 
bearing shewn by the azimuth-compass, is the vari- 
ation of the compass in that place of the Earth. 
The TRA- 403. THE TR AJECTORIUM LUN ARE. Thisma- 
c ^ ne * s * r delineating the paths of the Earth and 
Moon, shewing what sort of curves they make in 
the ethereal regions ; and was just mentioned in 



The TRAJECTORIUM LUNARE described. 453 



PLATE 
VII. 



the 266th article. S is the sun, and E the earth, 
whose centres are 8 1 inches distant from each other ; 
every inch answering to a million of miles, J 47. 
M is the moon, whose centre is ^ parts of an inch 
from the earth's in this machine, this being in just 
proportion to the Moon's distance from the Earth, 
$52. A A is a bar of wood, to be moved by hand 
round the axis g, which is fixed in the wheel y. 
The circumference of this wheel is to the circum- 
ference of the small wheel L (below the other end 
of the bar) as 365 J days is to 29|; or as a year is to 
a lunation. The wheels are grooved round their 
edges, and in the grooves is the cat-gut string GG 
crossing between the wheels at X. On the axis of 
the wheel L is the index F ; in which is fixed the 
moon's axis M for carrying her round the earth E 
(fixed on the axis of the wheel L) in the time that 
the index goes round a circle of 29-J equal parts, 
which are the days of the Moon's age. The wheel 
Y has the months and days of the year all round its 
limb ; and in the bar AA is fixed the index /, which 
points out the days of the months answering to the 
days of the moon's age shewn by the index F> in 
the circle of 29 J equal parts, at the other end of the 
bar. On the axis of the wheel L is put the piece , 
D below the cock C, in which this axis turns round ; 
and in D are put the pencils e and 772, directly under 
the earth E and moon M; so that m is carried 
round e, as Mis round E. 

Lay the machine on an even fioor, pressing Its usc 
gently on the wheel F, to cause its spiked feet (of 
which two appear at P and P, the third being sup- 
posed to be hid from sight by the wheel) to enter a 
little into the floor to secure the wheel from turning. 
Then lay a paper about four feet long under the 
pencils e. and m, cross- wise to the bar : which done 
move the bar slowly round the axis g of the wheel 
Y; and, as the earth E goes round the sun S, the 
Jioon M will go round the earth with a duly pro* 



454 The TIDE-DIAL described. 

portioned velocity; and the friction- wheel 
ning on the floor, will keep the bar from bearing 
too heavily on the pencils e and 772, which will de- 
lineate the paths of the earth and moon, as in Fig. 
2d, already described at large, 266, 267. As the 
index / points out the days of the months, the in- 
dex jF shews the Moon's age on these days in the 
circle of 29 equal parts. And as this last index 
points to the different days in its circle, the like 
numeral figures may be set to those parts of the 
curves of the earth's path and moon's, where the 
pencils e and m are at those times respectively, to 
shew the places of the earth and moon. If the pen- 
cil c be pushed a very little oif, as if from the pencil 
m y to about part of their distance, and the pencil 
772 pushed as much toward e to bring them to the 
same distance again, though not to the same points 
of space ; then as m goes round e, e will go as it 
were round the centre of gravity between the earth 
and moon m, 298 : but this motion will not 
sensibly alter the figure of the earth's path or the 
moon's. 

If a pin, as/>, be put through the pencil 777, with 
its head toward that of the pin q in the pencil e, the 
' head of the former will always keep to the head of 
the latter as m goes round c, and shews that the 
same side of the Moon is continually turned to the 
Earth. But the pin/?, which may be considered as 
an equatprial diameter of the moon will turn quite 
round the point 772, making all possible angles v.ith 
the line of its progress, or line of the moon's path. 
This is an ocular proof of the Moon's turning round 
her axis. 

TheTiDE- 404. The TIDE-DIAL. The outside parts of 

DIAL. t n i s machine consist of, 1. An eight-sided box, on 

Fig!Vii. * ne top, of which at the corners is shewn the phases 

of the Moon at the octants, quarters, and full. 

Within these is a circle of 29| equal parts, which 

, are the days of the Moon's age accounted from the 

Sun at new Moon, round to the Sun again. Within 



The TIDE-DIAL described. 455 

this circle is one of 24 hours divided into their re- 
spective halves and quarters. 2. A moving ellipti- 
cal plate, painted blue, to represent the rising of 
the tides under and opposite to the Moon ; and hav- 
ing the words, Hndi Water, Tide Falling, Low 
Water, Tide Rising, marked upon it. To one 
end of this plate is fixed the moon M, by the wire 
W, and goes along with it. 3. Above this ellipti- 
cal plate is a round one, with the points of the com- 
pass upon it, and also the names of above 200 places 
in the large machine (but only 32 in the figure, to 
avoid confusion) set over those points on which the 
Moon bears when she raises the tides to the great- 
est heights, at these places, twice in every lunar day : 
and to the north and south points .of this plate are 
fixed two indexes, / and K, which shew the times 
of high water, in the hour-circle, at all these places. 
4. Below the elliptical plate are four small plates, 
two of which project out from below its ends at 
new and full Moon ; and so, by lengthening the 
ellipse, shew the spring-tides, which are then raised 
to the greatest heights by the united attractions of 
the Sun and Moon, $ 302. The other two of these its use. 
small plates appear at low water when the Moon is 
in her quadratures, or at the sides of the elliptical 
plate to shew the neap-tides ; the Sun and Moon 
then acting cross-wise to each other. When any 
two of these small plates appear, the other two are 
hid ; and when the Moon is in her octants, they all 
disappear, there being neither spring nor neap- 
tides at those times. Within the box are a few 
wheels for performing these motions by the handle 
or winch H. 

Turn the handle until the moon M comes to 
any given day of her age in the circle of is9| equal 
parts, and the moon's wire W, will cut the time 
of t er coming to the meridian on that day, in the 
hour circle ; the XII under the sun being mid-day, 
and the opposite XII midnight ; then looking for 
the name of any given place on the round plate 

3 M 



456 The TIDE-DIAL described. 

(which makes 29| rotations while the moon M 
makes only one revolution from the sun to the sun 
again) turn the handle till that place comes to the 
word High Water under the moon, and the index 
which falls among the forenoc i- hours will shew the 
time of high water at that place in the forenoon of 
the given day : then turn the plate half round, till 
the same place comes to the opposite high-water- 
mark, and the index will shew the lime of high 
water in the afternoon at that place. And thus, as 
all the different places come successively under and 
opposite to the moon, the indexes shew the times 
of high water at them in both parts of the day : and 
when the same places come to the low- water-marks, 
the indexes shew the times of low water. For about 
three days before and after the times of new and full 
Moon, the two small plates come out a little way 
from below the high-water-marks on the elliptical 
plate, to shew that the tides rise still higher about 
these times : and about the quarters, the other two 
plates come out a little from under the low-water- 
marks toward the sun and on the opposite side, 
shewing that the tides of flood rise not then so 
high, nor do the tides of ebb fall so low, as at other 
times. 

By pulling the handle a little way outward, it 
is disengaged from the wheel work, and then the 
upper plate may be turned round quickly by hand, 
so that the moon may thus be brought to any given 
day of her age in about a quarter of a minute : and 
by pushing in the handle, it takes hold of the wheel- 
work again. 

The inside O n 3^ tne ax * s f t ^ ie handle //, is an endless 

work de- screw C, which turns the wheel FED of 24 teeth 

scribed. roun( j j n 24 revolutions of the handle : this wheel 

turns another ONG, of 48 teeth, and on its axis 

Plate ix. is the pinion jPQ of four leaves, which turns the 

Tig. VIH. w heel LKI of 59 teeth round in 29^ turnings or 

rotations of the wheel FED, or in 7U8 revolu- 



The DIAL-PLATE described. 457 

tions of the handle, which is the number of hours 
in a synodical revolution of the Moon. The round 
plate with the names of places upon it is fixed on 
the axis of the wheel FED ; and the elliptical or 
tide-plate with the moon fixed to it is upon the axis 
of the wheel LK1 ' ; consequently, the former makes 
29 revolutions in the time that the latter makes 
one. The whole wheel FED* with the endless 
screw C, and dotted part of the axis of the handle 
AB) together with the dotted part of the wheel 
OA'G, lie hid below the large wheel LKI. 

Fig. IXth represents the under side of the ellip- 
tical or tide-plate ahcd, with the four small plates 
ABCD, EFGH, IKLM, JVOPQ upon it : each 
of which has two slits, as 7T, SS, RR, UU, slid- 
ing on two pins, as nn, fixed in the elliptical plate f 
In the four small plates are fixed four pins, at 7F", 
X, F, and Z; all of which work in an elliptic groove 
oooo on the cover of the box below the elliptical 
plate ; the longest axis of this groove being in a right 
line with the sun and full moon. Consequently, 
when the moon is in conjunction or opposition, 
the pins /Fand X thrust out the plates ABCD and 
IKLM a. little beyond the ends of the elliptical plate 
at d and 6, to f and e ; while the pins F and Z 
draw in the plates EFGHand NOPQ quite under 
the elliptic plate to g and h. But, when the moon 
comes to her first or third quarter, the elliptic plate 
lies across the fixed elliptic groove in which the 
pins work; and therefore the end- plates ABCD 
and IKLMwcz drawn in below the great plate, and 
the other two plates EFGH.and NOPQ are thrust 
out beyond it to a and c. When the moon is in 
her octants, the pins T 7 , X, F, Z are in the parts 
o, o, 0, o of the elliptic groove, which parts are at 3 
mean between the greatest and least distances from 
the centre ^, and then all the four small plates dis,r 
appear, being hid by the great one, 



458 The ECLIPSAREON described. 

The 405. The ECLIPSAREON. This piece of me- 

Kilo" 8 *" c h an * sm exhibits the time, quantity, duration, and 
Plate' progress of solar eclipses, at all parts of the Earth. 
X.UL r fhe principal parts of this machine are, 1. A 

terrestrial globe A, turned round its axis J3 y by the 
handle or winch M; the axis B inclines 23^ de- 
grees, and has an index which goes round the 
hour-circle D in each rotation of the globe. 2. 
A circular plate jE, on the limb of which the 
months and days of the year are inserted. This 
plate supports the globe, and gives its axis the 
same position to the Sun, or to a candle properly 
placed, that the Earth's axis has to the Sun upon 
any day of the year, 338, by turning the plate 
till the given day of the month comes to the fixed 
pointer, or annual index G. 3. A crooked wire 
F, which points toward the middle of the Earth's 
enlightened disc at all times, and shews to what 
place of the Earth the Sun is vertical at any given 
time. 4. A penumbra, or thin circular plate of 
brass /, divided into 12 digits by 12 concentric 
circles, which represent a section of the Moon's 
penumbra, and is proportioned to the size of the 
globe ; so that the shadow of this plate, formed by 
the Sun or a candle placed at a convenient distance, 
with its rays transmitted through a convex lens to 
make them fall parallel on the globe, covers exactly 
all those places upon it that the Moon's shadow 
and penumbra do on the Earth ; so that the phen- 
umena of any solar eclipse may be shewn by this 
machine with candle-light almost as well as by the 
light of the Sun. 5. An upright frame HHHH y 
on the sides of which are scales of the Moon's lati- 
tude or declination from the ecliptic. To these 
scales are fitted two sliders A" and K, with indexes 
for adjusting the penumbra's centre to the Moon's 
latitude, as it is north or south ascending or de- 
scending. 6, A solar horizon C, dividing the 



The ECLIPSAREON described. 459 

enlightened hemisphere of the globe from that 
which is in the dark at any given time, and shew- 
ing at what places the general eclipse begins and 
eiids with the rising or setting Sun. 7. A handle 
M, which turns the globe round its axis by wheel- 
work, and at the same time moves the penumbra 
across the frame by threads over the pulleys Z/, Z/, L, 
with a velocity duly proportioned to that of the 
Moon's shadow over the Earth, as the earth turns 
on its axis. And as the Moon's motion is quicker 
or slower according to her different distances from 
the Earth, the penumbral motion is easily regulated 
in the machine by changing one of the pulleys. 

To rectify the machine for use. The true time TO rectify 
of new Moon and her latitude being known by the Jt< 
foregoing precepts, 353, et seq. if her latitude 
exceed the number of minutes or divisions on the 
scales (which are on the side of the frame hid from 
view in the figure of the machine) there can be no 
eclipse of the Sun at that conjunction ; but if it do 
not, the Sun will be eclipsed to some places of the 
Earth ; and, to shew the times and various appear- 
ances of the eclipse at those places, proceed in order 
as follows. 

To rectify the machine for performing by the 
light of the Sun. 1. Move the sliders ZiT, K, till their 
indexes point to the Moon's latitude on the scales, 
as it is north or south ascending or descending, at 
that time. 2. Turn the month-plate E till the day 
of the given new Moon comes to the annual index 
G. 3 . "Unscrew the collar JV a little on the axis of 
the handle, to loosen the contiguous socket on ^ 
which the threads that move the penumbra are 
wound, and set the penumbra by hand till its 
centre comes to the perpendicular thread in the 
middle of the frame ; which thread represents the 
axis of the ecliptic. 4. Turn the handle till the 
meridian of London on the globe comes just under 
the point of the crooked wire F; then stop, and 
turn the hour-circle D by hand till XII at nooit 



460 The ECLIPSAREON described. 

Comes to its index, and set the penumbra's middle 
to the thread. 5. Turn the handle till the hour- 
index points to the time of new Moon in the circle 
I) ; and holding it there, screw last the collar A* 
Lastly, elevate the machine till the Sun shines 
through the sight-holes in the small upright plates 
O, O, on the pedestal ; and the whole machine will 
be rectified. 

To rectify the machine for shewing by candle- 
light. Proceed in every respect as above, except in 
that part of the last paragraph where the Sun is men- 
tioned ; instead of which, place a candle before the 
machine, about four yards from it, so that the 
shadow of intersection of the cross threads in the 
middle of the frame may fall precisely on that part 
of the globe to which the crooked wire F points ; 
then, with a pair of compasses, take the distance 
between the penumbra's centre and intersection of 
the threads ; and cqiuil to that distance set the can- 
dle higher or lower, as the penumbra's centre is 
above or below the said intersection. Lastly, place 
a large convex lens between the machine and candle, 
so as that the candle may be ir. the focus of the lens, 
and then the rays will fall parallel, and cast a strong 
light on the globe. 

Its use. These things being done, (and they may be done 
sooner than they can be expressed) turn the handle 
backward, until the penumbra almost touches the 
side HF of the frame ; then turning gradually for- 
ward, observe the following phenomena. 1. Where 
the eastern edge of the shadow of the penurnbral 
plate / first touches the globe at the solar horizon : 
those who inhabit the corresponding part of the 
Earth see the eclipse begin on the uppermost edge 
of the Sun, just at the time of its rising. 2. In that 
place where the penumbra's centre first touches the 
globe, the inhabitants have the Sun rising upon 
them centrally eclipsed, 3. When the whole penum- 
bra just falls upon the globe, its western edge at the 
solar horizon touches" and leaves the place where 



The ECLIPSAREON described. 461 

the eclipse ends at Sun -rise on the lowermost edge. 
Continue turning ; and, 4. the cross lines in the 
centre of the penumbra will go over all those places 
on the globe where the Sun is centrally eclipsed. 5. 
When the eastern edge of the shadow touches any 
place of the globe, the eclipse begins there ; when 
the vertical line in the penumbra comes to any place, 
then is the greatest obscuration at that place ; and 
when the western edge of the penumbra leaves the 
place, the eclipse ends there ; the times of all which 
are shewn on the hour-circle ; and from the begin- 
ning to the end, the shadows of the concentric pe- 
numbral circles shew the number of digits eclipsed 
at all the intermediate times. 6. When the eastern 
edge of the penumbra leaves the globe at the solar 
horizon C, the inhabitants see the Sun beginning to 
be eclipsed on his lowermost edge at its setting. 
7. Where the penumbra's centre leaves the globe, 
the inhabitants see the Sun set centrally eclipsed. 
And lastly, where the penumbra is wholly depart- 
ing from the globe, the inhabitants see the eclipse 
ending on the uppermost part of the Sun's edge, at 
the time of its disappearing in the horizon. 

A". B. If any given day of the year on the plate 
E be set to the annual-index 6r, and the handle 
turned till the meridian of any place comes under 
the point of the crooked wire, and then the hour- 
circle D set by the hand till XII comes to its 
index ; in turning the globe round by the handle, 
when the said place touches the eastern edge of 
the hoop or solar horizon C, the index shews the 
time of Sun- setting at that place ; and when the 
place is just coming out from below the other edge 
of the hoop C, the index shews the time when 
the evening-twilight 'ends to it. When the place 
has gone through the dark part A, and comes abcut 
so as to touch under the back of the hoop C > on 



462 7 7ze E c L i rs A R E o N described. 

the other side, the index shews the time when the 
morning- twilight begins ; and when the same place 
is just coming out from below the edge of the hoop 
next the frame, the index points out the time of 
Sun-rising. And thus, the times of the Sun's ris- 
sing and setting are shewn at all places in one rota- 
tion of the globe, for any given day of the year : and 
the point oi' the crooked wire F shews all the places 
over which the Sun passes vertically on that day. 



A PLAIN METHOD 



OF FINDING THE 



DISTANCES OF ALL THE PLANETS 
FROM THE SUN, 



BY THE 

TRANSIT OF VENUS OVER THE SUN's 
DISC, IN THE YEAR 1761. 

TO WHICH IS SUBJOINED, 

AN ACCOUNT OF MR. HORROX's OBSERVATIONS 

OF THE TRANSIT OF VENUS IN 

THE YEAR 1639: 

AND ALSO, 

F THE DISTANCES OF ALL THE PLANETS FROM THE 

SUN, AS DEDUCED FROM OBSERVATIONS OF 

THE TRANSIT IN THE YEAR 17M. 



3N 



THE METHOD 

O FINDING 

THE DISTANCES OF THE PLANETS 

FROM THE SUN. 



CHAPTER XXIIL 

ARTICLE I. 

Concerning parallaxes, and their use in general. 

r |^ HE* approaching transit of Venus over the 
jL Sun has justly engaged the attention of as- 
tronomers, as it is a phenomenon seldom seen, and 
as the parallaxes of the Sun and planets, and their 
distances from one another, may be found with 
greater accuracy by it, than by any other method 
yet known. 

2. The parallax of the Sun, Moon, or any planet, 
is the distance between its true and apparent place 
in the heavens. The true place of any celestial ob- 
ject, referred to the starry heaven, is that in which 
it would appear if seen from the centre of the Earth; 
the apparent place is that in which it appears as seen 
from the Earth's surface. 

To explain this, let AJBDHbe the Earth (Fig. T. 
of Plate XiV.)> C its centre, M the Moon, and 
Z.XR an arc of the starry heaven. To an observer 
at C (supposing the Earth to be transparent) the 
Moon M will appear at 7, which is her true place, 

* The whole of this Dissertation Was published in the beginning 
of th'. year 1761, before the time :f the transit, except the 7th 
8th articles, which are added since that time. 



466 Tlic Method of folding the Distances 

referred to the starry firmament : but at the same 
instant, to an observer at A, she will appear at Uj 
below her true place among the stars. The angle 
AMC is called the Moon's parallax, and is equal to 
the opposite angle UMu 9 whose measure is the 
celestial arc Uu. The whole earth is but a point if 
compared with its distance from the fixed stars, and 
therefore we consider the stars as having no paral- 
lax at all. 

3. The nearer the object is to the horizon, the 
greater is its parallax ; the nearer it is to the zenith, 
the less. In the horizon it is greatest of all ; in the 
zenith it is nothing. Thus \z\.AL,t be the sensible 
horizon of an observer at A ; to him the Moon at 
L is in the horizon, and her parallax is the angle 
ALC, under which the Earth's semidiameter AC 
appears as seen from her. This angle is called the 
Moon's horizontal parallax, and is equal to the op- 
posite angle TLt 9 whose measure is the arc Tt in 
the starry heaven. As the Moon rises higher and 
higher to the points M, A", 0, P, in her diurnal 
course, the parallactic angles UMu, XNx, Toy 
diminish, and so do the arcs Uu, Xx, Yy, which 
are their measures, until the Moon comes to P*j 
and then she appears in the zenith Z without any 
parallax, her place being the same whether it be seen 
from A on the Earth's surface, or from Cits centre, 

4. If the observer at A could take the true mea- 
sure or quantity of the paraliactic angle ALC, he 
might by that means find the Moon's distance from 
the centre of the Earth. For, in the plane tri- 
angle LAC r the side AC, which is the Earth's 
semidiameter, the angle ALC, which is the Moon's 
horizontal parallax, and the right angle CAL y 
would be given. Therefore, by trigonometry, as 
the tangent of the parallactic angle ALC is to ra- 
dius, so is the Earth's semidiameter AC to the 
Moon's distance CL from the Earth's centre CV 
But because we consider the Earth's semidiameter 
as unity, and the logarithm of unity is nothing, sub* 



of the Planets from the Sun. 467 

tract the logarithmic tangent of the angle ALC 
from radius, and the remainder will be the logarithm 
of CX, and its c responding number is the num- 
ber of semi- diameters of the Earth which the Moon 
is distant from the Earth's centre. Thus, suppos- 
ing the angle ALC of the Moon's horizontal paral- 
lax to be 57' 18", 

From the radius 10.0000000 

Subtract the tangent of 57' 18" 8.2219207 



And there will remain 1.7780793 

which is the logarithm of 59.99, the number of semi- 
diameters of the Earth which are equal to the Moon's 
distance from the Earth's centre. Then, 59.99 be- 
ing multiplied by 3985, the number of miles con- 
tained in the Earth's semidiameter, will give 239060 
miles for the Moon's distance from the centre of the 
Earth, by this parallax. 

5. But the true quantity of the Moon's horizon- 
tal parallax cannot be accurately determined by ob- 
serving the Moon in the horizon, on account of the 
inconstancy of the horizontal refractions, which al- 
ways vary according to the state of the atmosphere; 
and at a mean rate, elevate the Moon's apparent 
place near the horizon half as much as her parallax 
depresses it. And therefore to have her par- 
allax more accurate, astronomers have thought of 
the following method, which seems to be a very 
good one, but hath not yet been put in practice. 

Let two observers be placed under the same me- 
ridian, one in the northern hemisphere, and the 
other in the southern, at such a distance from each 
other, that the arc of the celestial meridian inclu< d 
between their two zeniths may be at least 80 or 90 
degrees. Let each observer take the distance of 
the Moon's centre from his zenith, by means of n 
exceeding good instrument, at the moment oi ;>er 
passing the meridian: add these two zenith-distan- 
ces of the Moon together, and iheir excess above the 



468 The Method of finding the Distances 

distance between the two zeniths will be the distance 
between the two apparent places of the Moon. 
Then, as the sum of the natural sines ot the two ze- 
nith-distances of the Moon is to radius, so is the 
distance between her two apparent places to her hori- 
zontal parallax :' which being found, her distance 
from the Earth's centre may be found by the anal- 
ogy mentioned in $ 4. 

Thus, in Fig. 2. let FECQ. be the Earth, Jl/the 
Moon, and Zbaz an arc of the celestial meridian. 
Let ^be Vienna, whose latitude EVi* 48 20' north ; 
and C the Cape of Good Hope, whose latitude EC 
is 34 30' south : both which latitudes we suppose 
to be accurately determined before-hand by the ob- 
servers. As these two places are on the same me- 
ridian nVECs, and in different hemispheres, the 
sum of their latitudes 82 50' is their distance from 
each other. Z is the zenith of Vienna, and z the ze- 
nithof the Cape of Good Hope ; which two zeniths 
are also 82 50' distant from each other, in the 
common celestial meridian Zz. To the observer 
at Vienna, the Moon's centre will appear at a in the 
celestial meridian ; and at the same instant, to the ob- 
server at the Cape it will appear at b. Now- sup- 
pose the Moon's distance Za from the zenith of Vi- 
enna to be 38 1' 53" ; and her distance zb from the 
zenith of the Cape of Good Hope to be 46 4' 41" : 
the sum of these two zenith-distances (Z a+zb) 
is 84 6' 34", from which subtract 82 50', the 
distance Zz between the zeniths of these two 
places, and there will remain 1 16' 34" for 
the arc ba, or distance between the two apparent 
places of the Moon's centre as seen from ^andfrom C. 
Then, supposing the tabular radius to be 10000000, 
the natural sine of 38 1' 53" (the arc ZaJ is 
6160816, and the natural sine of 46 4' 41" (the 
arc Zb) is 7202821 ; the sum of both these 
sines is 13363637. Say, therefore, As 13363637 



cf the Planets from the Sun. '469 

is to 10000000, so is 1 16' 34" to 47' 18", which 
is the Moon's horizontal parallax. 

If the two places of observation be not exactly 
under the same meridian, their difference of longi- 
tude must be accurately taken, that proper al- 
lowance may be made for the Moon's change of 
declination while she is passing from the meridian of 
the one to the meridian of the other. 

6. The Earth's diameter, as seen from the 
Moon, subtends an angle of double the Moon's 
horizontal parallax ; which being supposed (as . 
above) to be 51' 18", or 3438", the Earth's diam- 
eter must be 1 54'' 36", or 6876". When the 
Moon's horizontsl parallax (which is variable on 
account of the eccentricity of her orbit) is 57' 18", 
her diameter subtends an angle of 31' 2", or 1862" : 
therefore the Earth's diameter is to the Moon's di- 
ameter, as 6876 is to 1862 ; that is, as 3.69 is to 1. 

And since the relative bulks of spherical bodies 
are as the cubes of their diameters, the Earth's 
bulk is to the Moon's bulk, as 49.4 is to 1. 

7. The parallax, and consequently the distance 
and bulk of any primary planet, might be found 
in the above manner, if the planet were near enough 
to the Earth, to make the difference of its two ap- 
parent places sufficiently sensible : but the nearest 
planet is too remote for the accuracy required. In 
order therefore to determine the distances and rela- 
tive bulks of the planets with any tolerable degree 
of precision, we must have recourse to a method 
less liable to error : and this the approaching tran- 
sit of Venus over the Sun's disc will afford us. 

8. From the time of any inferior conjunction of 
the Sun and Venus to the next, is 583 days 22 
hours 7 minutes. And if the plane of Venus's or- 
bit were coincident with the plane of the ecliptic, 
she would pass directly between the Earth and the 
Sun at each inferior conjunction, and would then 
appear like a d**k round spot on the Sun for ah 



470 The Method of finding the Distances 

7 hours and 3 quarters. But Venus's orbit (like 
the Moon's) only intersects the ecliptic in two op- 
posite points called its nodes. And therefore one 
half of it is on the north side of the ecliptic, and 
the other on the south : on which account Venus 
can never be seen on the Sun, but at those inferior 
conjunctions which happen in or near the nodes of 
her orbit. At all the other conjunctions, she either 
passes above or below the Sun ; and her dark side 
being then toward the Earth, she is invisible. 
The last time when this planet was seen like a spot 
on the Sun, was on the 24th of November, old 
style, in the year 1639. 

ARTICLE IT. 

Shewing hoiv to find the horizontal parallax of Fc- 
nus by observation, and from thence, by analogy , 
the parallax and distance of the Sun, and of all 
the planets from him. 

9. In Fig. 4. of Plate XIV. let DBA be the 
Earth, V Venus, and TSR the eastern limb of the 
Sun. To an observer at B the point / of that limb 
will be on the meridian, its place referred to the 
heaven will be at E, and Venus will appear just 
within it at S. Bui, at the same instant, to an ob- 
server at A, Venus is east of the Sun, in the right 
line AVF ; the point t of the Sun's limb appears 
at e in the heavens, and if Venus were then visible, 
she would appear at F. The angle CVA is the hori- 
zontal parallax of Venus, which we seek ; and is 
equal to the opposite angle FVE^ whose measure is 
the arc FE. ASC is the Sun's horizontal paral- 
lax, equal to the opposite angle eSE, whose mea- 
sure is the arc eE: and FAc (the same as VAvJ is 
Venus's horizontal parallax from the Sun, which 
may be found by ob:ening how much later in ab- 
solute time her total ingress on the Sun is, as seen 
from A, than as seen from B, which is the 



of the Planets from the Sun. 471 

time she takes to move from V to v in her orbit 
OVv. 

10. It appears by the tables of Venus's motion 
and the Sun's, that at the time of her ensuing tran- 
sit, she will move 4' of a degree on the Sun's disc in 
60 minutes of time ; and therefore she will move 4" 
of a degree in one minute of time. 

Now let us suppose, that A is 90 west of B, so 
that when it is noon at B, it will be VI in the morn- 
ing at A; that the total ingress as seen from B is at 
1 minute past XII, but that as seen from A it is at 7 
minutes 30 seconds past VI : deduct 6 hours for the 
difference of meridians of A and J9, and the remain- 
der will be 6 minutes 30 seconds for the time by 
which the total ingress of Venus on the Sun at S is 
later as seen from A than as seen from B : which 
time being converted into parts of a degree is 26", 
or the arc Fe of Venus's horizontal parallax from the 
Sun : for, as 1 minute of time is to 4 seconds of a 
degree, so is 6i minutes of time to 26 seconds of a 
degree. 

11. The times in which the planets perform their 
annual revolutions about the Sun, are already known 
by observation. From these times, and the univer- 
sal power of gravity by which the planets are retained 
in their orbits, it is demonstrable, that if the Earth's 
mean distance from the Sun be divided into 100000 
equal parts, Mercury's mean distance from the Sun 
must be equal to 38710 of these parts Venus's 
mean distance from the Sun, to 72333 Mars's 
mean distance, 152369 Jupiter's 520096 and Sa- 
turn's, 954006. Therefore, when the number of 
miles contained in the mean distance of any planet 
from the Sun is known, we can, by these propor- 
tions, find the mean distance in miles of all the rest. 

12. At the time of the ensuing transit, the Earth's 
distance from the Sun will be 1015 (the mean dis- 
tance being here considered as 1000), and Venus's 
distance from the Sun will be 720 (the mean distance 

3O 



472 The Method of finding the Distance* 

_ being considered as 723), which differences from the 

" mean distances arise from the elliptical figure of the 

planets' orbits Subtract 726 parts from 1015, and 

there will remain 289 parts for Venus's distance from 

the earth at that time. 

13. Now, since the horizontal parallaxes of the 
planets are* inversely as their distances from the 
Earth's centre, it is plain, that as Venus will be be- 
tween the Earth and the Sun on the day of her tran- 
sit, and consequently her parallax will be then great- 
er than the Sun's, if her horizontal parallax can be on 
that day ascertained by observation, the Sun's hori- 
zontal parallax may be found, and consequently his 
distance from the Earth.- Thus, suppose Venus's 
horizontal parallax should be found to be 36".S480; 
then, As the Sun's distance 1015 is to Venus's dis- 
tance 289, so is Venus's horizontal parallax 36". 
3480 to the Sun's horizontal parallax 10". 3493, on the 
day of her transit. And the difference of these two 
parallaxes, viz. 25".9987 (which may be esteemed 
26") will be the quantity of Venus's horizontal paral- 
lax from the Sun ; which is one of the elements for 
prejecting or delineating her transit over the Sun's 
disc, as will appear further on. 

To find the Sun's horizontal parallax at the time 
of his mean distance from the Earth, say, As 1000 
parts, the Sun's mean distance from the Earth's 
centre, is to 1015, his distance from it on the 



* To prove this, let S be the Sun (Fig-. 3.) V Venus, AB the Earth, 
Cits centre, and AC its semidiameter. The angle AVC is the hori- 
zontal parallax of Venus, and ASCthe horizontal parallax of the Sun. 
But by the property of plane triangles, as the sine of AVC (or of SVA 
its supplement to 180) is to the .sine of AVC, so is AS to AV, and so is 
CS to CV. N. B. In all angles less than a minute of a degree, the 
sines, tangents, and arcs, are so nearly equal, that they may, without 
error be used for one another. And here we make use of Gardiner's 
logarithmic tables, because they have the sines to every fc second of a 
degree. 



of the Planets from the Sun. 

day of the transit, so is 10",3493, his horizontal 
parallax on that day, to 10". 5045, his horizontal 
parallax at the time of his mean distance from the 
Earth's centre. 

14. The Sun's parallax being thus (or any other 
way supposed to be) found, at the time of his mean 
distance from the Earth, we may find his true dis- 
tance from it in semicliameters of the Earth, by the 
following analogy. As the sine (or tangent of so 
small an arc as that) of the Sun's parallax 10". 5045 
is to radius, so is unity, or the Earth's semidiameter, 
to the number of semidiameters of the Earth that the 
Sun is distant from its centre, which number, being 
multiplied by 3985, the number of miles contained 
in the Earth's semidiameter, will give the number of 
miles which the Sun is distant from the Earth's 
centre. 

Then, by 11, As 100000, the Earth's mean dis- 
tance from the Sun in parts, is to 38710, Mercury's 
mean distance from the Sun in parts, so is the Earth's 
mean distance from the Sun in miles to Mercury's 
mean distance from the Sun in miles. And, 

As 100000 is to 72333, so is the Earth's mean 
distance from the Sun in miles to Venus's mean dis- 
tance from the Sun in miles. Likewise, 

As 100000 is to 152369, so is the Earth's mean 
distance from the Sun in miles to Mars's mean dis- 
tance from the Sun in miles. Again, 

As 100000 is to 520096, so is the Earth's mean 
distance from the Sun in miles to Jupiter's mean dis- 
tance from the Sun in miles. Lastly, 

As 100000 is to 954006, so is the Earth's mean 
distance from the Sun in miles to Saturn's mean dis- 
tance from the Sun in miles. 

And thus, by having found the distance of any 
one of the planets from the Sun, we have sufficient 
data for finding the distances of all the rest. And 
then from their apparent diameters at these known 



474 The Method of finding the Distances 

distances, their real diameters and bulks may be 
found. 

15. The Earth's diameter, as seen from the Sun, 
subtends an angle of double the Sun's horizontal 
parallax, at the time of the Earth's mean distance 
from the Sun : and the Sun's diameter, as seen from 
the Earth at that time, subtends an angle of 32' 2", 
or 1922". Therefore the Sun's diameter is to the 
Earth's diameter, as 1922 is to 21. And since the 
relative bulks of spherical bodies are as the cubes of 
their diameters, the Sun's bulk is to the Earth's bulk, 
as 756058 is to 1 ; supposing the Sun's mean hori- 
zontal parallax to be 10". 5, as above. 

16. It is plain by Fig. 4. that whether Venus be 
at If or V, or in any other part of the right line BVS> 
it will make no difference in the time of her total in- 
gress on the Sun at , as seen from 2?; but as seen 
from A it will. For, if Venus be at V, her horizon- 
tal parallax from the Sun is the arc Fe y which mea- 
sures the angle FAe : but if she be nearer the Earth, 
as at U) her horizontal parallax from the Sun is the 
arc/, which measures the angle fAe; and this angle 
is greater than the angle FAe y by the difference of 
their measures fF. So that, as the distance of the 
celestial object from the Earth is less, its parallax is 
the greater. 

17. To find the parallax of Venus by the above 
method, it is necessary, 1. That the difference of 
meridians of the two places of observation be 90. 
2. That the time of Venus's total ingress on the 
Sun be when his eastern limb is either on the me- 
ridian of one of the places, or very near it. And, 
3. That each observer have his clock exactly regu- 
lated to the equal time at his place. But as it 
might, perhaps, be difficult to find two places on 
the Earth suited to the first and second of these re- 
quisites, we shall shew how this important problem 
may be solved by a single observer, if he be exact 



of the Planets from the Sun. 475 

as to his longitude, and have his clock truly adjusted 
to the equal time at his place. 

18. That part of Venus's orbit in which she will 
move during her transit on the Sun, may be consi- 
dered as a straight line , and therefore, a plane may be 
conceived to pass both through it and the Earth's 
centre. To every place on the Earth's surface cut 
by this plane, Venus will be seen on the Sun in the 
same path that she would describe as seen from the 
Earth's centre ; and therefore she will have no pa- 
rallax of latitude, either north or south ; but will have 
a greater or less parallax of longitude, as she is more 
or less distant from the meridian, at any time during - 
her transit. 

Matura, a town and fort on the south coast of the 
island of Ceylon, will be in this plane at the time of 
Venus's total ingress on the Sun ; and the Sun will 
then be 621 east of the meridian of that place. Con- 
sequently to an observer at Matura, Venus will have 
a considerable parallax of longitude eastward from 
the Sun, when she would appear to touch the Sun's 
eastern limb as seen from the Earth's centre, at 
which the astronomical tables suppose the observer 
to be placed, and give the times as seen from thence. 

19. According to these tables, Venus's total in- 
gress on the Sun will be 50 minutes after VII in the 
morning, at Matura*, supposing that place to be 80 
east longitude from the meridian of London, which is 
the observer's business to determine. Let us ima- 
gine that he finds it to be exactly so, but that to him 
the total ingress is at VII hours 55 minutes 46 se- 
conds, which is 5 minutes 46 seconds later than the 
true calculated time of total ingress, as seen from the 
Earth's centre. Then, as Venus's motion on (or 



* The time of total ingress at London, as seen from the Earth's cen- 
tre, is at 30 minutes after II in the morning ; and if Matura be just 
80 (or 5 hours 20 minutes) east of London, when it is 30 minutes past 
II in thft morning 1 at Lendm, it is 5U minutes past VII at Matxra* 



476 The Method of finding the Distances 

toward, or from) the Sun is at the rate of 4 minutes 
of a degree in an hour (by $ 10.) her motion must be 
23". 1 of a degree in 5 minutes 46 seconds of time: 
and this 23". 1 is her parallax eastward, from her to- 
tal ingress as seen from Matura, when her ingress 
would be total if seen from the Earth's centre. 

20. At VII hours 50 minutes in the morning, the 
Sun is 62^ from the meridian ; at VI in the morn- 
ing he is 90 from it : therefore, as the sine of 62| 
is to the sine of 23". 1 (which is Venus's parallax 
from her .true place on the Sun at VII hours 50 mi- 
nutes), so is radius or the sine of 90, to the sine of 
26", which is Venus's horizontal parallax from the 
Sun at VI. In logarithms thus : 

As the logarithmic sine of 62<> 30' - - - 9.9479289 
Is to the logarithmic sine of 23".l - - - 6.0481510 
So is the logarithmic radius - - - 10.0000000 



To the logarithmic sine of 26" very nearly - 6.1002221 

Divide the Sun's distance from the Earth, 1015, 
by his distance from Venus 726 (5 12.) and the quo- 
tient will be 1.3980; which being multiplied by 
Venus's horizontal parallax from the Sun 26", will 
give 36". 3480, for her horizontal parallax as seen 
from the Earth at that time. Then (by 13.) as the 
Sun's distance, 1015, is to Venus's distance 289, so 
is Venus's horizontal parallax 36". 3480 to the Sun's 
horizontal parallax 10". 3493. If Venus's horizontal 
parallax from the Sun be found by observation to ba 
greater or less than 26", the Sun's horizontal parallax 
must be greater or less than 10".3493 accordingly. 

21. And thus, by a single observation, the parallax 
of Venus, and consequently the parallax of the Sun, 
might be found, if we were sure that the astronomi- 
cal tables were quite correct as to the time of Venus's 
total ingress on the Sun. But although the tables 
may be safely depended upon for shewing the true 



of the Planets from the Sun. 

duration of the transit, which will not be quite 6 hours 
from the time of Venus's total ingress on the Sun's 
eastern limb, to the beginning of her egress from his 
western ; yet they may perhaps not give the true 
times of these two internal contacts : like a good 
common clock, which, though it may be trusted to 
for measuring a few hours of time, yet perhaps it may 
not be quite adjusted to the meridian of the place, 
and consequently not true as to any one hour ; which 
every one knows is generally the case. Therefore, to 
make sure work, the observer ought to watch both 
the moment of Venus's total ingress on the Sun, 
and her beginning of egress from him, so as to note 
precisely the times between these two instants, by 
means of a good clock : and by comparing the inter- 
val at his place with the true calculated interval as 
seen from the Earth's centre, which will be 5 hours 
58 minutes, he may find the parallax of Venus from 
the Sun both at her total ingress and beginning of 
egress. 

22. The manner of observing the transit should be 
as follows : The observer being provided with a 
good telescope, and a pendulum-clock well adjusted 
to the mean diurnal revolution of the Sun, and as 
near to the time at his place as conveniently may be; 
and having an assistant to watch the clock at the 
proper times, he must begin to observe the Sun's 
eastern limb through his telescope, twenty minutes 
at least before the computed time of Venus's total in- 
gress upon it, lest there should be an error in the 
time of the beginning as given by the tables. 

When he perceives a dent (as it were) to be made 
in the Sun's limb, by the interposition of the dark 
body of Venus, he must then continue to watch her 
through the telescope as the dent increases ; and his 
assistant must watch the time shewn by the clock, 
till the whole body of the planet appears just within 
the Sun's limb : and the moment when the bright 
limb of the Sun appears close by the east side of the 



The Method of finding the Distances 

dark limb of the planet, the observer, having a little 
hammer in his hand, is to strike a blow therewith on 
the table or wall ; the moment of which, the assist- 
ant notes by the clock, and writes it down. 

Then, let the planet pass on for about 2 hours 59 
minutes, in which time it will be got to the middle of 
its apparent path on tire Sun, and consequently will 
then be at its least apparent distance from the Sun's 
centre ; at which time, the observer must take its dis- 
tance from the Sun's centre by means of a good mi- 
crometer, in order to ascertain its true latitude or de- 
clination from the ecliptic, and thereby find the places 
of its nodes. 

This done, there is but little occasion to observe 
it any longer, until it comes so near the Sun's western 
limb, as almost to touch it. Then the observer must 
watch the planet carefully with his telescope. : and his 
assistant must watch the clock, so as to note the 
precise moment of the planet's touching the Sun's 
limb, which the assistant knows by the observer strik- 
ing a blow with his hammer. 

23. The assistant must be very careful in observing 
what minute on the dial-plate the minute-hand has past, 
when he has observed the second-hand at the instant 
the blow was struck by the hammer; otherwise, though 
he be tight as to the number of seconds of the current 
minute, he may be liable to make a mistake in the num- 
ber of minutes. 

24. To those places where the transit begins before 
XII at noon, and ends after it, Venus will have an 
eastern parallax from the Sun at the beginning, and 
a western parallax from the Sun at the end ; which 
will contract the duration of the transit, by caus- 
ing it to begin later and end sooner, at these places, 
than it does as seen from the Earth's centre ; which may- 
be explained in the following manner. 



of the Planets from the Sun. 479 

In Fig. 5. of Plate XIV let BMA be the Earth, 
V Venus, and S the Sun. The Earth's motion on 
its axis from west to east, or in the direction 
A MB, carries an observer on that side contrary 
to the motion of Venus in her orbit, which is in 
the direction UVW; and will therefore cause her 
motion to appear quicker on the Sun's disc, than 
it would appear to an observer placed at the Earth's 
centre C, or at either of its poles. For, if Venus 
were to stand still in her orbit at V for twelve hours, 
the observer on the Earth's surface would in that 
time be carried from A to B, through the arc AMB* 
When he was at A, he would see Venus on the Sun 
at R; when at M, he would see her at S; and when 
he was at B, he would see her at T: so that his own 
motion would cause the planet to appear in motion on 
the Sun through the line RST; which being in the 
direction of her apparent motion on the Sun as she 
moves in her orbit UJV, her motion will be accele* 
rated on the Sun to this observer, just as much as his 
own motion would shift her apparent place on the 
Sun, if she were at rest in her orbit at V. 

But as the whole duration of the transit, from first 
to last internal contact, will not be quite six hours; 
an observer, who has the Sun on his meridian at the 
middle of the transit, will be carried only from a to b 
during the whole time thereof. And therefore, the 
duration will be much less contracted by his own 
motion, than if the planet were to be twelve hours in 
passing over the Sun, as seen from the Earth's 
centre. 

25. The nearer Venus is to the Earth, the greater 
is her parallax, and the more will the true duration of 
her transit be contracted thereby ; the farther she is 
from the Earth, the contrary : so that the contraction 
will be in direct proportion to the parallax. There- 
fore, by observing, at proper places, how much the 
duration of the transit is less than its true duration at 
the Earth's centre, where it is 5 hours 58 minutes, 

3P 



180 The Method of finding the Distances 

as given by the astronomical tables, the parallax of 
Venus will be ascertained. 

26. The above method ( 17, Of seq.} is much 
the same as was prescribed long ago by Doctor Hal- 
ley ; but the calculations differ considerably from his ; 
as will appear in the next article, which contains a 
translation of the Doctor's whole dissertation on that 
subject. He had not computed his own tables when he 
wrote it, nor had he time before -hand to make a suffi- 
cient number of observations on the motion of Venus, 
so as to determine whether the nodes of her orbit are 
at rest or not ; and w r as therefore obliged to trust to 
other tables, which are now found to be erroneous. 

ARTICLE III. 

Containing Doctor HAL LEY'S Dissertation on the 
method of finding the Sun^s parallax and distance 
from the Earth, .by the transit of Venus over the 
Sun's disc, June the 6th, 1761. Translated from 
the Latin in Mottee's Abridgment of the Philoso- 
phical Transactions, Vol. I. page 243 ; with addi- 
tional notes. 

There are many things exceedingly paradoxical, 
and that seem quite incredible to the illiterate, which 
yet by means or mathematical principles may be easily 
solved. Scarce any problem will appear more hard 
and difficult, than that of determining the distance of 
the Sun from the Earth very near the truth : but even 
this, when we are made acquainted with some exact 
observations, taken at places iixed upon, and chosen 
before-hand, will without much labour be effected. 
And this is what I am now desirous to lay before this 
illustrious Society* (which I foretel will continue for 
ages), that I may explain before-hand to young astro- 
nomers, who may perhaps live to observe these things, 

* The Royal Society. 



of the Planets from the Sun. 481 

a method by which the immense distance of the Sun 
may be truly obtained, to within a five-hundredth part 
of what it really is. 

It is well known that the distance of the Sun from 
the Earth is by different astronomers supposed diffe- 
rent, according to what was judged most probable 
from the best conjecture that each could form. Pto- 
lemy and his followers, as also Copernicus and Tycho 
.Brake, thought it to be 1200 semidiameters of the 
Eanh; Kepler, 3500 nearly: Ricciolus doubles the 
distance mentioned by Kepler ; and Hevelius only in- 
creases it by one half. But the planets Venus and 
Mercury having, by the assistance of the telescope, 
been seen on the disc of the Sun, deprived of their 
borrowed brightness, it is at length found that the ap- . 
parent diameters of the planets are much less than they 
were formerly supposed ; and that the semidiameter of 
Venus seen from the Sun subtends an angle of no more 
than a fourth part of a minute, or 15 seconds, while the 
semidiameter of Mercury, at its mean distance from 
the Sun, is seen under an angle only of ten seconds ; 
that the semidiameter of Saturn seen from the Sun 
appears under the same angle ; and that the semidia- 
meter of Jupiter, the largest of all the planets, sub- 
tends an angle of no more than a third part of a minute 
at the Sun. Whence, keeping the proportion, some 
modern astronomers have thought, that the semidia- 
meter of the Earth, seen from the Sun, would sub- 
tend a mean angle between that larger one subtended 
by Jupiter, and that smaller one subtended by Saturn 
and Mercury ; and equal to that subtended by Venus 
(namely, fifteen seconds) : and have thence concluded, 
that the Sun is distant from the Karth almost 14000 
of the Earth's semidiameters. But the same authors 
have on another account somewhat increased this 
distance: for inasmuch as the Moon's diameter is 
a little more than a fourth part of the diameter of 
the Earth, if the Sun's parallax should be supposed 



The Method of finding the Distances 

fifteen seconds, it would follow that the body of the 
Moon is larger than that of Mercury ; that is, that a 
secondary planet would be greater than a primary ; 
which would seem inconsistent with the uniformity of 
the mundane system. And on the contrary, the same 
regularity and uniformity seems scarcely to admit that 
Venus, an inferior planet, that has no satellite, should 
be greater than our Earth, which stands higher in the 
system, and has such a splendid attendant. There- 
fore, to observe a mean, let us suppose the semidia- 
meter of the Earth seen from the Sun, or, which is the 
same thing, the Sun's horizontal parallax, to be twelve 
seconds and a half; according to which, the Moon 
\ will be less than Mercury, and the Earth larger than 
Venus ; and the Sun's distance from the Earth will 
come out nearly 16, 500 of the Earth's semidiameters. 
This distance I assent to at present, as the true one, 
till it shall become certain what it is, by the experi- 
ment which I propose. Nor am I induced to alter 
my opinion by the authority of those (however weighty 
it may be) who are for placing the Sun at an immense 
distance beyond the bounds here assigned, relying on 
observations made upon the vibrations of a pendulum, 
in order to determine those exceeding small angles ; 
but which, as it seems, are not sufficient to be depend- 
ed upon ; at least, by this method of investigating the 
parallax, it will sometimes come out nothing, or even 
negative ; that is, the distance would either become 
infinite, or greater than infinite ; which is absurd. And 
indeed, to confess the truth, it is hardly possible for a 
man to distinguish, with any degree of certainty, se- 
conds, or even ten seconds, with instruments, let them 
be ever so skilfully made : therefore, it is not at all to 
be wondered at, that the excessive nicety of this mat- 
ter has eluded the many and ingenious endeavours of 
such skilful operators. 

About forty years ago, while I was in the island 
of St. Helena^ observing the stars about the south 



of the Planets from the Sun. 

pole, I had an opportunity of observing, with the great- 
est diligence, Mercury passing over the disc of the 
Sun ; and (which succeeded better than 1 could have 
hoped for) I observed, with the greatest degree of ac- 
curacy, by means of a telescope 24 feet long, the very 
moment when Mercury entering upon the Sun seemed 
to touch its limb within, and also the moment when 
going off it struck the limb of the Sun's disc, form- 
ing the angle of interior contact : whence I found the 
interval of time, during which Mercury then appeared 
within the Sun's disc, even without an error of one 
second of time. For the lucid line intercepted between 
the dark limb of the planet and the bright limb of the 
Sun, although exceeding fine, is seen 'by the eye ; and 
the little dent made in the Sun's limb, by Mercury's 
entering the disc, appears to vanish in a moment ; and 
also that made by Mercury, when leaving the disc, 
seems to begin in an instant. When I perceived this, 
it immediately came into my mind, that the Sun's 
parallax might be accurately determined by such kind 
of observations as these ; provided Mercury were but 
nearer to the Earth, and had a greater parallax from 
the Sun ; but the difference of these parallaxes is so 
little, as always to be less than the solar parallax which 
we see ; and therefore Mercury, though frequently to 
be seen on the .Sun, is not to be looked upon as lit 
for our purpose. 

There remains then the transit of Venus over the 
Sun's disc ; whose parallax, being almost four times as 
great as the solar parallax, will cause very sensible dif- 
ferences between the times in which Venus will seem 
to be passing over the Sun at different parts of the 
Earth. And from these differences, if they be observ- 
ed as they ought, the Sun's parallax may be deter- 
mined even to a small part of a second. Nor do we 
require any other instruments for this purpose, than 
common telescopes and clocks, only good of their 
kind : and in the observers, nothing more is needful 



434 The Method of finding the Distances 

than fidelity, diligence, and a moderate skill in astrono- 
my. For there is no need that the latitude of the place 
should be scrupulously observed, nor that the hours 
themselves should be accurately determined with re- 
spect to the meridian : it is sufficient that the clocks 
IDC regulated according to the motion of the heavens, 
if the times be well reckoned from the total ingress of 
Venus into the Sun's disc, to the beginning of her 
egress from it ; that is, when the dark globe of Venus 
first begins to touch the bright limb of the Sun with- 
in ; which moments, I know, by my own experience, 
may be observed within a second of time. 

But on account of the very strict laws by which the 
motions of the planets are regulated, Venus is seldom 
seen within the Sun's disc ; and during the course of 
more than 120 years, it could not be seen once ; 
namely, from the year 1639 (when this most pleasing 
sight happened to that excellent youth, fforrox, our 
countryman, and to him only, since the creation) to 
the year 1761 ; in which year, according to the theo- 
ries which we have hitherto found agreeable to the 
celestial motions, Venus will again pass over the Sun 
on the* 26th of May, in the morning; so that at Lon- 
don, about six o'clock in the morning, we may expect 
to see it near the middle of the Sun's disc, and not 
above four minutes of a degree south of the Sun's 
centre. But the duration of this transit will be almost 
eight hours ; namely, fmrfi two o'clock in the morn- 
ing till almost ten. Hence the ingress will not be 
visible in England; but as the Sun will at that 
time be in the 16th degree of Gemini, having almost 
23 degrees north declination, it will be seen without 
setting at all in almost all parts of the north frigid 
zone : and therefore the inhabitants of the coast of 
Norway, beyond the city of Nidrosia, which is called 
Dronthdm, as far as the North Cape, will be able to 
observe Venus entering the Sun's disc ; and perhaps 

* The sixth of June, according to the new style. 



of the Planets from the Sun. 485 

the ingress of Venus upon the Sun, when rising, will 
be seen by the Scotch, in the northern parts of the 
kingdom, and by the inhabitants of the Shetland hies -, 
formerly called Thule. But at the time when Venus 
will be nearest the Sun's centre, the Sun will be ver- 
tical to the northern shores of the bay of Bengal* or 
rather over the kingdom tfPcgu; and therefore in the 
adjacent regions, as the Sun, when Venus enters his 
disc, will be almost four hours towards the east, and 
as many toward the west when she leaves him, the 
apparent motion of Venus on the Sun will be accele- 
rated by almost double the horizontal parallax of 
Venus from the Sun ; because Venus at that time is 
carried with a retrograde motion from east to west, 
while an eye placed upon the Earth's surface is whirl- 
ed the contrary way, from west to east*. 



* This has been already taken notice of in 24 ; but I shall here en- 
deavour to explain it more at large, together with some of the follow- 
ing part of the Doctor's Essay, by a figure. 

In Fig. 1. of Plate XV let Cbe the centre of the Earth, and Z the 
centre of the Sun. In the right line CvZ, make vZ to CZ as 726 is to 
1015 ( 12). Let acbdbe the Earth, v Venus's place in her orbit at the 
time of her conjunction with the Sun ; and let TSUbz the Sun, whose 
diameter is 31' 42". 

The motion of Venus in her orbit is in the direction Nvn, and the 
Earth's motion on its axis is according to the order of the 24 hours 
placed around it in the figure. Therefore, supposing the mouth of the 
Ganges to be at G, when Venus is at E in her orbit, and to be carried 
from G to by the Earth's motion on its axis, while Venus moves from 
JE to e in her orbit ; it is plain that the motions of Venus and the Ganges 
are contrary to each other. 

The true motion of Venus in her orbit, and consequently the space 
she seems to run over on the Sun's disc in any given time, could be 
seen only from the Earth's centre C, which is at rest with respect to 
its surface. And as seen from C, her path on the Sun would be in the 
right line TtU ; and her motion therein at the rate of four minutes of a 
degree in an hour. T is the point of the Sun's eastern limb which 
Venus seems to touch at the moment of her total ingress on the Sun, 
as seen from Cj when Venus is at E in her orbit; and U is the point of 
the Sun's western limb which she seems to touch at the moment of her 
beginning of egress from the Sun, as seen from C, when she is at c in 
ber orbit. 



486 The Method of finding the Distances 

Supposing the Sun's parallax (as we have said) 
to be 12-1", the parallax of Venus will be 43"; 
from which subtracting the parallax of the Sun, 
there will remain 30" at least for the horizontal 
parallax of Venus from the Sun ; and therefore the 
motion of Venus will be increased 45" at least by 
that parallax, while she passes over the Sun's disc, 
in those elevations of the pole which are in places 
near the tropic, and yet more in the neighbour- 
hood of the equator. Now Venus at that time 
will *move on the sun's disc, very nearly at the 
rate of four minutes of a degree in an hour ; and 
therefore 11 minutes of time at least are to be 
allowed for 45", or three fourths of a minute of 



When the mouth of the Ganges is at m (in revolving through the 
arc Gmg) the Sun is on its meridian. Therefore, since G and g are 
equally distant from m at the beginning and ending of the transit, it is 
plain that the Sun will be as far east of the meridian of the Ganges 
(at G) when the transit begins, as it will be west of the meridian of 
the same place (revolving from G to ) when the transit ends. 

But although the beginning of the transit, or rather the moment of 
Venus's total ingress upon the Sun at T, as seen from the Earth's 
centre, must be when Venus is at.E in her orbit, because she is then 
seen in the direction of the right line GET,- yet at the same instant of 
time, as seen from the Ganges at G, she will be short of her ingress on 
the Sun, being then seen eastward of him, in the right line GEK t 
which makes the angle KET (equal to the opposite angle GEC), with 
the right line GET. This angle is called the angle of Venus's parallax 
from the Sun, which retards the beginning of the transit as seen from 
the banks of the Ganges ; so that the Ganges G, must advance a little 
farther toward m, and Venus must move on in her orbit from E to R, 
before she can be seen from G (in the right line GRT) wholly within 
the Sun's disc at T. 

When Venus comes to e in her orbit, she will appear at U, 
as seen from the Earth's centre C, just beginning to leave the 
Sun; that is, at the beginning of her egress from his western 
limb: but at the same instant of time, as seen from the Ganges, 
which is then at g, she will be quite clear of the Sun toward 
the west; being then seen from g in the right line geL, which 
makes an angle, as UeL (equal to the opposite angle Ceg), 
with the right line CeU : and this is the angle of Venus's 



of the Planets from the Sun. 487 

a degree ; and by this space of time, the duration 
of this eclipse caused by Venus will, on account 
of the parallax, be shortened. And from this 
shortening of the time only, we might safely enough 
draw a conclusion concerning the parallax which 
we are in search of, provided the diameter of the 
Sun, and the latitude of Venus, were accurately 
known. But we cannot expect an exact computa- 
tion in a matter of such subtilty. 

We must endeavour therefore to obtain, if pos- 
sible, another observation, to be taken in those 
places where Venus will be in the middle of the 
Sun's disc at midnight; that is, in places under 
the opposite meridian to the former, or about 6 
hours or 90 degrees west of London ; and where 
Venus enters upon the Sun a little before its set- 



parallax from the Sun, as seen from the Ganges at $, when she 5s 
but just beginning to leave the Sun at {/, as seen from the Earth's 
centre C. 

Here it is plain, that the duration of the transit about the mouth 
of the Ganges (and also in the neighbouring places) will be dimi- 
nished by about double the quantity of Vemis's parallax from the 
Sun at the beginning and ending of the transit. For Venus must be 
at E in her orbit when she is wholly upon the Sun at T, as seen 
from the Earth's centre C: but at that time she is short of the Sun, 
as seen from the Ganges at G, by the whole quantity of her eastern 
parallax from the Sun at that time, which is the angle KET. [This 
angle, in fact, is only 23" ; though it is represented much larger in 
the figure, because the Earth therein is a vast deal too big.] Now, 
as Venus moves at the rate of 4' in an hour, she will move 23" in 5 
minutes 45 seconds : and therefore, the transit will begin later by 5 
minutes 45 seconds at the banks of the Ganges than at the Earth's 
centre. When the transit is ending at 7, as seen from the Earth's 
centre at C, Venus will be quite clear of the Sun (by the whole 
quantity of her western parallax from him) as seen from the Ganges, 
which is then at g : and this parallax will be 22", equal to the space 
through which Venus moves in 5 minutes 30 seconds of time : so 
that the transit will end 5.| minutes sooner as seen from the Ganges^ 
than as seen from the Earth's centre. 

Here the whole contraction of the duration of the transit at the 
mouth of the Ganges will be 31 minutes 15 seconds of time: for it 
is 5 minutes 45 seconds at the beginning, and 5 minutes 30 seconds 
at the end. 

SO. 



468 The Method of finding the Distances 

ting, and goes off a. little after its rising. And 
this will 'happen under the above-mentioned meri- 
dian, and where the elevation of the north pole is 
about 56 degrees; that is, in a part of Hudson's 
Bay, near a place called Port-Nelson. For, in this 
and the adjacent places, the parallax of Venus will 
increase ths duration of the transit by at least six 
minutes of time; because, while the Sun, from 
its setting to its rising, seems to pass under the pole, 
those places on the Earth's disc will be carried with 
a motion from east to west, contrary to the motion 
of the Ganges ; that is, with a motion conspiring 
with the motion of Venus ; and therefore Venus 
will seem to move more slowly on the Sun, and to 
be longer in passing over his disc.* 



* In Fig. I. of Plate XV. let aCbe the meridian of the eastern 
mouth of the Ganges; and AC" ;he meridian of Port-Nelson at the 
mouth of York River in Hudson's Bay, 56 north latitude. As 
the meridian of the Ganges revolves from a to c, the meridian of 
Port-Nelson will revolve from b to d; therefore, while the Ganges 
revolves from G to g, through the arc G?ng, Port-Nelson revolves 
the contrary way (as seen from the Sun or Venus) from P to fi 

through the arcjptt/?. Now, as the motion of Venus is from 

to e in her orbit, while she seems to pass over the Sun's disc in the 
right line TtU, as seen from the Earth's centre C, it is plain that 
tv Idle the motion of the Ganges is contrary to the motion of Venus 
in her orbit, and thereby shortens the duration of the transit at that 
place, the motion of Port-Ntlson is the same way as the motion of 
Venus, and will therefore increase the duration cf the transit : 
which may in some degree be illustrated by supposing, that while 
a ship is under sail, if two birds fly i.long the bide of the ship in con- 
trary directions to each other, the bird which flies contrary to the 
motion of the ship will pass by it sooner than the bird will, which 
flies the same way that the ship moves. 

In fine, it is plain by the figure, that the duration of the transit 
must be longer as seen from Port-Nelson, th^n as seen from the 
Earth's centre ; and longer as seen tr< :-m the Earth's centre, than 

as seen from the mouth of the Ganges F< r Port-Ntlaon must 

be at P, and Venus at A* in her orbit, wh>n she Appears wholly with- 
in the Sun at T: and the san;e place must be at/2, and Venus at n, 
when she appears at U beginning to leave the Sun. The Ganges 
must ue at G, and Venus at R, when she is seen from G upon 



of the Planets from the Sun. 489 

If therefore it should happen that this transit 
should be properly observed by skilful persons at 
boih these places, it is clear, that its duration 
will be 17 minutes longer, as seen from Port- 
Nelson, than as seen from the East -Indies. Nor is 
it oi much consequence (if the English shall at that 
time give any attention to this affair) whether the 
observation be made at Fort-George, commonly 
called Madras, or at Bencoolen on the western shore 
of the island of Sumatra, near the equator. But 
if the French should be disposed to take any pains 
herein, an observer may station himself convenient- 
ly enough at Pondicherry on the \vest shore of the 
bay oi Bengal, where the altitude of the pole is 
about 12 degrees. As to the Dittch, their cele- 
brated mart at Batavia will afford them a place of 
observation fit enough for this purpose, provided 
they also have but a disposition to assist in advanc- 
ing, in this particular, the knowledge of the hea- 
vens.- And indeed I could wish that many obser- 
vations of the same phenomenon might be taken by 
different persons at several places, both that we 
might arrive at a greater degree of certainty by 
their agreement, and also lest any single observer 
should be deprived, by the intervention of clouds, 
of a sight, which I know not whether any man liv- 
ing in this or the next age will ever see again ; and 
on which depends the certain and adequate solution 
of a problem the most noble, and at any other time 
not to be attained to. I recommend it, therefore, 
again and again, to those curious astronomers, 
who (when I am dead) will have an opportunity 
of observing these things, that they would remem- 

the Sun at T; and the same place must be at , and Venus at r, 
when she begins to leave the Sun at (7, as seen from g. So that 
Venus must move from JV to n in her orbit, while she is seen to pass 
over the Sun from Port-Nelson ; from E to e in passing over the 
Sun, as seen from the Earth's centre ; and only from R to r while 
she passes over the Sun, as seen from the banks of the Ganges. 



49t The Method of finding the Distances 

her this my admonition, and diligently apply them- 
selves with all their might to the making of this ob- 
servation ; and I earnestly wish them all imaginable 
success ; in the first place, that they may not, by 
the unseasonable obscurity of a cloudy sky, be de- 
prived of this most desirable sight ; and then, that 
having ascertained with more exactness the magni- 
tudes of the planetary orbits, it may redound to their 
immortal fame and glory. 

We have now shewn, that by this method the 
Sun's parallax may be investigated to within its 
five -hundredth part, which doubtless will appear 
wonderful to some. But if an accurate observation 
be made in each of the places above marked out, 
\ve have already demonstrated that the durations of 
this eclipse made by Venus will diifer from each 
other by 17 minutes of time; that is, upon a sup- 
position that the Sun's parallax is 12?". But if 
the difference shall be found by observation to be 
greater or less, the Sun's parallax will be greater 
or less, nearly in the same proportion. And since 
17 minutes of time are answerable to 12 seconds 
of solar parallax, for every second of parallax there 
will arise a difference of more than 80 seconds of 
time ; whence, if we have this difference true to 
two seconds, it will be certain what the Sun's pa- 
rallax is to within a 40th part of one second; and 
therefore his distance will be determined to within 
its 500dth part at least, if the parallax be not found 
less than what we have supposed : for 40 times 12$ 
make 500. 

And now I think I have explained this matter 
fully, and even more than I needed to have done, 
to those who understand astronomy ; and I would 
have them take notice, that on this occasion, I 
have had no regard to the latitude of Venus, both 
to avoid the inconvenience of a more intricate cal- 
culation, which would render the conclusion less 
evident ; and also because the motion of the nodes 



of the Planets from the Sun. 491 

of Venus is not yet discovered, nor can be deter- 
mined but by such conjunctions of the planet with 
the Sun as this is. For we conclude that Venus 
will pass 4 minutes below the Sun's centre, only 
in consequence of the supposition that the plane 
of Venus 's orbit is immoveable in the sphere of 
the fixed stars, and that its nodes remain in the 
same places where they were found in the year 
1639. But if Venus in the year 1761, should 
move over the Sun in a path more to the south, 
it will be manifest that her nodes have moved back- 
ward among the fixed stars ; and if more to the 
north, that they have moved forward ; and that at 
the rate of 5-J minutes of a degree in 100 Julian 
years, for every minute that Venus's path shall be 
more or less distant than the above-said 4 minutes 
from the Sun's centre. And the difference be- 
tween the duration of these eclipses will be some^ 
what less than 17 minutes of time, on account of 
Venus's south latitude ; but greater, if by the mo- 
tion of the nodes forward she should pass on the 
north of the Sun's centre. 

But for the sake of those who, though they are 
delighted with sidereal observations, may not yet 
have made themselves acquainted with the doctrine 
of parallaxes, I choose to explain the thing a little 
more fully by a scheme, and also by a calculation 
somewhat more accurate. 

Let us suppose that at London, in the year 1761, 
on the 6th of June, at 55 minutos after V in the 
morning, the Sun will be in Gemini 15 .37', and 
therefore that at its centre the ecliptic is inclined 
toward the north, in an angle of 6 10' ; and that 
the visible path of Venus on the Sun's disc at that 
time declines to the south, making an angle with 
the ecliptic of 8 28' : then the path of Venus will 
also be inclined to the south, with respect to the 
equator, intersecting the parallels of declination at 



492 The Method of finding the Distances 

an angle of 2 18'*, Let us also suppose, that Ve- 
nus, at the fore mentioned time, ^ ill be at her least 
distance from the Sun's centre, viz. only four mi- 
nutes to the south ; and that every hour she will 
describe a space of 4 minutes on the Sun, with a 
retrograde motion. The Sun's semidiameter will 
be 15' 51" nearly, and that of Venus 37|". And 
let us suppose, for trial's sake, that the difference of 
the horizontal parallaxes of Venus with the Sun 
(which we want) is 31", such as it comes out if the 
Sun's parallax be supposed 12i". Then, on the 
centre C( Plate XV Fig. 2.) let the little circle AB, 
representing the Earth's disc, be described, and let 
his semidiameter CB be 31"; and let the ecliptic 
parallels of 22 and 56 degrees of north latitude (for 
the Ganges and Port-kelson] be drawn within it, in 
the manner now used by Astronomers for construct- 
ing solar eclipses. Let BCg be the meridian in 
which the Sun is, and to this, let the right line FHG 
representing the path of Venus be inclined at an an- 
gle of 2 18' ; and let it be distant from the centre 
C240 such parts, whereof CB is 31. From Clet 
fall the right line CH> perpendicular to FG ; and 
suppose Venus to be at H at 55 minutes after V in 
the morning. Let the right line FHG be divided 
into the horary space III IV, IV V, V VI, &c. each 
equal to CH; that is, to 4 minutes of a degree. 
Also, let the right line LM be equal to the diffe- 

* This was an oversight in the Doctor, occasioned by his placing 
both the Earth's axis BCg (Fig. 2. of Plate XV.) and the axis of 
Venus's orbit C7/on the same side of the axis of the ecliptic CK; 
the former making an angle of 6 e 10' therewith, and the latter an 
angle of 8 g 28'; the difference of which angles is only 2 18'. But 
the truth is, that the Earth's axis, and the axis of Venus's orbit, will 
then lie on different sides of the axis of the ecliptic, the former mak- 
ing an angle of 6 therewith, and the latter an angle of 8 1. There- 
fore, the sum of these angles, which is 141 (and not their "difference 
2** 18'), is the inclination of Venus's 2 visible path to the equator 
and parallels of declination. 



of the Planets from the San. 493 

rence of the apparent semidiametcrs of the Sun and 
Venus, which is 15' 13i"; and a circle being de- 
scribed with the radius LM, on a centre taken in 
any point within the little circle AB representing the 
Earth's disc, will meet the right line FG in a point 
denoting the time at London when Venus shall touch 
the Sun's limb internally, as seen from the place of 
the Earth's surface that answers to the point assum- 
ed in the Earth's disc. And if a circle be describ- 
ed on the centre C, with the radius LM, it will meet 
the right line FG> in the points F and G ; and the,- 
spaces FH and GH will be each equal to 14' 4", 
which space Venus will appear to pass over in 3 
hours 40 minutes of time at London ; therefore F 
will fall in II hours 15 minutes, and G in IX hours 
35 minutes in the morning. Whence it is manifest 
that if the magnitude of the Earth, on account of its 
immense distance, should vanish as it were into a 
point ; or if, being deprived of a diurnal motion, it 
should always have the Sun vertical to the same 
point C; the whole duration of this eclipse would 
be 7 hours 20 minutes. But the Earth in that time 
being whirled through 1 10 degrees of longitude, with 
a motion contrary to the motion of Venus, and con- 
sequently the abovementioned duration being con- 
tracted, suppose 12 minutes, it will come out 7 
hours 8 minutes, or 107 degrees nearly. 

Now Venus will be at //, at her least distance 
from the Sun's centre, when in the meridian of the 
eastern mouth of the Ganges, where the altitude of 
the pole is about 22 degrees. The Sun therefore 
w ill be equally distant from the meridian of that 
place, at the moments of the ingress and egress of 
the planet, viz. 53 *. degrees ; as the points a and b 
(representing that place in the Earth's disc AB) are, 
in the greater parallel, from the meridian BCg. But 
the diameter efof that parallel will be to the distance 
ab, as the square of the radius to the rectangle under 
the sines of 53 J and 68 degrees; that is, of 1' 2" fc 



494 The Method of finding the Distances 

46" 13'". And by a good calculation (which, that 
I may not tire the reader, it is better to omit) I find 
that a circle described on a as a centre, with the ra- 
dius LM, will meet the right line FH'm the point 
M, at II hours 20 minutes 40 seconds; but that be- 
ing described round b as a centre, it will meet HG 
in the point A' at IX hours 29 minutes 22 seconds, 
according to the time reckoned at London: and 
therefore, Venus will be seen entirely within the Sun 
at the banks of the Ganges for 7 hours 8 minutes 
42 seconds : we have then rightly supposed that the 
duration will be 7 hours 8 minutes, since the part of 
a minute here is of no consequence. 

But adapting the calculation to Port-Nelson, I 
find, that the Sun being about to set, Venus will 
enter his disc ; and immediately after his rising she 
will leave the same. That place is carried in the 
intermediate time through the hemisphere opposite 
to the Sun, from c to d, with a motion conspiring 
with the motion of Venus ; and therefore, the stay 
of Venus on the Sun will be about 4 minutes 
longer, on account of the parallax ; so that it will 
be at least 7 hours 24 minutes, or 111 degrees of 
the equator. And since the latitude of the place 
is 56 degrees, as the square of the radius is to the 
rectangle contained under the sines 55 and 34 
degrees, so is AB, which is 1' 2", to cd, which is 
28" 33'". And if the calculation be justly made, 
it will appear that a circle described on c as a cen- 
tre, with the radius LM> will meet the right line 
FH'm O at II hours 12 minutes 45 seconds; and 
that such a circle described on d as a centre, 
will meet HG in P, at IX hours 36 minutes 37 
seconds ; and therefore the duration at Port -Nelson 
will be 7 hours 23 minutes 52 seconds, which is 
greater than at the mouth of the Ganges by 15 
minutes 10 seconds of time. But if Venus should 
pass over the Sun without having any latitude, the 
difference would be 18 minutes 40 seconds; and 



of the Planets from the Sun. 495 

if she should pass 4' north of the Sun's centre, the 
difference would amount to 21 minutes 40 seconds, 
and will be still greater, if the planet's north latitude 
be more increased. 

From the foregoing hypothesis it follows, that at 
London, wfren the Sun rises, Venus will have enter- 
ed his disc; and that, at IX hours 37 minutes in the 
morning, she will touch the limb of the Sun inter- 
nally at going off; and lastly, that she will not en- 
tirely leave the Sun till IX hours 56 minutes. 

It likewise follows from the same hypothesis, that 
the centre of Venus should just touch the Sun's 
northern limb in the year 1769", on the third of June, 
at XI o'clock at night. So that, on account of the 
parallax, it will appear in the northern parts of Nor- 
way, entirely within the Sun, which then does not set 
to those parts ; while, on the coasts of Peru and 
Chili, it will seem to travel over a small portion of 
the disc of the setting Sun ; and over that of the 
rising Sun at the Molucca Islands, and in their neigh- 
bourhood. But if the nodes of Venus be found to 
have a retrograde motion (as there is some reason to 
believe from some later observations they havej, then 
Venus will be seen every where within the Sun's 
disc ; and will afford a much better method for find- 
ing the Sun's parallax, by almost the greatest dif- 
ference in the duration of these eclipses that can pos- 
sibly happen. 

But how this parallax may be deduced from ob- 
servations made somewhere in the East Indies, in 
the year 1761, both of the ingress and egress of 
Venus, and compared with those made in its going 
off with us, namely, by applying the angles of a 
triangle given in specie to the circumference of three 
equal circles, shall be explained on some other oc- 
casion. 

3R 



496 The Method of finding the Distances 



ARTICLE IV. 

Showing that the whole method proposed by the Doc- 
tor cannot be put in practice, and why. 

27. In the above Dissertation, the Doctor has ex- 
plained his method with great modesty, and even 
with some doubtfulness with regard to its full suc- 
cess. For he tells us, that by means of this transit 
the Sun's parallax may only be determined within 
its five hundredth part, provided it be not less than 
12j"; that there may be a good observation made 
at Port-Nelson, as well as about the banks of the 
Ganges ; and that Venus does not pass more than 4 
minutes of a degree below the centre of the Sun's 
disc. He has taken all proper pains not to raise our 
expectations too high, and yet, from his well-known 
abilities, and character as a great astronomer, it seems 
mankind in general have laid greater stress upon his 
method, than he ever desired them to do. Only, as 
he wSs convinced it was the best method by which 
this important problem can ever be solved, he re- 
commended it warmly for that reason. He had not 
then made a sufficient number of observations, by 
which he could determine, with certainty, whether 
the nodes of Venus's orbit have any motion ; or if 
they have, whether it be backward or forward with 
respect to the stars. And consequently, having not 
then made his own tables, he was obliged to calcu- 
late from the best that he could find. But those ta- 
bles allow of no motion to Venus's nodes, and also 
reckon her conjunction with the Sun to be about 
half an hour too late. 

28. But more modern observations prove, that 
the nodes of Venus's orbit have a motion back- 
ward, or contrary to the order of the signs, with 
respect to the fixed stars. And this motion is al- 
lowed for in the Doctor's tables, a great part oi 
which were made from his own observations. And 






of the Planets from the Sun. 497 

it appears by these tables, that Venus will be so 
much farther past her descending node at the time of 
this transit, than she was past her ascending node at 
her transit, in November 1639; that instead of pas- 
sing only four minutes of a degree below the Sun's 
centre in this, she will pass almost 10 minutes of a 
degree below it : on which account, the line of her 
transit will be so much shortened, as will make her 
passage over the Sun's disc about an hour and 20 
minutes less than if she passed only 4 minutes below 
the Sun's centre at the middle of her transit. And 
therefore, her parallax from the Sun will be so mucl^ 
diminished, both at the beginning and end of her 
transit, and at all places from which the whole of it 
will be seen, that the difference of its durations, as 
seen from them, and as supposed to be seen from 
the Earth's centre, will not amount to 11 minutes of 
time. 

29. But this is not all ; for although the transit 
will begin before the Sun sets to Port-Nelson, it will 
be quite over before he rises to that place next morn- 
ing, on account of its ending so much sooner than 
as given by the tables to which the Doctor was oblig- 
ed to trust. So that we are quite deprived of the 
advantage that otherwise would have arisen from ob- 
servations made at Port-Nelson. 

30. In order to trace this affair through all its 
intricacies, and to render it as intelligible to the rea- 
der as I can, there will be an unavoidable necessity 
of dwelling much longer upon it than I could other- 
wise wish. And as it is impossible to lay down 
truly the parallels of latitude, and the situations of 
places at particular times, in such a small disc of the 
Earth as must be projected in such a sort of diagram 
as the Doctor has given, so as to measure thereby 
the exact times of the beginning and ending of the 
transit at any given place, unless the Sun's disc be 
made at least 30 inches diameter in the projection, 
and to which the Doctor did not quite trust without 
making some calculations ; I shall take a different 



498 The Method of jindmg the Distances 

method, in which the Earth's disc may be made as 
large as the operator pleases: but if he makes it only 
6 inches in diameter, he may measure the quantity 
of Venus's parallax from the Sun upon it, both in 
longitude and latitude, to the fourth part of a second, 
for any given time and place ; and then, by an easy 
calculation in the common rule of three, he may find 
the effect of the parallaxes on the duration of the 
transit. In this I shall first suppose with the Doc- 
tor, that the Sun's horizontal parallax is 12-j" ; and 
consequently, that Venus's horizontal parallax from 
the Sun is 31". And after projecting the transit, so 
as to find the total effect of the parallax upon its du- 
ration, I shall next show how nearly the Sun's real 
parallax may be found from the observed intervals 
between the times of Venus's egress from the Sun, 
at particular places of the earth ; which is the method 
now taken both by the English and French astro- 
nomers, and is a surer way whereby to come at the 
real quantity of the Sun's parallax, than by observ- 
ing how much the whole contraction of duration 
of the transit is, either at Bencoolen^ Batavia, or 
Pondicherry. 



ARTICLE V. 

Showing how to project the transit of Venus on the Sun's 
disc, as seen from different places of the Earth; so as 
tojindwhat its visible duration must be at any given 
place, according to any assumed parallax of the Sun; 
and from the observed intervals between the times of 
Venus* s egress from the Sun at particular places , to find 
the Surfs true horizontal parallax. 

31. The elements for this projection are as fol- 
lows : 

I. The true time of conjunction of the Sun and 
Venus ; which, as seen from the Earth's centre, 
and reckoned according to the equal time at 



of the Planets from the Sun. 499 

London, is on the 6th of June 1761, at 46 mi- 
nutes 17 seconds after V in the morning, accord- 
ing to Dr. H ALLEY'S tables. 

II. The geocentric latitude of Venus at that time, 
9' 43" south. 

III. The Sun's semidiameter, 15' 50". 

IV. The semidiameter of Venus (from the Doctor's 
Dissertation), 37|". 

V. The difference of the semidiameters of the Sun 
and Venus, 15' 1^". 

VI. Their sum, 16' *7j". 

VII. The visible angle which the transit-line makes 
with the ecliptic 8 31'; the angular point (or 
descending node) being 1 6' 18" eastward from 
the Sun, as seen irom the Earth ; the descending 
node being in t 14 29' 37", as seen from the 
Sun; and the Sun in n 15 35' 55", as seen from 
the Earth. 

VIII. The angle which the axis of Venus's visible 
path makes with the axis of the ecliptic, 8 31' ; 
the southern half of that axis being on the left 
hand (or eastward) of the axis of the ecliptic, as 
seen from the northern hemisphere of the Earth, 
which would be to the right hand, as seen from 
the Sun. 

IX. The angle which the Earth's axis makes with 
the axis of the ecliptic, as seen from the Sun, 
6; the southern half of the Earth's axis lying to 
the right hand of the axis of the ecliptic, in the 
projection which would be to the left hand, as 
seen from the Sun. 

X. The angle which the Earth's axis makes with 
the axis of Venus's visible path, 14 31'; viz. 
the Sum of No. VIII. and IX. 

XL The true motion of Venus on the Sun, given 
by the tables as if it were seen from the Earth's 
centre, 4 minutes of a degree in 60 minutes of 
time. 



500 The Method of finding the Distance* 

32. These elements being collected, make a scale 
of any convenient length, as that of Fig. 1. in Plate 
XVI, and divide it into 17 equal parts, each of which 
shall be taken for a minire of a degree, then divide 
the minute next to the left hand into 60 equal p^rts 
for seconds, by diagonal lines, as in the figure. 
The reason for dividing the scale into 17 parts or 
minutes is, because the sum of the semidiameters 
of the Sun and Venus exceeds 16 minutes of a de- 
gree. See No. VI. 

33. Draw the right line^QS (Fig. 2.) for a small 
part of the ecliptic, and perpendicular to it draw the 
right line CvE for the axis of the ecliptic on the 
southern half of the Sun's disc. 

34. Take the Sun's semidiameter, 15' 50" from 
the scale with your compasses ; and with that ex- 
tent, as a radius, set one foot in C as a centre, and 
describe the semicircle AEG for the southern half 
of the Sun's disc ; because the transit is on that half 
of the Sun. 

35. Take the geocentric latitude of Venus, 9' 
43", from the scale with your compasses ; and set 
that extent from C to v, on the axis of the ecliptic : 
and the point v shall be the place of Venus's centre 
on the Sun, at the tabular moment of her conjunc- 
tion with the Sun. 

36. Draw the right line CBD, making an angle 
of 8 31' with the axis of the ecliptic, toward the 
left hand ; and this line shall represent the axis of 
Venus's geocentric visible path on the Sun. 

37. Through the point of the conjunction v, in 
the axis of the ecliptic, draw the right line qtr for 
the geocentric visible path of Venus over the Sun's 
disc, at right angles to CBJD, the axis of her orbit, 
which axis will divide the line of her path into two 
equal parts qt and tr. 

38. Take Venus's horary motion on the Sun, 
4' from the scale with your compasses; and with 
that extent make marks along the transit-line qtr. 
The equal spaces, from mark to mark, show how 



of the Planets from the Sun. 501 

much of that line \ enus moves through in each 
huur, as seen from the Earth's centre, during her 
continuance on the Sun's disc. 

39. Divide each of these horary spaces, from 
mark to mark, into 60 equal parts for minutes of 
time; and set the hours to the proper marks in such 
a manner, that the true time ot conjunction of the 
Sun and Venus, 46| minutes after V in the morn- 
ing, may fall into the point v, where the transit-line 
cuts the axis of the ecliptic, bo the point v shall 
denote the place of Venus's centre on the Sun, at 
the instant of her ecliptical conjunction with the Sun, 
and t (in the axis CtD of her orbit) w ill be the mid- 
dle of her transit ; which is at 24 minutes after V in 
the morning, as seen from the Earth's centre, and 
reckoned by the equal time at London. 

40. Take the difference of the semidiameters of 
the Sun and Venus, 15' l^J", in your compasses 
from the scale ; and with that extent, setting one foot 
in the Sun's centre C, describe the arcs A* and T 
w ith the other crossing the transit- line in the points 
k and /; which are the points on the Sun's disc that 
are hid by the centre of Venus at the moments of her 
two internal contacts with the Sun's limb or edge, 
at J/and N ': the former of these is the moment of 
Venus's total ingress on the Sun, as seen from the 
Earth's centre, w 7 hich is at 28 minutes after II in 
the morning, as reckoned at London ; and the latter 
is the moment w r hen her egress from the Sun begins, 
as seen from the Earth's centre, which is 20 minutes 
after VIII in the morning at London. The interval 
between these two contacts is 5 hours 52 minutes. 

41. The central ingr-ess of Venus on the Sun is 
the moment when htr centre is on the Sun's eastern 
limb at M, which is at 15 minutes after two in the; 
morning : and her central egress from the Sun is 
the moment when her centre is on the Sun's western 
limb at w ; which is at 33 minutes aftey VIII in 



502 The Method of finding the Distances 

the morning, as seen from the Earth's centre, and 
reckoned according to the time at London. The in- 
terval between these times is 6 hours 18 minutes. 

42. Take the sum of the semidiameters of the 
Sun and Venus, 16' 2/-J", in your compasses from 
the scale ; and with that extent, setting one foot in 
the Sun's centre C, describe the arcs Q and R with 
the other, cutting the transit-line in the points q arid 
r, which are the points in open space (clear of the 
Sun) where the centre of Venus is, at the moments 
of her two external contacts with the Sun's limb 
at S and W; or the moments of the beginning and 
ending of the transit as seen from the Earth's cen- 
tre ; the former of which is at 3 minutes after II in 
the morning at London, and the latter at 45 minutes 
after VIIL The interval between these moments is 
6 hours 42 minutes. 

43. Take the semidiameter of Venus 37-J", in 
your compasses from the scale : and with that ex- 
tent as a radius, on the points q, k, t, /, r, as cen- 
tres, describe the circles HS, MI, OF, PN, WY, 
for the disc of Venus, at her first contact at S, her 
total ingress at M, her place on the Sun at the mid- 
dle of her transit, her beginning of egress at JV, and 
her last contact at IV. 

44. Those who have a mind to project the Earth's 
disc on the Sun, round the centre C, and to lay 
down the parallels of latitude and situations of places 
thereon, according to Dr. HAL LEY'S method, may 
draw 7 Cf for the axis of the Earth, produced to the 
southern edge of the Sun at/V and making an an- 
gle ECfoi' 6 with the axis of the ecliptic CE : 
but he will find it very difficult and uncertain to 
mark the places on that disc, unless he makes the 
Sun's semidiameter AC 15 inches at least : other- 
wise the line Cf is of no use at all in this projec- 
tion. The following method is better. 

45. In Fig. 3. of Plate XVI make the line AB 
of any convenient length, and divide it into 31 
equal parts, each of which may be taken for a second 



of the Planets from the Sun. 

of Venus's parallax either from or upon the Sun 
(her horizontal parallax from the Sun being sup- 
posed to be 31"); and taking the whole length 
AB in your compasses, set one foot in C (Fig. 4.) 
as a centre, and describe the circle AEBD for the 
Earth's enlightened disc, whose diameter is 62", or 
double the horizontal parallax of Venus from the 
Sun. In this disc, draw ACB for a small part of 
the ecliptic, and at right angles to it draw ECD for 
the axis of the ecliptic. Draw also NCS both for 
the Earth's axis and universal solar meridian, mak- 
ing an angle of 6 with the axis of the ecliptic, as 
seen from the Sun ; HCI for the axis of Venus's 
orbit, making an angle of 8 31' with ECD, the 
axis of the ecliptic ; and lastly, VCO for a small 
part of Venus's orbit, at right angles to its axis. 

46. This figure represents the Earth's enlightened 
disc, as seen from the Sun at the time of the transit. 
The parallels of latitude of London, the eastern 
mouth of the Ganges^ Bencoolen, and the island of 
St. Helena, are laid down in it, in the same manner 
as they would appear to an observer on the Sun, if 
they were really drawn in circles on the Earth's sur- 
face (like those on a common terrestrial globe) and 
could be visible at such a distance. The method 
of delineating these parallels is the same as already 
described in the XlXth chapter, for the construc- 
tion of solar eclipses. 

47. The points Where the curve-lines (called 
hour-circles) XI JV, XJV, &c. cut the parallels of 
latitude, or paths of the four places above mention- 
ed, are the points at which the places themselves 
would appear in the disc, as seen from the Sun, at 
these hours respectively. When either place comes 
to the solar meridian NCS by the Earth's rotation 
on its axis, it is noon at that place ; and the diffe- 
rence, in absolute time, between the noon at that 
place and the noon at any other place, is in propor- 
tion to the difference of longitude of these two 
places, reckoning one hour lor every 1.5 degrees of 

3 S 



504 The Method of finding the Distances 

longitude, and 4 minutes for each degree : adding 
the time if the longitude be east, but subtracting it 
if the longitude be west. 

48. The distance of either of these places from 
HCI (the axis of Venus's* orbit) at any hour or 
part of an hour, being measured upon the scale AB 
in Fig. 3. will be equal to the parallax of Venus 
from the Sun in the direction of her path , and this 
parallax, being always contrary to the position of the 
place, is eastward as long as the place keeps on the 
left hand of the axis of the orbit of Venus, as seen 
from the sun ; and westward when the place gets to 
the right hand of that axis. So that, to all the places 
which are posited in the hemisphere HVI of the 
disc, at any given time, Venus has an eastern paral- 
lax ; but when the Earth's diurnal motion carries 
the same places into the hemisphere HOI, the paral- 
lax of Venus is westward. 

49. When Venus has a parallax toward the east, 
as seen from any given place on the Earth's surface, 
either at the time of her total ingress, or beginning 
of egress, as seen from the Earth's centre ; add the 
time answering to this parallax to the time of ingress 
or egress at the Earth's centre, and the sum will be 
the time, as seen from the given place on the Earth's 
surface : but when the parallax is westward, sub- 
tract the time answering to this parallax from the 
time of total ingress or beginning of egress, as seen 
from the Earth's centre, and the remainder will be 
the time, as seen from the given place on the sur- 
face, so far as it is affected by this parallax. The 
reason of this is plain to every one who considers, 

* In a former edition of this, I made a mistake, in taking- the pa- 
rallax in longitude instead of the parallax in the d'n-ection of the orbit 
of Venus ; and the parallax in latitude instead of the parallax in lines 
perpendicular to her orbit. But in this edition, these errors are cor- 
rected ; which make some small differences in the quantities of the 
parallaxes, and in the times depending on them ; as will appear by 
comparing them in this with those in the former edition 



of the Planets from the Sun. 505 

that an eastern parallax keeps the planet back, and 
a western parallax carries it forward, with respect to 
its ti ue place or position, at any instant of time, as 
seen from the Earth's centre. 

50. The nearest distance of any given place from 
VCO^ the plane of Venus's orbit tit any hour or 
part of an hour, being measured on the scale AB in 
Fig. 3. will be equal to Venus's parallax in lines 
perpendicular to her path ; which is northward from 
the true line of her path on the Sun, as seen from 
the Earth's centre, if the given place be on the south 
side of the plane of her orbit J^CO on the Earth's 
disc ; and the contrary, if the given place be on the 
north side of that plane ; that is, the parallax is al- 
ways contrary to the situation of the place on the 
Earth's disc, with respect to the plane of Venus's 
orbit on it. 

51. As the line of Venus's transit is on the 
southern hemisphere of the Sun's disc, it is plain 
that a northern parallax will cause her to describe a 
longer line on the Sun, than she would if she had no 
such parallax ; and a southern parallax will cause her 
to describe a shorter line on the Sun, than if she had 
no such parallax. And the longer this line is, the 
sooner will her total ingress be, and the later will 
be her beginning of egress ; and just the contrary, 
if the line be shorter. But to all places situate on 
the north side of the plane of her orbit, in the hemis- 
phere VHO) the parallax in lines perpendicular to 
her orbit is south ; and to all places situate on the 
south side of the plane of her orbit, in the hemis- 
phere FT0 9 this parallax is north. Therefore, the 
line of the transit will be shorter to all places in the 
hemisphere 7HO, than it will be, as seen from the 
Earth's centre, where there is no parallax ; and long- 
er to all places in the hemisphere 710. So that the 
time answering to this parallax must be added to the 
time of total ingress, as seen from the Earth's centre, 
and subtracted from the beginning of egress, as 



506 The Method of finding the Distances 

seen from the Earth's centre, in order to have the 
true time of total ingress and beginning of egress as 
seen from places in the hemisphere VHO : and just 
the reverse for places in the hemisphere VIO. It 
was proper to mention these circumstances, for the 
reader's more easily conceiving the reason of apply- 
ing the times answering to these parallaxes in the 
subsequent part of this article : for it is their sum in 
some cases, and their difference in others, which be- 
ing applied to the times of total ingress and beginning 
of egress as seen from the Earth's centre, that will 
give the times of these phenomena as seen from given 
places on the Earth's surface. 

52. The angle which the Sun's semidiameter 
subtends, as seen from the Earth, at all times of the 
year, has been so well ascertained by late observa- 
tions, that we can make no doubt of its being 15' 50" 
on the day of the transit ; and Venus's latitude has 
also been so well ascertained at many different times 
of late, that we have very good reason to believe it 
will be 9' 43" south of the Sun's centre at the time 
of her conjunction with the Sun. If then her semi- 
diameter at that time be 37^" (as mentioned by Dr. 
HALLEY) it appears by the projection (Fig. 2.) that 
her total ingress on the Sun, as seen from the Earth's 
centre, will be at 28 minutes after two in the morn- 
ing (HO.), and her beginning of egress from the Sun 
will be 20 minutes after VIII, according to the time 
reckoned at London. 

53. As the total ingress will not be visible at Lon- 
don we shall not here trouble the reader about Ve- 
nus's parallax at that time. But by projecting the 
situation of London on the Earth's disc (Fig. 4.) for 
the time when the egress begins, we find it will then 
be at /, as seen from the Sun. 

Draw Id parallel to Venus's orbit FCO, and lu 
perpendicular to it : the former is Venus's eastern 
parallax in the direction of her path at the beginning 
of her egress from the Sun, and the latter is her 



of the Planets from the Sun. 507 

southern parallax in a direction at right angles to her 
path at the same time. Take these in your com- 
passes, and measure them on the scale AB (Fig. 3.) 
and you will find the former parallax to be 10*", 
and the latter 211". 

54. As Venus's true motion on the Sun is at the 
rate of four minutes of a degree in 60 minutes of 
time (See No. XI. qf 31.) say, as 4 minutes of a 
degree is to 60 minutes of time, so is 10J" of a de- 
gree to 2 minutes 41 seconds of time ; which being 
added to VIII hours 20 minutes (because this paral- 
lax is eastward, 49.) gives VIII hours 22 minutes 
41 seconds, for the beginning of egress at London 
as affected only by this parallax. But as Venus has 
a southern parallax at that time, her beginning of 
egress will be sooner ; for this parallax shortens the 
line of her visible transit at London. 

55. Take the distance Ct (Fig. 2.), or nearest ap- 
proach of the centres of the Sun and Venus in your 
compasses, and measure it on the scale (Fig. 1.), 
and it will be found to be 9' 36^" ; and as the pa- 
rallax of Venus from the Sun in a direction which 
is at right angles to her path is 21|" south, add it to 
9' 361", and the sum will be 9' 58" ; which is to 
be taken from the scale in Fig. 1. and set from C 
to L in Fig. 2. And then, if a line be drawn pa- 
rallel to tl, it will terminate at the point p in the arc 
Z 1 , where Venus's centre will be at the beginning of 
her egress, as seen from London*. But as her cen- 
tre is at / when her egress begins as seen from the 
Earth's centre, take Lp in your compasses, and 
setting that extent from t toward / on the central 
transit-line, you will find it to be 5 minutes shorter 
than //. therefore subtract 5 minutes from VIII hours 
22 minutes 41 seconds, and there will remain VIII 

* The reason why the lines oLp, aBb,ct, and th, which are the vi- 
sible transits at London, the Ganges mouth, Bencoolen, and St. Helena, 
are not parallel to the central transit-line hi, is because the paral- 
laxes in latitude are different at the times of ingress and egress, as 
seen from each of these places. The method of drawing these lines 
will be shown byand-by. 



508 The Method of finding the Distances 

hours 17 minutes 41 seconds for the visible begin- 
ning of egress in the morning at London. 

56. At V hours 24 minutes (which is the middle 
of the transit, as seen from the Earth's centre) Lon- 
don will be at L on the Earth's disc (Fig. 4.) as seen 
from the Sun. The parallax La of Venus from the 
Sun in the direction of her path is then 12-J" ; by 
which, working as above directed, we find the mid- 
dle of the transit, as seen from London, will be at V 
hours 20 minutes 53 seconds. This is not affected 
by Lt the parallax at right angles to the path of Ve- 
nus. But Lt measures 27" on the scale AE (Fig. 
3.) : therefore take '27" from the scale in Fig. 1. and 
set it from t to L, on the axis of Venus's path in 
Fig. 2. and laying a ruler to the point />, and the 
above- found point of t gres^ /?, draw oLp for the line 
of the transit as seen from London. 

57. The eastern mouth of the river Ganges is 89 
degrees east from the meridian of London; and 
therefore, when the time at London is 28 minutes 
after II in the morning ( 40.) it is 24 minutes past 
VIII in the morning (by 47.) at the mouth of the 
Ganges ; and when it is twenty minutes past VIII in 
the morning at London ( 40.) it is 16 minutes past 
II in the afternoon at the Ganges. Therefore, by 
projecting that place upon the Earth's disc, as seen 
from the Sun, it will be at G (in Fig. 4.), at the time 
of Venus's total ingress, as seen from the Earth's cen- 
tre, and at g when her egress begins. 

Draw Ge and gr parallel to the orbit of Venus 
VCO, and measure them on the scale AB in Fig. 3. 
the former will be 21" for Venus's eastern parallax 
in the direction of her path, at the above-mentioned 
time of her total ingress, and the latter will be 16*" 
for her western parallax at the time when her egress 
begins. The former parallax gives 5 minutes 15 
seconds of time (by the analogy in \ 54.) to be ad- 
ded to VIII hours 24 minutes, and the latter paral- 
lax gives 4 minutes 11 seconds to be subtracted 
from II hours 16 minutes; by which we have VIII 



of the Planets from the Sun. 509 

hours 29 minutes 15 seconds, for the time of total 
ingress, as seen from the banks of the Ganges, and 
II hours 1 1 minutes 49 seconds from the beginning 
of egress, as affected by these parallaxes. 

Draw Of perpendicular to Vrnus's orbit VOC, 
and by measurement on the scale AB (Fig. 3.) it 
\viil be found to contain 10" : take 10" from the 
scale in Fig. 1. and find, by trials, a point c, in the 
arch JV, where, if one foot of the compasses be placed, 
the other will just touch the central transit-line kl. 
Take the nearest distance from this point c to CL, 
the axis of Venus's orbit, and applying it from t to- 
ward k, you will find it fall a minute short of k ; 
which shows, that Venus's parallax in this direction 
shortens the beginning of the line of her visible tran- 
sit at the Ganges by one minute of time. Therefore, 
as this makes the visible ingress a minute later, add 
one minute to the above VIII hours 29 minutes 15 
seconds, and it will give VIII hours 30 minutes 15 
seconds for the lime of total ingress in the morning, 
as seen from -he eastern mouth of the Ganges. At 
the beginning of egress, the parallax gp in the same 
direction is 21?" (by measurement on the scale AB), 
which will protract the beginning of egress by about 
30 seconds of time, and must therefore be added to 
the above II hours 1 1 minutes 49 seconds, which 
will make the visible beginning of egress to be at II 
hours 12 minutes 19 seconds in the afternoon. 

58. Bencoolen is 102 degrees east from the meri- 
dian of London ; and therefore, when the time is 28 
minutes past 1 f in the morning at London, it is 16 
minutes past IX in the morning at Bencoolen; and 
when it is 20 minutes past VIII in the morning at 
London, it is 8 minutes past III in the afternoon at 
Bencoolen. Therefore, in Fig. 4. Bencoolen will be 
at B at the time of Venus's total ingress, as seen 
from the Earth's centre ; and at b when her egress 
begins. 



510 7%? Method of finding the Distances 

Draw El and bk parallel to Venus's orbit 
and measure them on the scale : the former will be 
found to be 22" for Venus's eastern parallax in the 
direction of her path at the time of her total ingress ; 
and the latter to be 19-J" for her western parallax in 
the same direction when her egress begins, as seen 
from the Earth's centre. The first of these parallaxes 
gives 5 minutes 30 seconds (by the analogy in 54.) 
to be added to IX hours 16 minutes, and the latter 
parallax gives 4 minutes 52 seconds to be subtracted 
from III hours 8 minutes ; whence we have IX 
hours 21 minutes 30 seconds for the time of total 
ingress at Bencoolen : and III hours 3 minutes and 
8 seconds for the time when the egress begins there, 
as affected by these two parallaxes. 

59. Draw bv and bm perpendicular to Venus's 
orbit VCO, and measure them on the scale AB : the 
former will be 5" for Venus's northern parallax in a 
direction perpendicular to her path, as seen from 
Bencoolen^ at the time of her total ingress ; and the 
latter will be 15" for her northern parallax in that 
direction when her egress begins. Take these pa- 
rallaxes from the scale, Fig. 1. in your compasses, 
and find, by trials, two points in the arcs JVand T 
(Fig. 2.) where if one foot of the compasses be 
placed, the other will touch the central transit- line 
kl: draw a line from a to 6, for the line of Venus's 
transit as seen from Bencoolen ; the centre of Venus 
being at a, as seen from Bencoolen, at the moment 
of her total ingress ; and at b at the moment when 
her egress begins. 

But as seen from the Earth's centre, the centre 
of Venus is at k in the former case, and at / in the 
latter : so that we find the line of the transit is 
longer as seen from Bencoolen than as seen from the 
Earth's centre, which is the effect of Venus's north- 
ern parallax. Take Ba in your compasses, and 
setting that extent backward from t toward .g, on 
the central transit-line, you will find it will reach 
two minutes beyond k : and taking the extent Bb 



of the Planets from the Sun. 511 

in your compasses, and setting it forward from t to- 
ward iv, on the central transit- line, it will be found 
to reach 3 minutes beyond /. Consequently, if we 
subtract 2 minutes from IX hours 21 minutes 30 
seconds (above found), we have IX hours 19 mi- 
nutes 30 seconds in the morning, for the time of 
total ingress, as seen from Bencoolen : and if we add 
3 minutes to the above-found III hours 3 minutes 
$ seconds, we shall have III hours 6 minutes 8 se- 
conds afternoon, for the time when the egress be- 
gins, as seen from Bencoolen. 

60. The whole duration of the transit, from the 
total ingress to the beginning of egress, as seen from 
the Earth's centre, is 5 hours 52 minutes (by 40.); 
but the whole duration from the total ingress to the 
beginning of egress, as seen from Bencoolen, is only 
5 hours 46 minutes 38 seconds : which is 5 minutes 
22 seconds less than as seen from the Earth's cen- 
tre : and this 5 minutes 22 seconds is the whole 
effect of the parallaxes (both in longitude and lati- 
tude) on the duration of the transit at Bencoolen. 

But the duration, as seen at the mouth of the 
Ganges, from ingress to egress, is still less ; for it 
is only 5 hours 42 minutes 4 seconds ; which is 9 
minutes 56 seconds less than as seen from the Earth's 
centre, and 4 minutes 34 seconds less than as seen 
at Bencoolen. 

61. The island of St. Helena (to which only a 
small part of the transit is visible at the end) will 
be at H (as in Fig. 4.-) when the egress begins as 
seen from the Earth's centre. And since the mid- 
dle of that island is 6 west from the meridian of 
London, and the said egress begins when the time 
at London is 20 minutes past VIII in the morning, 
it will then be only 56 minutes past VII in the 
morning at St. Helena. 

Draw Hn parallel to Venus's orbit VCO, and 
Ho perpendicular to it ; and by measuring them on 
the scale AB (Fig. 3.) the former will be found to 
amount to 29" for Venus's eastern parallax in the 

3T 



5,12 The Method of finding the Distances 

direction of her path, as seen from St. Helena, when 
her egress begins, as seen from the Earth's centre ; 
and the latter to be 6" for her northern parallax in 
a direction at right angles to her path. 

By the analogy in $ 54, the parallax in the direc- 
tion of the path of Venus gives 10 minutes 2 se- 
conds of time; which being added (on account of 
its being eastward) to VII hours 56 minutes, gives 
VIII hours 6 minutes 2 seconds for the beginning 
of egress at St. Helena, as affected by this parallax. 
But 6" of parallax in a perpendicular direction to 
her path (applied as in the case of Bcncoolen) length- 
ens out the end of the transit-line by one minute ; 
\vhich being added to VIII hours 6 minutes 2 se- 
conds, gives VIII hours 7 minutes 2 seconds for the 
beginning of egress, as seen from St. Helena. 

62. We shall now collect the above-mentioned 
times into a small table, that they may be seen at 
once, as follows : M signifies morning, A afternoon. 



Total ingress. 

H. M.S. 

f The Earth's centre II 28 OM 
} London - - - Invisible M 
^ The Ganges mouth VIII 30 15 M 
\ Bencoolen - - IX 19 30 M 
{.St. Helena - - Invisible M 



Beg. of egress. 

H. M. S. 

VIII 20 OM 

VIII 17 41M 

II 12 19 A 

III 68^ 

V11I 7 1 2M 



Duration. 
H. M. S. 
5 52 0* 



5 42 4 
5 46 38 



63. The times at the three last-mentioned places 
are reduced to the meridian of London, by sub- 
tracting 5 hours 56 minutes from the times of in- 
gress and egress at the Ganges; 6 hours 48 mi- 
nutes from the times at Bencoolen ; and adding 24 

* This duration as seen from the Earth's centre, is on supposition 
that the semidiameter of Venus would be found equal to 37 1 ", on the 
bun's disc as stated by Dr. If alley (see Art. V. 31.), to which all 
the other durations are accommodated. But, from later observa- 
tions, it is highly probable, that the semidiameter of Venus will be 
found not to exceed 30" on the Sun ; and if so, the duration between 
the two internal contacts, as seen from the Earth's centre, will be 5 
hours 58 minutes ; and the duration as seen from the above-men- 
tioned places, will be lengthened very nearly in the same proportion. 



of the Planets from the Sun. 513 

minutes to the time of beginning of egress at St. 
Helena: and being thus reduced, they are as fol- 
lows : 



Total Ingress. 

H.M.S. 

Times at C Ganges mouth 11 34 15 M 
London < Hencoolen - - II 31 30 A/ 
for & Helena - - Invisible M 



Beg. of egress. 

II. M.S? 

V11I 16 19 M-) Dura- 
V11I 18 8MC lions as 
V1I1 31 2A/S above. 



64 All this is on supposition, that we have the 
true longitudes of the three last- mentioned places, 
that the Sun's horizontal parallax is 12 ;/ that the 
true latitude of Venus is given, and that her semi- 
diameter will subtend an angle of 37-1" on the Sun's 
disc. P 

As for the longitudes, we must suppose them true, 
until the observers ascertain them, which is a very 
important part of their business; and without which 
they can by no means find the interval of absolute 
lime that -elapses between either the ingress or egress, 
as seen from any two given places : and there is 
much greater dependence to be had on this elapse, 
than upon the whole contraction of duration at any 
given place, as it will undoubtedly afford a surer 
basis for determining the Sun's parallax. 

65. I have good reason to believe that the latitude 
of Venus, as given in 31, will be found by obser- 
vation to be very near the truth ; but that the time 
of conjunction there mentioned will be found later 
than the true time by almost 5 minutes ; that Venus's 
semidiameter will subtend an angle of no more than 
30" on the Sun's disc ; and that the middle of her 
transit as seen from the Earth's centre, will be at 24 
minutes after V in the morning, as reckoned by the 
equal time at London. 

66. Subtract V11I hours 17 minutes 41 seconds, 
the time when the egress begins at London, from 
VIII hours 31 minutes 2 seconds, the time reckoned 
ut London when the egress begins at St. Helena , and 



514 The Method of finding the Distances 

there will remain 13 minutes 21 seconds (or 801 se- 
conds) for their difference or elapse, in absolute time, 
between the beginning of egress, as seen from these 
two places. 

Divide 801 seconds by the Sun's parallax 12i", 
and the quotient will be 64 seconds and a small frac- 
tion. So that for each second of a degree in the 
Sun's horizontal parallax (supposing it to be 1%%') 
there will be a difference or elapse of 64 seconds of 
absolute time between the beginning of egress as 
seen from London, and as seen from St. Helena; 
and consequently 32 seconds of time for every half 
second of the Sun's parallax; 16 seconds of time for 
every fourth part of a second of the Sun's parallax ; 
8 seconds of time for the< eighth part of a second of 
the Sun's parallax; and full 4 seconds for a sixteenth 
part of the Sun's parallax. For in so small an angle 
as that of the Sun's parallax, the arc is not sensibly 
different from either its sine or its tangent: and 
therefore the quantity of this parallax is in direct 
proportion to the absolute difference in the time of 
egress arising from it at different parts of the Earth. 

67. Therefore, when this difference is ascertained 
by good observations, made at different places, and 
compared together, the true quantity of the Sun's 
parallax will be very nearly determined. For, 
since it may be presumed that the beginning of 
egress can be observed within 2 seconds of its real 
time, the Sun's parallax may then be found within 
the 32d part of a second of its true quantity ; and 
consequently, his distance may be found within a 
400th part of the whole, provided his parallax be 
not less than 123" ; for 32 times 12-J is 400. 

68. But since Dn. HAL LEY has assured us, that 
he had observed the two internal contacts of the 
planet Mercury with the Sun's edge so exactly as 
not to err one second in the time, we may well im- 
agine that the internal contacts of Venus with the 
Sun may be observed with as great accuracy. So 



of the Planets from the Sun. 515 

that we may hope to have the abs