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~. Centrifugal Force. The centrifugal force must arise from an
impulse originally given to the planets when they commenced their
motions ; since, without such an impulse, they would have simply
moved toward the sun and have been incorporated with it. And if the
centrifugal force were now destroyed, the planets would all move in
straight lines to the sun ; while, if the attraction of the sun were sus-
pended, they would move off into space in tangent lines to their orbits.
Let A B (Fig. 20) represent the amount of the centripetal, and A C that
of the centrifugal force, for a given time; then completing the parallelo-
gram, and drawing the diagonal A D, we find the point which the body
when acted on by both forces will reach in that time. E, F, and G may be
shown in a similar way to be the points reached by the body at the end of
successive periods of time of an equal length ; and thus, if the forces acted
by impulses, the body would describe the broken line formed by the diag-
onals of the parallelograms ; but as the force of gravitation is a continuous
force, the revolving body describes a curve, which may either be a circle or
an ellipse.
35. The planets' orbits are ellipses, having the sun or cen-
tral body in one of the foci.
a. Kepler's Laws. This is the first of the three celebrated truths
pertaining to the planetary motions, discovered by Kepler after many
years of investigation, and announced by him in 1609 ; hence, called
" Kepler's Laws." Previous to this time, the general belief among
astronomers had been that the planets' orbits are circular in form, since
QUESTIONS. a. By whom discovered, and how? 6. Origin of the centrifugal force f
Explain from diagram. 35. What is the shape of the planets' orhits? a. By whom
discovered ? Previous belief.
OF THE PLACETS,
31
they conceived the circle to be the most perfect and beautiful of curves ;
but, according to this theory, they had found very great difficulty in
accounting for the irregularities in the apparent motions of the planets.
b. The Epicycle.* This was, however, partially accomplished
by ingeniously supposing that the planet, instead of revolving in a
simple orbit, revolved in a small circle, called an epicycle, the centre
of which moved around in a circular orbit. This hypothesis was in-
vented, it is supposed, about two centuries B. C., and was adopted by
Ptolemy and all the great astronomers, including Copernicus himself,
who could not account for the apparent irregularities in the motions
of Mars, which has a very eccentric orbit, on any other hypothesis.
The explanation by the epicycle is illustrated by the annexed diagram.
The small circle represents Fig. 21.
the epicycle, the centre of which
moves in the large circle around
the sun, S. At A the planet is
nearest to the sun ; but while it
performs one-quarter of a revo-
lution in the epicycle, the latter
also moves over one-quarter of
its orbit, and thus the planet is
carried to B, and in a similar
manner to C,-its farthest point
from the sun, and thence through
D to A again. The difference
between its greatest distance
from the sun C S, and its least
distance A S, is equal to the di-
ameter of the epicycle. KPICTCLB.
c. Tycho Brahe. Such ingenious but cumbrous hypotheses could
only be sustained by the most imperfect observations made with the
rudest instruments ; but when astronomy, as an art of observation,
came to be cultivated, they were necessarily exploded. Tycho Brahe
is justly to be considered the founder of modern practical astronomy.
He was born in 1546, in Sweden, and so great a reputation did he
* From the Greek words epi, meaning upon, and cycle, a circle ; that is, a
circle upon a circle.
QUESTIONS. 6. What is the hypothesis of the epicycle ? Explain by the diagram.
c. Tycbo Brahe ? Value of his labors, and use made of them by Kepler ?
32 THE ORBITAL REVOLUTIONS
acquire, that Ferdinand, king of Denmark, built for him, on an island
at the mouth of the Baltic, a magnificent observatory, which he styled
" Uraniberg. or the City of the Heavens." His accurate observations
of the planets were the means of conducting Kepler to the discovery
of his famous laws. No less than nineteen different hypotheses were
made by Kepler, before he could bring his mind to abandon the theory
of the circular motion of the planets, and then he assumed the ellipse,
as being the next most beautiful curve. The adoption of this hypo-
thesis at once reconciled the computed with the observed place of Mars ;
and, on applying it to the other planets, he found still more convincing
proof of its truth.
36. The straight line that joins the sun or central body
with the planet at any point of its orbit, is called the BADIUS-
VECTOR.*
37. The point of a planet's orbit nearest to the sun is
called its PERIHELION ; f the point farthest from the sun, its
APHELION.J
fl. Apsides. The aphelion and perihelion are. of course, the ex-
tremities of the major axis. These two points are sometimes called the
Apsides,% and the line that joins them, the Line of Apsides.
b. One-half of the sum of the aphelion and perihelion distances of a
planet is, of course, the mean distance. This is always equal to the
distance of a planet from the sun when it is at either extremity of its
minor axis. [See Introduction, Art. 29, &.]
38. The radius-vector of a planet's orbit passes over equal
spaces in equal times. This is the second of Kepler's laws.
If 8 (Fig. 22) represent the sun in the focus of a planet's elliptical orbit, A
will be the aphelion, P the perihelion, and A S, B S, C S, etc., the radius-
* Vector, in the Latin, means that which carries. The radius-vector is con-
ceived to carry the planet as it moves around in its orbit,
t From the Greek peri, meaning around or near ; and helios, the sun.
J From apo, meaning/rom, and helios. Apo in combination becomes aph.
% Apsis, plural apsides, is from the Greek, and means a joining.
QUESTIONS. 36. Define radius-vector. ST. Define perihelion and aphelion, a, Ap.
sides and apsis line. b. What is mean distance? 33. What is Kepler's second law?
Explain from the diagram.
OF THE PLANETS. 33
rector in different positions of the plan-
et. The planet moves in its orbit so
that the spaces A S B, B S C, etc., may
be equal, if described in equal times.
It has therefore to move much faster
in the perihelion than in the aphelion,
since at the former point the spaces P
must be wider in order to make up
for their diminished length.
a. Orbital Veloctiy. The ve-
locity of a planet must therefore be
variable when it moves in an ellip- ELLIPTICAL OBBIT.
tical orbit, being greatest at the
perihelion, least at the aphelion, and alternately increasing and dimin-
ishing between these points.
b. The second law of Kepler is equally true for every kind of orbit,
including ciicular orbits ; but in the latter, the radius of the circle
would be the radius-vector, and not only would the spaces described
be equal, but also the different portions of the orbit, and consequently,
the velocity would be uniform. The orbits of the satellites of Jupiter
and Uranus are almost, if not exactly, circular.
39. The squares of the periodic times of the planets are in
proportion to the cubes of their mean distances from the
sun, or central body.
a. That is to say, if we square the times which any two planets
require to complete a revolution around the sun, and then cube their
mean distances, the ratio of the squares will be equal to that of the
cubes. This law applies to the secondary as well as the primary
planets.
b. History. This is the third and most celebrated of Kepler's laws.
It establishes a most beautiful harmony in the Solar System. In his
work on " Harmonics," Kepler first made it known, with a perfect
burst of philosophic rapture. " What I prophesied, twenty-two years
ago, that for which I have devoted the best part of my life to astro-
nomical contemplations, at length I have brought to light, and have
QUESTIONS. n. Velocity of a planet when variable ? 6. When uniform ? 39. Re-
lation of periodic times to distances ? n. Is it true of the satellites ? b. History of its
discovery ? (Repeat the three laws of Kepler.)
34 THE ORBITAL REVOLUTIONS
recognized its truth beyond my most sanguine expectations. It is now
eighteen months since I got the first glimpse of light, three months
since the dawn ; very few days since the unveiled sun, most admirable
to gaze on, burst out upon me. Nothing holds me ; I will indulge
in my sacred fury. If you forgive me, I rejoice ; if you are angry, I
can bear it. The die is cast, the book is written, to be read either now
or by posterity, I care not which : it may well wait a century for a
reader, as God has waited six thousand years for an interpreter of Ms
works"
Sir John Herschel remarks of this law, " Of all the laws to which
induction from pure observation has ever conducted man, this thiid
law of Kepler may justly be regarded as the most remarkable, and the
most pregnant with important consequences."
c. Demonstration cf Kepler's Laws. These laws were deduced
by Kepler, as matters of fact, from the recorded observations of him-
self and others ; but he failed to show the principle on which they are
founded, and by which they are connected with each other. This was
reserved for Newton, who, by the discovery and application of the law
of gravitation, confirmed the truth of these laws by exact mathematical
reasoning and calculation.
d. Kepler's Third Law not quite true. The third law is, how-
ever, absolutely correct only when we consider the planets as mathe-
matical points, without mass. Owing to the immense mass of the
sun, this is relatively so nearly the fact, that the variation from the
truth is very slight.
40. The eccentricity of the large planets' orbits is very
small, that of Mercury being the greatest, and Venus the
least. The orbits of the Minor Planets are generally remark-
able for their great eccentricity.
a. Comparative Eccentricities. The eccentricity of a planet's
orbit is measured by comparing it with one-half of the major axis.
The following is an approximate statement of the eccentricities of the
large planets : Mercury, ; Mars, f,, ; Saturn, -fa ; Jupiter, 2 J f ; Ura,
nus, -^ ; Earth, - 6 L o ; Neptune ,-} T ; Venus, 7^5. The greatest of any
of the minor planets is a little over ^.
QTTFSTIONS. c. By whom was their truth mathematically proved ? d. What modi-
fication of Kepler's third law is required ? 40. What is the amount of eccentricity of
the planets' orbits ? a. State their comparative eccentricities.
OF THE PLANETS.
35
The annexed diagram will aid in giv- Fig. 23.
ing the student a correct idea of the
figure of the planets' orbits. This dia-
gram represents an ellipse, the eccentri-
city of which is , or much greater than
that of the most eccentric of the minor
planets. It will be apparent, therefore,
that the actual figure of the planets' or-
bits is but slightly different from that of a
circle. If drawn on paper, the eye could
not detect the difference.
41. The MEAN PLACE of a
planet is that in which it would
be if it moved in a circle, and of
course, with uniform velocity ; the TEUE PLACE is that in
which it is actually situated at any particular time.
42. The angular distance of the true place from the mean
place, measured from the sun as a centre, is called the Equa-
tion of the Centre.
Fig. 24.
ELLIPSE ECCENTEICITY, f.
MEAN AND TEUE PLACES OF A PLANET.
In the above diagram, the ellipse represents the actual orbit of the planet,
QUESTIONS. 41. What is mean place? True place? 42. Equation of the centre?
Explain from the diagram.
36 THE OKBITAL KEVOLUTIONS
and the dotted circle the corresponding circular orbit. The points marked
T represent the true places, and those marked M, the mean places of the
planet. As the radius-vector passes over greater portions of the orbit in
the perihelion than in the aphelion, the mean place is before or east of the
true place, as the body moves from aphelion to perihelion, and behind or
west of it in the other half of its revolution. The angle contained between
the radius-vector and the radius of the circle is the equation of the centre.
43. The planets do not all revolve around the sun in the
same plane, but in planes slightly inclined to each other.
The angle which the plane of a planet's orbit makes with
that of the earth's orbit is called the Inclination of its
Orbit.
44. Of all the primary planets, Mercury has the greatest
inclination of orbit (7), and Uranus the least (46'). The
Minor Planets are remarkable for a much greater inclination
of their orbits than that of the other planets.
a. Since the planets' orbits are all inclined to that of the earth, each
one must cross the plane of it in two points. These two points are
called the Nodes j one the ascending node, and the other the descend
ing node.
Fig. 25.
B
INCLINATION OF ORBITS.
Fig. 25 represents an oblique view of the orbits of the earth and Venus.
E is the ascending, and F, the descending node. E F the line of nodes,
and A S G the angle of inclination of the orbit.
QUESTIONS. 43. What is meant by inclination of orbit f 44. Which planet has the
greatest ? Which has the least ? Orbits of the Minor Planets why remarkable ?
OF THE PLANETS.
37
45. The NODES * of a planet's orbit are the two opposite
points at which it crosses the plane of the earth's orbit.
46. The ASCENDING NODE is that at which the planet
crosses from south to north ; the DESCENDING NODE, that
at which it crosses from north to south. The straight line
which joins these points is called the Line of Nodes.
Q is the sign of the ascending node ; , of the descending node.
Fig. 26.
INCLINATION OF PLANETS' ORBITS.
Fig. 26 represents the position of the plane of each orbit in relation to
that of the earth. The small amount of deviation from one uniform plane
will be at once apparent. These planets, however, on account of their vast
distance from the sun, depart very far from the plane of the earth's orbit.
Thus, Mars, although having only 2 of inclination, may be nearly 5 mil-
lions of miles from this plane ; and Neptune, about 85 millions.
* From the Latin word nodus, meaning a, knot.
QUESTIONS. 45. What are nodes? 46. What is the ascending node? Descending
node ? Line of nodes ?
CHAPTER Y.
DISTANCES, PERIODIC TIMES, AND ROTATIONS OF THE
PLANETS.
47. The distances of the planets from the sun are so great
that they can only be expressed in millions of miles.
a. Idea of a Million. A million is so vast a number that we can
form rio true conception of it without dividing it into portions. To
count a million, at the rate of 5 per second, would require about 2|-
days, counting without intermission, night and day. A railroad car,
traveling at the rate of 80 miles per hour, night and day, would require
nearly four years to pass over a million of miles. In stating the dis-
tances of the planets, the rate of the express train may be employed as
a standard of comparison, so that the pupil may obtain something
more than merely a knowledge of figures in learning these almost
inconceivable distances.
48. The following are the mean distances of the planets
from the sun, expressed in approximate round numbers :
Mercury, . 35 millions. Jupiter, . 476 millions.
Venus, . 66 " Saturn, . 872 "
Earth, . . 9U " Uranus, . 1,754
Mars, . . 139* " Neptune, 2,746
Minor Planets, . . 260 millions (average).
a. Illustration. Multiply each of these numbers expressing mil-
lions by four, and we shall find the time which an express train start-
ing from the sun would require to reach each of the planets. In the
case of the nearest planet, this period would be 140 years, and of the
most remote, almost 11,000 years. A cannon ball moving at the rate
of 500 miles an hour, would not reach Neptune in less than 623 years.
QUESTIONS 4T. Distances of planets how expressed ? a. Idea of a million ? 48. State
the mean distances of the primary planets from the sun. a. What illustration is given ?
PERIODIC TIMES OF THE PLANETS. 39
b. Bode's Law. A comparison of the distances given above will
show a very curious numerical relation existing among them, each
distance being nearly double that next inferior to it. A more exact
statement of this numerical relation was published in 1772 by Profes-
sor Bode, of Berlin, although not discovered by him : it has usually
been designated " Bode's Law." Take the numbers
0, 3, 6, 12, 24, 48, 96, 192, 384;
each of which, excepting the second, is double the next preceding ;
add to each 4, and we obtain
4, 7, 10, 16, 28, 52, 100, 196, 388;
which numbers very nearly represent the relative proportion of the
planets' distances, including the average distance of the Minor Planets.
In the case of Neptune, the law very decidedly fails, and, conse-
quently, has ceased to have the importance attributed to it previous
to the discovery of this planet in 1846.
PERIODIC TIMES OF THE PLANETS.
49. The following are the periods of time occupied by the
planets respectively in completing one revolution around
the sun :
Mercury, . 88 days. Jupiter, . 12 yrs. (nearly.)
Venus, . 224.J " Saturn, . 291 "
Earth, . . 365J " Uranus, . 84~ "
Mars, . . 1 yr. 322 days. Neptune, 165 "
Thus the year of Neptune is about 700 times as long as that of
Mercury.
50. Of all the primary planets, Mercury moves in its orbit
with the greatest velocity, and Neptune with the least; the
velocities of the planets diminishing as their distances from
the sun increase.
a. This is in accordance with Kepler's third law ; since the ratio of
the periodic times increases faster than that of the distances ; the square
QUESTIONS. b. What is Bode's law? 49. State the periodic times of the primary
planets. 60. Which planet moves with the greatest velocity ? Which, the least ?
a. Why is this?
40 AXIAL KOTATIONS OF THE .PLANETS.
of the former being equal to the cube of the latter. Thus, if the dis
tance of one planet is four times as great as that of another, the
periodic time will not be simply four times as long, but eight times as
long ; that is, the square root of the cube. (y / 4 3 ^/64 = 8). Hence,
as the planet has a longer time in proportion to the distance traveled,
its velocity must be diminished.
b. Comparative Velocities. The following table exhibits the mean
hourly motion of the primary planets in their orbits :
Mercury, . . 104,000 miles. Jupiter, . . 28,700 miles.
Venus, . . 77,000 " Saturn, . . 21,000 "
Earth, . . . 65,500 " Uranus, . . 15,000 "
Mars, . . . 53,000 " Neptune, . . 12,000 "
c. Illustration. What an amazing subject for contemplation does
this table present ! For example, the weight of the earth in tons is
computed to be about 6,000,000,000,000,000,000,000 ; that is to say, six
thousand million million times a million, or 6,000 X 1,000,000 X 1,000,-
000 X 1,000,000. Yet this body so inconceivably vast is rushing
through the abyss of space with a velocity of 1,000 miles per minute,
or about 15 miles during every pulsation of the heart. But the earth
in comparison with the body around which it is revolving is as a single
grain of wheat compared with four bushels.
d. To find the Hourly Motion. This can be done by the applica-
tion of very simple principles. The orbits being nearly circles, twice
the mean distance will give us the diameter, and 3f times the diameter
will give the circumference, or whole distance traveled in the periodic
time. Then finding the number of hours in this time, and dividing the
whole distance by this number, we obtain the hourly motion. Thus,
Mercury's mean distance is 35 million miles; then 35X2X3^ = 220
millions, the whole distance traveled in 88 days, or 88 X 24 = 2112 hours ;
and 220 million -s- 2112 = 104,166 miles.
AXIAL ROTATIONS OF THE PLANETS.
51. Besides revolving around the sun, the planets revolve
upon their axes in the same direction as they revolve in
their orbits; that is, from west to east. (See Art. 18, a.)
This is called their DIUBNAL KOTATION.
QUESTIONS. 6. State the comparative velocities of the planets. c. Illustration ?
d. How is the hourly motion in the orbit found ? 51. What is meant by diurnal
rotation?
AXIAL ROTATIONS OF THE PLANETS. 41
52. The Axis of a planet is the imaginary straight line
passing through its centre, on which we conceive it to
rotate.
53. A planet must rotate with its axis either perpen-
dicular or oblique to the plane of its orbit. The axes of the
planets are all considerably oblique, excepting that of Jupi-
ter, which is only 3 from the perpendicular ; that of Venus
is supposed to be 75.
54. The angle which the axis of a planet makes with a
perpendicular to its orbit, is called its INCLINATION or Axis.
Pig. 27.
INCLINATION OF JUPITEB, EABTH, AND VENUS.
a. The inclination of the axis of each planet, as far as it has been
discovered, is as follows :
Mercury, . . (unknown.) Jupiter, . . 38.
Venus, . .75. (?) Saturn, . . 26J?.
Earth, . . . 23^, Uranus, . . (unknown.)
Mars, . . . 28i, Neptune, . .
b. How to Discover the Rotation. The usual method of dis-
covering the rotation of a planet is to examine the disc with a powerful
telescope, so as to find, if possible, any spots upon it, and then to detect
any regular movement of such spots across the disc. Let the pupil
stand a short distance from a terrestrial globe, and let it be caused to
revolve, and he will observe the marks upon it move across, and alter-
QUKBTIONS. 52. What is the axis of a planet ? 53. Are the axes perpendicular, or
oblique ? 54. What is inclination of axis f a. State the axial inclination of each
planet, b. How is the axial rotation of a planet discovered ?
42 AXIAL ROTATIONS OF THE PLANETS.
nately disappear and re-appear. The same tiling must, of course, occur
in our observation of the planets, if they have a diurnal motion.
55. The times of rotation of the planets respectively are
as follows :
Mercury, . . 24} hours. Jupiter, . . 10 hours.
Venus, . . 23i " Saturn, . .101 "
Earth, ... 24 " Uranus, . . 9^ " ( ? )
Mars, . . . 24A " Neptune, . (unknown.)
a. It will be observed that the terrestrial planets all perform their
rotations in about 24 hours ; but that the maj or planets require less
than one-half that time.
b. Sun's Rotation. The sun also rotates upon an axis, but requires
about 608 hours, or 25 ^ days to complete one rotation. The inclina-
tion of its axis to the plane of the earth's orbit is about 7^.
QUESTIONS. 55. State the time of the rotation of each planet, a. What distinction,
in this respect, between major and terrestrial planets ? 6. Does the sun rotate ? In
what time ?
CHAPTER VI.
ASPECTS OF THE PLANETS.
56. The ASPECTS of the planets are their apparent posi-
tions with respect to the sun or to each other. The principal
aspects, that is, those most frequently referred to, are Con-
junction, Quadrature, and Opposition.
57. A planet is said to be in CONJUNCTION with the sun
when it is in the same part of the heavens.
That is, if the sun is in
the east, the planet must also
be in the east, both being
seen, if visible, precisely in
the same direction. It is evi-
dent that in the case of the
inferior planets, this may oc-
cur in two ways ; namely,
when the planet is at that
point of its orbit which is
nearest to the earth or at the \
point most remote ; or, in \
other words, when the earth P^\
and planet are both on the \
same side of the sun, or on
opposite sides. Of course a
superior planet, to be in con-
junction, must be on the oppo-
site side of the sun from the earth.
Fig. 28.
SUPERIOR CONJUNCTION
SUP R10R
\
INFERIOR
OPPOSITION
ASPECTS.
58. Conjunction may be Inferior or Superior. Inferior
QUESTIONS. 56. What is meant by aspects of the planets? 57. When is a planet
in conjunction ? 58. Of how many kinds ? What is inferior conjunction? Superior ?
44 ASPECTS OF THE PLANETS.
conjunction is that in which the planet is between the earth
and the sun; superior conjunction is that in which the
planet is on the opposite side of the sun from the earth.
59. A planet is said to be in OPPOSITION with the sun
when it is in the opposite part of the heavens.
a. That is, while the sun is in the east, the planet, if in opposition,
must be in the west. If Jupiter, for example, should he rising just as
the sun is setting, or vice versa, it would be in opposition. It is obvious
that the superior planets only can be in opposition, and that when in
that position, they are at the points of their orbits nearest to the earth.
b. These different aspects obviously depend upon the angular, or
apparent, distance of a planet from the sun. [See Introduction, Art.
18, ]. In conjunction, there is no angular distance, unless we regard
the difference in the planes of the orbits ; and when the planet is in
conjunction and at either of the nodes, none whatever. In opposition,
the angular distance is 180.
60. The angular distance of a planet from the sun is called
its ELONGATION.
61. A planet is said to be in QUADRATURE when its elon-
gation is 90.
a. The position of quadrature in the heavens is half-way between con-
junction and opposition, the planet being so situated that the straight
lines that connect the earth with the sun and planet, respectively, make
a right angle with each other. Thus if a planet were in quadrature,
it would be in the south, or near it, either at sunset or sunrise, accord-
ing as it were either east or west of the sun. It will be obvious, from
Fig. 28, that, viewed from the earth as a centre, the position of quad-
rature in the orbit is not half-way between conjunction and opposition,
but much nearer the latter.
b. There are, in all, five aspects of the planets, depending on their
relative positions. The following are their names, the angular dis-
tances, and the characters used to denote them :
QUESTIONS 59. When is a planet in opposition? a. Which planets can be in oppo-
sition? b. What is the angular distance of a planet in conjunction? In opposition?
60. What is elongation? 61. Quadrature? a. Where is quadrature relatively to con-
junction and opposition ? ft. Enumerate and define the five aspects, and write the sign
of each.
ASPECTS OF THE PLANETS.
45
Conjunction,
Sextile, . .
Quartile, . .
6 0.
* 60.
n 90.
Trine, . .
Opposition,
120.
180.
Fig. 29.
In the diagram, the graduated semicircle cuts the sides of all the angles
which have their vertices at E, and serves to measure the angular distance
of each planet from the sun. V and V" represent Venus in superior and
inferior conjunction, the elongation being, at those points, ; while at V,
it is at its point of greatest elongation. It will be obvious from this dia-
gram that no inferior planet can be 90 from the sun. M represents Mars
in opposition, and M' the same planet in quadrature. The aspect of M and
V or V" is opposition ; of M' and V or V", quartile.
62. The time which elapses between two similar elonga-
tions of a planet is called its Synodic * Period.
a. Thus the interval between two successive conjnnctions or oppo-
sitions is the synodic period. The synodic period would be the true
periodic time if the earth were at rest ; but the earth is moving in its
orbit in the same direction as the planet, with a velocity less than that
* From the Greek words syn, meaning together, and odos, which means a
pathway.
QUESTIONS. 62. What is the synodic period ? a. Why not the true period ? Illus-
trate by the diagram. How to calculate the synodic period of the inferior planets ?
(Fig. 30) Of the superior planets? (Fig. 31.)
4G
ASPECTS OF THE PLANETS.
SYNODIC PEEIOD. INFEBIOB PLANETS.
of the inferior planets and greater than that of the superior. Hence,
the synodic period of an inferior planet must always be greater than
the periodic time, while that of the superior planets is generally less.
Fig- 3O. The diagram represents Venus at V 1
in inferior conjunction with the sun, the
earth being at E 1 . Now conceive Venus
to move around once, so as to return to
V 1 ; the earth will then have gone over
about I2f of her orbit, and reached E 2 ,
and Venus will not overtake her until
she reaches E 3 , passing her first position,
and hence making one revolution, and
the part E 1 ES besides, while Venus
makes two revolutions, and of course a
corresponding part of her orbit besides.
This part of the orbit of each is about
TO of the whole, in the case of Venus.
For since Venus completes a revolu-
tion, or 360, in 224* days, she moves
about 1.6 per day; while the earth moves about .98 per day ; hence Venus
gains .62 per day; but she has 360 to gain, as she leaves V, and 300 -*-
.62 =582 days. The true synodic period is 584 days. Now, 584 n-224.} =
2.6, number of revolutions of Venus during one synodic period ; and 584
-j- 365i = 1.6, number of revolutions of the earth ; and 2.6 rev. 2 rev. = T a 5
rev.rrE 1 3 or Vi V 3 .
The synodic periods of the superior plan-
ets, are illustrated in the annexed diagram.
Let J 1 represent Jupiter in opposition, the
earth being at E 1 . As Jupiter's periodic
time is about 12 years, when the earth, after
performing a revolution, returns to E 1 ,
Jupiter has passed over T 1 5 of its orbit, and
reached J*, and the earth moving a short
distance farther overtakes it at J 3 . In this
case, the superior planet only moves over
a fraction of its orbit, while the earth moves
over the same fraction of its orbit, and one
whole revolution. We can find the synodic
period of Jupiter from the true period, in
SYNODIC PEHIOD, supEBioB pLANET8. tne f]l wm g manner : As Jupiter per-
forms only & of a revolution while the
earth performs a whole one, the earth gains H of a revolution, while perform-
ing one ; but to overtake Jupiter when starting from E 1 , after opposition,
Fig. 31.
ASPECTS OF THE PLANETS. 47
she has to gain an entire revolution, and 1-Hi = r?. Now ? of 3654 days
= 399 days (nearly) ; which is the synodic period of Jupiter.
If the periodic time of any superior planet were exactly double that of
the earth, its synodic period and periodic time would be equal. This is
nearly true of Mars ; its periodic time being 1 yr. 322 days, and its synodic
period, 2 yrs. 50 days.
63. When a planet appears in the evening, just after sun-
set, it is called an Evening Star ; when in the morning, just
before sunrise, it is called a Morning Star.
a The inferior planets being always less than 90 from the sun, can
only appear as morning or evening stars. Mercury being a small
planet, and never having but a small amount of elongation, is a diffi-
cult object to see ; Venus, being a large planet, and having a greater
apparent distance from the sun, is a very brilliant and beautiful object,
either as an evening or morning star. When the former, her elonga-
tion must of course be east ; when the latter, west. The su} erior
planets are morning or evening stars at different degrees of elongation,
since they may be visible from sunset to sunrise.
Fig. 32.
VENTTS AS MORNING AN7> EVENING STAB.
In the diagram, Fig. 32, Venus is represented as a morning and evening
QTTFBTTONS. 63. What is meant by morning star? By evening star? a. What is
said of the inferior planets, in this respect ? Explain fron. the diagram.
48 ASPECTS OF THE PLANETS.
star. While Venus is on the side of the sun as represented at V, she must
be an evening star, since, as the earth turns, any place at P must, as it
turns from the sun at the time of sunset, still keep Venus in view by the
angular distance contained between the lines drawn to the place from the
sun and Venus respectively ; but when Venus is at V, the other side of the
sun, the rotation of the earth would bring Venus into view tit any place as
P, before the sun. (The student should carefully notice the direction of
the motion as indicated by the arrows.) Venus, of course, remains the
same side of the sun during one-half of the synodic period, or 292 days.
QUESTIONS FOE EXEKCISE.
1. When a planet is in quadrature, what is its elongation ?
2. What is its elongation when in inferior conjunction ?
3. What is its elongation in superior conjunction ?
4. How many degrees of elongation has it when in opposition ?
5. Which of the planets can be in inferior conjunction ?
6. Which can be in superior conjunction ?
7. Which, can be in opposition ?
8. Which can be in quadrature ?
9. Can the elongation of Mercury or Venus exceed 90 ?
10. Can that of Jupiter ?
11. What is the greatest elongation of a superior planet ?
12. When Venus is in inferior conjunction, and Mars in opposition,
what is their angular distance from each other ? [See Fig. 29.]
18. What is their angular distance when Venus is in inferior con-
junction, and Mars in superior conjunction ?
14. How many degrees are they apart when Venus is in superior
conjunction and Mars is in quadrature ?
15. When the elongation of Venus is 30, and that of Mars is 120,
what is their angular distance from each other ?
16. If Venus is 50 from Mars, and the latter body is in quadrature,
what is the elongation of Venus ?
CHAPTER VII.
THE EARTH.
64. That the earth is, in its general form, a spherical body,
is plainly indicated by a few simple facts :
1. Navigators are able to sail entirely around it either in
an eastward or a westward direction ;
2. The earth and the sky always seem to meet in a circle,
when the view is unobstructed ;
3. The top of a distant object always appears above this
circle, before the lower parts ; as the sails of a ship before
its hull ;
4> The elevation of the spectator causes this circle to sink,
so as to show more of the earth's surface, and equally on
all sides ;
5. The apparent movements of the heavenly bodies
around the earth, some in large circles, some in small circles ;
one particular star in the heavens not appearing to have
any motion at all.
a. This last circumstance is accounted for by supposing that the
earth's axis points to this star. Hence it is called the North, or Pole Star.
/>. The first practical proof that the earth is spherical was afforded
by the voyage of Magellan, whose squadron, in 1519-22, sailed entirely
around the earth.
SECTION I.
LATITUDE AND LONGITUDE.
65. Points are located upon the surface of the earth by
measuring their distances from certain established circles
What five circumstances indicate that the general form of the earth
is spherical ? a. What is the north star ? 65. How are points located on the earth's
Surface.
50 LATITUDE AND LONGITUDE.
conceived to be drawn upon it. The position of these cir-
cles is determined by their relation to two fixed points,
called the POLES.
66. The poles are the two extremities of the earth's axis,
one being called the NORTH POLE, and the other the SOUTH
POLE.
a. As the earth turns on its axis from west to east, it causes all the
other heavenly bodies to seem to revolve around it from east to west,
in circles contracting in size towards the fixed point of the heavens,
called the celestial pole, near which is the pole-star. The celestial
poles correspond to the poles of the earth, being the two points at which
the earth's axis, if extended, would meet the sphere of the heavens.
67. The great circle exactly midway between the two
poles is called the EQUATOR. Its plane divides the earth
into northern and southern hemispheres.
68. The great circles that pass through the poles are
called meridian circles ; the half of a meridian circle that
Fig. 33. extends from pole to pole, is called a Me-
Meridian ^
a. Meridian circles must, of course be per-
pendicular to the equator and the plane of any
one of them would divide the earth into eastern
and western hemispheres. A great circle that
is perpendicular .to another is sometimes called
a secondary to it. Thus the meridian circles
are secondaries to the equator.
69. The position of a place on the surface of the earth is
indicated by its latitude and longitude. LATITUDE is dis-
tance north or south from the equator ; LONGITUDE, distance
east or west from some established meridian, called a First,
or Prime, Meridian.
66. What are the poles ? n. What are the celestial poles? 67. What is
the equator? 68. What are meridian circles? Meridians? n. Their relation to the
equator? What is a secondary ? 69. What is latitude ? Longitude?
LATITUDE AND LONGITUDE. 51
Pig. 34. 70. Small circles parallel to the equa-
tor are called PARALLELS OF LATITUDE.
71. Latitude is reckoned on a meridian,
from the equator to the poles ; longitude
is reckoned from the prime meridian
round to the opposite meridian.
a. Distance from any great circle must be
reckoned on a secondary to that circle. It
will be easily perceived by the pupil that the poles have the greatest
possible latitude namely, 90 ; and that places situated under the me-
ridian opposite the prime meridian, have the greatest longitude, or
180 east or west ; also, that a place situated at the intersection of the
prime meridian with the equator can have neither longitude nor
latitude.
b. Difference of Time. Difference of Longitude causes difference
of time. Since the earth turns toward the east, any place east of
another place, must have later time y because it is sooner carried, by the
motion of the earth, under the sun ; and, as an entire rotation, or 360,
is performed in 24 hours, 15 of longitude must be equivalent to one
hour of time. Thus, London is 74 east of New York ; and, conse-
quently, when it is noon at New York, it is 5 o'clock in the afternoon
at London, the sun having passed the meridian five hours earlier.
c. Difference of Longitude may be converted into Difference
of Time, by multiplying the degrees and minutes by 4 ; the former of
which will then be minutes of time ; and the latter, seconds. For
since , J 5 the number of degrees is equal to the number of hours, f ,or
4 times, the degrees must be equal to the minutes ; and, for the same
reason, 4 times the minutes of space must be equal to seconds of
time.
(I. To convert Difference of Time into Difference of Longitude,
reduce the hours to minutes, and divide by 4. For since 15 times the
hours are equal to the degrees, / - of 15, or {, the minutes must be
equal to the degrees.
QUKSTIONS. 70. What are parallels of latitude ? 71. How are latitude and longitude
reckoned? a. Where is the latitude greatest ? The longitude? What point or place
on the earth's surface has neither latitude nor longitude ? fo. How does difference of
longitude cause difference of time? r. How to convert diff-rcnce of longitude into
difference of time? rf. How to convert difference of time into difference of longitude.
LATITUDE AND LONGITUDE.
PROBLEMS FOR THE GLOBE.
PROBLEM I. To find the latitude and longitude of a
place : Bring the given place to the graduated side of the
brass meridian [the circle of brass that encompasses the
globe], which is numbered from the equator to the poles :
and the degree of the meridian, over the place will be the
latitude ; and the degree of the equator, under the meridian,
east or west of the prime meridian, will be the longitude.
Verify the following by the globe :
LAT. I,ONG.
LONDON, . . . 5U N. ; 0.
PARIS, . . . 49 N. ; 2^ E.
WASHINGTON, . 39 N. ; 77 W.
CINCINNATI, . 39 N. ; 84 W.
C. GOOD HOPE, 34 S. ; 18^ E.
BERLIN, . . 52 N. ; 13^ E.
MADRAS, . . 13 N. ; 80 E.
SANTIAGO, . . 32F S. ; 70| W.
PROBLEM II. The latitude and longitude of a place
being given, to find the place : Find the degree of longitude
on the equator, bring it to the brass meridian, and under
the given degree of latitude, on the meridian, will be the
place required.
EXAMPLES.
1. What place is in lat. 30 N., and long. 90 W. ? Am. New Orleans
2. What place " " 42 \ N., " 71 W.? An*. Boston.
3. What place " " 40f N., " 74 W. ? Ana. New York.
PROBLEM III. To find the difference of latitude or Ion
gitude between any two places : Find the latitude or longitude
of both places ; if on the same side of the equator or merid-
ian, subtract one from the other ; if on different sides, add
them ; the result will be the answer required.
EXAMPLES.
Find the difference of latitude and longitude of
\. London and Naples. Am. Lat. 10^, long. 14 8 .
2. New York and San Francisco. Ans. Lat. 3, long. 58./-
3. Stockholm and Rio Janeiro. Ans. Lat. 82, long. 61.
LATITUDE AND LONGITUDE. 53
PROBLEM /F. To find all the places that have the same
latitude as any given place : Bring the given place to the
brass meridian, and observe its latitude ; turn the globe
round, and all places that pass under the same degree of the
meridian will be those required.
EXAMPLES.
What places have the same, or nearly the same, latitude as
1. MADRID? Ana. Minorca, Naples, Constantinople, Kokand, Salt
Lake City, Pittsburgh, New York.
2. HAVANA ? Ans. Muscat, Calcutta, Canton, C. St. Lucas, Mazatlan.
PROBLEM V. To find the places that have the same longi-
tude as any given place : Bring the given place to the grad-
uated side of the brass meridian, and all places under the
meridian will be those required.
EXAMPLE
What places have the same, or nearly the same, longitude as
LONDON ? Ans. Havre, Bordeaux, Valencia, Oran, Gulf of Guinea.
PROBLEM VL A time and place being given, to find
what o'clock it is at any other place : Bring the place at which
the time is given to the brass meridian, set the index to the
given time, and turn the globe till the other place comes to
the meridian, and the index will point to the time required.
NOTE. If the place be east of the given place, turn the globe westward ;
if west, turn it eastward.
This problem can be performed without the globe by finding the differ-
ence of longitude, as indicated in Art. 71, c, d.
EXAMPLES.
1. When it is noon at New York, what o'clock is it at London ?
Ans. 5 o'clock P.M. (nearly).
2. When it is 10 o'clock A.M. at St. Petersburg, what o'clock is it at
the City of Mexico ? Ans. 1 hour 20 min. A.M.
3. When it is 9 o'clock P.M. at Rome, what o'clock is it at San Fran-
cisco? Ans. Noon.
54 THE HORIZON.
PROBLEM VII. To find the distancce between any two
places : Lay the graduated edge of the quadrant over both
places, so that the division marked may be on one of them ;
and the number of degrees between them, reduced to miles,
will be the distance required.
NOTE. If geographic miles are required, multiply the degrees by CO; if
statute miles, by 091.
EXAMPLES.
Find the distance in geographic, and statute miles between
1. NORTH CAPE and CAPE MATAPAN. Am. 2,100 geog. miles ; 2,413f
statute miles.
2. Rio JANEIRO and CAPE FAREWELL. Ans. 4,980 geog. miles ; 5,736 j
statute miles.
SECTION II.
THE HORIZON.
72. The HORIZON * OF A PLACE is the circle which sepa-
rates the visible part of the heavens from the invisible.
(i. The surface of the earth appears, to a person standing upon it,
like a great plane, extending equally on all sides, and limited by a cir-
cle at which the earth and sky appear to meet. As the elevation of
the spectator increases, the greater is the extent of surface embraced
within this circle, and the more extensive the visible heavens as com-
pared with the invisible, On the other hand, an eye situated exactly
on the earth's surface sees but a point of it, but still beholds a circle
bounding the visible heavens, the plane of which would touch the
earth's surface at the exact point where the eye is located. This circle
is called the Sensible or Visible Horizon ; and the depression of it, due
to the elevation of the spectator, the Dip of the Horizon. The follow-
ing definitions may therefore be given of each :
73. The SENSIBLE HORIZON is that circle of the celestial
* From the Greek word horizo, meaning to bound.
QUESTIONS. 72. What is the horizon of a place ? a. General phenomena connected
with the horizon ? 73. What is the sensible horizon ?
THE HORIZON.
55
sphere the plane of which touches the earth at the place of
the spectator.
a. By the Celestial Sphere is meant the concave sphere of the heavens,
in which the heavenly bodies appear to be placed, the observer being
at the centre within, and looking upward.
74. The DIP OF THE HORIZOX is the depression of the
sensible horizon caused by the elevation of the spectator,
and bringing a circular portion of the earth's surface into
view.
In the diagram, let the small circle
whose centre is E, represent the
earth, the portion of the large circle
V Z V a part of the celestial sphere,
and P the point, or place, of the spec-
tator. Then the tangent S P S will
represent the plane of the sensible
horizon, and S Z S the visible heavens.
Conceive the observer to stand above
the surface at II ; the tangents H V
and II V' will then, at their points of
contact, D and D, limit the visible
part of the earth's surface, and at
their extremities, V and V 7 , the visi-
ble heavens. S V or S V will be, of course, the dip of the horizon. At the
point P, the visible part of the heavens is less than the invisible ; but at so
great an elevation as H P (represented as about 1,000 miles), the visible
part would be much greater than the invisible, and a large part of the
earth's surface, denoted by the arc D D, would come into view. The dip,
however, at any attainable height is very small, and only an inconsiderable
portion of the earth's surface can ever be seen. The line R R represents the
plane of a great circle, which divides the celestial sphere into equal parts,
passing through the centre of the earth, and situated at a distance from
the plane of the sensible horizon equal to the semi-diameter of the earth,
or nearly 4,000 miles.
75. The great circle of the celestial sphere which is paral-
lel to the sensible horizon, is called the RATIONAL HORIZON.
SENSIBLE AND BATIONAL HORIZON.
QUFSTIONS. a. What is meant by the celestial sphere f 74. What is the dip of the
horizon t Explain by the diagram. 75. What is the rational horizon ?
56 THE HORIZON.
It divides the earth and the celestial sphere into upper and
lower hemispheres.
The terms upper and lower, above and below, and the like, are only
applicable to the horizon. The rational horizon is the real horizon ;
it is the standard circle for referring the apparent positions of all the
heavenly bodies.
76. The poles of the horizon are called the ZENITH and
the NADIR. The zenith is the point directly overhead ; the
nadir is the point opposite to the zenith, and directly under
our feet.
The one is the pole of the visible, or upper, hemisphere ; the other,
the pole of the invisible, or lower. Each is, of course, 90 from the
horizon.
77. Great circles conceived to pass through the zenith and
nadir are called VERTICAL CIRCLES, or VERTICALS.
a. Vertical circles, being perpendicular to the horizon, are secondaries
to it. The position of a body in the celestial sphere is defined by its
distance from the rational horizon, and some selected vertical circle ;
just as the position of a place on the earth's surface is determined by
its latitude and longitude. The vertical selected for this purpose is
that which the centre of the sun reaches and passes at noon. This
circle, of course, passes through the north and south points of the
horizon, and also through the celestial poles, its plane intersecting the
earth so as to form a terrestrial meridian. It is therefore called the
Meridian of flie Place.
78. The MERIDIAN OF A PLACE is the vertical circle
which passes through the north and south points of the
horizon of that place. It divides the celestial sphere into
eastern and western hemispheres.
a. When a body is on the meridian, it is said to culminate, because
it is at that time at its greatest distance above the horizon during
24 hours.
QUESTIONS. 76. What are the zenith and the nadir ? 11. What are vertical circles ?
a. How is the position of a body in the celestial sphere defined ? 78. What is the me-
ridian of a place ? a. When is a body said to culminate ?
THE H O It I Z N .
57
79. The distance of a body above the horizon is called its
ALTITUDE. It is reckoned on a vertical circle, from the
horizon to the zenith.
At the horizon, therefore, the altitude is ; at the zenith, 90.
80. The distance of a body east or west from the meridian
is called its AZIMUTH. It is reckoned on the horizon.
a. Prime Vertical 5 Amplitude. The altitude and azimuth of a
body would be sufficient to define its position in the visible heavens ;
but astronomers sometimes employ another vertical as a standard of
reference, namely, that which passes through the east and west points
of the horizon, cutting the meridian at right angles. This is called
the Prime Vertical ; and the distance of a body from it, north or south,
is call the Amplitude. These are, at
present, but little used. By the am-
plitude of the sun is generally meant
the distance at which it rises from
the east, or sets from the west point
of the horizon.
In the diagram, let N E S W repre-
sent the rational horizon, the circle
passing through N S, the meridian, and
that passing through E W, the prime
vertical ; then if A be the position of
the sun at rising, A E will represent its
amplitude, and A N, its azimuth ; the
altitude being O c .
Sadir
81. The ZENITH DISTANCE of a body is its distance from
the zenith reckoned on a vertical circle.
The zenith distance is the complement of the altitude, that is, the
difference between it and 90.
82. The circles which the heavenly bodies may be con-
ceived to describe during their apparent daily revolution
around the earth, are called CIRCLES OF DAILY MOTION.
QUESTIONS. 79. What is altitude? 80. Azimuth? a. What is the prime vertical ?
What is amplitude? 81. What is zenith distance? 82. What are circles o* daily
motion ?
58
THE HORIZON.
Fig. 37.
Parallel Sphere
JSadir
Pig. 38.
Right Sphere
Zemtfc
Pole
-Nadir
Fig. 39.
Oblique Sphere
a. Positions of the Sphere. The circles of
daily motion are parallel, perpendicular, or ob-
lique to the horizon, according to the place of the
observer upon the surface of the earth. When
standing exactly at either of the poles, he would
have the celestial pole in the zenith, and the
circles of daily motion would be parallel to the
horizon ; this position is called a Pan allel Sp7iere.
At the equator, the celestial poles would be in the
horizon, and the circles of daily motion perpen-
dicular to it ; this position is called a Right
Sphere. At any place between the equator and
the pole the circles would be oblique
to the horizon, and the pole would be
raised to an altitude equal to the lati-
tude of the place ; this is called an
Oblique Sphere.
It. In a parallel sphere, one-half of all
the circles of daily motion are wholly
above the horizon, and the heavenly
bodies do not appear to rise and set,
but to move around in parallel circles
contracting in size toward the zenith ;
in a right sphere, all the circles are
divided equally by the horizon, there
being as much of each above as below it ;
in an oblique sphere, some of the circles of
daily motion are wholly above the horizon,
others wholly below it, and all between
these, divided unequally by it. All this
will be rendered apparent by the accompa-
nying diagrams.
83. The circle of an oblique sphere
in which the stars never set is called
the CIRCLE OF PERPETUAL APPARI-
Pole
QUFSTIONS. ft. What are the three positions of the sphere ? Define each. ft. TTow
are the circles of daily motion divided by the horizon in each? 83. What is the circle
of perpetual apparition ? Of perpetual occultation ?
PARALLAX.
59
TION ; that in which they never rise, the CIRCLE OF PER-
PETUAL OCCULTATION.
84. That part of a circle of daily motion which is above
the horizon, and which a body describes from its rising to
its setting, is called the DIURNAL ARC ; the part below the
horizon is called the NOCTURNAL ARC.
In the diagram of the oblique sphere (Fig. 39), H H represents the ra-
tional horizon, Z and N the zenith and nadir, P P the poles, E E'the equa-
tor extended to the heavens, and the dotted lines, circles of daily motion.
Then Z E will be the same number of degrees as the latitude, E H will be
the altitude at which the equinoctial or equator intersects the meridian,
and P II will be the altitude of the celestial pole. Now E P is equal to Z H,
each being 90 ; hence, by subtracting Z P from each, we find E Z = P H ;
that is, the altitude of the pole equal to the latitude.
PARALLAX.
85. The TRUE ALTITUDE of a body is the distance at
which it would appear to be from the horizon, if it could be
viewed from the centre of the earth.
In the diagram let the Fig. 4O.
email circle represent the
earth, having its centre at E ;
A, B, and C, a body as seen at
different altitudes from the
place, P ; E H, the plane of
the rational horizon ; P h, the
plane of the sensible horizon,
and E Z, the direction of the
zenith. At A, the body being
in the sensible horizon, its ap-
parent altitude will be noth-
ing ; but if viewed from E, it
would appear to be above the
horizon a distance equal to the
angle mE H, or its equal m A h,
since the difference in direction between the lines E H or Ph, and E m is the
difference between the apparent and true altitude. At B, there is evidently
QUESTIONS. 84. Define diurnal arc, and nocturnal arc.
is the true altitude of a body?
Explain Fig. 39. 85. What
60 PARALLAX.
a less difference of direction between the lines P n and E o, and when the
body is at C, the centre of the earth, the place of the observer, and the po-
sition of the body being all on the same straight line, the true is the same
as the apparent altitude. It is evident that the apparent altitude is always
less than the true altitude, except when the body is seen in the zenith, as at
C ; and that there is the greatest difference when the body is in the horizon,
as at A.
86. The difference between the true and apparent altitude
of a heavenly body is called its PARALLAX.
87. The parallax of a body is greatest when it is in the
horizon, and diminishes towards the zenith, where it is
nothing. The parallax of a body when in the horizon is
called its Horizontal Parallax.
In the preceding diagram, the angle m A h, or its equal P A E, is called
the angle of parallax, o B n, or P B E, is the angle of parallax for the posi-
tion B. The angular distance of the sensible and rational horizons is, of
course, the horizontal parallax.
a The greater the distance of a body from the earth, the smaller is
the angle of parallax.
Fig. 41. Thus the horizon-
tal parallax of a body
at A, (Fig. 41.) is A E
H, or P A E ; but at
B, it is the smaller
angle B E H, or P B E. The horizontal parallax of any body is really the
angle subtended by the semi-diameter of the earth at the distance of the
body ; and, of course, the greater the distance, the smaller the angle.
6. The horizontal parallax of the moon is nearly 1 ; that of the
sun, less than 9". In a subsequent chapter, it will be shown that
by finding the parallax of a body, we can determine its distance from
the earth.
88. Since the apparent altitude of a body is less than the
true altitude by the amount of parallax, the effect of paral-
lax is said to be to diminish the altitude. The apparent
QUESTIONS. 86. What is parallax? 87. Where is it greatest? What is horizontal
parallax? Explain Fig. 41. a. What relation between the distance of a body and its
parallax ? Explain by the diagram, b. What is the horizontal parallax of the moon
and sun ? 88. What is the effect of parallax ?
REFRACTION. 61
altitude is therefore corrected by adding the amount of
parallax due to the particular elevation and the distance of
the body.
a. Other corrections would also have to be made to obtain the exact
altitude ; namely, for the dip of the horizon caused by the elevation of
the spectator, and for the effect of the atmosphere upon the direction
of the rays of light which pass through it. The latter of these is
called Refraction.
REFRACTION.
89. REFRACTION, in astronomy, is the change of direction
which the rays of light undergo in passing through the
earth's atmosphere.
a. It is a general fact that the rays of light when passing obliquely,
from one medium into another of a different density, are turned from
their course, and made to pass more obliquely, if the medium which
they enter is rarer, and less obliquely, if it is denser than that which
they leave. Thus, in passing from air into water, or from water into
glass, the direction would be less oblique ; but in passing from water
into air, more oblique.
Suppose n m to represent the surface of water, Fig 42 .
and S a ray of light, entering the water at O.
Instead of keeping on in the direction 8 O, it is
bent toward the perpendicular A B, and thus
passes less obliquely.
b. Now, as the earth's atmosphere is not of
uniform density, but grows more and more
dense toward the surface of the earth, the
rays of light which proceed from any body
are constantly bent more and more toward a perpendicular direction ;
and since we see an object in the direction in which the ray of light
strikes the eye, the apparent altitude of the body will be increased.
QUESTIONS. a. What other corrections required for true altitude? 89. What is
refraction ? . State the general law. Explain by the diagram, b. Why is the alti-
tude increased by refraction ? Explain by the diagram.
REFRACTION.
Suppose E to represent the
earth, and A B C D, portions
or strata of the atmosphere, of
different densities, P, the place
of observation. Suppose a ray
of light from the star S, strike
the atmosphere at a; on ac-
count of refraction, instead of
proceeding in the direction S
A, it describes a &, b c, and c P,
reaching the spectator at P,
and in the direction of c P ; so
that the star appears in that
/ E \ \ \ \ direction at S', and is thus
ABCD ABCD elevated above its true posi-
tion at S. As the atmosphere
does not consist of distinct strata, as represented, but diminishes uniformly
in density from the surface of the earth, the broken line a b c P, is in real-
ity a curve, and the line S' P, a tangent to it at the point P.
90. The effect of refraction is greatest upon a body when
it is in the horizon, and diminishes toward the zenith, where
it is nothing. At the horizon, it amounts to about 33
minutes.
a. There is no refraction at the zenith, because at that point every
ray of light strikes the atmosphere perpendicularly, and refraction only
takes place when the direction of the rays is oblique ; at the horizon,
they are more oblique than they can be at any point above it ; hence
the refraction is greatest there.
91. At the horizon, the amount of refraction is somewhai
greater than the apparent diameter of the sun or moon ; and
hence these bodies appear to be above the horizon when
they are actually below it.
a. The times of the rising of all the heavenly bodies are, therefore,
accelerated, and those of their setting retarded, by refraction ; each
one appears to be above the horizon before it has actually risen, and
is seen above the horizon after it has actually set.
. 90. What is the effect of refraction at the zenith and horizon ? Why ?
91. What is the amount of refraction at the horizon? a. Effect on the rising and set-
ting of the heavenly hodies ?
APPARENT MOTIONS OF THE SUN. 63
6. Refraction very rapidly diminishes from the horizon towards the
zenith. At the horizon its mean value is 33' ; at 10 of altitude, 15 i' ;
at 30, li' ; at 45, 57" ; at 80, 10" ; at 90, 0.
SECTION III.
APPARENT MOTIONS OF THE SUN AND STARS.
92. The sun has two apparent motions around the earth ;
namely, a diurnal motion from east to west, and an annual
motion from west to east. The first is caused by the rota-
tion of the earth on its axis, and the second, by its revolu-
tion around the sun.
(l. The student should be careful to verify by his own observations
the following statements respecting the sun's apparent motions :
1. Apparent Daily Motion. The sun rises exactly at the east point
of the horizon, and sets at the west point, twice a year ; namely, about
the 20th of March and 23d of September ; and, on these days, it crosses
the meridian at an altitude equal to the complement of the latitude ;
that is, at the point where the celestial equator crosses the meridian.
2. From March 20th to June 21st, the points at which the sun rises
and sets move from the east and west toward the north, and its merid-
ian altitude constantly increases ; from June 21st till Sept. 23rd, the
points of rising and setting move back toward the east and west, and
the meridian altitude diminishes ; from Sept. 23rd to Dec. 22nd, the
points of rising and setting move toward the south, and the meridian
altitude diminishes ; from Dec. 22nd to March 20th, the points of rising
and setting move back toward the east and west, and the meridian alti-
tude increases. There is thus a constant movement of the points of
rising and setting alternately from north to south, and a constant
variation, up and down, of the point of culmination, except that the
sun culminates at the same altitude for several days, about the 21st of
QUESTIONS. b. How fast does refraction diminish from the horizon? 92. What ap-
parent motions has the sun ? How caused ? a. State the daily phenomena connected
with the apparent motions of the sun. What changes in the points of rising and set-
ting ? In the point of culmination ? Solstices and equinoxes ?
64 APPARENT MOTIONS OF
June and the 22nd of December. These two stationary points of cul-
mination are called the Solstices.* The points ut which the culmina-
tion of the sun coincides with that of the celestial equator are called
the Equinoxes,\ because when the sun is at either of these points, the
days and nights are exactly equal to each other.
3. Apparent Annual Motion. The sun appears to move toward
the east among the stars ; for, if on any evening at sunset, or a short
time after, we notice the distance of the sun from any star that may be
visible, we shall find, in a few evenings, that this distance has grown
less ; and hence, as the stars are fixed points, that the sun has moved
toward the east. This motion will continue from month to month
until the sun will be in conjunction with the star; and then for six
months the star will be no longer visible, but at the end of that time,
will show itself above the eastern edge of the horizon just as the sun
sets below the western ; and at the expiration of one year from the
first observation, will have returned to the same relative position with
the sun. In this way the sun appears to move from star to star toward
the east, completing its circuit in 365 J- days.
93. The great circle of the celestial sphere in which the
sun appears to revolve around the earth every year, is called
the ECLIPTIC.
The ecliptic may also be defined as the great circle of the celestial
sphere in which it is intersected by the plane of the earth's orbit. Hence
the plane of the ecliptic is the plane of the earth's orbit.
94. The great circle of the celestial sphere exactly over
the equator is called the EQUINOCTIAL, or CELESTIAL
EQUATOR.
The student must conceive these circles as marked out on the sky,
the one crossing the other. (See diagram, Fig. 44.)
95. Since the earth's axis is inclined to the plane of its
*From the Latin words sol, meaning the sun, and sto, meaning to stand.
t From the Latin words equus, meaning equal, and nox, meaning night. The
arrival of the sun at either of these points produces equal days and nights.
QUESTIONS. State the phenomena connected with the snn's apparent annual motion.
03. What is the ecliptic ? 94. What is the equinoctial ? 95. What is meant by the
obliquity of the ecliptic ? Why is it 23 J ?
THE SUN AND STAES. 65
orbit, or the plane of the ecliptic, making with it an angle
of 66A, the ecliptic and equinoctial must cross each other
at an angle of 23 ,J. This angle is called the OBLIQUITY OF
THE ECLIPTIC.
Fig. 44.
pOLE_OF_CUp r/c
P LE OF ECLIPTIC
ECLIPTIC AND EQUINOCTIAL.
a. The obliquity of the ecliptic, and, of course, the inclination of the
axis, are indicated by the difference between the highest and lowest
daily culminating points of the sun, being equal to one-half of this dif
ference. For when it is at the equinoctial, it must culminate where
the equinoctial crosses the meridian, that is, at an altitude equal to the
complement of the latitude ; and when it is north or south of the equi-
i. How is the obliquity of the ecliptic indicated?
66
APPARENT MOTIONS OF
noctial, it must culminate as far above or below the culminating point
of the equinoctial. But this never exceeds 23 i either way ; hence,
the obliquity or inclination must be 23 . This departure of the sun
from the equinoctial, as indicated by its daily motion, is called its
Declination.
b. To find the greatest and least meridian altitude of the sun at any
place, the following rule may be given : Find the complement of the
latitude, and to it add 23 for the greatest altitude ; and from it sub-
tract 23i for the least. Thus for
Fig. 45. New york the lat of which is
about 40, L : 90 - 40F = 49
comp. of lat. Hence, 49^ + 23^
= 73, greatest altitude ; and 49^
23jr = 26, least altitude.
In the diagram, P P represents
the celestial poles, E E the equi-
H noctial, Z N the zenith and nadir,
H H the horizon, 8 the position of
the sun when 23| north of the
equinoctial, and S' its position
when 23i south of the equinoctial ;
then E H will represent its alti-
tude when at the equinoctial, E H
+ E S, its greatest meridian alti-
; and E H E S', its
G3EATE8T ANI> LEAST ALTITUDE OF THE SUN.
96. The two opposite points of the ecliptic, where it
crosses the equinoctial, are called .the EQUINOCTIAL POINTS,
or EQUINOXES. The one which the sun passes in March is
called the Vernal Equinox ; that which it passes in Septem-
ber, the Autumnal Equinox.
97. The two opposite points of the ecliptic at which the
sun is farthest from +he equinoctial, are called the SOLSTITIAL
POINTS, or SOLSTICES. The one north of the equinoctial is
called the Summer Solstice ; the one south of it, the Winter
Solstice.
QUESTIONS ft. How to find the greatest and least meridian altitude of the sun?
Explain by the diagram. 06. What are the equinoxes? How distinguished? 97. The
solstices, and how distinguished ?
THE SUN AND STABS. 67
a. The equinoxes and solstices are sometimes called the cardinal
points of the ecliptic ; they are 90 from each other, and, of course,
divide the ecliptic into four equal parts.
98. The DECLINATION of a heavenly body is its distance,
north or south, from the equinoctial.
a. Declination corresponds to terrestrial latitude. At the equinoxes,
the decimation of the sun is ; at the solstices, it is 23, which is the
greatest declination the sun can have.
b. In a right sphere, the amplitude of the sun when it is rising or
setting, is exactly equal to its declination. [Let the student verity this
by an artificial globe.]
99. CIRCLES OF DECLINATION are great circles of the
celestial sphere that pass through the poles, and are perpen-
dicular to the equinoctial.
a. Hour Circles. Circles of declination correspond to meridian
circles on the earth. When drawn at intervals of 15, they are called
Hour Circles, because the heavenly bodies, in their apparent diurnal
revolution round the earth, pass from one to the other every hour ;
since 360 + 24 = 15.
b. Hour Angle. The angle included between the hour circle pass-
ing through a body and the meridian of the place of observation is
called the Hour Angle of the body.
c. Colures. The circle of declination that passes through the equi-
noctial points is called the Equinoctial Colure; that which passes
through the solstitial points is called the Solstitial Colure.
That in the arctic circle is called the North Frigid Zone ;
QUESTIONS. a. Why has the earth's surface been divided into zones? 125. Define
the zones. How named? 126. Where is the torrid zone? 127. Where are the tern
perate zones ? 128. The frigid zones ?
THE EAKTH.
that in the antarctic circle, the South Frigid Zone. Each
extends 23^ degrees from the pole, and is 47 degrees across.
SECTION VI.
THE FIGUEE AND SIZE OF THE EABTH.
129. THE FIGURE OF THE EARTH is that of an oblate
spheroid, differing but slightly from a perfect sphere.
a. Proofs that the Earth is Spheroidal. Several and diverse
proofs may be given to establish tkis fact.
1. The effect of the centrifugal force would necessarily give it this
form ; for, since this force causes bodies to fly off from the centre of
motion, the water, or any other yielding materials of which the earth
is composed, would recede as far as possible from the axis of rotation,
and thus passing from the poles to the equator, cause the earth to
bulge out at those parts. Sir Isaac Newton, from this consideration,
very nearly ascertained the amount of oblateness in the earth's figure,
before any actual discovery of it had been made.
Fig. 57.
to become elliptical in form.
2. The attraction exerted by tht
tor than at any other part, and
toward either of the poles. This
This change in the form
of a rotating body may be
illustrated by an apparatus
represented in Fig. 57. This
consists of one or more cir-
cular hoops of an elastic ma-
terial, fastened at the lower
end of the axis, but free to
move up and down, at the
upper end. When set in
rapid rotation, they lose
their circular form and are
bulged out at the points
farthest from the axis, so as
! earth at its surface is less at the equa-
increases as we go from the equator
is shown by a pendulum's vibrating
QUESTIONS. 129. What is the figure
Illustrate it and explain by the diagram.
of the earth? . What is the first proof?
What is the second proof?
THE EARTH.
89
Fig. 58.
less rapidly at the equator than at places nearer the poles ; and this
can be accounted for only by supposing that the equatorial parts of the
earth are the farthest from its centre, and the poles the nearest to it ;
since the attraction of gravitation diminishes as the distance increases.
3. The length of a degree on the meridian is different in different
latitudes, showing a variation in the curvature of the earth's surface at
different parts. If the earth were an exact sphere, the meridians would
be perfect circles, and consequently of the same curvature at every part ;
hence, if we find, by exact measurement, that the curvature is not the
same, we know that they are not exact circles. This is what has been
ascertained. The length of a degree on the meridian has been measured
at different latitudes ; and it has been found that it is longer the nearer
we go to the poles, showing that the earth is flattened at these parts.
Let the ellipse, Fig. 58, repre-
sent the form of the earth. Since
the curvature at P is much less
than that at E, the radius of the
curve a b will be longer than that
of c d ; hence, if the angle a o b is
equal to the angle c m d, the arc a 6
which is farther from the centre
than c d, must be the longer. Of
course, this would be equally true
of an angle of 1 ; and thus, the
arc subtending one degree of an-
gular measurement at the poles
must be longer than the corre-
sponding arc at the equator, if the earth is spheroidal.
b. To Find the Size of the Earth. The angular distance of two
places situated under the same meridian, measured from the earth's cen-
tre, is the arc of the meridian contained between the places. This angle
is found by observing the change of position, with respect to the hori-
zon or zenith, which a star appears to undergo when viewed from two
different points on the earth's surface, one being exactly north of the
other. The apparent displacement of the star is the angular distance,
or meridian arc, contained between the two places. Then, having
measured the distance in miles between the places, we can find by a
QtmmoNS. How is this fact (shown? What is the third proof? Illustrate it
Explain by the diagram. 6. How is the size qf the earth found ? Explain by the
diagram.
90
THE EARTH.
simple proportion, the circumference of the earth. For, suppose the
angular distance is found to be 2, and the actual distance 172.76
miles ; then 2 : 360 : : 172.76 miles : 24,877 miles. This must be the
circumference of the earth ; and dividing 24,877 miles by 3.1416, the
ratio of the circumference to the diameter, we obtain its diameter.
To understand why
a change in the place
of the spectator causes
a displacement of the
star, let E (Fig. 59)
represent the centre of
the earth, P and P
places on the earth, Z
and Z' the zenith of
\ each respectively, S,
\ the direction of a star
situated at an immense
distance beyond. At
P, the zenith distance
of the star is a c, or the angle S P Z ; at P, the other place, it is 6 d, or the
angle 8 P Z', greater than S P Z by the angle e P d, which is equal to the
angle PEP. Thus, the star appears farther from the zenith Z' than
from Z at P by the arc of the meridian, P P.
130. The oblateness of the earth's figure is equal only to
s Js part of its diameter, or 26^ miles.
a. So small is this variation from an exact sphere, that if a body
were made of the precise form of the earth, having its longest diame-
ter three feet in length, the shortest would be only one-eighth of an
inch less, an amount entirely imperceptible.
6. The longest diameter of the earth is 7,925| miles ; the shortest
diameter 7,899 ; the mean diameter 7,912 miles.
131. The spheroidal figure of the earth is the cause of the
precession of the equinoxes.
a. Precession Explained. For since this excess of matter at the
equator is situated out of the plane of the ecliptic, the attraction of
QUESTIONS. 130. What is the degree of oblateness of the earth ? Illustration ?
b. What are the exact dimensions of the earth ? 131. What does the spheroidal figure
of the earth cause ? a. Explain how precession is caused ?
THE EARTH 91
the sun and moon acts obliquely upon it, and thus tends to draw the
planes of the equinoctial and ecliptic together ; which tendency, by
the rotation of the earth on its axis, is converted into a sliding move-
ment, as it were, of one circle upon the other, both preserving very
nearly the same inclination.
Fig. 60,
Thus (Fig. 60) the attraction of the sun, acting obliquely upon the protu-
berance, or excess of matter, at E and E', tends to draw it toward the plane
of the ecliptic ; and this it would finally accomplish were the earth's rota-
tion suspended ; so that the plane of the equator would be made to
coincide with that of the ecliptic. But the effect is a sliding of the equator
over the line of the ecliptic, and thus a change of the points of inter-
section.
b. Revolution of the Poles. Since the equator moves round on
the ecliptic, the poles of the earth must revolve around those of the
ecliptic, and consequently change their apparent position among the
stars. Hence, the star which is now so near the north celestial pole
will not always be the pole-star ; but in about 13,000 years, that is,
one-half the period of an entire revolution, will be 47 from it.
c. Why the Equinoctial Points move toward the West. It may
not be obvious why the equinoctial points move toward the west ; but
perhaps the following diagram and explanation will render it clear :
Let E E (Fig. 61) represent the equator, and e e the ecliptic, A the first
degree of Aries, or vernal equinox ; a 6 the amount of force exerted to
draw the equator toward the ecliptic in a given time, and a d the amount
of rotation performed in that time. By the principle of resultant motion,
the excess of matter and, of course, the earth with it, would move in the
QUKSTIONS. ft. Effect on the position of the poles? c. Why does the equinox move
toward the west ? Explain by the diagram (Fig. 61).
diagonal a c, thus changing the direction of the equator from E E to g h^
and causing the point of intersection to recede from A to A'. It will be
obvious that the angle of inclination at A must be very nearly equal to
that at A'.
d. Obliquity of the Ecliptic Variable. There is a very slow dimi-
nution of the obliquity of the ecliptic, amounting to 46V m a century.
At present (1867), the obliquity is 23 27' 24". The limit of the varia-
tion is 1 21', to pass through which arc it requires about 10,000 years.
SECTION VII.
TIME.
132. The apparent motions of the sun and stars, caused
by the real motions of the earth, afford standards for the
measurement of time.
133. The time which elapses between a star's leaving the
meridian of a place until it returns to it again is called a
SIDEREAL* DAY.
d. This is the time of one complete revolution of the celestial
sphere, and is the exact period of one rotation of the earth on its axis.
It is an absolutely uniform standard, having undergone not the
slightest appreciable change from the date of the earliest recorded
* From the Latin word sidus, which means a star.
QTTESTIONS. d. What change takes place in the obliquity of the ecliptic ? 132. What
are the standards for measuring time ? 133. What is a sidereal day ? a. Is it uniform f
TIME.
93
observations. Indeed, it is the only absolutely uniform motion ob-
served in the heavens.
134. A SOLAR DAY is the period which elapses from
the sun's leaving the meridian of a place until it returns to
it again.
a. As the sun is constantly changing its place among the stars,
owing to the annual revolution of the earth, this period must be
longer than a sidereal day ; for the sun having moved toward the east
during the time of a rotation, the earth must turn farther in order to
bring the place again into the same relative position with the sun.
This will be understood by examining the annexed diagram.
Let 1 represent Fig 62 .
the earth in one po-
sition of its orbit,
and 2 the position
to which it advances
during one day ; P,
the place at which
the sun is on the
meridian at 1; P',
the same place after
one complete rota-
tion, as shown by
the parallel P' 8.
It will be evident
that in order to
bring P' under the
meridian, so that
the sun may appear
to cross it, the earth
will have to turn a
space represented
by the arc P' M, which will make the solar day so much longer than the
sidereal day.
135. The solar day exceeds the sidereal day by an average
difference of four minutes.
QTTKBTIONB. 134. What is a solar day ? . Why are the solar days longer than the
sidereal ? Explain by the diagram. 135. What is the average difference ?
94
TIME.
136. Owing to the variable motion of the earth in its
orbit, and the obliquity of the ecliptic, this difference is not
the same throughout the year ; and consequently the solar
days are of unequal length.
Why the Solar Days are Unequal. The first cause assigned for
the inequality of the solar days will be easily understood, by referring to
Fig. 62 ; since it will be at once apparent that the length of the arc P' M
must depend upon the length of the interval between 1 and 2. If these
intervals vary, the arcs which represent the excess over a rotation turned
by the earth in order to bring the sun on the meridian, must also vary, and
in the same proportion. Hence, they must be longest when the earth is
in perihelion, and shortest when it is in aphelion.
Fig. 63.
The second cause,
namely, the obliquity
of the ecliptic, needs
an independent illus-
tration: Let API
(Fig. 63) represent
the northern hemi-
sphere; A E I the
equinoctial, and A e
I the ecliptic. Let
the ecliptic be divid-
ed into equal por-
tions, A 6, 6 c, c df, etc., and draw meridians through the points of division,
intersecting the equinoctial in B, C, D, etc. The divisions of the ecliptic
will be equal arcs of longitude, and the divisions of the equinoctial will be
the corresponding arcs of right ascension, and hence passed over by the sun
in equal periods of time. These arcs of right ascension, it will be apparent,
are not equal ; for A 6, which is oblique to A B, must subtend a smaller arc,
A B, than d e which is nearly parallel to its arc D E. Thus the arcs of right
ascension are shortest at the equinoxes, and longest at the solstices;
while the divisions coincide at all these four points.
137. A MEAN SOLAR DAY is the average of all the solar
days throughout the year. It is divided into twenty-four
hours, and commences when the sun is on the lower meridian,
that is, at midnight.
QUESTIONS. 136. Why are the solar days unequal? Explain by the diagrams.
What is a mean solar day ?
137.
TIME. 95
a. Because used for the general purposes of civil and social life, it
is also called the civil day. Clocks are regulated to show its beginning
and end, and the equal division of it into hours, minutes, and seconds.
As already stated, it is four minutes longer than a sidereal day.
ft. If the solar days were equal in length, the sun would always be
on the meridian at 12 o'clock ; that is, apparent noon would coincide
with mean noon the noon of the clock. But this is not the case, and
therefore to make the observed noon, as indicated by the sun, corre-
spond with the noon of the clock, a correction has generally to be
made, either by adding or subtracting a certain amount of time. This
correction is called the equation of time.
138. The EQUATION or TIME is the difference between
apparent and mean time ; that is, the difference between
time as shown by the sun, and that shown by a well-regu-
lated clock.
a. The unequal motion of the earth in its orbit causes the sun to
be in advance of the clock from aphelion to perihelion, that is, from
July 1st to January 1st ; and behind it from January 1st to Jul 1st ;
while they both coincide at those points. The obliquity of the ecliptic
causes the sun to be in advance of the clock from Aries to Cancer,
behind it from Cancer to Libra, in advance again from Libra to Capri-
corn, and behind again from Capricorn to Aries ; and makes them
both agree at those four points. To verify this let the student exam-
ine Fig. 63. When these two causes act together, as is the case in
the first three months and the last three months of the year, the equa-
tion of time is the greatest.
139. The equation of time is greatest in the beginning of
November, the sun being then about 16| minutes in advance
of the clock.
a. Hence, to deduce true noon from apparent noon, at that time it is
necessary to subtract 16', minutes from the observed time. The sun is at
the greatest distance behind the clock about February 10th, the equation
QUESTIONS. a. Why called a civil day ? ft. What is meant by apparent and mean
noon ? Do they coincide ? 138. What is the equation of time ? . When is the sun
in advance of the clock? When behind it? 139. When is the equation of time the
greatest ?
9G TIME.
being then 14^ minutes, and, of course, to be added, in order to find
the correct time.
140. Mean and apparent time coincide four times a year,
namely ; April 15th, June 15th, September 1st, and Decem-
ber 24th. The equation of time then becomes nothing.
b. To Find the Equation of Time by the Globe. The part of
the equation of time that depends upon the obliquity of the ecliptic
can be found by the globe, in the following manner : Bring the sun's
place in the ecliptic to the brass meridian, and find its longitude and
right ascension ; the difference reduced to time (counting four minutes
to a degree), will be the equation. If the right ascension exceed the
longitude, the sun is slower than the clock ; if the longitude exceed
the right ascension, the sun is faster than the clock.
Thus, on the 28th of January, the longitude of the sun is about 308, the
right ascension 310 ; hence the sun is 10 minutes slower than the clock.
QUESTIONS. What is the equation of time October 19th ? Ans. Sun 10
minutes faster than the clock.
What is it August 13th ? Ans. Sun 8 minutes slower than
the clock.
141. A SIDEREAL YEAR is the period of time that
elapses from the sun's leaving any star until it returns to
the same again.
a. This is the true period of the annual revolution of the earth,
and is equal to 365 days, 6 hours, 9 minutes, 9 seconds. Owing, how
ever, to the precession of the equinoxes, the sun advances through all
the signs, from either equinox to the same again, in a shorter period.
142. A TROPICAL YEAR is the period that elapses from
the sun's leaving the vernal equinox until it arrives at it
again. It is 20 min. 20 sec. shorter than the sidereal year.
a. Its length is, therefore, 365 d 5 h 48 m 49* which is the civil year, or
the year of the calendar, deducting the 5 h 48 m 49' ; and as this is
very nearly one-fourth of a day, one day is added every fourth year,
QUESTIONS. 140. When is the equation of time nothing ? 141. What is a sidereal
year? 142. What is a tropical year ? How much shorter than a sidereal year? a.
What is its length ? What other names has it ?
QUESTIONS FOB EXERCISE. 97
which makes what is called leap year, or bissextile. The tropical
year is sometimes called an equinoctial or solar year.
b. The sidereal year is not exactly the period which the earth
requires to pass from perihelion to perihelion again, since the perihe-
lion is moving slowly toward the east (Art. 123, c). This period is
called the anomalistic year. It is about 4^ minutes longer than the
sidereal year.
QUESTIONS FOR EXERCISE.
These questions are to be answered by applying the principles explained
in the preceding sections, and without the use of the globe,
1. What is the latitude of the north pole ?
2. What is the latitude of a place under the equator ?
3. New York is about 49 degrees from the north pole ; what is its
latitude ?
4. How many degrees is it from the south pole ?
5. What is the latitude of a place under the Tropic of Cancer ?
6. What under the Antarctic Circle? Under the Tropic of Cap-
ricorn?
7. What is the greatest altitude of a heavenly body ?
8. Where is the altitude greatest ? Where is it least ?
9. If the zenith distance of a body is 15, what is its altitude ?
10. How many degrees wide id the circle of perpetual apparition in
the latitude of New York ?
11. How wide is it at the north pole ? At the equator ?
12. If the declination of a star is 60 N., does it ever set in New York ?
13. Does it rise in latitude 30 S. ?
14. At what points is the declination of the sun greatest ?
15. At what points is its declination nothing ?
16. What is the right ascension of the sun in the first degree of Can-
cer? What in the first degree of Capricorn ? In the first degree of
Libra ? In the vernal equinox ?
17. What is the longitude of the sun in the summer solstice ? In the
winter solstice ? In the autumnal equinox ?
18. When the sun is in either of the equinoxes, what is its merid-
ian altitude in New York ? In London ? At Cape Horn ? At North
Cape?
QUESTIONS. ft. What is an anomalistic year ? Why longer than a sidereal year ?
98 QUESTIONS FOR EXERCISE.
19. What is the greatest meridian altitude of the sun in New York ?
What is the least 1
20. If the declination of a star is 30 N., what is its meridian alti-
tude in New York ? Its zenith distance ?
21. What must its declination be to be seen in the zenith at New
York?
22. When is it longest day in New York ? At Cape Horn ?
23. If a star were seen on the meridian 40 from the zenith, what
would be its altitude, azimuth, and amplitude ?
24. If the meridian altitude of a star in Havana is 50, what is its
declination ?
25. What are the amplitude, azimuth, zenith distance, and altitude
of a star just rising 15 from the east?
26. What is the right ascension of the sun when its declination is
23FS.?
27. What is its declination when its longitude is 90 ?
28. What is its right ascension when its longitude is 180 ?
29. Where is a planet situated when its latitude is ?
30. In what position is Mars when it has the same longitude as the
sun?
31. At what point of a planet's orbit is the centripetal force greatest ?
The centrifugal force ?
32. If the inclination of the earth's axis had been 30, how wide
would each of the zones have been ?
33. If it had been 45, how wide would the torrid zone have been ?
The temperate zones ?
34. If the earth's axis were perpendicular, where would perpetual
summer prevail ? Perpetual winter ?
35. What would be the seasons, if the earth's axis coincided with
the plane of the ecliptic ?
36. Is constant day as long at the south as at the north pole ?
CHAPTER VIII.
THE SUX.
143. The SUN is the source of light and heat to all the
other bodies of the solar system, and the support of life and
vegetation on the surface of the earth, or any of the other
planets.
All the forces displayed on our planet, whether mechanical, chem-
ical, or vital, spring from the sun and his exhaustless rajs ; and yet,
it is calculated, that the earth, with its limited grasp, only receives the
two hundred and thirty millionth part of the whole force radiated and
dispensed by this vast and splendid luminary.
144. The greatest distance of the sun from the earth is
very nearly 93 millions of miles ; and its least distance
about 90 millions ; making the mean distance, as previously
stated, about 91A millions.
a. History of its Discovery. The distance of the sun from the
earth has been, from the earliest times, a subject of close and earnest
investigation to astronomers. Ptolemy and those contemporary with
him, and in more modern times Copernicus and Tycho Brahe, supposed
it to be equal to only 1200 times the radius of the earth, or less than five
millions of miles ; Kepler thought it to be about fourteen millions of
miles ; Halley, sixty -six millions ; and it was not until the middle of
the last century (1769), that any reliable determination of this impor-
tant fact was reached. This was accomplished by finding the horizontal
parallax of the sun by means of observations made at different parts
of the earth, of the transit of. Venus, which took place in that year.
QUESTIONS. 143. What is the sun ? 144 What is its distance from the earth ? a.
Opinions of various astronomers ?
100 THE SUN.
b. When an inferior planet happens to be at or near one of its
nodes, at the time of inferior conjunction, it appears like a round black
spot on the disc of the sun, and moves across it from east to west.
This passage across the disc is called a transit. The transits of Venus
have been of very great interest because employed to determine the
solar parallax. The method will be explained hereafter.
145. The distance of the sun from the earth is ascertained
by finding its horizontal parallax. According to a recent
determination, this is a little less than 9".
a. This has been found by a series of observations on Mars, made at
the time of its opposition in 1860 and 1862, it being in those years at
about its nearest point to the earth. More exactly stated, the solar
parallax is 8. 94".
b. It has been already shown (Art. 87, .), that the angle of parallax
varies with the distance. The method of determining the distance from
the parallax is as follows :
Fig. 64. Let E (Fig. 64) repre-
P sent the centre of the
earth, P, a place on its
surface, and S, the cen-
tre of the sun. Then
P S E is the angle of
horizontal parallax, or
the angle which the ra-
dius of the earth subtends at the distance of the sun. Now, in every right-
angled triangle, such as P S E, the ratio of either side to the hypothenuse
depends on the angle opposite the side ; so that however long the sides of
the triangle may he, the ratio is the same, provided the angle is the same.
Hence, as tables have been calculated containing the ratio of every possi-
ble angle, we can always find, by referring to these tables, this ratio when
we know the angle. In the triangle S P E, S E, the hypothenuse, is the
distance of the sun, and P E, the radius of the earth, equal to 3956 miles.
The opposite angle P S E, is the horizontal parallax, or 8.94". For this
angle we find the ratio to be about .0000432; that is, P E = S E X .0000432 ;
PE
and hence S E = 7)000433 ? but 3956 * -0000432 = 91,5 "4,074, which is about
the mean distance of the sun.
QUESTIONS. 6. What is a transit ? 145. How is the distance of the sun found ? ff.
What is the solar parallax ? ft. How is the distance of the sun deduced from the par-
allax ?
THE SUK. 101
C. The ratio of either side of a right-angled triangle to the hypoth-
enuse, dependent upon any particular angle, is called the sine of that
angle. Thus, the sine of 30 is .5 or ; that is, if brie of the, angles of ,
a right-angled triangle is 30, the side opposite {&&$& Mty'bp one^
half the hypothenuse. _, J ' , 3 , tl
(1. Hence, it may be given as a general rule*, th^tt J #e radiid? ofltye j >
earth divided by the sine of the Jwrizontal parallax of any body is equal
to its distance from the earth.
NOTE. It is important that the student should keep the above definition
and rule in memory, as they will be employed in several subsequent calcu-
lations.
14G. The apparent diameter of the sun, or the angle
which it subtends in the celestial sphere, is about 32', or a
little more than one-ha.lf of a degree.
a. This is the mean value ; the greatest being 32' 86'' ; and the least
31' 32", This variation in the apparent size of the sun is caused by
the elliptical orbit of the e^rth ; it being greatest when the earth is
in perihelion, and least in aphelion. The apparent diameters of the
sun, at different periods of the year, are measures of the different
lengths of the radius-vector of the earth's orbit, and thus lead to a
knowledge of its exact figure.
b. Since the greatest apparent diameter is 32.6 r , and the least 31.533',
their ratio Is as 1.034 to 1 (nearly), and one-half the difference, or .017,
is about the eccentricity of the earth's orbit.
147. The actual diameter of the sun is 852,900 miles, or
107| times the diameter of the earth.
a. This is found by a calculation based upon the principle of the
right-angled triangle, pxplained in Art. 145. The method is as fol-
lows :
Let S (Fig. 65) be the centre of the sun, E the place of the e^irth. Then S A
E is a right-angled triangle, in which the hypothenuse S E is the distance of
the sun from tjie earth., A S the radius pf the sun, and the^xngle A E S
QUESTIONS. <. What Is the vine of an angle? d. Give the general rule. 146.
What is the apnarent diameter of the sun? a. How does it vary ? b. How may the
eccentricity of the earth's orbit be found? 147. What is the actual diameter of the
sun? n, TIow found? Explain from the diagram.
102 THE 8 UK.
Pig - 65 ' one-half the apparent
diameter, or lt>'. The
ratio corresponding to
this angle, or the sine
of the angle, is .00466 ;
hence, 91,500,COO X
.00466 = 426,390, the
semi-diameter of the
sun ; and, therefore, the diameter is 852,780 miles, which is very nearly its
exact length.
148. The figure of the sun appears to be that of a perfect
sphere, no observations having as yet detected any indica-
tions of oblateness.
a Surface and Volume. Since the surfaces of spheres are as tlie
squares of their diameters, and the volumes as the cubes, it follows
that the surface of the sun must be 11,620 times that of the earth, and
its volume 1,252,000 times ; or, in round numbers, one million and a
quarter of worlds as large as the earth must be rolled into one to form
a body of the bulk of the sun.
149. The mass of the sun is 315,000 times as great as
that of the earth.
a. The method of finding this will be explained in a subsequent
article. Since the volume of the sun is 1,252,000, while the mass, or
quantity of matter is only 315,000, as compared with the earth, it fol-
lows that the density of the sun must be only that of the earth.
Now, the earth's density has been found by certain experiments to be
about 5 1 (5.67) times that of water ; hence, that of the sun must be less
than !$ that of water (1.42).
b. From the comparative lightness of its substance, Kerschel infers
that an intense heat prevails in its interior, imparting an expansibility
sufficient to resist the force of gravitation, which, otherwise, would
cause the body to shrink into smaller dimensions.
c. The volume of the sun is, as already stated, about 500 times that
of all the planets ; the mass is, however, about 700 times as great.
QUESTIONS. 148. What is the figure of the sun ? n. What is said of its surface and
volume ? 149. What is its mass ? . Its relative mass and density ? b. What is
the inference drawn by Sir John Herschel? c. Mass of the sun compared with that
of the planets ?
THE SUN.
103
This shows that the density of the sun is greater than the average density
of the planets.
150. The sun rotates from west to east on an axis nearly
perpendicular to the plane of the ecliptic, the period ot
rotation being about 25 1 days (25 d 7 h 48 m ).
151. This is proved by the spots which are seen upon its
disc, and which appear to move across it, occupying about
two weeks in their passage.
Fig, ee.
A SPOT PASSING ACBO88 TITE DISC.
days, the time of one rotation. (See Fig. 67).
6. It may appear singular, at the first view, to infer an eastward rota-
tion of the sun from an apparent westward motion of the spots ; but
it must be remembered that the sides of the sun and earth presented
to each other at any time are moving in opposite directions in space,
while both bodies move in the same direction in circular motion.
c. Discovery of the Spots The discovery of spots on the solar
disc is noticed in history as early as 807 A. D. ; but their true appear-
ance and extent were unknown until the invention of the telescope, in
the beginning of the 17th century, at which time (in 1611) they were
attentively observed by Galileo and others. In recent years, the sun
has received a very great deal of attention from astronomers, and
many interesting facts have been made known respecting its appearance
and physical constitution.
152. The inclination of the sun's axis to the ecliptic is
7| ; and, in consequence of this inclination, the spots
appear to move across the disc in lines of various directions
and form, sometimes being straight and sometimes curved.
SEPTEMBER
N
APPUSENT PATHS OF SOLAR SPOTS.
Fig. 68 illustrates this. In March, when the south pole is presented to
the spectator, the paths assume the appearance indicated in the first circle ;
in June, they are straight and oblique, because the observer is in the plane
QUESTIONS. b. Why do the spo^s seem to move from east to vest? c. History of
their discovery f 152. What is the inclination of the sun's axis ?
THE SUN. 105
of the sun's equator ; while in September, the observer being north of its
equator, the north pole is turned toward him, and they are as represented
in the third circle. [The inclination of the axis is exaggerated in the
diagram.]
153. APPEARANCE OF THE SPOTS. When the spots are
examined by means of a telescope, they present the appear-
ance of irregular black patches surrounded with a dusky
border or fringe, the whole sometimes encompassed with a
bright surface or ridge. The black portion in the centre is
called the umbra or nucleus ; the dusky border, the penum-
bra ; and the bright surfaces seen around the spots, or by
themselves on other parts of the disc, are called faculce.
-- i
BOLAB SPOTS.
a. Sometimes the nucleus is absent ; and sometimes spots are seen
without any penumbra. The nucleus is not of a uniform blackness,
but generally contains an intensely black spot in the centre. These
spots usually appear in clusters, numbering from two to sixty or sev-
enty, or even many more.
154. VARIABILITY OF THE SPOTS. The solar spots con-
stantly undergo very great changes in number, form, size,
and general appearance.
QTJESTIONS. 158. Explain the appearance of the spots. . What diversity in their
appearance ? 154 What changes do they undergo ?
106 THE SUN.
a. Sometimes the sun's disc will be entirely free from them, and
will continue so for weeks and months ; at other times, they will burst
forth and spread over certain parts of it in great numbers. After
twenty-five years of continued observations, M. Schwabe, a German
astronomer, discovered that there was a periodical increase and de-
crease of the number and size of the spots ; and Prof. Wolf, of Zurich,
by comparing the observations made during the last hundred years,
has shown that this period has varied between 8 and 16 years. These
periods are thought by some to depend upon physical influences exerted
by some of the planets, particularly Venus and Jupiter, when in cer-
tain positions of their orbits.
Fig. 70.
m
SUN-SPOT, JULY 29, 1860, STTfttVTN'G TITR " WTT.T.OW-LE\P M STRUCTURE.
b. The spots are mostly confined to two zones parallel to the equator,
and extending from 5 to 35 from it ; and they appear to have a tend-
ency to arrange themselves in lines parallel to the equator.
c. The duration of single spots is also very variable. A spot has
been seen to make its appearance and vanish within twenty-four
QUESTIONS. -rr. What periods have heen established? b. To what zone are the
spots mostly confined ? c. Their duration ?
THE SUN. 107
hours ; while others have continued for nine or ten weeks, without,
much change of appearance.
d. Their magnitude also presents very great diversity. Spots are
not unfrequently seen that subtend an angle of more than 60", or
nearly seven times the sun's horizontal parallax ; the diameter of such
spots must therefore be more than 25,000 miles. A spot in June, 1843,
continued visible to the naked eye for a whole week, its length being
estimated at 74,000 miles. One observed in 1839, by Capt. Davis, had
a linear extent of 186,000 miles.
Fig. 70 represents a large spot as seen and drawn by Mr. Nasmyth, an
English astronomer, in 1860. It shows the umbra, penumbra, the latter
arching the former as well as surrounding it, and also the dotted or mottled
surface of the sun, as seen through a powerful telescope. The penumbra
presents the appearances to which Mr. Nasmyth has applied the name of
44 willow leaves," from their fancied resemblance to such objects.
155. THEORIES AS TO THE PHYSICAL CONSTITUTION OF
THE SUN. The most generally received hypothesis as to
the nature of the sun is that it is an opaque body surrounded
by an atmosphere of luminous matter, and that the spots
are openings in the atmosphere, through which the dark
body of the sun becomes visible.
a. This hypothesis was first advanced by Dr. Wilson, of Glasgow,
in 1769. In 1793, Sir William Herschel suggested the hypothesis that
two atmospheres encompass the sun ; the first or lower one being
formed of a partially opaque or cloudy stratum reflecting light, but
emitting none of itself ; and the second consisting of luminous mat-
ter, which is the source of the sun's light, and gives to the disc its
form and limit. This luminous atmosphere has been sometimes called
the photosphere.
b. The existence of a third atmosphere, very nearly transparent,
and extending a great distance above the photosphere, is clearly indi-
cated by the diminished brightness of the sun's disc toward the edges.
c. Wilson's and Herschel's hypotheses, as developed and modified
. . Their magnitude? 155. What generally received hypothesis as to
the cause of the spots ? a. By whom advanced ? ft. What evidence of a third atmos-
phere? f. How do Wilson' 8 and Herschers hypotheses explain the phenomena?
Cause of the openings ?
108 THE SUN.
by more recent observers, explain all the phenomena of the spots.
The black umbra is the body of the sun, while the penumbra is the
non-luminous atmosphere, or cloudy stratum, rendered visible by the
larger opening in the photosphere above it. When this opening is
smaller, no penumbra is visible ; and when there is no opening in the
cloudy stratum, no black nucleus is visible. These openings or rents
are supposed by Sir John Herschel to be caused by changes of tern-
perature, in a manner similar to the production of tornadoes and other
agitations of the earth's atmosphere.
156. The spots and other appearances on the sun's disc
indicate, without doubt, the existence of a luminous atmos-
phere, consisting of gaseous matter in an incandescent
state, like the flame of an ordinary gas-burner, and
another atmosphere, also gaseous, and almost perfectly trans-
parent, extending to a considerable distance beyond.
a. The gasoous character of the atmosphere, denied by Sir William
Herschel, seems to have been conclusively proved by M. Arago, by means
of an ingenious application of the principle of polarized light. M. Faye
estimates the height or extent of the photosphere at 4,000 miles.
b. KirchhofFs Hypothesis. A simpler hypothesis than Wilson's
and HerschePs has within the last five years been advanced by Kirchhoff,
a German physicist, and others, to account for the phenomena of the
spots, consistently with the established facts, as above stated. Accord-
ing to this hypothesis the nucleus of the sun is an incandescent, solid
or liquid mass, the vapors arising from which form the atmospheres,
the denser and lower one being luminous from the incandescent particles
that float in it. Changes of temperature in this atmosphere give rise
to tornadoes and other violent agitations ; and descending currents pro-
duce the openings, which are dark because filled with clouds of various
degrees of condensation. This theory, and the experiments upon which
it is based, are receiving, at present, much attention from astronomers
and physicists ; and there is reason to believe, that when fully devel-
oped, it will entirely supersede the cumbrous and therefore improbable
hypothesis so long and so ingeniously sustained.
QUESTIONS. 156. What is certainly indicated by the phenomena ? a. Gaseous char-
acter of the atmosphere ? b. Explain Kirchhoffs hypothesis.
THE SUN.
Fig. 7L
109
ARTH
**
APPARENT MAGNITUDES OF THE 8TTN.
157. The apparent diameter of the sun at each of the
planets diminishes in proportion as the distance increases.
Thus, at Mercury, it is 2^ times as great as at the earth ;
but at Neptune, only ^ as large.
a. The surface of the solar disc at Mercury must therefore be
about 6,000 times as great as at Neptune, and the intensity of its
light and heat in the same proportion.
ft. Various experiments seem to show that the light of the sun at
the earth is equal to that of 600,000 full moons ; (Wollaston estimated
it at 800,000.) The light of the sun at Neptune must therefore be
equal to about 670 times that of the full moon at the earth. The
electric light is the only light that approximates in intensity to the
light of the sun.
c. The intensity of heat at the surface of the sun has been esti-
mated to be 300,000 times that received at any point of the earth's sur-
face. Sir John Herschel supposes that it would be sufficient to melt a
cylinder of ice 45 miles in diameter, plunged into the sun, at the rate
of 200,000 miles a second.
158. In addition to the rotation on its axis, the sun
appears to have a progressive motion in space, revolving
with all its attendant bodies around some remote star or
centre.
QUESTIONS. 157. How does the sun appear at the different planets? a. Its surface,
light, and heat, at Mercury and Neptune? b. Light of the sun? c. Intensity of its
heat? 15S. Motion of the sun and solar system in space ?
110
ZODIACAL LIGHT.
or about -fa of the
earth's surface; and its volume (ft ) 3 , or about -^ that of the earth.
Its mass is estimated to be about -^ of the earth's ; and consequently
its density must be considerably less, about .
PHASES OF THE MOON.
165. The moon, when she first becomes visible in the
west, is seen as a slender crescent ; but from evening to
evening her form expands as her angular distance eastward
from the sun increases, until when in quadrature, or 90
from the sun, half of her disc is visible. When she has
departed so far to the east that she rises just as the sun sets,
the whole of her disc is seen, and she is said to be full.
After this she becomes the waning moon, rising later and
later, and growing less and less, until she may be seen in
the east as a bright crescent just before sunrise. A short
time after this she disappears, and then becomes visible
again in the west. These different appearances, called the
phases of the moon, prove that she revolves around the earth
from west to east.
166. When the moon is in conjunction, the dark side
being turned toward us, she is called new moon ; when she
is in quadrature and shows half of her disc, she is called
half-moon; when she is in opposition, she is called full
moon. When she is in quadrature after conjunction, she is
said to be in her first quarter ; when in quadrature after
opposition, in her last quarter.
QUESTIONS. b. The surface, volume, and mass of the moon? 165. Describe the
phases of the moon ? 166. What is the phase in conjunction, etc. ?
THE MOOtf.
Fig. 74.
115
PHASES OP THR MOON
167. When she is between conjunction and quadrature
she assumes the crescent form, and is then said to be horned ;
when she is between opposition and quadrature, she exhibits
more than one-half of her disc, but not the whole, and is
said to be gibbous.
The positions of new and full moon are sometimes called the
tyzygies*
1C8. The phases of the moon are the different portions of
her illuminated surface which she presents to the earth as
she revolves around it.
* From the Greek word syzygia, meaning a yoking together.
QUESTIONS. 16T. When is the moon said to be horned? Gibbous? What are the
syzygies? 168. Define the phases.
V
116 THE MOON.
Fig. 75. In Fig. 75, let the par.
tially darkened circle
represent the moon ; 8^
the direction of the sun ;
E, the direction of the
earth on one side of the
moon, and E', its direc-
tion on the opposite side .
Then a 6 will represent
the line which separates
the illuminated and
" ' darkened hemispheres of
MOON HOBNKD AND GIBBOUS. the moon ; and c d, that
which separates the hemisphere turned toward the earth from that turned
away from it. At E, a c being the only part of the disc visible, the moon
appears horned ; while at E', b c being visible, the form is gibbous.
a. Hence we can find the time of a revolution of the moon by
observing the phases. If the earth were at rest, the time from one
new or full moon to the next would be exactly the period of a revolution ;
but as the earth is constantly advancing in her orbit, when the moon
has completed a revolution, she has to move still farther in order to
come into the same relative position with the earth and sun.
169. The time from one new moon to the next is 29A
days. This is the synodic period, and is called a sy nodical
month, or lunation.
a. Sidereal Period Calculated. In a year, or 365 \ days, the
moon makes 365^ -=- 29 -K or 12 , 4 ft synodic revolutions ; but the side-
real, or actual, revolutions of the moon must be one more ; because
each synodic revolution is equal to one sidereal revolution and a part
of another, equal, in angular measurement, to the advance of the earth
in her orbit during each synodic revolution of the moon. Hence, the
moon performs 13^ sidereal revolutions in 3651 days : but 365; day
-^-13,VV:= 27 : V days (nearly), which is, therefore, the time of one
sidereal revolution.
In Fig. 76, let A B represent the advance of the earth in its orbit, while
the moon completes a synodic revolution, that is, moves from c, the posi-
tion of inferior conjunction, till she arrives at the same relative position
QUEBTIONR. a. What can we find by the phases ? 169. What is a synodical month,
or lunation ? a. How to find the sidereal period ? Explain by the diagram.
THE MOON.
117
with the sun at E. But when she reaches this point, she has completed a
sidereal revolution, and has also moved from D to E, a distance, it will be
Fisr. 76.
8IDEEEAL AND 6TNODICAL REVOLUTION.
seen, equal in angular measurement to A B ; since the arc A B bears the
same proportion to the earth's orbit that E D does to that of the moon.
170. Owing to the constant advance of the moon in her
orbit, she rises and, of course, arrives at the meridian and
sets, about 50 minutes later each successive day.
a. This is the average interval of time between the successive ris-
ings of the moon ; for since she moves through the ecliptic in 29 days,
her daily advance is equal to about 12i ; but a place upon the earth's
surface moves 15 in one hour, and hence, requires nearly 50 minutes
to overtake the moon. If the moon's orbit or the ecliptic, since the
inclination is very small, always made the same angle with the hori-
zon, this would be the constant interval ; but, in consequence of the
obliquity of the ecliptic, this angle continually varies during each
lunation.
171. The HARVEST MOON is the full moon that occurs
in high latitudes, near the time of the autumnal equinox, in
September and October, when she rises but a little later for
several successive evenings, and thus affords light for col-
lecting the harvest.
a. By means of the globe, it may be easily shown that the ecliptic
is most oblique to the horizon in the signs Pisces and Aries, and least
so in Virgo and Libra ; so that when the moon is in the former signs,
in this latitude, she rises only about half an hour later, but when in
QUESTIONS. 170. Why does the moon rise later each evening? a. Why are the
intervals unequal ? 171. What is harvest moon ? . How to explain this phenomenon?
118
THE MOON.
the latter, more than an hour. This difference is, however, only
noticed when the moon happens to be full while in Pisces or Aries,
and thus rises, for several evenings, in the higher latitudes, but
a few minutes later. These full moons must occur, of course, in
September and October, when the sun is in the opposite signs, Virgo
and Libra. In the former month, the full moon in England is called
the Harvest Moon ; in the latter, sometimes, the Hunter's Moon.
Let H S H M (Fig. 77) represent
the horizon; S, the position of the
sun at sunset ; M, the full moon
just rising ; SAM, the part of the
equator, and S B M, the part of the
ecliptic above the horizon, the sun
being in Libra, the autumnal equi-
nox, and the moon in Aries, the
vernal equinox. Since the southern
half of the ecliptic lies east of Libra,
it will be evident that in or near
this position the ecliptic must make
the smallest angle with the horizon ;
and consequently, while the moon
makes her daily advance in her
orbit, M 6, she only descends below
the horizon a distance equal to A 6 ; while, if her orbit made a greater
angle with the horizon, as S A M, she would, by advancing through the
equal arc M a, descend below the horizon a distance equal to h a.
b. In the Polar Regions, since the full moon must be opposite to
the sun, it remains constantly above the horizon ; and during about 15
days passes through its changes without rising or setting, appearing
to move around the horizon ; and at the pole, in a circle exactly parallel
to it. At the time of the solstice, it is first seen in the west in its first
quarter, and continues constantly visible till the last quarter. These
brilliant moonlight nights serve partially to compensate the inhabit-
ants of those dreary regions for the long absence of the sun.
c. Moonlight in Winter. The moonlight nights in the temperate
latitudes are longer and more brilliant in winter than in summer;
especially about the time of the winter solstice. For when the sun is
in Capricorn, 23^ south of the equinoctial, the full moon is in the op-
HARVEBT MOON.
QUESTIONS. 6. The moon as seen at the polar regions ? c. Moonlight in winter ?
THE MOON. 119
posite sign, Cancer, 23 north of the equinoctial, and therefore
culminates at a great altitude ; and, if she happens to be also at the
point of her orbit, 5 J 7 north of the ecliptic, at her greatest altitude,
which is equal to the complement of the latitude plus 23 plus 5|.
In New York, this is 49 + 23^ -f 5| = 77 38'.
172. Observations with the telescope show that the moon
always presents very nearly the same hemisphere to the
earth. This proves that it rotates on its axis once during
each sidereal month, or 27 3 days.
a. The unassisted eye is able easily to perceive that the dusky
spots on the disc of the moon constantly keep in the same relative po-
sition and present the same appearance ; and this could not occur if
she rotated so as to present in succession different hemispheres to the
earth. Just as we infer a rotation of the sun from the apparent
motion of the solar spots, so we know that the moon rotates during
one revolution around the earth, by the observed fact that the lunar
spots have no apparent motion ; since, if the moon performed no rota-
tion, the spots on its disc would move across it from west to east,
keeping pace with the moon's motion in the ecliptic, and completing
one apparent revolution in 29^ days.
Fig. 78.
c c
J \f
That the moon must perform one rotation during each sidereal month,
in order to keep the same side turned toward the earth, will be evident
from the annexed diagram (Fig. 78). Let the line 1, 2, 3, etc., represent
a portion of the earth's orbit, and the dotted curve the real orbit of the moon,
as it is carried by the earth around the sun during one lunation. When
QUESTIONS. 172. How do we know that the moon rotates ? a. How to explain this?
120 THE MOON.
the earth is at 1, the moon is full ; at 2, last quarter ; at 3, new ; at 4, first
quarter ; and at 5, full again. The line a b indicates the position of the
moon at the commencement of a rotation ; and the parallel line c d, its
position if it had only completed a rotation at the end of the lunation ; lout
it is evident that in order to keep the same face to the earth at 5, it must
have turned more than one rotation by the angle contained between c d
and ef. Hence, during a synodic period, or lunation, the moon performs
more than one rotation, which she completes in a sidereal period, or 2?'
days.
173. The real orbit of the moon, as she is carried by the
earth around the sun, crosses the earth's orbit every 14.J ,
but departs so little from it that it is always concave to the
sun.
a. It will be evident from Fig. 78, that the moon crosses the earth's
orbit twice during each lunation, or 29^ days ; but there are nearly 12^
lunations in a year ; hence the moon must cross the earth's orbit 25
times during one year ; and 360 -5- 25 = 14^ (nearly).
b. The Lunar Orbit. The orbit of the moon, if correctly repre-
sented in relation to that of the earth, would present the appearance
of a continuous curve, never crossing itself, and so slightly deviating
from the earth's orbit as, unless drawn on a very large scale, scarcely
to be distinguished from it. This will be evident when it is considered
that the moon's distance from the earth is only about - 4 - |p - of the earth's
distance from the 3un. Why the lunar orbit is always concave to the
sun, will be made clear by the following diagram :
Let the dotted curve ABODE represent the moon's orbit crossing 1 that
of the earth at A, C, and E. At A, the moon is in first quarter, and west of
the earth (although east of the sun) ; at B, it has made one-fourth of a revolu-
tion, and is opposite to the sun and full ; at C, it is in last quarter, being
east of the earth ; at D, it is new ; and at E, again west of the earth and
in first quarter, having thus completed one lunation. The arc A C or C E
being known, it it easy to compute the distance of the chord A C or C E
from the arc. This will be found to be about 750,000 miles ; but as the
moon's distance from the earth is only 240,000 miles, its orbit can never be
beyond the chord, but must, as at C D E, be within it ; and hence, must be
always concave to the sun. In the diagram, the principle only is illustrated,
QUESTIONS. 173. Describe the real orbit of the moon. a. How often does it cross
the earth's orbit ? 6. Why always concave to the sun ? Explain from the diagram.
THE MOON
Fig. 79.
the relative distance of the moon being greatly exaggerated, as well as the
orbital movement of the earth during the lunation. The arc A C E in the
diagram is more than 130 , whereas it should be only about 29.
c. Librations of the Moon. As the orbit of the moon is elliptical,
her velocity is not uniform, sometimes exceeding that of her rotation,
and at other times exceeded by it. In consequence of this, a small
portion of the hemisphere turned away from the earth becomes visi-
ble alternately at the eastern and western limbs. This is called the
libration* in longitude. A portion of her surface is also exhibited
alternately at each pole, caused by the inclination of her axis to the
plane of her orbit. This is called the libration in latitude.
The greatest extent of the libration in longitude is 7 53' ; in lati-
tude, 6 47' ; and the whole amount of the moon's surface made visible
by both is about yfo. There is also a third libration caused by the
difference in the angle under which the moon is viewed at anyplace
when on the meridian from that at which we see it when at or near
the horizon. This is called the diurnal libration. It is, however,
quite inconsiderable, amounting to only 32" when greatest, and bring-
ing into view but T ^ of the moon's surface. Hence, -, 5 (fo fi o of the
lunar surface is all that we are ever able to see ; -f-g-fc having never
been gazed at by any human eye.
* Libration means a balancing, and is applied in consequence of the ap-
parent rolling or vibratory motion of the moon from one side to the other.
QUESTIONS. c. What are librations ? Of how many kinds ? Explain each,
much of the moon's surface have we ever been able to see ?
How
1.22 THE MOON.
d. Position of the Lunar Axis. The moon's axis leans toward
its orbit 6 39' ; hence, this is the angle which the plane of its equator
makes with that of its orbit ; and observation determines that the
plane parallel to the ecliptic lies between these two planes / therefore,
the inclination of the moon's axis to the plane of the ecliptic is equal
to 6 39' 5 8', (the inclination of the orbit) ; that is, 1 31'.
It is a curious fact that the line of equinoxes of the moon constantly
coincides with the line of nodes of its orbit, the ascending node of its
orbit being situated at the descending node of its equator. Hence the
lunar equinoxes retrograde with the nodes, and the pole of the moon
revolves around that of the ecliptic, requiring 18? years to complete
the circuit.
Fig- 80. Fig. 80 represents
the moon in two po-
sitions of her orbit,
O O; at 1, in the
ascending node, and
at 2, when she has
her greatest north-
ern latitude. E E
represents the plane
of the ecliptic, and
E' E', a plane paral-
lel to it, each pass-
ing between the
planes of the moon's equator and orbit, and at the point where the former
descends below the latter. The angular distance between the planes E E
and E' E', of course, never exceeds 5f , which is about ten times the appar-
ent diameter of the moon as seen from the earth. Hence, the greatest
distance between these planes is about ten times the diameter of the moon,
or 21,600 miles, which at the distance of the sun subtends an angle of
about 49", and to this extent may affect the inclination of the axis to the
ecliptic.
174. Owing to the small inclination of the moon's axis
to the plane of the ecliptic (1 31'), she can have but very
little change of seasons, and that not constant, because her
axis does not always point in the same direction.
a. From what has been said above (Art. 173, d), it will be evident
QUESTIONS. d. Explain and illustrate the position of the lunar axis. What curious
fact is mentioned ? 174. What change of seasons has the moon ? a. What change n
the equinoxes and solstices?
THE MOOtf. 123
that the lunar solstices and equinoxes change places with each other
every 9^ years ; whereas, the period required for a similar change in
the earth, occasioned by precession, is about 13,000 years.
175. A lunar day must be nearly 15 times as long as one
of our days, and a lunar night of the same length ; since
any place on the moon's surface requires 29^ days to return
to the same relative position with the sun. Hence the sun
must remain above the horizon during one half of that
period, and below it the other half.
a. Mountains situated at either of the lunar poles must have per-
petual day ; for the sun there can never be more than \\ below the
horizon ; and on so small a body as the moon, the horizon would dip
that amount at an elevation of about \ mile.
b. The Earth's Light. On one hemisphere of the moon, the long
night must be relieved by the light of the earth, which exhibits the
same phases to the moon as the latter does to the earth, except that
they are reversed ; that is, when the moon is new to us, the earth is
full to the moon ; and when the lunar form is but a slender crescent,
the earth is gibbous, showing itself with almost full splendor. Now,
as the earth's disc contains about 14 times as much surface as that of
the moon, the light of the earth must cause a very considerable illu-
mination.
c. The effect of this is seen when the moon is just emerging from
conjunction, the dark part of her disc being slightly illumined by the
light of the nearly full earth, so that the full, round form of the
moon's disc becomes visible, the bright crescent appearing at the edge
toward the sun. This is sometimes called " the old moon in the new
moon's arms."
d. The Earth appears Stationary to the Moon. The earth,
although it exhibits phases to the moon, does not appear to revolve
around it, but remains at every place on the lunar hemisphere which
is turned toward it, nearly at a fixed point in the heavens ; this point
varying, of course, with the change of place of the observer. This
will be obvious, when it is considered that the rotation of the moon
would give the earth an apparent motion from east to west; but the
QUESTIONS. 1T5. What is the length of a lunar day and night ? a. Where is there
perpetual day ? b. The earth's light effect on the moon? c. " The old moon in the
new moon's arms ?'' d. Why must the earth appear stationary to the moon ?
124 THE MOON.
motion of the moon in her orbit would give it an apparent motion at
the same rate, from west to east ; hence, one counteracts the other, and
the earth appears to be almost stationary, only shifting its position
backward and forward by the amount of libration.
176. Appearances indicate that the moon has very little,
if any, atmosphere ; and that its surface is as devoid of
water as of air.
a. When viewed with a telescope, the surface of the moon appears
entirely unobscured by any clouds or vapors floating over it ; and
when the moon's edge comes in contact with a star, the latter is im-
mediately extinguished ; whereas, if there were an atmosphere, it
would, from the effect of refraction, rest on the edge for a short time ;
that is, it would be visible when a short distance actually behind the
moon. Observations of this kind have been made with so much
nicety, that it is believed that an atmosphere two thousand times less
dense than that of the earth could not have escaped detection. If any
atmosphere therefore exists, it must be rarer than the attenuated air
in the exhausted receiver of the most perfect air-pump.
b. The absence of water follows from that of air ; since, without
the latter, the heat of the sun would be incapable of preserving the
temperature above the freezing point ; as we see on the tops of terres-
trial mountains, which are constantly covered with snow, from the
extreme rarefaction of the air at those heights. If water existed, it
would therefore soon be converted into ice ; but we see no indications
of it even in this form.
c. Some have accounted for this by supposing that the internal heat
of the moon was once very great, as is that of the earth at the present
time ; but that having cooled, the moon has contracted in volume, and
that vast caverns have thus been formed in its interior, into which the
water has penetrated, and, of course, disappeared. Indeed, it is obvi-
ous that only great internal heat could keep an ocean upon the surface
of a body like the earth or moon.
SELENOGRAPHY.
177. That part of the moon's surface which is turned
toward the earth has been very carefully observed, and all
QUESTIONS. 1T6. Has the moon any atmosphere ? a. How is this known ? 6. Why
no water? c. How accounted for ? ITT. What is selenography ?
THE MOON.
125
the objects upon it delineated upon maps or charts, so as to
show their exact forms and relative positions. This branch
of astronomical science is called SELENOGKAPHY.*
a,. This department of the astronomer's labors has been prosecuted
with extraordinary zeal and industry by the Prussian astronomers,
Beer and Madler. Their chart, measuring 37 inches in diameter,
exhibits the lunar surface with the most astonishing minuteness and
accuracy. Other charts have also been constructed ; and the moon is
still receiving a very scrutinizing survey by a number of eminent
astronomers, each taking a separate belt or zone, with the object of
arriving at still greater minuteness of delineation.
178. The moon's disc when viewed through a telescope
presents a diversified appearance of dusky and bright spots ;
the latter being evidently elevated portions of the surface,
and the former, plains or valleys.
u. The dusky patches were once thought to be seas, and they still
Pig. 81.
PHOTOGRAPHIC VIEWS OF THE MOON. D, L(l Rue.
* From the Greek word selerie, the moon, and graphy, a description.
QUESTIONS.^. Construction of lunar charts? ITS. How does the moon appeal
when viewed through a telescope ? . What are the dusky patches ?
126
THE MOON.
retain these names in selenography, although without any such literal
meaning ; thus, one is called Mare Tranquillitatis, or Sea of Tranquil,
lity ; another, Mare Nectaris, Sea of Nectar, etc.
b. Lunar Mountains. Mountains on the moon's surface are indi-
cated by the bright spots that appear scattered over the disc, and
beyond the terminator, or line that separates the dark from the illumi-
nated part of the disc, and by the shadows cast upon the surface of the
mo3n when the sun shines obliquely upon these elevations.
c. These mountains are of various forms, including with others, the
following :
1. Rugged and precipitous ranges, many of a circular form, enclos-
ing great plains, called on this account, " Bulwark Plains," from 40 to
Fig. 82.
COPERNICUS, FEOM A DBAWING BY SIR JOHN HEB8CHKL.
120 miles in diameter ; 2. Lofty mountains, of a circular form,
enclosing an area from 10 to 60 miles in diameter, resembling the crater
QUESTIONS. &. How are mountains indicated ? c. What classes of mountain for
mations ?
THE MOON".
12?
of a volcano but of vast size, and sometimes containing in the centre one
or more lofty peaks : such formations are called Ring Mountains;
3. Smaller cavities, called craters, also enclosing a visible space, and a
central mound ; and 4. Deep hollows, called holes, showing no enclosed
area.
From the Ring Mountains, streaks of light and shade radiate on all
sides, spreading to a distance of several hundred miles. These are
called radiating streaks. They are attributed by some to the streams
of lava which once flowed in all directions from these evidently vol-
canic mountains.
(1. Copernicus. (Fig. 82) This is one of the grandest of the
Ring Mountains. It is 56 miles in diameter, and has a central
mountain, two of whose six peaks are quite conspicuous. The
summit, a narrow ridge, nearly circular, rises 11,000 feet above the
bottom. It is very brilliant in the full moon, sometimes resembling a
string ot pearls. It lies on the terminator a day or two after first
quarter. Another of the Ring Mountains (Tycho) is visible to the
naked eye, in the southeast quadrant of the moon. It is 54 miles
across, and is 16,600 feet high.
e. Height of Lunar Mountains. Beer and Madler have calcu-
Fig. 83.
lated the height of more than 1000
mountains, several of which reach
an elevation of 23,000 feet, which
is nearly equal to that of the loftiest
terrestrial peaks ; and, of course,
relatively very much greater.
To understand the principle on
which the altitude of the lunar mount-
ains is found, let E (Fig. 83) repre-
sent the position of the earth, C, the
centre of the moon, S, the direc-
tion of a ray of the sun, falling on the
top of a mountain at M, which there-
fore appears to an observer at E, at
the distance A M from the terminator
at A. Now, this distance can be found
by angular measurement and. calcula T
tion. Suppose it to be about & of the apparent diameter of the disc, or
QUESTIONS. d. Describe Copernicus, e. Height of lunar mountains ? How found ?
128 THE MOOX.
about V ; then A M will be & of the moon's diameter, or about 72 miles.
Then, from the properties of the right-angled triangle, (A C) 2 + (A M)* =
(C M)2 ; that is, (1080) 2 + (72)* = (C M) = 1,171,584 ; the square root of which,
1082.4, will be C M. As this is the sum of the moon's radius and the
height of the mountain, the latter must be 1082.4 1080 = 2.4 miles.
/. The General Physical Condition of the Moon's Surface,
therefore, as far as we can observe it, is characterized by uniform deso-
lation and sterility. Sir John Herschel says, that among the lunar
mountains is seen in its greatest perfection, the true volcanic charac-
ter, as observed in the crater of Mt. Vesuvius and elsewhere, except
that the internal depth of these lunar craters is sometimes two or
three times as great as the external height, and that they are of vastly
greater magnitude. By means of the great telescope of Lord Rosse,
the interior of some of these craters is seen to be strewed with huge
blocks, and the exterior crossed by deep gullies radiating from the
centre. No reliable indication of any active volcano has ever been
obtained ; although, Sir William Herschel, in 1787, asserted that he
had seen three lunar volcanoes in actual operation.
(/. Are there People in the Moon ? This question has often been
discussed, but idly ; since no positive evidence can be adduced on one
side or the other. The distance of the moon is too great for us to
detect any artificial structures, as buildings, walls, roads, etc., if there
were any ; and certainly, without air or water, no animals such as
inhabit our own planet could exist there. But the Almighty Creator
can place animals and intelligent beings in any part of the universe,
and accommodate them to the peculiar circumstances of tlieir abode ;
and it would perhaps be strange if He had left even our little satel-
lite without an intelligent witness of His infinite power and benefi-
cence.
IRREGULARITIES OF THE MOON'S MOTIONS.
179. The attraction of the sun acting unequally on the
moon in different parts of its orbit gives rise to very many
disturbances and irregularities in its motion ; so that it is a
very difficult problem to calculate its exact place at any
given time.
QUESTIONS. /. Physical condition of the moon's surface ? g. Is the moon inhabited ?
179. Lunar irregularities how caused ?
THE MOON. 129
a. The sun's attracting force upon the moon acts directly in con-
junction and opposition, but, on account of the difference in the
distance, is greater in the former position than in the latter ; while at
the quadratures, it acts obliquely, thus giving rise to a variety of dis-
turbances, or perturbations.
b. The attraction of the sun upon the moon is absolutely more than
twice as great as that of the earth ; but being very nearly equal
on both earth and moon, they move with regard to each other
almost as if they were not attracted at all by the sun. If the attrac-
tion of the sun upon the earth were suspended, the moon would
abandon the earth, and either revolve around the sun, or move directly
to it. As the distance of the earth and moon from each other is so
small relatively to their distance from the sun (about - 3 -i 4 -), their mutual
attractions are not much disturbed by the action of the sun ; but they
are to some extent. Thus, in conjunction, the moon is attracted more
than the earth, but in opposition, less ; so that the tendency of the
sun's force is to pull them apart when in either of these positions. In
the quadratures, however, the sun's force acts obliquely, and con-
sequently tends to pull them together. Hence, we may say, the
attraction of the earth upon the moon is diminished in the syzygies,
and increased in the quadratures.
c. The following are the principal irregularities or inequalities to
which the moon's motion is subject : (Those completed in short periods
are called periodical; those that require very long periods for their
completion are called secular)
1. Ejection, which is the largest of these inequalities, is the variation
in the moon's longitude, due to the action of the sun, above referred to.
It depends upon the moon's angular distance from the sun, and the
eccentricity of its orbit. By it the equation of the centre of the moon
is diminished in syzygies and increased in quadratures. It may influ-
ence the moon's longitude to the extent of 1 SO*. This irregularity
was discovered by Ptolemy.
2. The variation, which also affects the longitude of the moon to
the extent of 3(X. It arises from the disturbing force of the sun, act-
ing upon the moon when in the octants, or points half-way between
the syzygies and quadratures. This was discovered by Tycho Brahe,
QUESTIONS. a. How does the sun's force act? b. Its effect in syzygies and quadra-
tures? c. What is evection ? The variation ?
130 THE MOON.
and was the first lunar inequality explained by Sir Isaac Newton by
applying the law of gravitation.
3. The annual equation, which results from the varying velocity of
the earth in its orbit. It may affect the moon's longitude about 11'.
4. The parallactic inequality, arising from variations in the disturb-
ing force of the sun upon the moon according as the latter is in that
part of its orbit nearest to, or farthest from, the sun. It may affect the
moon's longitude to the extent of 2'.
5. The secular acceleration of the moon's mean motion, caused by
the diminution of the eccentricity of the earth's orbit. At present it
amounts to 10" every 100 years, the periodic time of the moon being
constantly diminished to that extent. This was discovered by Halley
in 1693, by comparing the periodic time of the moon, as deduced from
Chaldean observations of eclipses made at Babylon, 720 and 719 B.C.,
with Arabian observations made in the 8th and 9th centuries A.D.
La Place demonstrated its cause. At a very distant period, this
inequality will, of course, be reversed, becoming a retardation instead
of an acceleration.
d. Other irregularities have been discovered, caused by the disturb-
ing action of Venus. These various inequalities constitute what is
called the Lunar Theory ; and when they are all applied, the computed
place of the moon should precisely agree with the observed place.
QUESTIONS. The annual equation ? The parallactic inequality ? The secular accele-
ration ? d. What other inequalities ? The Lunar Theory ?
CHAPTER X.
ECLIPSES.
180. An ECLIPSE * is the concealment or obscuration of
the disc of the sun or moon by an interception of the sun's
rays. Eclipses are, therefore, either Solar or Lunar.
181. A SOLAR ECLIPSE is caused by the passage of the
moon between the earth and sun so as to conceal the sun
from our view.
182. A LUNAR ECLIPSE is caused by the passage of the
moon through the earth's shadow.
a. By a shadow is meant simply the space from which the light of a
luminous body is wholly intercepted by the interposition of some
opaque body. Since light proceeds from a luminous body in straight
lines, and in all directions, the darkened space formed behind the
earth or moon must be conical ; that is, of the form of a cone, circular
at the base and terminating at a point ; since the sun or luminous
body is larger than either of the opaque bodies. The shadow is some-
times called by its Latin name, umbra.
b Besides the totally darkened space called the umbra, there is
formed on each side a space from which the light is only partially
excluded ; this is called the penumbra.^ The relations of the umbra
* From the Greek word ekleipsis, which means a, fainting away. The ecliptic
is so called because eclipses only take place when the moon is in its plane.
t From the Latin word pene, meaning almost, and umbra, meaning a
shadow.
QUESTIONS. 180. What is an eclipse? Of how many kinds? .181. How is a solar
eclipse caused? 182. A lunar eclipse? a. How is a shadow defined? The form oi
the earth's or moon's shadow ? ft. Define the terms umbra and penumbra.
132 ECLIPSES.
to the penumbra will be understood by inspecting the annexed dia-
gram (Fig. 84).
Pig. 84.
80LAB AND LUNAB ECLIPSES.
183. If the moon moved exactly in the plane of the
earth's orbit, a solar eclipse would occur at every new moon,
and a lunar eclipse at every full moon ; but as the moon's
orbit is inclined to that of the earth, an eclipse can only
happen when the moon is at or near one of its nodes.
a. When the moon is new or full at a considerable distance from
its node, it is too far above or too far below the plane of the ecliptic to
intercept the sun's rays from the earth, or to pass within the limits of
the earth's shadow. It will be easily understood that no eclipse can
occur unless the sun, earth, and moon are situated exactly or nearly
in the same straight line. [See Fig. 84.]
ft. The limit north or south of the ecliptic within which an eclipse
must occur is larger in the case of solar than in the case of lunar
eclipses. In the former it varies from 1 35' to 1 24' ; in the latter,
from 63' to 52'.
QUESTIONS. 183. Where must the moou be when an eclipse occurs ? . How sx-
plained? b. What is the limit in latitude for solar and lunar eclipses ? Explain and
demonstrate each by Fig. 85.
ECLIPSES 133
Fig. 85.
To explain how this is found, let S be the centre of the sun, and O the
centre of the earth, S O E being the plane of the ecliptic ; let also P be
the position of the moon at the limit for a solar eclipse, and V, its position
for a lunar eclipse. The angular distance of the moon's centre from the
ecliptic in each case is the limit required; S O m is that angle for the for-
mer, and n O E, for the latter. Now, S O m is equal toSOB + POm +
B O P ; and S O B is the apparent semi-diameter of the sun, and P O m is
that of the moon. But, O P C, being exterior to the triangle B O P, is
equal to the sum of the two interior angles O B P and BOP, and hence
B O P is equal to O P C O B C, or the moon's horizontal parallax
minus that of the sun. Therefore, the solar limit in latitude is equal to the
sum of the apparent semi-diameters of the sun and moon increased by the differ-
ence between the horizontal parallax of each ; or 16i' + 161' -f 1 2' = 1 35', when
greatest (omitting the sun's parallax, which is very small) ; and 15J' + 14V
+ 535' - 1 24', when least. Hence, when the moon's latitude at the time
of inferior conjunction does not exceed the former, an eclipse may occur;
when it does not exceed the latter, an eclipse must occur.
The angle of limit for a lunar eclipse is n O E, obviously less than S Om.
It is composed of the angle n O V, or the apparent semi-diameter of the
moon, and the angle V O E, or the angle subtended by one-half of the
diameter of the shadow, where the moon traverses it. Now, V O E = O V D
-OEV, and OEV=AOS-OAD; hence VOE = OVD + OAD
A O S. But V D is the moon's horizontal parallax, O A D is that of
the sun, and A O S is the sun's apparent semi-diameter. Consequently,
n O E, or the lunar limit in latitude, is equal to the sum of the horizontal
parallax of the sun and moon, diminished by the sun's apparent semi-diameter,
and increased by that of the moon. That is, 62' 15J' + 161' = 63', when
greatest ; and 53^ 16^+14^ = 52', when least. These calculations, being
made only for illustration, are but approximatively correct.
184. The distance in longitude, either side of the node,
QUESTION. 184. What is meant by the ecliptic limit?
134
ECLIPSES.
within which an eclipse can occur, is called the ECLIPTIC
LIMIT.
185. The solar ecliptic limit extends about 17 on each
side of the node ; the lunar ecliptic limit, about 12.
a. This difference follows from the difference in the limits in lati-
tude, the ecliptic limits in longitude being computed from those in
latitude.
Fig. 86. For in Fig. 86, let B N be
a portion of the ecliptic,
A N, a part of the moon's
orbit, N, the node, A B, the
solar limit in latitude and
C D, the lunar. It will be
at once apparent that since
A B is greater than C D, it
must be farther from the node. To calculate the exact amount, there are
given, in the right-angled triangle A N B, the angle at N = 5} ; the side
A B or C D, and the right angle at B, to find the side B N or D N, which
can easily be done by the higher mathematics.
b. Since the limits in latitude vary, those in longitude also vary,
the amount given above being the mean. The greatest solar ecliptic
limit is 18 36' ; and the least, 15 2(X ; the greatest lunar ecliptic limit
is 12 24' ; and the least, 9 23'. Within the former, an eclipse may
happen ; within the latter, it must.
Fig. 87.
* *
m $
PATH OF THE STTN OBO88ED BY THAT OK THE MOON.
Fig. 87 illustrates the relative position of the sun and moon's orbits,
with respect to the ecliptic limits. In the centre the moon is exactly at the
ascending node; while at the extremes, it is at the limits both in latitude
and longitude. Except at the node, the moon, it will be apparent, only
partially covers the disc of the sun, within the limits on each side.
QUESTIONS. 185. What is the extent of the solar and lunar ecliptic limits f a. Why
do they differ ? b. Why is each not always the same ?
ECLIPSES. 135
186. Since the solar ecliptic limits are wider than the
lunar, eclipses of the sun are more frequent than those of
the moon.
187. The greatest number of eclipses that can happen in
a year is seven ; five of the sun and two of the moon, or four
of the sun and three of the moon. The least number is
two, both of which must be of the sun.
a. The usual number is four, and it is rare to have more than six.
From the above statement, it will be seen that the greatest number of
solar eclipses is five, and the least two ; and that the greatest number
of lunar eclipses is three, while none at all may occur during the year.
b Number of Solar Eclipses. Since the sun crosses the line of
nodes twice each year, and his monthly progress in the ecliptic is about
29, while a solar eclipse must occur if the moon is within 15 20' of
either node, or within a space of 30 40 7 , there must evidently be a
solar eclipse each time the sun passes the node, or twice each year.
Now, if the sun, at the time of new moon is 18 west of the node, it
may be eclipsed (Art. 185, 6) ; and if it were, there would be another
eclipse at the next new moon, for the sun would have advanced less
than 11 east of the node. Again, in six lunations from the first new
moon referred to, the sun would have advanced 174, and consequently
would be 174 18, or 156 east of one node, and 24 west of the
other ; but the node is itself moving to the west about 1 every luna-
tion ; and hence, the sun would be only 24 9, or 15, from the
node, so that a third eclipse would take place ; and after another
lunation, a fourth, since the sun would then be less than 15 from the
node. Now, owing to the retrogradation of the nodes, the sun passes
from one to the same again in 346 days ; and hence, if it passed one at
the beginning of the year, it would pass it again toward the end of
the year, and there would be three passages of a node in that time ;
so that if four eclipses had previously taken place, there might be still
another toward the end of the year, making Jive in all.
c. Number of Lunar Eclipses. As the space on each side of the
node, within which a lunar eclipse must occur, is only about 9, or 19
QUESTIONS. 186. What eclipses are more frequent? Why? 1ST. What is the
greatest number of eclipses in a year? The least? . The usual number? How
many solar eclipses may happen ? Lunar eclipses ? ft. How is this proved in respect
to solar eclipses ? c. Lunar eclipses ?
136 ECLIPSES.
on both sides, it is obvious that there might be no lunar eclipse during
the year ; but, since an eclipse may occur within a space of 25 (12 24
on each side of the node), it follows that one lunar eclipse may occur
at each passage of the sun, or three during the year. But three lunar
eclipses can not be preceded by five solar eclipses in the same year ; for
two solar eclipses can not take place at each node, unless, at the first one,
the sun is at least about 15 west of the node, so that there would not
be enough space at the end of the year for both a solar and a lunar
eclipse.
188. Solar eclipses do not actually occur as often as lunar
eclipses at any particular place ; because the latter are always
visible to an entire hemisphere, whereas the former are only
visible to that part of the earth's surface covered by the
moon's shadow or its penumbra,
a. That the moon, in a lunar eclipse, is concealed from an entire
hemisphere, will be obvious from the fact that the diameter of the
earth's shadow where the moon crosses it is always more than twice as
great as the diameter of the moon, and is sometimes nearly three times
as great. For the angle VOW (Fig. 85) is equal to the sum of the hori
zontal parallax of the sun and moon, diminished by the apparent semi
diameter of the sun (183, b). The greatest parallax of the moon is about
62', and the least, 53 \' ; and the least apparent semi-diameter of the
the sun is 152', and the greatest, 16V > hence, the angle V W is,
when greatest, 44 V (omitting the sun's parallax) ; and when least, 37V J
the mean being about 40!|'. As this is the angular value of the semi-
diameter of the shadow, it must be doubled for the whole, which
therefore is, when greatest, 88^' ; least, 74^' ; mean, 81|'. Hence,
as the moon's apparent diameter is, when greatest, 33' ; least, 29^' ;
mean, 31?', the truth of the above statement will be apparent.
b. Length of the Earth's Shadow. This can be readily found by
comparing the triangles A S E and DEO (Fig. 85), which being both
right-angled triangles, and having all their angles respectively
equal, have, by a principle of geometry, proportional sides ; so that
AS:DO::SE:OE. But D 0, the semi-diameter of the earth, is about
Ttnr f -A.S, the semi-diameter of the sun; hence OE, the length of
QUESTIONS. 188. What eclipses are the more frequent at any place ? Why ? .
Why is the moon concealed from an entire hemisphere ? 6. What is the length of the
earth's shadow ? How demonstrated ?
ECLIPSES.
137
th shadow, must be To -- 7 of S E ; and therefore, S must be |f of the
whole distance S E, and, of course, SE, \$l of SO; but OE, the
length of the shadow, is equal to S E S O ; hence it is equal to -fa of
S 0, or the distance of the earth from the sun. Therefore its greatest
length is about 877,000 miles, and its least, 850,000 miles ; that is, at
its mean length, a little more than the diameter of the sun.
Fig. 88.
c. Length of the Moon's Shadow. This can be found by a similar
calculation. Let S (Fig. 88) be the centre of the sun, and O, that of the
moon ; P will then be the end of the shadow, and P its length ; and,
inthetrianglesASPandOMP,AS:MO::SP:OP. Now, MO is
about TJ T of A S ; hence O P is y^ of S P, and S 0, \\\ of S P ; or S P,
\\\ of S O ; therefore O P is - 3 ^ of S 0, the distance of the moon from the
sun. Now, the moon's distance from the earth varies between 252,000
miles and 226,000 miles ; and the earth's distance from the sun,
between 93 millions and 90 millions ; hence, at the mean distance of
the earth and moon, the length of the shadow is about 232,000 miles,
or 6,000 miles from the earth's centre, and 2,000 miles from its surface.
When the earth is in aphelion and the moon in perigee, it extends
about 10,000 miles beyond the earth's centre, or 14,000 miles from the
surface a b, which is the maximum. When the earth is in perihelion
and the moon in apogee, the shadow is about 228,000 miles long,
while the moon is 252,000 miles from the earth's centre ; so that it
fails to reach the surface of the earth by 20,000 miles.
fl. Breadth of the Moon's Shadow. When the end of the
shadow extends to the greatest distance beyond the earth's centre, the
amount of surface covered by it is the greatest possible. Let a b (Fig.
88) be the diameter of the shadow where it intersects the earth ; and
QUESTIONS. c. The length of the moon's shadow? How demonstrated ? d. How
much of the earth's surface may he obscured by the moon's shadow ? How proved ?
How much by the moon's penumbra ?
138 ECLIPSES.
since it is a very small arc, we may find its approximate length by con-
sidering it a straight line. We shall then have, by comparing the
triangles, A P : a P : : A S : %a b ; but a P is 14,000 miles (183 c), and A P is
93,014,000 miles. Hence, 93,014,000 : 14,000 : : 426,000 : \a b =64 miles+.
Therefore a 6, or the breadth of the shadow where it intersects the
earth is about 128 miles. The breadth of the portion of the earth's
surface covered by the shadow is, really, 1 54', or 130 miles. This is the
maximum. The breadth of the greatest portion of the earth's surface
ever covered by the moon's penumbra is 70 17', or 4,850 miles.
189. When the whole of the sun's or moon's disc is con-
cealed, the eclipse is said to be total ; when only a part of
it is concealed, it is said to be partial.
190. In order to measure the extent of the eclipse, the
apparent diameters of the sun and moon are divided into
twelve equal parts, called digits.
Fig. 89.
A PARTIAL ECLIPSE OF THE BUN AND MOON.
a. The conditions of a total and a partial eclipse will be apparent
from the explanations already given. When the centres of the sun
and moon coincide, that is, when the latter is exactly at the node, the
eclipse is said to be central. A central eclipse of the moon must, of
course, be total ; but a solar eclipse may be central without being
total ; since sometimes, as it has been demonstrated, the shadow of the
moon does not reach the earth. The moon, when this is the case, covers
QUESTIONS. 189. When is an eclipse total? When partial ? 190. What are digits 1
a. What is a central eclipse ?
ECLIPSES. 139
only the central part of the sun's disc, leaving a ring of luminous sur-
face visible around the opaque body. This is called an annular *
eclipse.
191. An ANNULAR ECLIPSE is an eclipse of the sun, which
happens when the moon is too far from the earth to conceal
the whole of the sun's disc, leaving a bright ring around the
dark body of the moon.
192. The time at which an eclipse will occur may be dis-
covered by finding the mean longitudes of the sun and node
at each new or full moon throughout the year, and compar-
ing the difference of the longitudes with the ecliptic limits.
Fig. 00.
AN ANNULAR ECLIP8R.
a. Cycle of Eclipses. Eclipses of both the sun and moon recur
in nearly the same order, and at the same intervals, after the expiration
of 18 years and 10 or 11 days (according as there may be 5 or 4 leap-
years in this period). For a lunation is about 29.53 days, and the time
of a revolution of the sun with respect to the node, 346.62 days, which
periods are nearly in the ratio of 19 to 223 ; so that 223 lunations are
almost equal to 19 revolutions of the sun ; and 346.62 days X 19= 18*
llf, d . This is called the cycle or period of eclipses. The eclipses which
occur during one such period being: noted, subsequent eclipses may
easily be predicted ; as their order is the same, only they are 10 or 11
days later in the month, and about eight hours later in the day ; so
* From the Latin word annulus, meaning a ring.
QUFBTIONR 191. What is an annular eclipse ? How caused? 192. How to predict an
eclipse ? a. What is the cycle of eclipses ? How calculated ? How named by the Chaldeans ?
140 ECLIPSES.
that in one cycle eclipses may be visible, and in the next invisible, to a
particular place. During this period there are generally 41 solar and
29 lunar eclipses. This cycle was known to the ancient Egyptians
and Chaldeans, and called by them Saros.
193. The phenomena connected with a total eclipse of the
sun are of a peculiarly interesting character, and have been
observed by astronomers with great attention and industry.
a. To an ignorant mind, this occurrence must be the occasion of
very great awe, if not actual terror. A universal gloom overspreads
the face of the earth as the great luminary of day appears to be ex-
piring in the sky ; the stars and planets become visible, and the animal
creation give signs of terror at the dismal and alarming aspect of
nature. Armies about to engage in battle have thrown down their
arms and fled in dismay froin the seeming angor of heaven. This was
the case at the eclipse predicted by Thales, which occurred on the eve
of the battle between the Medes and Lydians, 584 B.C.
ft. Phenomena of a Solar Eclipse, The following are the most
interesting of the phenomena presented Curing a total eclipse of the
sun :
1. The change of color in the sky from its ordinary blue or azure
tinge to a dusky, livid color intermixed with purple. Kepler men-
tions that during the solar eclipse in 1590, the reapers in Styria noticed
that every thing had a yellowish tinge. The darkness is not, however,
total, but sufficiently great to prevent persons' reading.
2. The corona, or halo of light which appears to surround the moon
while it covers the disc of the sun. This is, at the present time, sup-
posed to be caused by the atmosphere of the sun.
3. When the moon has almost covered the disc of the sun, leaving
only a line of light at the edge, this line is broken up into small por-
tions, so as to appear like a band of brilliant points. This phenomenon
is called Baily's leads, from Mr. Francis Baily, who was the first to
describe it minutely, in 1836. This is supposed to be caused by the
irregularities of the moon's surface, serrating its dark edge, and pro-
jected on the sun's brilliant disc.
4. Pink or rose-colored protuberances which project from the margin
of the moon's disc when the obscuration is total. One measured by
QUESTIONS. 193. The phenomena connected with a total eclipse ? a. Effect on igno-
rant minds? ft. State the most interesting phenomena presented by a solar eclipse?
The corona? Baily's beads? Rose-colored protuberances? Explain the cause cf each.
ECLIPSES. 141
De La Rue, in 1860, was found to be at least 44,000 miles in vertical
height above the sun's surface. They have been seen by most observ-
ers. No entirely satisfactory cause has been assigned for these
appearances, although it seems to be settled that their origin is in
the sun and not the moon ; and it is thought by some that they are
clouds floating in the atmosphere of the sun, their peculiar color being
caused by the absorption of the other colors, as sometimes occurs in
the case of clouds in our own atmosphere.
c. Appearance of a Lunar Eclipse. In a total lunar eclipse, the
moon does not become wholly invisible, but assumes a dull, reddish
hue, which arises from the refraction of the sun's rays by the earth's
atmosphere. The red color is caused by the absorption of the blue
rays in passing through the atmosphere, just as the western sky as-
sumes a ruddy hue when illuminated in the evening by the solar light.
Sometimes, however, it happens that the moon is rendered very nearly
invisible, as was the case in 1643 and 1816 ; and the degree of distinct-
ness of the moon's appearance varies considerably at different times,
owing to the different conditions of the atmosphere.
d. Earliest Observations of Lunar Eclipses. These were made
by the Chaldeans, the first recorded eclipse having taken place in 720
B.C. This eclipse was total at Babylon, and occurred about 9 o'clock
P.M. The record of the occurrence of eclipses is often very useful in
fixing the dates of history.
194. An OCCULTATION" is the concealment of a planet or
star by the interposition of the moon or some other body.
The occultation of a planet or star by the moon is a very interesting
and beautiful phenomenon. From new moon to fall moon, she
advances eastward with the dark edge foremost, so that the occulted
body disappears at the dark edge and re-appears at the enlightened
edge. In the other part of her orbit this is reversed. The former
phenomenon is of course the more striking, the star or planet appear-
ing to be extinguished of itself.
QUESTIONS. c. Describe the appearance of a lunar eclipse, d. Earliest observations
by whom made ? 194. What is an occultation ?
CHAPTER XI.
THE TIDES.
195. TIDES are the alternate rising and falling of the
water in the ocean, bays, rivers, etc., occurring twice in about
twenty-five hours.
196. FLOOD TIDE is the rising of the water, and at its
highest point is called high water. EBB TIDE is the falling
of the water, and at its lowest point is called loiv water.
197. The tides are caused by the unequal attraction of the
sun and moon upon the opposite sides of the earth.
~-by whom discovered ? Their appa-
rent motions ? a. How designated ?
JUPITER 179
but are more generally designated by the numerals I., II., III., IV.,
according to their order from Jupiter
256. Their PERIODIC TIMES are, respectively, l d 18 h ; 3 d
13 h ; 7 d 4 h ; and 16 d lG h . The longest, it will be seen, is but
a little more than half that of the moon.
. It will also be perceived that the second is very nearly twice the
first ; and the third, twice the second.
257. Their diameters in approximate numbers, are L, 2,300
miles ; II., 2,070 miles ; III., 3,400 miles ; IV., 2,900 miles ;
all, excepting the second, being larger than the moon
a. These figures are based upon the measurements of their discs and
a comparison of their apparent diameters with that of the planet as
seen simultaneously. Thus, suppose the apparent diameter of Jupiter
in opposition is found to be 45", and the third satellite is measured at
H" ; the diameter of the satellite must then be & that of the primary
planet, and 85,000 X & = 3,400.
b. As seen from Jupiter these bodies present quite large discs ; the
apparent diameter of I. being 36' ; of II., 19' ; of III., 18' ; and of IV.,
9'. The first is therefore somewhat larger in appearance than that of
the moon. The firmament of Jupiter must present a very beautiful
diversity of phenomena. These various moons, all of which are occa-
sionally above the horizon at one time, go through their phases within
a few days ; the first within 42 hours. To an inhabitant of the first
satellite, the apparent diameter of Jupiter must be 19 ; that is, about
86 times as great as the moon ; while the amount of illuminated sur-
face presented by it must be nearly 1300 times as great.
c. Although their volumes are quite large, their masses are very
inconsiderable, owing to their very small densities, which are I., JG ',
II., -sfe ; III., h ; IV., -A, the earth being 1. All are, thus, considerably
lighter than water, and the first very much lighter than cork.
258. Their DISTANCES from Jupiter are, respectively,
264,000 miles, 423,000 miles, 678,000 miles, and 1,188,000
miles.
a. These are found by measuring their greatest elongations from
QUESTIONS. -256. Periodic times of the satellites ? 15T. Their diameters ? a. How
found? /*. Apparent size at Jupiter? Apparent size of Jupiter at satellites? c.
Masses and densities ? 253. Their distances from the primary ? a. How found T
180 JUPITER.
the planet, and comparing these with its apparent diameter. Thus,
the greatest elongations are respectively, 136", 217", 349", and 611";
the apparent equatorial diameter of the planet being 45". Dividing each
elongation by 45", we find the ratio to the planet's diameter of the
distances of the satellites respectively. These are nearly I., 3 ; II., 4.8 ;
III., 7.7; IV., 13.6. Fig. 106 shows the comparative extent of these
elongations.
Fig. 106.
JUPITKR AND ITS SATELLITES AT THEIB OBEATE8T ELONGATIONS.
b. The entire system of Jupiter is thus comprehended within a circular
space of less than 2|- millions of miles in diameter, and subtends at its
distance from the earth an angle less than 22', or about f the apparent
diameter of the moon. A telescope, the field of view of which would
include one-half the area of the moon's disc, would exhibit Jupiter and
all his satellites, as represented in Fig. 106.
c. A comparison of the periodic times and distances as above given
will prove that they agree with Kepler's third law. Thus, taking I.
and II. as an example, we find ($!) 2 = 41 (nearly), and (IH) 3 = 4.1
(nearly) ; hence, (85) 2 : (42) 2 : : (423,000) 3 :(264,000) 3 .
259. The ORBITS of these bodies are almost circular, and
very nearly in the plane of the planet's equator. They
therefore make only a very small angle with the plane of its
orbit (about 3).
260. The ECLIPSES, OCCULTATIONS, and TRANSITS of the
satellites present an endless series of interesting and useful
phenomena ; and the situation of their orbits causes them
to occur with very great frequency.
a. I., II., and III. are eclipsed at every revolution : but so peculiarly
related to each other are their motions that their simultaneous eclipse
is impossible. Laplace demonstrated that the mean longitude of I.,
plus twice that of III , minus three times that of II., is always equal to
QUESTIONS. ft. Angular space covered by the system? c. Kepler's law how
applied? 259. Figure and position of the orbits? 260. Eclipses? Why frequent? a.
Ho'V many eclipses may occur at Jupiter during a Jovian year ?
JUPITER. 181
180. Hence, when two are eclipsed, the other must "be on the oppo-
site side of the planet. This is called the libration of the satellites,
All four are, however, occasionally invisible, being concealed either
behind or in front of the planet. This occurred last in August, 1867. It
has been computed that, during a year of Jupiter, an inhabitant of the
planet might behold 4,500 solar and lunar eclipses.
b. During the transits the satellites appear like bright spots passing
from east to west across the disc, preceded or folio wed by their shadows,
which seem like small round dots as black as ink.
Vis- 107.
ECLIPSES, OOOTTLTATUVNB, ATTH TRANSITS OP JUTITKli's SATELLITES.
In Fig. 107, to an observer at E, I. is represented as eclipsed ; II., as just
passing into the shadow of the planet ; III., just before a transit, the shadow
vreceding ; and IV., at the point of occultation. At E', I. has just passed behind
the disc ; IL is in occultation ; III., a transit, both shadow and satellite being
on the disc, the shadow preceding ; IV., just emerging from behind the
planet ; at E", I. and II. are behind the disc, III. is in transit, but the
fhadow follows the satellite; IV., just after an eclipse.
261. Since the occurrence of these eclipses can be exactly
predicted, they serve to mark points of absolute time ; so
tbat if the precise moment at which they will occur at any
QUESTIONS b. How do the satellites app.ar in a transit? 261. Why are these
eclipses useful f
182 SATUKK.
particular place has been computed, and the actual time of
their occurrence at any other place is noted, a comparison
of the two will give the difference of time, and, of course,
the difference of longitude, between the two places.
a. Thus, if a mariner perceives, by the nautical almanac, that the
eclipse of a satellite will occur at 9 o'clock P.M., Washington time,
and he notices that the eclipse does not take place till 11 o'clock P.M.,
he can infer that his position is 2 hours, or 30, east of Washington.
b. Velocity of Light found by the Eclipses of Jupiter's Sat-
ellites. In the prediction of these eclipses, a constant variation was for
several years found to exist between the calculated and observed time
of the occurrence, with this additional fact, that the eclipse was later
as Jupiter receded from the earth and earlier as it approached the
earth ; being about 16 m 35 B earlier in opposition than in conjunction.
These observations were made by Olaus Roemer, a Danish astronomer ;
and in 1675 he promulgated the theory, to account for the phenomena,
that the passage of light from a luminous body is not instantaneous,
but moves with a certain definite but immense velocity, requiring 16 m
35 to cross the earth's orbit This theory has been universally
accepted, and certain experiments recently made in France, by M.
Fizeau and others, have confirmed it. The velocity of light must
therefore be 184,000 miles a second. For 183,000,000 miles (distance
across the earth's orbit) divided by 995^ (number of seconds in 16
35^), gives 184,000 (nearly) Light must therefore require 8i min-
utes to pass from the sun to the earth. So great a velocity is entirely
inconceivable.
III. SATURN b
262. SATURN, the second of the major planets, is the
centre of a very large and peculiar system, being attended
by eight satellites and encompassed by several rings. It
shines with a dull yellowish light.
a. Name and Sign. Saturn, in the ancient mythology, was one of
the older deities, and presided over time, the seasons, etc. He was
represented as a very old man carrying a scythe in one hand. The
sign of the planet is a rude representation of a scythe.
QUESTIONS. a. Illustration? ft. What important dte-overy made by Roemer? In
vrhatway? What is the velocity of light ? 262. General description of Saturn? a.
Name and sign ?
SATURH. 183
263. The aphelion distance of Saturn is about 921 mil-
lions of miles; the perihelion distance, 823 millions; the
mean distance being therefore 872 millions.
. This is nearly twice the distance of Jupiter, between which and
Saturn there is a vast space of nearly 400 millions of miles, in linear
breadth, through which there rolls no planetary body. Light requires
about U k to pass from the sun to Saturn.
264 The ECCENTRICITY of Saturn's orbit is nearly 50
millions of miles, or about .056 of its mean distance, being
but little greater, relatively, than that of Jupiter,
265 The INCLINATION OF ITS ORBIT to the plane of the
ecliptic is about 2J (2 29' 36").
266. Its SYNODIC PERIOD is 378 days (378.07 d ), and its
SIDEREAL PERIOD, 10,759 days or about 29^ years.
a. For 378.07^365 .25* = 1.03514; and 378 07* -* .03514 = 10759*
(nearly) The year of Saturn contains, therefore, about 25,000 of its
own days.
267. The greatest apparent diameter of Saturn is 21"; its
least, 14.]". Its real equatorial diameter is about 74,000 miles.
a. For the least distance from the earth is 823 millions of miles
93 millions = 730 millions . and the sine of 10" is about .000050G8,
which being multiplied by 730,000,000 will give 37,000 (nearly) the
semi-diameter.
268. The OBLATENESS of Saturn is greater than that of
any other planet, being a little more than y^ of its equatorial
diameter, or 7,800 miles.
a. Hence its polar diameter is only 66,200 miles ; its mean diame-
ter being 70,100 miles.
269. The AXIAL ROTATION is performed in about 10 J
hours (10 h 29 m 17 s ).
. This was the determination reached by Sir William Herschel by
QUESTIONS. 263. Distance from the sun ? . Interval between Jupiter and Saturn *
264. Eccentricity? 265. Inclination of orbit? 266. Synodic and sidereal periods?
a. How computed ? 267. Apparent and real diameters ? 268. Oblateness ? 269. Time
of rotation ? a. How and by whom found ?
184 SATUEN.
means of observations made on the belts which, like those of Jupiter,
cross the planet's disc. Subsequent observations have indicated but
little variation from it.
b. The equatorial velocity of Saturn is, therefore, more than 22,000
miles an hour ; and as its density is very small, being only /,- of the
earth's, its oblateness should be, according to the law stated in Art.
/24\ 2
251, &, ( iQL ) X V- = 40i ; that is, 40^ times as great as the earth's.
But ifo X 40 = - 6 V = -1355 (nearly), or about -ft. So that its observed
oblateness is much less than it ought to be in accordance with this law.
The measurement of Saturn's apparent diameter is, however, so diffi-
cult, in consequence of the rings, that there may be considerable error
in the statement of its oblateness given above.
c. Volume, Mass, and Density. The volume of Saturn as com-
pared with that of the earth, is (^VfY 3 ) 3 695^ , and its muss lias been
found to be 90 ; hence its density is (as above stated), 90 -^ 095 .7 = -/,-
(nearly ) t the earth's being 1; or 5^ X /j =.726 as compared with
water ; that is, somewhat lighter than oak wood.
d. Superficial Gravity. This must be, according to the figures
above giifen, (&%-)* X 90 =1.15 (nearly). Hence, a body at the sur-
face of Saturn weighs only about | more than at the surface of the
earth, notwithstanding the immense size of that planet.
The INCLINATION- OF ITS AXIS toward the plane of
its orbit is about 27 (26 48' 40"), or a little greater than
that of the earth.
a. That is, its axis makes an angle of 27 with & perpendicular to its
orbit. The angle which it makes with the plane of its orbit is 90
27 = 63 The position of the axis is such that its inclination toward
the plane of the ecliptic is about 28 10' ; and like that of the earth
and those of the other planets, as far as it has been ascertained, the
axis remains parallel to itself during the orbital motion.
b. The Seasons of Saturn must therefore be similar to those of
the earth, but like the year, 29^ times as long.
c. Solar Light and Heat The distance of Saturn from the sun
QUESTIONS. ft. How floes the oblateness, computed by -Velocity and mass, compare
\rith that found by observation? c. Volume, mass, and density ?
September 19, 1848.
c. The following are their periods and distances from the primary ;
PEBOD6.
DISTANCES.
PERIODS.
DISTANCES.
1. MIMAS
tt|
121,000 I 6. RHEA
4 12V,
343,000
2v ENCELADUS
Id 9h
155,0;M) j j C. TITAN
16 23.
7C 6,000
8. TETHYS
l121h
191,000
7. HYPEEION j 21 7h
1,006,000
4 DIONE
2 IS-
246,00)
j 8. JAPETUS 79 1 8-
2,313,000
277. The largest of the satellites is Titan, its diameter
being 3,300 miles, which is larger than that of Mercury*
The sizes of the others are very much less.
a. That of Japetus is 1,800 miles ; Rhea, 1,200 ; Mimas ; 1,000
Tethys and Dione, 500 ; Enceladus and Hyperion, unknown.
b. The orbit of Japetus subtends an angle of only 21 ^ ; so that this
magnificent system of Saturn with his rings and eight satellites, at
its immense distance from the earth, is contained within a space in the
heavens less than one-half the disc of the moon.
c. In 1862, while the ring was invisible, the rare phenomenon
occurred of a transit of Titan across the disc of the primary. T 1
Shadow was observed by Dawes and others. The same phenome'
was observed by Sir William Herschel in 1789.
d. The variations in the light of Titan indicated to Sir V
fierechel an axial rotation of the satellite, which, like that of
Satellites whose periods have been discovered, is performed in
time as the revolution around the primary.
278. The CELESTIAL PHENOMENA at Saturn mr
QUESTIONS. 6. History of their discovery ? c. Their periods and t
Which is the largest satellite ? Its size ? a. Diameter of each of the i
6. Space in the heavens occupied by the Saturnian system ? c. Transit ^ in : -.*&,
Celestial phenomena at Saturn ?
i i
URANUS. 18.1
a scene of extreme beauty and grandeur. The starry vault,
besides being diversified by so many satellites, presenting
every variety of phase, must be spanned, in certain parts of
the planet, and during different portions of its long year,
by broad, luminous arches, extending to different elevations,
according to the place of the observer, and receiving upon
their central parts the shadow of the planet.
IV. URANUS, tf
279. URANUS was discovered in 1781 by Sir William
Herschel. It shines with a pale and faint light, and to the
unassisted eye is scarcely distinguishable from the smallest
of the visible stars.
a. History of its Discovery. This planet had been observed by
several astronomers previous to its discovery by Herschel, but had
been mapped ts a star at least twenty times between 1690 and 1771,
its planetary character not having been discerned ; and even Ilerschel,
on noticing that its appearance was different from that of a star, was
not aware that he had discovered a new planet, but supposed it to be
a comet, and so announced it to the world, April 19th, 1781. It was,
however, in a few months, evident that the body was moving in an
orbit much too circular for a comet ; but its planetary character, sug-
,ated first by Lexell, in June, 1781, was not fully established until
i '3, when Laplace partly calculated the elements of its orbit. This,
^er, does not detract from the merit of Herschel, in making this
y ; for, the attention of astronomers having been called to this
one of a peculiar character, and not sidereal, it was a simple
etermine whether it was a planet or a comet. The merit of
ery consisted in that delicacy of observation, that skill in the
-uments, and, more than all, that unfailing perseverance
'terized Herschel, and made him the great astronomer of
and Sign. Herschel proposed to call the new planet
QUESTIONS. 279. When and by whom was Uranus discovered ? Its appearance ?
a. I .story of its discovery ? b. Origin of the name and sign >
1 92 U R A K U S .
" Georgium Sidus," George's Star, in compliment to his friend and
patron, King George III. This name not being accepted by foreign
astronomers, Lalande proposed to name it " Herschel," after its great
discoverer ; and by this designation it was, for some time, quite gener-
ally known. The scientific world has now definitely settled upon the
name, suggested by Bode, of Uranus, which, in the Grecian mythology,
was the name of the oldest of the deities, the father of Saturn, as
Saturn was the father of Jupiter. The name of the discoverer is,
however, partly connected with the planet by the sign, which is the
letter H with a suspended orb.
280. The aphelion distance of Uranus is about 1,836
millions of miles ; its perihelion distance, 1,672 millions ;
the mean distance being 1,754 millions, which is more than
19 times (19.183) that of the earth.
a. Light requires 2 hours 33^ minutes to pass from the sun to
Uranus ; for 8 m X 19.183 = 153.464" 1 = 2 h 33^ m (nearly). Sunrise and
sunset are therefore not perceived by the inhabitants of Uranus for
two hours and a half after they really occur, for the light which pro-
ceeds from the sun when it touches the plane of the horizon does not
reach the eye until 2^ hours afterward.
b. The distance of this planet from the sun is so vast that the
greatest elongation of the earth as seen from it is only about 2. That
of Jupiter is only 16^, while its apparent diameter is but little greater
than that of Mercury as seen from the earth. Even Saturn departs
only about 29 from the sun, its apparent diameter being less than 20".
The inhabitants of the planet, if any there be, must therefore possess
much less opportunity than ourselves to become acquainted with the
constituent members of the great system to which they belong.
281. The ECCENTRICITY of the orbit of Uranus is about
82 millions of miles, or about .047 of its mean distance.
282. The INCLINATION" OF ITS ORBIT is less than that of
any other planet, being only 46.J'.
QUESTIONS. 280. What is its distance from the sun ? a. What time does light
require to pass from the sun to Uranus? Effect on apparent sunrise and sunset? It.
Elongations and apparent diameters of the planets as seen from Uranus? 281. Eccen-
tricity of its orbit ? 282. Inclinatiou of its orbit ?
URANUS. 193
a. Nevertheless, so vast is its distance that, at its greatest latitude,
it may depart from the plane of the ecliptic more than 24 millions of
miles.
283. Its SYNODIC PERIOD is 369.65 days ; and therefore
its sidereal period is 30,687 days, or about 84 years.
a. The computation may be made as in the case of the other planets :
360.65 -r- 365.25 = 1.012046 +; that is, Uranus performs about .012046 of
a sidereal revolution during the synodic period. Hence, 369. 65 d -r- .012046 =
30,687 d ( nearly) is the sidereal period.
6. In the case of a very distant planet, the sidereal period may be
readily found by observing the daily arc of movement of the planet
when in quadrature : for, at that time, the line joining tne earth and
planet is a tangent to the earth's orbit (see Fig. 28), so that, for a short
time, the earth moves either toward or from the planet, and does not
affect the apparent motion of the latter , while its distance is so great
that its geocentric increase in longitude is almost equal to its helio-
centric. Now, the apparent daily increase of the longitude of Uranus
in quadrature is 42.23", and 360 -f- 42.23" = 30,689, which gives a
near approximation to the true sidereal period.
284. The greatest apparent diameter of TJrarius is about
4" ; and as 1", at the least distance of this planet, subtends
8,350 miles, the real diameter must be 33,400 miles. (By
more exact calculations, it is found to be 33,247 miles.)
ft. The cblateness has not positively been ascertained. Miidler esti-
mates it to be as much as -^ The volume of Uranus is about 72 times
that of the earth ; but its mass is only 13 times ; hence its density is
less than that of the earth, or about equal to that of water.
285. As the disc of Uranus presents neither belts nor
spots, the period of its rotation and its axial inclination still
remain unknown. It is thought, from the positions of the
orbits of the satellites, that the inclination of its axis is
QUESTIONS. a. Possible distance from the plane of the ecliptic ? 283. Synodic and
sidereal periods? a. How calculated ? l>. How may the sidereal period be found by
the daily increment of longitude? T84. Apparent and real diameter of Uranus ? a.
Oblateness? Volume? Mass? Density? 285. Diurnal rotation?
made with the best instruments to detect the others. In 1847 two others,
situated within the orbit of the nearest discovered by Herschel, were
detected, one by Lassell and the other by O. Struve.
&. The following are the names of these satellites, with their periods
and distances
PERIODS.
DISTANCES.
PERIODS.
DISTANCES.
1 ABItiL
2. UMJHHEI.
2J 12h
41 3p
123,000 I
171,000
3. TlTANIA
4. OliEBOX
8^11"
181 17h
281,000
376,000
c. Their orbits are inclined to the plane of that of the primary at
an angle of 79 ; bat, as their motion is retrograde, it seems probable
that the poles have been reversed in position, the south pole being
north of the ecliptic, and vice versa. The inclination is properly, there-
fore, 101.
V. NEPTUNE
287. NEPTUNE is the most distant planet known to belong
to the solar system. It was first observed in 1846 by Dr. Galle
at Berlin ; but its existence had been predicted, and its posi-
tion in the heavens very nearly ascertained by the calculations
of M. Leverrier, in France, and Mr. Adams, in England ;
th^se calculations being based upon certain observed irregu-
larities in the motion of Uranus.
QUESTIONS 86. How many satellites attend Uranus? Direction of their orbital
motion? ft. History of their discovery ? b. Names, periods, and distances? c. Posi-
tion of their orbits and polet ? 287. By whom, and how was Neptune discovered?
NEPTUNE. 195
a. History of its Discovery. The discovery of this planet was
one of the proudest achievements of mathematical science in its appli-
cation to astronomy, and afforded a more striking proof of the truth of
the great law of universal gravitation than had previously been ascer-
tained. After the discovery of Uranus, in 1781, it was ascertained that
the planet had several times been observed by astronomers, and its
place recorded as a star. These positions of the planet could not,
however, be reconciled with those recorded after its actual discovery ;
and observation soon showed that its motion was at certain points
increased, and at others diminished, by some force acting beyond it
and in the plane of its orbit. These facts suggested the existence of
another planet, revolving in an orbit exterior to that of Uranus, and,
according to Bode's law, extending nearly twice as far from the sun.
Adams and Leverrier almost simultaneously undertook to find, by
mathematical analysis, where this planet must be in order to produce
these perturbations. The former reached the solution of this wonder-
ful problem first, and, in October, 1845, after three years of toil,
communicated to Mr. Airy, Astronomer Royal, the result, pointing out
the position of the planet and the elements of its orbit. The search
for the planet was not, however, commenced until Leverrier published
the result of his labors, which was found to agree so closely with that
attained by Adams, that astronomers both in France and England
prepared to construct maps of the part of the heavens indicated, in
order to detect the planet.
In this they were anticipated by the Berlin observer, who, being
informed by Leverrier of the result of his computations, and having
by a fortunate coincidence just received a newly prepared star-map of
the 21st hour of right ascension (the part of the heavens designated by
Leverrier), immediately compared it with the stars, and found one of
them missing. The observations of the following evening, by detect-
ing a retrograde motion of this star, established its true character. It
was the planet sought for, and, wonderful to relate, was found only
52' from the place assigned by Leverrier. He had also stated its appa-"
rent diameter at 3.3'' ; it was found by actual measurement to be 3".
Adams's determination of the place of the supposed planet differed
from the true place by about 2.
b. Name and Sign. This planet, according t"> the system of
mythological designations, was, after considerable discussion, called
QUESTIONS. a. Circumstances connected with its discovery? How nearly was its
true place predicted ? ft. Name and sign ?
196 NEPTUNE.
Neptune. The sign is the head of a trident the peculiar symbol of
this deity.
288. The APHELION DISTANCE of Neptune is 2,770 mil-
lions of miles ; its perihelion distance, 2,722 millions ; its
mean distance being 2,746 millions.
u. This is about 30 times the distance of the earth ; but according
to Bode's law, it should have been 38.8 times ; so that this remarkable
relation of the planets, failing in this instance, ceases to be a law, and
becomes, apparently, only a curious Coincidence.
b. So immense is the distance of Neptune that only Saturn and
Uranus can be seen from it. If there are astronomers, however, on the
planet, they must have much better opportunities than ourselves for
becoming acquainted with the distances of the stars ; since, at oppo-
site periods of their long year, they are situated at positions in space
about 5.500 millions of miles apart.
c. Since the distance of Neptune from the sun is 30 times that of
the earth, light requires 8 m X 30 = 4 h , to reach that planet
289. The ECCENTRICITY of the orbit of Neptune is about
24 millions of miles, which is only .0087 of its mean" dis-
tance ; so that it is, relatively, but little more than one-half
that of the earth's orbit.
290. The INCLINATION OF ITS OKBIT to the plane of the
ecliptic is very small, being only 1| (1 47').
a. The sine of 1 47' is .031 ; hence Neptune, when at its mean dis-
tance from the sun, and at the point of greatest latitude north or south
of the ecliptic, must be more than 85 millions of miles from the plane
of that circle ; for, 2.746,000,000 X .031 = 85,126,000.
291. Its SYNODIC PERIOD is about 3674 days (367.48234) ;
hence its SIDEREAL PERIOD is 60,127 days, or about 164.]
years.
a. It is more difficult to calculate the sidereal periods of these
QUESTIONS. 288. Aphelion, perihelion, and mean distances ? a. Does it agree with
Bode's law ? 6. Which planets can he seen at Neptune ? c. How long does light
require to pass from the sun to Neptune? 289. Eccentricity of its orbit? 290. Incli-
nation ? a. How far may it depart from the plane of the ecliptic? How is this calcu-
lated ? 291. Synodic period ? Sidereal period ? a. How calculated ?
NEPTUNE. 197
remote planets ; since the synodic period is so nearly equal to the side-
real period of the earth, that the fraction of a revolution performed
during the latter is very small. In the case of Neptune it is a little
over .0061118; that is, 367.48234 d -~- 365. 25 d = 1.0061118 -f-; and 367.-
48234 d -=- .0061118 = 60,127 days (nearly).
292. The APPARENT DIAMETER of Neptune when greatest
is 2.9" ; hence its real diameter must be nearly 37,000 mik-s,
a. For the least distance of Neptune from the earth is 2,722 millions
93 millions = 2,629 millions ; now the sine of 2.9" is .000014 : and
2,629 millions multiplied by this small fraction will give 36,806 miles.
b. Volume, Mass, and Density. The volume of Neptune, if cal-
culated by the method previously explained, will be found to be very
nearly 99 times as great as that of the earth, and consequently is only
about i L f as large as Jupiter. Its mass is nearly 17 times (16.76) as
great as the earth's [Prof, Pierce] ; consequently its density must be
about ^ that of the earth, or somewhat more than -^ as heavy as water.
c. Solar Light and Heat. The apparent diameter of the sun as
Been at Neptune must be a little more thanl' , for, 32 -r- 30.037 (ratio of
of Neptune's distance to the earth's) 64"(nearly). Hence, the sun at this
planet looks but little larger than Venus ; but its light is vastly more
brilliant. For, since the intensity of light varies inversely as tne
square of the distance, and (30.037) 2 = 902 (nearly), the light at Nep-
tune must be q{ )2 of that at the earth, and hence is nearly equal to
that of 670 full moons (157, 6). This is probably as great as that
which would be produced by 20,000 stars shining at once in the firma-
ment, each equal to Venus when its splendor is greatest.
293. A SATELLITE of this planet was discovered by Lassell
in October, 1846, and was afterward observed by several
other astronomers.
a. From observations made about the same time the existence of
another satellite was suspected, as well as a ring analogous to that of
Saturn ; but the most diligent and careful scrutiny with very powerful
telescopes has failed to detect any indications of the truth of these
conjectures.
QUESTIONS. 292. Apparent diameter of Neptune? Its real diameter? a. How
found? b. Its volume, mass, and density? c. How great is the intensity of solar
light and heat? How found? 293. By whom and when was the satellite discovered?
a. What conjectures as to another satellite, etc. ?
198 NEPTUNE.
b. Distance of the Satellite. The observations made by eminent
astronomers (principally those of M. Struve, Mr. Lassell, and Mr.
Bond) have shown that the greatest elongation of the satellite from
its primary is 18 ", the apparent diameter of the latter being at the
same time 2.8". Hence its distance must be 18" -:- 2.8" = 6| diame-
ters, or 12f- radii, of the planet : and 18,500 X 12$ 238,000 miles, or
about the same as the moon's distance from the earth.
C. Inclination, Period, and Rotation. The orbit of this satellite is
nearly circular, and is inclined to the orbit of Neptune in an angle of
29. Its motion, like that of the satellites of Uranus, is retrograde, or
from east to west Its sidereal period, as determined by Lassell at Malta,
in 1852, is 5 d 21 h . Periodical changes in its brightness were observed
by Lassell, which indicated that this satellite, like others in the sys-
tem, rotates on its axis in the same time that it revolves around its
primary.
d. Are there Planets beyond Neptune? This is a question
which we are at present entirely unable to answer. Future genera-
tions may, with greater resources of science and mechanical skill,
disclose new marvels in our system, and detect other bodies obedient
to the dominion of its great central sun. The nearest of the stars is
known to be nearly 7,000 times as far from Neptune as that body is
from the sun ; and it is by no means improbable, therefore, that so
vast a space should contain planetary bodies reached by the solar
attraction, but very far beyond the sphere of any other central lumi-
nary. It will require, however, far greater means than we possess to
bring this to a practical determination.
QUESTIONS. b. What is the distance of this satellite from the primary? How cal
culated ? c. Its inclination of orbit? Orbital revolution period and direction ? Axial
rotation ? d, is Neptune the remotest planet ?
CHAPTER XIV.
THE MINOR PLANETS, OE ASTEROIDS.
294. The MINOR PLANETS are a large number of small
bodies revolving around the sun between the orbits of Mars
and Jupiter. The number discovered up to the present
time (1869) is 106.
a. Discovery of Ceres and Pallas. The existence of so large an
interval between Mars and Jupiter, compared with the relative dis-
tances of the other planets, for a long time engaged the attention and
incited the researches of astronomers. Kepler conjectured that a
planet existed in this part of the system, too small to be detected ; and
this opinion received considerable support from the publication of
Bode's law in 1772. When Uranus was discovered, in 1781, and its
distance was found to conform to this law, the German astronomers
became so confident of the truth of this bold conjecture of Kepler, that,
in 1800, they formed, under the leadership of Baron de Zach, an asso-
ciation of 24 observers to divide the zodiac into sections and make a
thorough search for the supposed planet. This systematic exploration
had, however, been scarcely commenced, when, in 1801, Piazzi, an
Italian astronomer, while engaged in constructing a catalogue of stars,
detected a new planet. It was called by him Geres. In the next year,
while looking for the new planet, Olbers discovered another, which he
called Pallas.
b Discovery of Juno and Vesta Theory of Olbers. The ex-
treme minuteness of the new planets, and the near approach of their
orbits at the nodes, led Olbers to suppose that they might be the frag-
ments of a much larger planet once revolving in this part of the
system, and shattered by some extraordinary convulsion. Believing
QUESTIONS. 294 What are the minor planets? Their number? a. How and by
whom were Ceres and Pallas discovered ? 6. Juno and Vesta ? Theory of Olbers ?
200 MINOR PLANETS.
that other fragments existed, and that they must pass near the nodes
of those already found, he resolved to search carefully in the direction
of those points ; but while he was thus engaged, Harding, of the
observatory of Lilienthal, discovered, in 1804, very near one of those
points, a third planet, which he called Juno. Olbers, still further stim-
ulated by this event to continue the investigation which he had
commenced, was at length, in 1807, rewarded by discovering a fourth
planet, Vesta, near the opposite node. From this date until 1845, no
additional discovery was made. These small planets were called
Asteroids by Herschel, from their resemblance, in appearance, to stars.
c. Discovery of the other Minor Planets. In 1845, M. Hencke,
an amateur astronomer of Driessen, after a series of observations con-
tinued for fifteen years with the use of the Berlin star-maps, discovered
Astrcea, the fifth of this singular zone of telescopic planets. The
others have been discovered in the following order : In 1847, Hebe,
Iris, Flora ; 1848, Metis ; 1849, Hygeia ; 1850, Partheriope, Victoria,
and Egeria ; 1851, Ire'ne and Eunomia ; 1852, Psyche, Thetis, Mel-
pom' ene, Fortu'na, Massilia, Lutetia, Calliope, and Thalia; 1853,
Themis, Phoce'a Proserpina, and Enter' pe ; 1854, Bello'na, Amphi-
tri'te, Urania, Euphros'yne, Pomo'na, and Polyhym'nia ; 1855, Circe,
Leuco'thea, Atalan'ta, and Fides ; 1856, Le'da, Lcetita, Harmonia,
Daphne, and Isis ; 1857, Ariadne, Ny'sa, Eugenia, Hestia, Mel'ete,
Aglaia, Doris, PU'les, and Virginia; 1858, Neman' sa, Euro'pa, Ca-
lypso, Alexandra, and Pandora ; 1859, Mnemosyne ; 1860, Concordia,
Dan'ae, Olympia, Erato, and Echo ; 1861, Ausonia, Angelina, Cyb'ele,
Ma'ia, Asia, Hesperia, Leto, Panope'a, Feronia, and Ni'obe; 1862,
Clyt'ie, Oalate'a, Euryd'ice, Fre'ia, and Frig'ga; 1863, Diana and
Euryn'ome ; 1864, Sappho, Terpsichore, and Alcmene ; 1865, Beatrix,
Clio, and lo ; 1866, Sem'ele, Sylvia, This"be, <>, Antiope, ; 1867, <>
<>, <8>, <>; 1868,, , , ,, @>, <, @>> @> (> The
largest number discovered in any single year is eleven (in 1869); and in
the three years, '57, '61, and '69, no less than thirty were discovered.
d. Names of the Discoverers. Dr. Luther, at the observatory of
Bilk, near Dusseldorf, has discovered no less than 16, and is at the
head of planet discoverers ; Mr. Herman Goldyhmidt, an amateur
QUESTIONS. c. What time elapsed before Ash-sen was discovered ? Mention those
discovered in each subsequent year. In what year were the largest number discov-
ered? Who has discovered the greatest number? d. What other discoverers are
named ? How many of the minor planets were discovered in the United States? How
ore thene bodies designated ?
MINOR PLANETS. 201
astronomer of Paris, has discovered 14; Mr. Hind, a distinguished
English astronomer, 10 ; De Gasparia, at Naples, 9 ; M. Chacornac, at
Marseilles and Paris, 6 ; Mr. Pogson, an English astronomer, 6 (3 at
Oxford, and 3 at Madras) ; Dr. C. H. F. Peters, at Clinton, N. Y., 8 ;
M. Tempel, at Marseilles, 6 ; Mr. Ferguson, at Washington, 3 ; Mr. Wat-
son, at Ann Arbor, Michigan, 9 ; Mr. Tuttle, at Cambridge, Mass., 2 ;
several other observers, 1 or 2 each. Twenty-three of these planets have
been discovered in this country. Instead of the names above given, the
minor planets are now generally distinguished by numerals according to
the order of their discovery. Several of these bodies were discovered by
two or more observers independently.
295. The AVERAGE DISTANCE of these planets from the
sun is about 260 millions of miles. That of the nearest,
Flora, is about 201 millions ; that of the most distant,
Sylvia, is nearly 320 millions. The entire width of the zone
in which they revolve is, however, about 190 millions of miles.
296. The INCLINATION OF THEIR ORBITS is very diverse ;
more than one-third of the whole have a greater inclination
than 8, and consequently extend beyond the zodiac. The
greatest is that of Pallas, amounting to 34 42' ; the least,
that of Massilia, which is only 41'.
297. The ECCENTRICITY of their orbits is equally variable ;
the most eccentric being that of Polyhymnia, which is
.337, or more than one-third ; the least eccentric is that of
Europa, which is only .004, or ^i^.
. These orbits are not concentric ; but if represented on a plane
surface, would appear to cross each other, so as to give the idea of
constant and inevitable collisions. " If," says D' Arrest, of Copenhagen,
" these orbits were figured under the form of material rings, these rings
would be found so entangled, that it would be possible, by means of
one among them taken at a hazard, to lift up all the rest." The orbits
do not, however, actually intersect each other, because they are situ-
ated in different planes ; but some of them approach within very short
QUESTIONS. 205. Average distance? Which is the nearest? The farthest? 296.
Inclination of their orbits? How many heyond the zodiac ? The most inclined ? The
least? 29T. Eccentricity? Greatest? Least? a. Position of their orbits ?
202 MINOR PLANETS.
distances of each other. The orbit of Fortuna, for example, approaches
the orbit of Metis within less than the moon's distance from the earth.
This is also true of the orbits of Astrsea and Massilia, and those of
Lutetia and Juno.
298. The LARGEST of the minor planets is Pallas, the
diameter of which is variously estimated at from 300 to 700
miles. These bodies are generally so small that it is quite
impossible to measure their apparent diameters, or to say
which is the smallest. The brightest of these planets is
Vesta ; the faintest, Atalanta. Vesta, Ceres, and Pallas
have been seen with the naked eye, having the appearance
of very small stars.
299. The SIDEREAL PERIOD of Flora is 3] years ; that
of Sylvia is about 6^ years. The average period of the
whole is about 4} years.
a. Origin of the Minor Planets. The theory of Gibers has
already been alluded to ; it supposes that these little planets are the
fragments of a much larger one, which by an extraordinary catastro-
phe was, in remote antiquity, shivered to pieces. Prof. Alexander
has endeavored to compute the size and form of this planet He sup-
poses that it was not of the form of a globe, but shaped like a lens
or wafer, the equatorial and polar diameters being respectively, 70,000
miles and 8 miles ; that the time of its rotation was about 3^ days ;
and that it burst in consequence of its great velocity, as grindstones
and fly-wheels sometimes do. This theory of an exploded planet has
not been generally accepted, since it is highly improbable, and sup-
ported by no analogous facts.
b. Nebular Hypothesis. This was invented by Laplace to account
for the formation of the solar system by the operation of ordinary
physical laws. He conceived that the matter of which the various
bodies belonging to this system are composed, originally had an enor-
mously high temperature and existed in the condition of gas or vapor,
filling a vast space ; that as this mass cooled, and, of course, unequally,
currents were formed within it, which, tending to different points or
QUESTIONS. 298. Which is the largest of the planets ? The brightest ? The faintest ?
299. Average sidereal period ? Longest? Shortest? a. Origin of the minor planets ?
Asteroid planet ? b. Nebular hypothesis ?
MINOfi PLANETS. 203
centres, gave it finally a slow rotation ; that this increased by degrees,
until the centrifugal force exceeded the attraction of the central mass,
and a zone or ring became detached, of a lower temperature, but still
vaporous or liquid; and that thus successive rings were formed, which
breaking up as they rotated, the parts finally came together and
formed spheroidal masses revolving around the original mass. If these
rings condensed without breaking up they would continue to revolve
as rings, like those of Saturn ; if, on the other hand, they broke up
into small parts, none sufficiently large to attract all the others, they
would condense into fragments and continue to revolve as small
planets, like the asteroids. The larger planet masses, being still in a
vaporous condition, would, as they cooled and condensed, throw off
rings like the original mass , and in this manner either satellites or rings
would be formed. The residue of the original nebulous mass he con-
ceived to be the sun.
Such is a brief outline of this celebrated and most ingenious
hypothesis, an hypothesis which every subsequent discovery has
seemed to harmonize with and confirm. Whatever theory be adopted
to account for the development of the solar system and the exist-
ence of this zone of small planets, it must not be forgotten that the
infinite power and intelligence of the Great Creator could alone
have brought them into being. The only question is, in what way did
He exert this power, and in what manner did He ordain that all these
wonderful orbs should come into existence as witnesses of His omnipo-
tence and benevolent design.
c. Decrease in Brightness of the Successive Groups. The
brightest of the minor planets seem to have been discovered, for each
successive group is less conspicuous than those preceding it. The
first ten resemble stars of the eighth magnitude [the brightest stars
are of the first] ; the last ten are but little brighter than stars of the
twelfth magnitude. It is not anticipated, therefore, that others will
hereafter be detected with the readiness and frequency which have
marked the discoveries of the last ten years. The labor required in
the discovery of these little bodies is almost inconceivable. The
most successful discoverers have attained the object of their efforts
only after mapping down every minute star in certain zones of the
heavens ; and to do this required a patient and toilsome watching
during every clSar night for many months.
QUESTIONS. c. What decrease iti brightness is referred to ? bifificulties in discover-
ing these bodies ?
CHAPTER XV.
MUTUAL ATTRACTIONS OF THE PLANETS.
300. The PLANETS, while revolving around the sun,
constantly disturb each other's motions, and thus give rise
to numerous irregularities, similar to those which take
place in the revolution of the moon around the earth.
301. These irregularities are called inequalities or per-
turbations. They are either periodic or secular, the former
requiring short, the latter very long periods of time for their
completion.
t. Problem of the Three Bodies. To compute the exact place
of a planet at any time requires that all the inequalities due to the
disturbing action of other planets should be taken into account ; and
to do this has tasked to the utmost the highest powers of the human
intellect. The problem is, however, simplified by the fact that, as the
sun's attraction is so much greater than that of the other bodies, the
place of the planet can be found by first supposing that it revolves in
an exact elliptical orbit, and then calculating the amount of disturbance
due to each other planet in succession ; the aggregate of the results
thus obtained giving the proper correction to be applied in order to
ascertain the true place. This has been called the The Problem of the
Three Bodies, because it involves the investigation of the motion of
one body revolving around another, and continually disturbed by the
attraction of a third. To determine, therefore, all the inequalities to
which any planet is subject, it is necessary to solve this problem sepa-
rately for every other planet by which it may be disturbed. Its
complete solution surpasses the powers of the most skillful mathe-
matician.
QUESTIONS. 300. How do the planets disturb each other? 01. What are the irregu-
larities called ? Of how many kinds ? . What is the " Problem of the Three Dodice ?"
ATTRACTIONS OF THE PLANETS. 205
302. The ELEMENTS OF A PLANET'S ORBIT are the facts
which it is necessary to know in order to determine the pre-
cise situation of the planet at any instant. They are 1.
Tfie position of the line of nodes ; 2. The inclination of the
orbit to the plane of the ecliptic ; 3. The place of the peri-
helion ; 4. TJie eccentricity ; 5. Tlie major axis.
a. Elements 1, 2, and 8 determine the position of the orbit ; 4, its
figure ; and 5, its size. In order to find the place of the planet, it is
necessary also to know the periodic time, and the place of the planet at
any particular epoch.
b. Heliocentric and Geocentric Place. The true position of a
planet is that in which it would appear to be situated if viewed from
the sun, that is, its heliocentric place ; hence, one important point in
ascertaining a planet's true position is to deduce its heliocentric place
from its geocentric place, or situation as seen from the earth.
303. The only INVARIABLE ELEMENT is the length of the
major axis ; every other, in the case of each planet, under-
goes certain small changes, such as those which have been
described in the orbits and motions of the earth and moon.
. Thus the inclinations of the orbits of Mercury, Venus, and
Uranus are increasing ; those of Mars, Jupiter, and Saturn are dimin-
ishing ; the greatest variation being that of Jupiter, which is 23" in a
century. A similar variation occurs in the positions of the nodes and
perihelion, and in the amount of eccentricity. In the case of the earth,
as has been stated (Art. 125, e), the latter is diminishing ; and this is
also true of Venus, Saturn, and Uranus ; while that of Mercury, Mars,
and Jupiter is increasing. The greatest variation is that of Saturn,
which is about .00031 of its mean distance in a century. This is rela-
tively about 7i times as great as that of the earth, and amounts
absolutely to about 2,700 miles a year ; while the absolute annual
variation of the earth's eccentricity is only 36^ miles. All these
changes are confined within certain very narrow limits, after reaching
which they occur in an opposite direction.
QUESTIONS. 302. What are the elements of a planet's orbit ? a. What is determined
by them ? What else must be known to determine a planet's place ? ft. What is meant
by the heliocentric and geocentric places of a planet ? 203. Which clement is In variable 5 ?
a. What examples are given of variable elements ?
206 ATTRACTIONS OF THE PLANETS.
304. The MOTIONS OF THE PLANETS are retarded or
accelerated by their mutual attractions, according to their
positions with respect to each other and to the sun ; but as
action and reaction are equal and in opposite directions,
whenever one is accelerated the other which acts upon it
must be retarded.
Thus, in Fig. 93, page 151, the planet at M must have its motion accel-
erated by that of the earth at E, while the latter must be retarded ; but the
acceleration of M is greater than the retardation of E, because the disturb-
ing force at M acts more nearly in the direction of the planet's motion.
After conjunction this is reversed ; the motion of the earth being accelerated
and that of the planet retarded.
a. If the planets' orbits were exactly circular, the amount of accel-
eration in one part of the orbit would be counterbalanced by the
retardation in the other, and the inequalities would, in a synodic
period, cancel each other : but as the orbits are elliptical, the successive
conjunctions must occur at diffe rent parts of the orbits, where the plan-
ets are at different distances from each other ; so that the inequalities
must increase while the conjunctions occur in one part of the orbit,
and diminish while they take place in the other. If the conjunctions
always occurred in the same part of the orbit, the inequalities would
constantly accumulate, and the system would be destroyed. This is
nearly the case with Jupiter and Saturn.
b. Great Inequality of Jupiter and Saturn. The periodic times
of Jupiter and Saturn are respectively 4,332 days and 10,759 days ; and
hence, 5 of the former are nearly equal to 2 of the latter ; so that, in 5
revolutions of Jupiter, or about 59 of our years, the conjunctions take
place at nearly the same points of their orbits. The synodic period of
these two planets is 19.86 years : and during the 17th and 18th cen-
turies the conjunctions constantly occurred almost at their points
of nearest approach to each other, so that Jupiter's period appeared to
be shortened and Saturn's lengthened, greatly to the perplexity of
astronomers, till Laplace demonstrated the cause. Similar coincidences
exist in the periods of Venus and the earth, but the disturbance accu-
mulates only for a short period. It will be obvious, therefore, that the
QTTOSTIONS. 304. How are the motions of the planets accelerated or retarded' ".
Effect in circular orhits? In elliptical orbits, 6. Great inequality of Jupiter and
Saturn what is meant hy it?
ATTRACTIONS OF THE PLANETS. 207
stability of the system, since the orbits are not circular, depends on the
periods' being incommensurable.
305. Since the attraction of gravitation is reciprocal, the
sun is attracted by the planets, and each primary planet is
attracted by its satellites ; and, therefore, instead of revolv-
ing one around the other as a centre, they in fact revolve
around their common centre of gravity.
a. By the centre of gravity of two or more bodies connected together
in any way, is meant the point around which they all balance eacii
other. The centre of gravity of the solar system moves in a small
and very irregular orbit, since it results from the joint action of all the
planets Its distance from the centre of the sun can never be equal to
the diameter of the latter ; and within this limit the centre of the sun
must revolve around it.
306. MASSES OF THE PLANETS. The amount of attrac-
tion exerted by one body upon another is an exact measure
of its mass. The masses of the planets that are attended
by satellites are found by comparing the attraction of the
sun upon the planets, with the attraction which they exert
themselves upon their satellites. The masses of the planets
not attended by satellites are found by ascertaining the
amount of disturbance which they occasion in the motions
of bodies in their vicinity.
a. Comparative Masses of the Sun and Planets. To determine
these it will be most convenient to resort to simple algebraic represen-
tation. Let M be the mass of the sun, and ra that of the earth ; F and
/, their respective forces of attraction, P and p, their periodic times,
and D and d, their distances. Then, according to the law of gravita-
tion, the ratio of the attractions is equal to the direct ratio of the
masses multiplied by the inverse ratio of the squares of the distances.
That is, - = X ^ ; hence, (dividing by ^ we have = - x
QUESTIONS. 305. Do the planets revolve around the sun as n centre t a. What is
meant by the centre of gravity ? What is the shape and magnitude of the sun's orbit,
and the orbit of the centre of gravity ? 306. What is the general method of determin-
ing the masses of the planets ? a. How to find the comparative masses of the sun and
planets ? What calculation is made for the sun and earth ? The earth and Saturn ?
208 ATTRACTIONS OF THE PLANETS.
D 3
-=- . But it can be shown by simple geometry that the forces are
directly as the distances and inversely as the squares of the periodic
TT T^ /nl \l" T^3
times. That is, - = - x Therefore by substitution, =
/ ' d P 8 m d*
X |ij ; that is, the ratio of the masses is equal to the direct ratio of the
cubes of the distances multiplied by the inverse ratio of the squares of the
periodic times. ^Hence the muss oi the sun (that of the earth being one) is
tion, we take no account of the attraction of the earth upon the sun
or of the moon upon the earth ; but this is so small that it would
not affect the result materially.
The above formula is applicable to the case of any planet that is
attended by satellites. Thus, the masses of the earth and Saturn may
be compared by the periodic times and distances of the moon and any
of the satellites of Saturn. The distance of Dione is 245,846 miles, and
its periodic time about 66 hours ; hence the cube of the ratio of the
distance of this satellite and tliat of the moon multiplied by the
square of the ratio of their periodic times, or (Hf t-JS) 8 X (^) 5 , will
give the mass of Saturn, the earth being 1 By performing the work
the result will be found to be 89 -f, which is very nearly correct.
The mass of the sun as compared with the earth can also be found
by finding the force of gravity at the surface of the earth and compar-
ing it with the force of the sun upon the earth, as determined by the
distance and orbital velocity of the latter.
T)3 TVT P^
b. From the third of the above formulae it is obvious that -^ = X -5
and this is evidently applicable to planets revolving around the same cen-
vr
tral body. But in that case, the mass being the same, becomes equal
D 3 P*
to 1 ; and, therefore,-^ = 9 ; that is, the squares of the periodic
times are in propm'tion to the cubes of the mean distances ; which is
Kepler's great law.
QTTESTION.-6. What demonstration of Kepler's third law is given?
CHAPTER XVI.
COMETS.
307. COMETS are bodies of a nebulous or cloudy appear-
ance that revolve around the sun in very eccentric or
irregular orbits, and are generally accompanied by a long
and luminous train, called the tail
308. They generally consist of three parts ; the nucleus,
or bright and apparently solid part in the centre ; the coma,
or nebulous substance which envelops it; and the tail,
which extends on the side from the sun.
a. The name comet is derived from this nebulous appearance which
the ancients fancifully likened to hair [in the Greek, come], and hence
called these bodies eometce, or hairy bodies. When the luminous train
precedes the comet, it is sometimes called the Icard.
b. The appearance of comets is not uniform, the same comet chang-
ing" very much at different times. Some comets have no nucleus,
others, no tails ; while still others have several tails.
c. These bodies when at a long distance from the earth and sun are
distinguished from planets by the size and position of their orbits, and
the direction of their motions. Uranus, it will be remembered, was
for some time thought to be a comet, and was recognized as a plane
tary body only after its orbit had been proved to be almost circular, and
nearly in the plane of the ecliptic.
309. Comets either revolve around the sun in elliptic
orbits, or move in curve lines called by mathematicians para-
lolas and hyperbolas. Elliptic comets may be considered as
QTIFSTIONS. 30T. What are cornets? 308. Of what parts do they consist? a.
Origin of the name 6. Is the appearance of a comet uniform ? c. How distinguished
from planets ? 809. In what kind of orbits do they revolve ?
210
COMETS.
belonging to the solar system ; the others, only as visitants
of it, since they come from distant regions of space, move
around one side of the sun, and then pass swiftly away in
paths that never return into themselves, but are constantly
divergent.
D'ig. liO.
OBBITS OF COMETS.
a. These paths are curve lines of peculiar properties ; they are called
" conic sections," because they may be formed by cutting a cone in
various ways. Thus, if a cone be cut by a plane parallel to its base
the curve formed will be a circle; if both sides of the cone be cut
obliquely by a plane, the curve will be an ellipse ; both of these curves
are continuous lines, returning into themselves. But if the cone be
cut by a plane parallel to either side and intersecting the base, the curve
formed will be a parabola ; and if a plane be passed through the cone
so as to intersect the base at an angle greater than that of the plane
of the parabola, the resulting curve will be a hyperbola. The parabola
and hyperbola are not continuous but divergent curves ; hence they
do not return into themselves. The parabola is like an ellipse with
only one focus, or an eccentricity infinitely great ; and when only a
QUESTION . Conic sections?
COMETS. 211
portion of it is given, it is very difficult to distinguish h from an ellipse.
The hyperbola is more easily distinguished, because its arms or branches
are more divergent.
In Fig. 110 these three kinds of paths are represented; A and P being the
aphelion and perihelion of an elliptic orbit ; a P 6, the two branches of a para-
bolic path ; and e P d, those of a hyperbolic path. The greater divergency
of the last will be obvious; also, that the elliptic and parabolic curves coincide
from 1 to 2, so as to be entirely undistinguishable. The motion indicated
by the arrows is direct.
310. The ELEMENTS of a comet's orbit are, 1. The longitude
of the perihelion ; 2. The longitude of the ascending node ;
3. The inclination to the plane of the ecliptic ; 4. The eccen-
tricity ; 5. The direction of the motion; 6. The perihelion
distance from the sun.
311. The elements of more than 240 cometary orbits have
been computed ; and of these only 19 are known to be elliptic,
and 5 hyperbolic. The remainder are either parabolic, or
elliptic of very great eccentricity.
a. Besides the 19 elliptic comets mentioned, there are 37 that are
believed to be elliptic although they have not been proved to be so ;
and 11 others more doubtful. There are also 10 doubtful hyperbolic
comets ; leaving, out of 242 comets whose elements have been com-
puted, 160 with parabolic orbits, or orbits having an eccentricity too
great to be ascertained with accuracy.
312. The ELLIPTIC COMETS are divided into two classes ;
those of short periods and those of long periods. The for-
mer are seven in number, and have all reappeared several
times, their identitv being satisfactorily established by an
entire correspondence of their elements. The most noted
of these is the comet of Encke, the period of which is about
3| years, eighteen returns of it having been recorded.
a. The others are De Vice's, the period of which is 5 years ; Win-
necke's, 5$ years , Br or sen's, 5% years ; Biela's, 6| years ; D' Arrest' 8,
QUESTIONS. 310. What are the elements of a comet's orbit? 311. How many have
been calculated ? . Different kinds of orbits ? 312. Classes of the elliptic comet* ? a.
Which are of short period ?
COMETS.
6f years ; Faye's, 7 years. These comets are named after the distin-
guished astronomers who first discovered them, or determined their
periods and predicted their returns. Several others are thought to be
comets of short periods.
b. These comets have comparatively small orbits, the mean distance
of each being less than that of Jupiter, and all revolving within the
orbit of Saturn. The inclination of the orbits is comparatively small,
the average being about 12. The greatest is 31, and the least 3.
They all revolve from west to east. They are not conspicuous objects,
but have been generally visible only with the aid of a telescope.
313. With the exception of a few comets, the periods of
which have been computed to be about 75 years, all the
remaining elliptic comets are thought to be of very long
periods, some more than 100,000 years.
a. The comet of 1744 is estimated to require nearly 123,000 years
to complete one revolution ; that of 1844, 102,000 years ; and the great
comet of 1680, about 9,000 years. The period of a comet can not, how-
ever, be ascertained with precision during one appearance, since only
a very small part of its orbit is described during the short time it
remains visible. There is, consequently, considerable uncertainty in
these determinations. To the great comet of 1811, the two periods of
2,301 and 3,065 years have been assigned.
314. Of all the comets whose orbits have been ascertained,
about one-half are direct, that is, revolve from west to east ;
the remainder are retrograde. Their inclinations are very
diverse, some revolving within the zodiac, others at right
angles with the ecliptic.
a. There is a decided tendency in the periodic comets to revolve in
orbits but little inclined to the ecliptic , while the greatest number of
comets are found moving in or near a plane inclined 50 to the ecliptic.
Most of the elliptic and hyperbolic comets are direct; of the parabolic,
retrograde.
6. About three-fourths of all the comets have their perihelia within
the orbit of the earth ; and nearly all the others, within the orbit of
QUESTIONS. ft. Size and inclination of the orbits ? 313. Comets of long period ? a.
Examples ? 814. Direction of the motion of comets ? a. Tendencies of the periodic
comets ? 6. Situation of the perihelia? Aphelia ? How found ?
COMETS. 213
the nearest asteroid. Only one is situated more than 400,000,000
miles from the sun. Some comets, on the other hand, come into close
proximity to the sun. The great comet of 1680 approached within
600,000 miles of it ; and that of 1843 was less than 75,000 miles. The
aphelion distances of some of these comets are inconceivably great.
The comet of 1811 recedes to a distance from the sun equal to 14 times
that of Neptune, or more than 40,COO millions of miles ; the greatest
known (that of 1844) must be nearly 400,000 millions of miles.
The aphelion distance can be found from the eccentricity and peri-
helion distance. The latter in the case of the comet of 1844 is about
80,000,000 miles ; the eccentricity, .9996 of the semi-axis. Hence 1
.9996 .0004 of the semi-axis must be the perihelion distance; and
80,000,000 -r- .0004 = 200,000,000,000 = semi-axis.
c. The velocity of comets as they move through their perihelia is
amazingly great. That of 1680 was 880,000 miles an hour ; and that
of 1843, about 1,260,000 miles an hour, or 350 miles per second. The
latter body swept around the sun from one side to the other in about
two hours.
315. The NUMBER OF COMETS is supposed to be very great.
From the earliest period up to the present time more than
800 have been recorded, of which nearly 300 have had their
orbits computed, and of the latter 54 have been identified
as returns of previous comets.
a. Since it is only within the last 100 years that optical aid has
been made available in searching for comets, it is supposed that the
actual number of comets that have come within view, in both hemi-
spheres, is not less than 4,000 or 5,000. M. Arago estimates that the
greatest possible number in the solar system can not exceed 350,000.
316. The SIZE of comets, including both envelope and
nucleus, very much exceeds that of the largest planet ; the
nucleus is, however, comparatively small, the diameter of the
largest measured being about 8,000 miles (that of 1845).
a. The nucleus of the comet of 1858 (Donati's) was 5,600 miles in diam-
eter ; that of 1811, only 428 miles. The coma of the latter was found to
QUESTIONS. c. Velocity of comets? 315. The number of comets? a. Probable
number that have visited, or that belong to, the system? 316. Size of comets? a.
Examples ? Change of size at different times?
COMETS.
be 1,125,000 miles ; and that of Encke, 281,000 miles. The dimensions
of comets, however, vary greatly at different parts of their orbits, con-
tracting as they approach the sun, and expanding as they recede from
it. Thus Encke's comet in October, 1838, was more than 250,000 miles
in diameter ; but in December, contracted to 3,000 miles.
317. The MASSES AND DENSITIES of the comets must be
inconceivably small; since, notwithstanding their great
magnitudes, they move among the planets and their satel-
lites without in the least, as far as it can be observed,
affecting their motions ; although they are themselves greatly
disturbed by the attractions of the planets.
a. Their densities are, without doubt, many thousand times less than
atmospheric air. Stars are seen very clearly through the nebulous
coma and train of a comet, notwithstanding that the light has to pass
sometimes through millions of miles of the substance.
318. The TAILS of comets are often of immense length,
and are generally of a bent or curved form, extending on the
side from the sun and nearly in a line with the radius-
vector of the orbit. The tail increases in length as the
comet approaches the sun, but attains its greatest dimensions
a short time after the perihelion passage, and then gradually
diminishes.
a. In respect to magnitude, the tails of comets are the most stupen
dous objects which the discoveries of astronomers have presented to
our contemplation. That of the comet of 1680 was more than 100,000,-
000 miles in length , while the comet of 1843 presented a train
200,000,000 miles long, which was shot forth from the head of the
comet in the incredibly short space of twenty days. The increase of
the tail and the decrease of the head of the comet as it approaches the
sun, are among the most striking phenomena presented by these bodies
b. The tails ol comets are not of uniform breadth, but diverge or
spread out as they extend from the head. The middle of the tail
usually presents a dark stripe which divides it longitudinally into two
parts. This appearance is usually explained by the supposition that
QUESTIONS. 31 T. Masses and densities 1 a. Why is the density thought to he small ?
318. Position and length of tails? a. Examples? Change in length at different times f
b. Appearance of tails ? How explained ?
COMETS. 215
the tail is hollow, being a kind of conical shell of vapor ; and as we
look through a considerable thickness of the vapor, at the edges, it
appears brighter there than in the middle where the quantity is com-
paratively small.
c. The diminution of the size of comets as they approach the sun is
probably to some extent only apparent ; since their substance must
necessarily be vaporized as they approach the sun, and much of it so
attenuated as to become invisible. There is no doubt also that a consid-
erable portion is exhausted in the formation of the tail ; and that as
the comet moves in its orbit it loses by disruption considerable portions
which pass away into space.
319. Observations with the polariscope have shown that
the tails of comets shine by reflected light ; but that the
nucleus and coma emit quite a strong radiance of their own.
a. If the head of the comet shone by reflected light alone, its appar-
ent brightness would be inversely proportional to the product of the
squares of the distances from the sun and earth ; but this is contrary
to observation. Donati's comet (that of 1858), according to this rule,
should have been 188 times as bright when near its perihelion in Octo-
ber as it was in June ; whereas it was actually 6,300 times as bright, its
own light having increased in the ratio of 33 to 1.
b. Some astronomers suppose the nucleus to be a solid, partially or
wholly converted into vapor by the intense heat of the sun ; others,
that it is of the same nature as the coma, only more dense. It was the
opinion of Sir William Herschel, and is still a very generally accepted
one, that the nucleus is surrounded with a transparent atmosphere of
vast extent, within which the nebulous envelop floats like clouds in
the earth's atmosphere. This nebulous matter appears to be con-
tinually driven off by some force emanating from the sun, and thus
f rms the luminous train. At their perihelia comets must generally
be subjected to a heat far more intense than would be required to melt
the hardest substance found on the surface of the earth. Prof. Norton
thinks that the tail is formed by two streams, in opposite magnetic or
electric states, expelled from opposite points, or poles, of the nucleus,
and bent back by the sun's repulsive force until they nearly meet, being
separated by only a narrow interval, which appears as the dark stripe
noticed in the tail.
QUESTIONS. c. Change in the size of comets how explained ? 810. Are comets self-
luminous ? a. Why thought to be so ? &. Nature of the nucleus and the tail ?
216 COMETS.
HEMARKABLE COMETS.
320. COMET OF 1680. This was the comet that Newton
subjected to the calculations by which he showed that these
Fig . lu . bodies revolve in
one of the conic
sections, and that
they are retained
in their orbits by
the same force
that binds the
planets to the
sun. It was very
GBEAT OOMET OF 1680. remarkable for
its splendor, and for the extent of its train, which stretched
over an arc of 70 in the heavens, and reached the amazing
length of 120,000,000 miles. With the exception of the
comet of 1843, it approached nearer to the sun than any
other known, and moved through its perihelion with a
velocity of 880,000 miles an hour.
a. Its perihelion distance is .0062 (the earth's distance being 1), and
its eccentricity, according to Encke, is .99998 Now, 91,500,000 X
.0062 = 567,300 ; and 1 .99998 = .00002. Hence 567,300 -i- .00002 =
28,365,000,000, which is its semi axis; and if we multiply this by 2,
and subtract the perihelion distance from the product, we shall find
the aphelion distance, which is equal to nearly 57,000 millions of miles.
The period corresponding to this orbit is 8,814 years. Some ascribe to
this comet a much shorter period ; and others, a hyperbolic orbit.
321. HALLEY'S COMET. This comet derives its name
from Sir Edmund Halley, a celebrated English astron-
omer, who calculated its orbit and predicted its return. It
appeared in 1682, and Halley noticing a close resemblance
QUESTIONS. 320. How is the comet of 1680 described ? a. Its distance and period ?
321. Halley 1 s comet?
COMETS.
in its elements to those of JN*
1531 and 1607, concluded
that the comets of these
years were different appear-
ances of the same comet, and
ventured to predict its re-
appearance in 1758 or 1759.
This prediction was real-
ized by the return of the
comet in March, 1759; and
it again appeared in 1835.
These different appearances, HAU.RY-B COMET, isss.
it will be observed, were about 75 years apart ; and others of
an earlier date have also been recognized.
a. History of the Prediction. This celebrated prediction of
Halley may be considered almost the first fruits of Sir Isaac Newton's
demonstration of the laws of planetary motion as contained in his
famous work, the Princlpla. published in 1687. The comet of 1682
had been an object of interest to both Halley and Newton, and its
path had been calculated by Picard, Flamstead, and others, It occur-
red to Halley that this comet might be identical with others previously
recorded ; and fortunately the comet of 1607 liad been observed by
Kepler and Longomontanus, and that of 1531, by Apian at Ingolstadt j
the path in each case being quite accurately determined. The coinci-
dence which Halley noticed in these paths gave him confidence in the
prediction which he made. He observed, however, that as the comet
in the interval between 1607 and 1682, passed near Jupiter, its
velocity must have been increased and its period shortened ; so that
the next interval would be 76 years or upward, and the comet would
return at the end of 1758 or the beginning of 1759. Subsequent
researches gave increased force to this prediction ; for it appeared that
comets had been seen in 1456 and 1378, whose paths seemed to have
been nearly identical with that of the comet of 1682.
b. The Prediction Realized. As the time drew near, the attention
of the scientific world was awakened to the subject ; and it was
QUESTIONS. a. History of the prediction? b. How was it realized?
218 COMETS.
resolved to compute more exactly the time of the comet's appearance,
by applying all the additional resources of mathematical science that
seventy-five years had brought forth. This was a gigantic undertaking-,
since it was necessary to calculate the distance of each of the two
planets, Jupiter and Saturn, from the comet, and the exact amount of
their disturbance, separately, for every successive degree, and for two
revolutions of the comet, or 150 years. Clairaut and Lalande, two
French mathematicians, undertook the work, the latter being assisted
in the arithmetical portion of it by Madame Lapaute ; and after six
months spent in calculations, from morning to night, this enormous
sum was worked out, and the day of the comet's return to its perihe-
lion was announced. This was April llth. It actually passed its
perihelion March 13th, or about 22 days previously to the predicted
time Clairaut, however, stated in announcing his prediction that the
comet might be accelerated or delayed by the attraction of an undis-
covered planet beyond the orbit of Saturn, thus anticipating, in
imagination, the discovery of Uranus which Herschel made 22 years
afterward. Halley did not live to witness the realization of his
prediction, having died in 1743.
c. The Return in 1835. The time of its perihelion passage in
1835 was computed by several mathematicians, the mean of all the
results being November 12th. The comet was observed to pass its
perihelion on the 16th of that month. It continued visible in the
southern hemisphere for several months, and then disappeared, not to
be seen again until 1911.
d. The mean distance of this comet is a little less than that of Uranus.
Its perihelion distance is about 60 millions of miles; its aphelion
distance more than 3,200 millions. Its motion is retrograde, and the
inclination of its orbit about 18. History shows that it has reg-
ularly returned during a period of more than 18 centuries, its first
recorded appearance being in 11 B.C. It seems however, to have been
a far more conspicuous object in its ancient visitations than at its more
recent returns. In 1066 and 1456, it was an object of immense size
and splendor, and created wide-spread alarm.
322. ENCKE'S COMET is remarkable for its short period and
frequent returns. Its period and elliptic orbit were deter-
QUESTIONS. c. Return in 1836 ? d. Distance, etc. ? 322. Encke's comet ?
COMETS. 219
mined by Professor Encke Fi s- H3.
at its fourth recorded ap-
pearance in 1819. Its
last return took place in
1868 ; the next will occur
in January, 1872. This
comet has generally ap-
peared without any lumi-
nous train ; but in 1848,
it had a tail about 1
long, turned from the ENCKE' s COMET.
sun, and a shorter one directed toward that luminary. In
its latest returns it has been very faint and difficult of
observation.
. Mass of Mercury. The return of 1838 led to the establishment
of an important fact. In August, 1835, this comet passed very near
Mercury ; and Encke showed that, if Laplace's value of Mercury's mass
were correct, the comet's motion would be greatly disturbed ; but as
this was found not to be the case, it was obvious that the received
determination of Mercury's mass needed correction. A much lower
value has since been adopted ; but astronomers do not entirely agree
as to this element. Encke's value is about ^ that of the earth ; but
Leverrier's is a little more than i 1 ,;. Laplace's had been about .
b. The Resisting Medium. A still more interesting discovery has
been evolved from observations of this comet. Professor Encke found
that at each return, the arrival of the comet at its perihelion took
place about 2 : | hours earlier than the most exact calculations predicted ,
and that this constant acceleration had amounted since 178G to about
2 j days. As this could not be attributed to the disturbing influence of
any unknown body, he conceived that it could be caused only by a
resisting medium filling the interplanetary spaces ; since the effect of
such a medium would be to diminish the centrifugal force, and thus
bring the body nearer to the sun : so that its orbit would be con.
tracted and its periodic time made constantly shorter. A very ethereal
fluid would be sufficient to produce this result in the case of a body so
light as a comet ; while it would have no appreciable effect on the
QUESTIONS. . How was the mass of Mercury found ? b. Resisting medium ?
220
COMETS.
planets on account of their great mass and enormous momentum. A
similar acceleration takes place in the case of Faye's comet.
323. LEXELI/S COMET. This body is particularly noted
for the amount of disturbance which it has suffered in pass-
ing among the planets. From observations made in 1770,
Lexell calculated its period at about 5 A years ; and it was
a large and bright object, the diameter of its head being
about 2 3. It has, however, never been seen since, its orbit
having been entirely changed by planetary disturbance.
a. Investigation showed that it really returned in 1776, but was so
situated as to be continually hid by the sun's rays ; that in 1779, it
passed so near Jupiter that its orbit was greatly enlarged, so that it no
longer comes near the earth. The fact that it never appeared previous
to 1770, is accounted for in a similar way ; its orbit having in 1767 been
changed by the attraction of Jupiter, from one of large to one of small
dimensions. On July 1st, 1770, the distance of this comet from the earth
was less than 1,500,000 miles.
324. COMET OF 1744.
This was the finest comet
of the 18th century, and
according to some ob-
servers, had six tails spread
out in the form of a fan.
Euler calculated its ellip-
tic orbit, and assigned to
it a period of 122,683
years. Its motion was
direct.
COMET OF n44 325. BIELA'S COMET.
This is one of the elliptic comets of short period ; its perihe-
lion lying just within the orbit of the earth, and its aphelion
a little beyond that of Jupiter. The orbit of this body
Fig. 114.
QUESTIONS. 323. Lexell's comet why noted? er How accounted for ? 324. Comet
of 1744? 325 Biela'scomet?
COMETS. 221
nearly crosses the actual path of the earth ; and in 1832,
Gibers calculated that it would come within 20,000 miles of
the earth, so that the latter body would be enveloped in its
mass. The earth, however, did not reach the node until one
month after the comet had passed it.
a. In 1845, this comet became elongated in form and finally sepa-
rated into two comets, which traveled together for more than three
months ; their greatest distance apart being about 160,000 miles. The
two parts were again seen at the next return of the comet in 1852, but
the interval had increased to 1,250,000 miles. It has not been seen since
Fig. 115.
COMET OF 1811.
326. COMET OF 1811. This comet was very remarkable
for its unusual magnitude and splendor. It was atten-
tively observed by Sir William Herschel, who describes it as
having a nucleus 428 miles in diameter, which was ruddy in
hue, while the nebulous mass surrounding it was of a blu-
ish-green tinge. Its tail was of peculiar form and appearance,
extending about 25, with a breadth of nearly 6.
n. The investigation of its elements by Argelander is the most com-
plete ever made He assigns it a period of more than 3,000 years, and
estimates its aphelion distance at 40,121 millions of miles.
327. COMET OF 1843,-This comet was also remarkable for its
QUESTIONS. . Its separation? 326. Comet of 1811 ? a. Its elements ? 32T. Comet
of 1843?
GREAT COMET OF 1843.
extraordinary size and splendor, it being visible in some parts
of the world during the day time. It had a tail 60 long, and
approached within a very short distance of the sun, about
75,000 miles from its surface. Its period is variously esti-
mated at from 175 to 376 years. Its motion is retrograde.
328. DONATI'S COMET. This is the great comet of 1858,
named after Donati, by whom it was first seen at Florence.
As it approached its perihelion it attained a very great mag-
nitude and splendor, and was particularly distinguished for
the magnificence of its train. Its period has been estimated
at nearly 1,900 years.
329. RECENT COMETS. About thirty comets have ap-
peared since that of Donati, the elements of which have
been calculated. The most remarkable were the comet of
1861, described as one of the most magnificent on record,
having a tail 100 long ; and that of 1862, which was very
interesting for the peculiar phenomena which it presented
of luminous jets, issuing in a continuous series from its
nucleus.
QUESTIONS __ 328. Donati' s comet?
Other comets.
CHAPTER XVII.
METEORS OB SHOOTING STA11S.
330. METEORS* or SHOOTING STARS are small luminous
bodies that move rapidly through the atmosphere, followed
by trains of light, and quickly vanishing from view. They
sometimes appear in numbers so great as to seem like
showers of stars.
a. Star-Showers Periodical. These star-showers are found to
occur at certain periods. Every year, about November 14th, there is
a larger fall than usual of meteors ; but about every 33 years, it has
been noticed, there is a great star-shower. Those which occurred in
November, 1866-7, had been predicted from observations of previous
events of the kind. Thus a star-shower occurred in November, 1832-3,
also in 1799 ; and there are eighteen recorded observations of the phe-
nomena from 1698 to 902, all corresponding in period to that mentioned
above.
b. Great Star-Showers. The shower of 1799 was awful and sub-
lime beyond conception. It was witnessed by Humboldt and his
companion, M Bonpland, at Cumana, in South America, and is thus
described by them : " Toward the morning of the 13th of November,
1799, we witnessed a most extraordinary scene of shooting meteors.
Thousands of bolides and falling stars succeeded each other during four
hours. Their direction was very regularly from north to south , and
from the beginning of the phenomenon there was not a space in the
firmament, equal in extent to three diameters of the moon, which was
not filled every instant with bolides or falling stars. All the meteors
* From the Greek word meteora, meaning things in the air.
QFFBTIOXS. 330. What are meteors? a. What periods have been observed in their
occurrence ? b. What instances of great showers ?
224 METEORS OR SHOOTING STARS.
left luminous traces, or phosphorescent bands behind them, which
lasted seven or eight seconds." The same phenomena were witnessed
throughout nearly the whole of North and South America, and in some
parts of Europe. The most splendid display of shooting stars on
record was that of November 13th, 1833, and is especially interesting as
having served to point out the periodicity in these i-hemmena. Over the
northern portion of the American continent tLe spectacle was of tli3
most imposing grandeur ; and in many \ arts of the country the popula-
tion were terror-stricken at the awfulness of the scene. The ignorant
slaves of the southern States supposed that the wcrld was en fire, and
filled the air with shrieks of horror and cries for mercy. TLe shower
of 1866 was anticipated with great interest ; end in New York and
other places arrangements were made to announce the cccurrence,
during the night of November 14th, by ringing the bells from the
watch-towers. The display, however, was not witnessed in this coun-
try, but in England was quite brilliant ; as many as 8,000 being
counted at the Greenwich observatory. Another shower of less extent
occurred in November, 1867.
331. METEORIC EPOCHS are particular times of the year
at which large displays of shooting stars have been observed
to occur at certain intervals. The principal of these are
November 13th-14th, and August 6th-llth.
a. Three others have been established with consielerable certainty ;
namely, in January, April, and December, and still others indicated,
that are doubtful. There are 56 meteoric days in the year ; those in
August and November being the richest.
b. August Meteors. Of 315 recorded meteoric displays, 63 seem
to have occurred at this epoch. The first eleven, with one exception,
were observed in China, between 811 A.D., and 933 A.D., and occurred a
few days previous to August 1st. The period of this shower is exactly
the same as the sidereal year , and therefore it occurs about a day later
in 71 tropical or civil years. Its maximum period is much longer than
that of the November meteors, being estimated at 105 years.
332. METEORS are supposed to be small bodies collected in
QUESTIONS. 331. What are the principal meteoric epochs? a. What others? How
many meteoric days in a year? b. August meteors dates of their occurrence and
periods ? 332. What are meteors supposed to be ?
METEORS Oil SHOOTING STARS. 225
rings or clusters, and revolving around the sun in eccentric
orbits. They appear to resemble comets in their nature and
origin, and, liko those bodies, sometimes revolve from cast
to west.
a. Origin of Meteors. The immense velocity of these bodies,
which is about equal to twice that of the earth in its orbit, or 86 miles
a second, and the great elevation at which they become visible, the
average being 60 miles, indicate that they are not of terrestrial, but
cosmical, origin ; that is, they emanate from the interplanetary regions,
and being brought within the sphere of the earth's attraction, precipi-
tate themselves upon its surface. Moving with so great a velocity
through the higher regions of the air, they become so intensely heated
by friction that they ignite, and are either converted into vapor, or,
when very large, explode and descend to the earth's surface as mete-
oric stones, or aerolites* The brilliancy and color of meteors are
variable ; some are as bright as Venus or Jupiter. About two-thirds
are white ; the remainder yellow, orange, or green.
&. Number of Meteors. The average number of shooting stars
seen in a clear, moonless night by a single observer is 8 per hour ; a
sufficient number of observers would perceive 30 per hour, which is
equivalent to 720 per day, seen by the naked eye at any point of the
earth's surface, if the sun, moon, and clouds were absent. But the
number visible over the whole earth is about 10,500 times that seen at
a single point ; and therefore the average number daily entering the
atmosphere, and sufficiently large to be seen by the naked eye, is more
than 7^ millions ; while at least 50 times as many can be seen through
the telescope ; so that about 400 millions must descend to the earth
during each day. It becomes therefore an interesting question how
much foreign matter may be added to the earth ani its atmosphere by
these meteoric falls.
333. FIRE BALLS are large meteors that make their
appearance at a great height above the earth's surface,
moving with immense velocity, and accompanied by luminous
*From the Greek word aer, meaning the air, and lithos, a stone.
QUESTIONS. n. Their origin? Cause of their ignition? Aerolites? Color of me-
teors? b. Number of meteors? 333. What are fire balls ?
226 METEORS OH SHOOTING STARS.
trains. They generally explode with a loud noise, and
sometimes descend to the earth in large masses.
a. No deposit has been known to reach the earth from ordinary
shooting stars ; probably, because being very small they are dissipated
in the air ; but scarcely a year passes without the fall of aerolites in
some parts of the earth, either singly or in clusters. Some estimate
the whole number that fall annually at 700; others, much higher.
The most ancient fall of meteoric stones on record is that mentioned
by Livy, which occurred on the Alban Hill, near Rome, about the year
654 B.C. There are very many remarkable occurrences of this kind
on record, some of the masses being of immense size, and the explo-
sion so violent as to sound like thunder. In 1783 a fire ball of
extraordinary magnitude was seen in Scotland, England, and France.
It produced a rumbling sound like distant thunder, although its height
was 50 miles when it exploded. Its diameter was estimated at about
half a mile, and its velocity was as great as that of the earth in its orbit.
In 1859, between 9 and 10 o'clock A.M., a meteor of immense size was
seen in the eastern part of the United States. Its apparent diameter
was nearly equal to that of the sun ; and it had a train several degrees
in length, plainly visible in the sunshine. Its disappearance on the
coast of the Atlantic was followed by several terrific explosions. Some
of these meteors have been supposed to pass the earth, moving away
into space ; others to revolve in an orbit around it, becoming small
satellites. A French astronomer assigns to one of the latter a period of
revolution of 3 hours and 20 minutes, and a distance from the earth of
5,000 miles.
b. Composition and Size of Aerolites. The materials composing
these bodies are always nearly the same, consisting largely of iron,
and in no case of any other elementary substances than are found on
the earth. Some have been discovered of immense size ; one, a mass
of iron and nickel, found in Siberia, weighs 1,680 Ibs. At Buenos Ayres
there is a mass partly buried in the ground 7.^ feet in length, and sup-
posed to weigh about sixteen tons. A similar block, weighing about
six tons, was discovered a few years ago in Brazil. Many others exist.
All these are doubtless of cosmical origin, having been very small
QUESTIONS. a. Frequency of the fall of aerolites? Earliest recorded instance?
Remarkable instances ? Do they all reach the earth? It. Composition of aerolites?
Their size ? Additions to the earth, Venus, and Mercury from this cause ? Effect on
Mercury's period?
METEORS OB SHOOTING STARS. 227
planets revolving around the sun, but brought within the earth's
attraction ; and there is no doubt that, before the solar system had
reached its present condition, the additions made to the matter of
the earth in this way were quite considerable. This is supposed
still to be the case with Venus and Mercury, moving as they are
through the thicker portions of the great ling which we call the
zodiacal light. Now, as Mercury's orbit is very eccentric, it receives at
its aphelion a large number of these meteors whose periods are longer
than its own ; and this would have the effect to diminish its mean
motion and lengthen its period. Such an effect has actually been
discovered.
c. Meteoric Dust, etc. There are oa record many instances of
showers of dark -colored dust, which have fallen from the higher
regions of the atmosphere, and which seem from the composition of
the dust to be of meteoric origin. These falls are often preceded or
attended by a flashing of light as well as by a loud noise, sometimes
resembling thunder. In March, 1813, a shower of red dust fell in
Tuscany, discoloring the snow which then lay on the ground ; and at
the same time, a few miles distant, there occurred a shower of aero-
lites, lasting about two hours, and accompanied by a noise as of the
dashing of waves The phenomena of Hack and red rain and snow are
attributed to a similar cause. Since, as has been shown, several mil-
lions of meteors pass into the atmosphere during the year, there is no
doubt that large quantities of dust, too fine to be visible, descend to
the earth's surface. Some of this dust has been detected upon the
tops of mountains in soil which had never been previously disturbed
by man. Partial obscurations of the sun's light, occasioning what are
recorded as dark days, and the passage of large black masses across
the sun's disc, too rapid to be spots, are probably meteoric phenomena.
334. The NOVEMBER METEORS are supposed to revolve
around the sun in an orbit of considerable eccentricity,
inclined to the plane of the ecliptic in an angle of 17^,
and extending at its aphelion somewhat beyond the orbit of
Uranus, its perihelion being very nearly at that of the earth.
They move in a ring of unequal width and density, the
QUESTIONS. c. Showers of dust ? Black and red rain ? 334. Orbit of the November
meteors ? Why visible only every 33 years?
228 METEORS OB SHOOTING STABS.
thickest part crossing the earth's orbit every 33 years, and
requiring nearly two years to complete the passage.
a. The elements of this orbit correspond almost precisely with
those of the comet which made its appearance in January, 1866 ; so
that it seems probable that the comet is a very large meteor of the
November stream. The elements of the orbit of the August meteors
have been found, in a similar manner, to coincide with those of the
third comet of 1862 ; showing that the comet and these meteors belong
to the same ring. This seems also to be true of the first comet of
1861 and the April meteors.
b. The point from which the November meteors seem to radiate is
in the constellation Leo ; because, as the earth at that time of the year
is moving toward that point, they appear to rush from it. Their veloc-
ity appears to be double that of the earth, although only equal to it ;
because they move in an opposite direction and almost in the same
plane. When the earth plunges into the meteoric stream a great star-
shower occurs.
c. Physical Origin. Meteors are supposed by some to be small
fragments of nebulous matter detached in vast numbers from the
larger masses which are seen in the regions of the stars, or from
that of which the solar system was originally formed, tlieir origin
being precisely the same as that of the comets, which indeed may
be considered as, in reality, only meteors of vast size. It is also
probable that, like Biela's comet, others have been divided and
subdivided so as finally to be separated into small fragments moving
in the orbit of the original comet, and thus constituting a meteoric
ring or stream.
d. The following general conclusions with regard to meteors in the
solar system have been suggested : 1. Biela's comet in 1845 passed very
near, if not through, the November stream, and was probably divided
in this way ; 2. The rings of Saturn are dense meteoric streams, the
principal or permanent division being due to the disturbing influence
of the satellites ; 3. The asteroids are a stream or ring of meteors,
the largest being the minor planets which have been discovered ; 4.
The meteoric masses encountered by Encke's comet may account for
the shortening of the period of the latter without the hypothesis of a
resisting medium.
QUESTIONS. a. Resemblance to comets ? ft. Radiant point of November meteors ?
c. Physical origin of the meteors ? d. Generalizations with regard to meteors in the
solar system ?
CHAPTER XVIII.
THE STARS.
335. The STARS are luminous bodies like the sun, out
situated at so vast a distance from the earth that they seem
like brilliant points, and always in nearly the same positions
with respect to each other.
a. The scintillation or twinkling of the stars is due to the
inequalities in density, moisture, etc., of the different strata of the
atmosphere through which the rays of light pass. In tropical regions,
where the atmospheric strata are more homogeneous, this scintillation
is rarely observed ; so that, as remarked by Humboldt, " the celestial
vault of these countries has a peculiarly calm and soft character."
6. Parallax of the Stars. The usual method of finding the par-
allax of a body by viewing it at different parts of the earth's surface
is entirely useless in the case of the stars, as the displacement thus occa-
sioned in the positions of any of them is utterly inappreciable ; the
radius of the earth at a distance so immense being practically but a
mathematical point. If, however, we view the same star at intervals
of six months, our stations of observation will be about 180 millions
of miles apart ; and the amount of displacement thus occasioned, when
reduced to the centre of the orbit, is the stellar parallax, called some-
times the annual parallax.
336. The ANNUAL PARALLAX is the change which' would
take place in the position of a star if it could be viewed
from the centre of the orbit, instead of the orbit itself.
a. In other words, it is the angle subtended by the semi-axis of the
QUESTIONS. 335. What are the stars? ft. Cause of the scintillation ? ft. Parallax of
the etars, how found ? 386. How is annual parallax defined? a. Greatest parallax ?
230 THE STAKS.
earth's orbit at the distance of the star. The greatest parallax yet
discovered in the case of any star is somewhat less than 1" (0.9187"),
BO that the earth's orbit itself is but little more than a mere point at
the nearest star. To determine this small parallax exactly is prob-
ably the most difficult problem in practical astronomy.
b. Distance Calculated. The sine of 0.9187" is about .000004464,
which is the ratio of the semi-axis of the earth's orbit to the distance
of the star. Hence the distance of the star must be 224,000 times the
semi-axis of the earth's orbit, or 91 millions of miles ; and 91,500,000
X 224,000 20,496,000,000,000 miles, or nearly 20^ trillions of miles.
Light, moving with a velocity of 184,000 miles a second, requires more
than 3^ years to pass across this enormous interval, an interval more
than 7,000 times the distance of Neptune from the sun. However
large the stars may be, therefore, their attraction upon the solar system
must be altogether too feeble to disturb the motions cf its component
bodies in the least. The parallax of twelve stars has been determined
with considerable precision, the smallest being 0.046 ', cr about one-
twentieth that mentioned above ; this star must therefore be about
410 trillions of miles from us, a distance which light would not traverse
in less than 70.3 years.
337. MAGNITUDES. The stars are divided into classes
according to their apparent brightness, the brightest being
distinguished as stars of the first magnitude, the next of the
second, and so on. Stars of the first six magnitudes are visi-
ble to the naked eye ; but the telescope reveals the existence
of others so feeble in light as to be classed as of the seven-
teenth magnitude.
a. This classification is based exclusively on appearance, and indi-
cates nothing as to the real magnitudes of the bodies in question. Sir
John Herschel gives the following comparative estimate of the amount
of light emitted by stars of the first six magnitudes :
6th magnitude 1 3d magnitude = 12
5th = 2
4th =6
2d = 25
1st " =100
QUESTIONS. b. Distance of the stars, how calculated ? Of how many stars hag
the parallax been found? The least? 337. Magnitudes of the Ftars ? How many?
. What does mag :itude indicate? Comparative brilliancy of each ?
THE STABS. 231
This is not uniformly the relative brightness of stars thus denominated ;
Sirius, the brightest star in the heavens, being 324 times as brilliant as
an average star of the 6th magnitude.
338. The WHOLE NUMBER of stars visible to the naked
eye in the northern hemisphere is about 2,400; in both
hemispheres, more than 4,500.
a. These are distributed by Argelander according to their magni-
tudes as follows : 1st magnitude, 9 ; 2d, 34 , 3rd, 96 ; 4th, 214 ; 5th,
550 ; 6th, 1439 ; total in northern hemisphere, 2,342. If the southern
hemisphere is equally rich in stars, the whole number must be 4,684 ;
some estimate it at 6,000 or 7,000. The stars are probably less bright
in proportion as their distance is greater; and hence the number
increases as we descend to the lower magnitudes. Argelander's
estimate for the 9th magnitude is 142,000. Viewed through the tele-
scope, the stars can be counted by millions.
THE CONSTELLATIONS.
339. To facilitate the naming and location of the stars,
the heavens are divided into particular spaces, represented
on the globe or map as occupied by the figures of animals
or other objects. These spaces and the groups of stars
which they contain are called constellations, or asterisms.
a. Thus tliere are the constellations Aries, the Ram ; Leo, the
Lion ; Gemini, the Twins, etc. The general position of a star, accord-
ing to this system, is defined by stating in what part of the figure it is
situated ; as, the eye of the Bull, the heart of the Lion, etc. Its exact
position is, of course, only to be denned by its right ascension and
declination, or longitude and latitude. This system of grouping the
stars into constellations is supposed to be very ancient. Ptolemy
counted only forty-eight constellations ; but, since his time, the num-
ber has been augmented to 109.
340. The stars belonging to each constellation are distin-
guished by particular names ; as jSirius, Regulus, Arcturus,
etc., and by letters or numerals.
QUESTIONS- 338. What number of visible stars? . How distributed? 339. Con-
stellations? a. How used ? Number enumerated by Ptolemy? By modem astronomers f
::4D. Mode of designating the stars?
232
THE STAKS.
a. Only the most conspicuous stars have particular names ; the most
usual mode of designation being the use of the letters of the Greek
alphabet, alpha (a) being given to the brightest star, beta (i3) to the
next, and so on. When the twenty-four letters of this alphabet are
exhausted, the Roman letters are used, and subsequently the Arabic
numerals, the latter being applied according to the positions of the
stars in the constellation, the most eastern being designated 1, which
is thus the first star to cross the meridian.
ft. The Greek Alphabet. The following are the letters of the
Greek alphabet, with their names. It will be convenient for the student
to become familiar with them, as they are very frequently employed.
a Alpha
T] Eta
v Nu
T Tau
Beta
Theta
Xi
v Upsilon
y Gamma
t Iota
o Omicron
S86r -fiwrr,
Ptolemy.
28
226"
78*
'29
VULPECULA KT AN8KR.
The /Vw S-orpionis
Heart of the Scorpion
245
26 S
ALT \ IB
SPICA
FoMALHAtTT
j. Aqniloe,
x Virgini*
a Pimrix AtUfi.
Neck of the Eagle
Sheaf of Virgo
Southern Fish
300' 8i N
200' 10i* S
343 805 S
RKOULUS 01 Leoni*
Heart of the Lion
150 12r N
DEXRH * dugnl
Tail of the Swan
309"! 45' N
ALPIIKRATZ a. Andromeflce,
Head of Andromeda
r|2sr N
DUHIIR !* UfMce M ijori*
Great Bear
i 1C4
oar N
CASTOR
POLLUX
a Geminorum \
3 ffsminorum j
Heads of Gemini
'
112
114
32 N
2S>- N
POLE-STAR
a U>'*(K Minor-is
Tail of Little Bear
2
18i*
882* N
ALPHARD
i f/i/'/rcK
Heart of Hydra
J
140
S S
HAS ALHAGUS
a Ophiucki
Head of Serpent-bearer
>
262
i2r N
MAKKAB
a Peyaxi
Wing of Pegasus
2
845
145 N
ScilKAT
ft Pe'gaxi
Thigh of Pegasus
2
345
27iN
ALGENIB
y Pefftifti
Wins of Pegasus
2
2
u| N
ALGOL
ft Perxei
Head of Medusa
2i 45 401 N
DKNEBOLA
ft Leonix
Tail of the Lion
2|i 176 15 N
ALPIIKOCA
a. Coronce Bar.
Northern Crown
2i
282
27 N
BENKTNASCH
ALDKKAMIN
VlNDEMIATRtX
TJ U -see Major is
a Cep/iei
e Virginia
Tip of the Great Bear's Tail
Breast of Cepheus
Right Arm of Virsro
I 3
8
206
318
194
50 N
62 N
1H N
COR CAROLI
a Cnn-um Venaticorum
The Hunting Docs
8
398
39 N
ALCYONE
i\ Tauri
The Pleiades
8
55
28fN
QUESTIONS. 343. To what extent are star-names used? Mention some of the prin-
cipal.
THE STARS. 241
PROBLEMS FOR THE CELESTIAL GLOBE.
PROBLEM I. To find the place of a constellation or star on
the globe : Bring the degree of right ascension belonging to
the constellation or star to the meridian ; and under the
proper degree of declination will be the constellation or
star, the place of which is required.
NOTE. The student should be exercised in finding the places of all the
constellations or stars laid down in the lists, according to this rule. The
place of a planet or comet may also be found by this rule when its right
ascension and declination are given.
PROBLEM II. To find the appearance of the heavens at any
place, the hour of the day and the day of the month being given :
Make the elevation of the pole equal to the latitude of the
place ; find the sun's place in the ecliptic, bring it to the
meridian, and set the index to 12. If the time be before
noon, turn the globe eastward; if after noon, turn it west-
ward till the index has passed over as many hours as the
time wants of noon, or is past noon. The surface of the globe
above the wooden horizon will then show the appearance of
the heavens for the time.
NOTE. The student must conceive himself situated at the centre of the
globe looking out.
PROBLEM III. To find the declination and right ascen-
sion of any constellation or star : Proceed in the same
manner as to find the latitude and longitude of a place on
the terrestrial globe.
STAR FIGURES
344. Particular stars can be easily recognized in the heav-
ens by noticing the configurations which they form with
each other, or by using the more conspicuous stars as
" pointers ;" that is, by assuming two bright stars so situated
QTTESTION, 344. How to find particular stars ?
242 THE STAES.
that a straight line drawn through both will point directly
to the less prominent star whose position it is desired to
ascertain.
. This is sometimes called the method of " alignments," and is
that usually employed by astronomers. A few examples are here
given in order to enable the student to find some of the most conspic-
uous of the stars.
1. The Great Dipper, or Charles's Wain. This consists of seven
bright stars, in the Great Bear, so situated as to resemble a dipper
with a bent or curved handle, four of the stars forming the bowl, and
three, the handle. It is situated within the circle of perpetual appari-
tion, and hence is always visible, although in different positions as it
revolves around the pole. The two stars at the far side of the bowl
(a and 0) are called the " pointers" because a line drawn through them
would reach the" pote-star, which can, therefore, always be found by
discovering- the Great Dipper. The pole-star, by modern astronomers
called Polaris, by the 1 Greeks Cynosura, and by the Arabians Alrucca-
lah, is situated abolit 1 from the pole, and forms the extremity of
the upwardly curved handle of a small dipper, which occupies a
reversed position froni that of the Great Dipper, and consists of quite
faint stars.
2. Trapezium of Draco. About 90 east of the Great Dipper are
four stars so arranged as to form an irregular quadrangle or trapezium.
These are in the head of Draco, and with another, a little to the west,
situated in the nose (Rastaberi), form almost the letter V, pointing to
the west.
3. The Chair of Cassiopeia. This consists of five stars of the 3d
magnitude, which, with one or two smaller ones, form the figure of an
inverted Chair ; it is situated almost precisely at the opposite side of the
pole from the Dipper, being nearly 180 from it and in about the same
declination ; it can thus be easily found.
4. The Great Square of Pegasus. South of the Chair and a little to
the west, are four stars about 15 apart, forming a large square. They
are quite bright stars and the figure is very obvious. The north-eastern
star is Alpheratz, in the head of Andromeda ; the south-eastern, Alge-
nib ; the south-western, Markab ; and the north-western, Scheat.
Algenib and Alpheratz are on the equinoctial colure, which being con-
tinued toward the north passes through Caph, in Cassiopeia.
QUESTIONS. ft. "What star-figures are described? What is the situation of each?
THE STA11S. 243
5. The Great Y of Bootes. This consists of the bright and pecu-
liarly ruddy star Arcturus, at the lower extremity of the letter;
Mirach, at the fork ; Seginus, at the extremity of the western arm ;
and Alphecca, in Corona Borealis, at that of the eastern. This figure
is less than 45' to the south-east of the Great Dipper. Arcturus and
Seginus form with Cor Caroli, situated toward the west, a large triangle ;
and a similar but a larger figure is also formed by Arcturus with Dene-
bola, about 35 west, and Spica Virginia, about as far south.
6. The Diamond of Virgo is a large and very striking figure formed
of Cor Caroli and Spica Virginis, at the extremities of its longest
diagonal, and Arcturus and Denebola at those of the shortest. The
former are about 50 apart ; the hitter 35j. The figure extends from
north to south.
7. The Cross of Cygnus. This consists of five stars so arranged
as to form a large and regular cross, the one at the upper extremity
being Deneb, a star of the first magnitude. This figure is very mani-
fest and is situated about 35 to the west of the Square of Pegasus.
The star at the lower extremity of the cross is called Albirco. Deneb,
or Deneb Cygni (Deneb means tail), is sometimes called Arided. A
short distance toward the west from the Cross is the bright star Vega,
forming with two faint stars near it a small triangle, the base being
turned toward the side of the cross.
8. The Sickle of Leo. If the line joining the " pointers " of the
Great Dipper be continued toward the south, it will pass through a most
beautiful object, having the complete form of a sickle, the bright star
Regulux being at the extremity of the handle, and the curve of the
blade toward the north-east.
9. The V of Taurus. This is a group of stars situated in the head
of the Bull, the brightest of which is Aldebaran, a ruddy star of the
first magnitude, and situated at the left upper extremity of the letter.
Aldebaran is an Arabic word and means, " that which follows :" it was
applied to this star because it follows the Pleiades. This group of
stars is called the Hyades. A little to the north-west is the famous
cluster of small stars called the Pleiades, said once to consist of seven
stars, although now we only discover six, of which Alcyone is the
brightest,
10. The " Bands of Orion." These are in a splendid group of
stars to the south-east of Taurus, and situated under the equinoctial,
consisting of four brilliant stars in the form of a long quadrangle
244 THE STARS.
intersected in the middle by three stars arranged at equal distances in
a straight line, and pointing to Sirius, the most splendid star in the
heavens, on one side, and the Hyades and Pleiades on the other. These
three stars have been called by some " The Yard ; " in the Book of Job
they are called the Bands of Orion. A line of faint stars projects from
these toward the south : these are sometimes called " The Ell." At the
north-east extremity of the quadrangle is Betefgeuse ; at the south-east,
Saiph ; at the south-west, Rigel ; and at the north-west, Bellatrix.
tl. The Crescent of Crater. To the south-east of the Sickle may
be distinctly seen a beautiful crescent or semi-circle opening toward
the west, consisting of stars of the sixth magnitude. They form the
outlines of Crater ; and nearly south of the Sickle is the bright star
Cor Hydras, almost solitary in the heavens.
12. The Dipper of Sagittarius. This is a very striking figure con-
sisting of five stars of the 3d and 4th magnitudes, forming a straight-
handled dipper turned bottom upward. It is a considerable distance
south of Lyra, but comes to the meridian a very short time after it.
The stars at the mouth of the dipper are about 5 apart.
Familiarized with these few configurations, it will not be difficult
for the student, with the assistance of the globe or a planisphere, to
acquire a knowledge of the other visible stars and their positions in
the constellations to which they belong.
345. The APPARENT PLACES of the stars are constantly
changing in consequence of the precession of the equinoxes.
Their right ascensions and declinations are either increasing
or diminishing, according to their situation, as the equinoctial
pole revolves around that of the ecliptic.
a. The star Polaris is about H from the pole, and is making a
constant approach to it ; which it will continue to do until its dis-
tance is about \. It will then recede till in about 12,000 years the
bright star Vega, which is now 51 20' from the pole will be less than
5 from it, and will therefore be the pole-star. About 4,000 years ago
a Draconis was the polar star, being about 10' from the pole.
346. NUTATION. The precession of the equinoxes is not
a uniform movement, hut is subject to periodical variations
QUESTIONS. 345. Are the stars absolutely " fixed r What change constantly occurs!
. What change in the pole-star ? 346. What is nutation ? How caused ?
THE STARS. 245
occasioned by the different positions of the sun and moon
with respect to the plane of the equinoctial. When the sun
is at the equinox its effect is nothing; at the solstice it is
at its maximum ; and thus arises, in connection with the
general revolution of the pole, a vibratory motion of the
earth's axis, called nutation.*
347. The SOLAR NUTATION is very slight and goes through
all its changes in one year ; but that of the moon, depend-
ing on the position of its nodes with respect to the earth's
equinoxes, requires a period of 18^ years. The latter is what
is ordinarily meant by nutation.
a. By the lunar nutation alone, the pole of the equator would be
made to describe, in 18^ years, a small ellipse, about 18^" by 13J", the
longer axis being in the direction of the ecliptic pole ; but being car-
ried by the general movement of precession round the pole of the
ecliptic at the rate of 50" annually, it actually moves in a circle the
circumference of which is an undulating curve, somewhat like the real
orbit of the moon, the limit of the undulation either way being 9V'.
6. The discovery of the nutation of the earth's axis was made by
Dr. James Bradley in 1727, by noticing slight variations in the right
ascensions and declinations of the stars of which neither precession
nor any other known source of disturbance would account. The true
cause of the phenomena soon suggested itself to his mind, but could
not be confirmed until after 18^ years of observation. It was there-
fore not announced till 1745.
348. ABERRATION. This is a change in the apparent
places of the stars, which arises from the motion of the
earth in its orbit, combined with the progressive motion of
light.
(i. This displacemqnt qf the; stars was first observed by Hooke
while attempting to discover a parallax in y Draconis but the true
explanation of its cause was given by Dr. Bradley in 1727, the year
^Nutation is derived from a Latin word wjiich means a nodding.
QUESTIONS. 347. Periods of the solar and lunar nutations? , Effect of the lunar
nutation ? b. By whoiu and how discorered ? 84$, What is aberration ? . Ho\r
and when discoyered f
246 THE STABS.
in which the death of Ne vton took place. It was one of the most
interesting and important astronomical discoveries ever made, and
afforded an entire confirmation of the progressive motion of light, dis-
covered by Roemer about 50 years previously.
b. Cause of Aberration. An object is always seen in the direction
in which the rays of light coming from it strike the eye. Now this
depends not only on the actual direction of the rays themselves, but
on our own motion with reference to them ; for if a ray is proceeding
perpendicularly from an object and we are moving directly across it, it
will appear to strike against the eye in an oblique direction, and thus
the object will, in appearance, be thrown forward of its true place, by
an angle depending for its size upon the ratio of the velocity of our
own motion to that of light. This change of direction of the rays of
light is similar to that which takes place in the drops of rain when
we are running in a shower, and the rain descends perpendicularly ; for
then it beats in our faces as it would if we were standing still and the
wind were blowing it obliquely against us.
c. Amount of Aberration. Since the velocity of light is 184,000
miles a second while that of the earth is but little more than 18 miles.
the ratio of the latter to the former is about .0001, which is the sine of
an angle of 20^' ; and this accordingly is the amount of displacement
due to aberration, when the star is so situated that the rays proceed-
ing from it are perpendicular to the plane of the earth's orbit, the
star in that case appearing each year to describe a small circle having
a radius of 20.^". When the rays are oblique to this plane, the circle is
foreshortened into an ellipse, and the amount of displacement varies,
being 20^" only when the rays are perpendicular to the earth's motion ;
while in the case of stars situated in the plane of the ecliptic, there ia
merely an apparent oscillation, in a straight line, amounting to 41"
during each revolution of the earth.
(I. The phenomena connected with aberration are thus very compli-
cated ; and as they are all satisfactorily explained by the hypotheses of
the earth's motion and that of light, both receive a confirmation from
this important discovery.
349. THE GALAXY, OK MILKY WAY is that faint lumi-
nous zone which encompasses the heavens, and which, when
QUESTIONS. b. Its cause ? c. Amount of displacement caused by it ? <7. What is
proved by it ? 349. What is the Galaxy or Milky Way ?
THE STARS. 24?
examined with a telescope, is found to consist of myriads cf
stars. Its general course is inclined to the equinoctial at an
angle of 63, and intersects it at about 105 and 285 cf
right ascension. Its inclination to the plane of the ecliptic
is consequently about 40.
a. This nebulous zone is of very unequal breadth, not exceeding in
some parts 3 ; while in others it is 10 or even 16 ; the average
breadth being about 10. It passes through Cassiopeia, Perseus,
Gemini, Orion, Monoceros, Argo, the Southern Cross, Centaurus, Ophiu-
chus, Serpens, Aquila, Sagitta, Cygnus, and Cepheus. From a Centauri
to Cygnus it is divided into two parts, the whole breadth including the
two branches being about 22. It exhibits other divisions at several
points of its course.
350. Its appearance is not uniform, some parts being
exceedingly brilliant ; while others present the appearance of
dark patches, or regions comparatively destitute of stars.
a. Near the Southern Cross, where its general appearance is most
brilliant, there occurs a singular dark, pear-shaped space, obvious to
the most careless observer. To this remarkable patch the early navi-
gators gave the name of the coal-sack. A similar vacant space occurs in
the northern hemisphere at Cygnus.
b. The number of stars in the Milky Way is inconceivably
great. Sir William Herschel states that on one occasion he calculated
that 116,000 stars passed through the field of his telescope in a quarter
of an hour, and on another that as many as 258,000 stars were seen to
pass in 41 minutes. The total number, therefore, can only be esti-
mated in millions. Struve's estimate of the whole number visible in
Sir William Herschel's great reflecting telescope is 20^ millions ; and
tlie number brought into view by the still more powerful instrument
cf Lord Rosse must be very much greater.
351. The PREVAILING THEORY with regard to the Milky
Way is, that it is an immense cluster of stars having the gen-
eral form of a mill-stone, split at one side into two folds, cr
QUESTIONS. Its position ? a. Its breadth? What constellations does it pass through ?
851. Appearanco of the Mi'ky Way ? a. The " coal-sack ?" b. Number of stars in
the Galaxy? 351. What is it supposed to be ? Its figure ?
248 THE STARS.
thicknesses, inclined at a small angle to each other ; that all
the stars visible to us belong to this system ; and that the
sun is a member of it and is situated not far from the mid-
dle of its thickness, and near the point of its separation.
(i. The fact that the Milky Way is composed of vast numbers of
stars was conjectured by Pythagoras and other ancient astronomers,
but was not positively discovered till Galileo directed his telescore
to the heavens. The hypothesis that it is a vast cluster of which tie
sun and visible stars are members, was first suggested by Th< mas
Wright in a work entitled the " Theory of the Universe," published
in 1750. This subject received a careful and prolonged investigation
by Sir William Herschel, the results of which he published in 1184,
and which seems to establish the hypothesis mentioned in the text.
This opinion he arrived at by taking observations at different distances
from the zone of the Galaxy, and counting the stars within the field of
view. On the supposition that the stars are uniformly distributed
throughout the system, the number thus presented would indicate the
extent of the cluster in the direction in which they were seen ; and in
this manner some general idea of its form would be obtained.
b. Galactic Circle and Poles. The extensive survey made by
Sir William Herschel of the stars in the northern hemisphere, and con-
tinued by his son, Sir John Herschel, in the southern, has proved that
there are two points of the celestial sphere, diametrically opposite to
each other, at which the stars are very thinly scattered ; while at and
near the circle of which these are the poles the stars are so densely
crowded as to be absolutely countless. This circle lies very near the
middle course of the Milky Way, and hence is called the Galactic
Circle ; the points at which the stars are least dense are called the
Galactic Poles. It is also found that the decrease of the density of
the visible stars in proceeding either way from the plane of the
Galactic Circle conforms to the same law, but that the density in the
southern hemisphere is at each latitude greater than at the correspond-
ing latitude in the northern.
The annexed figure represents the general form of a section of this Tr ast
cluster, or stratum of stars, S being the place of the sun ; S/, the position
of the plane of the Galactic Circle ; 6 5, the Galactic Poles. It will be
QUESTIONS. n. By whom was this theory first suggested ? Herschel's investigations?
Mode of estimating its form ? b. What are the Galactic circle and poles ? How found ?
THE STARS. 249
obvious that at the visual lines S e and S/ the stars must appear most
dense, and at S6 least ; while at intermediate points, the density will vary
with the obliquity of the visual lines ; and as S/ is nearer the northern
confines of the stratum than the southern, more stars must be visible in
Fig. 117.
SECTION OF THE GALACTIC STRATUM.
the southern hemisphere than in the northern ; the number of stars depend-
ing in each direction upon the length of the visual line. The apparent
separation of the Milky Way is accounted for by supposing the sun to be
placed, as indicated, near the point where the two branches diverge.
c. Dimensions of the Galactic System. The thickness of this
stratum of stars Herscliel supposed to be about 80 times the distance
of the nearest star from the solar system ; but that its extreme length
is equal to 2,000 times that distance. To move from one extreme point
of this vast space to the other, light would require about 7,000 years.
352. PROPER MOTION OF THE STARS. The stars do not
always remain precisely in the same places with respect to
each other, but in long periods of time perceptibly change
their relative positions, some approaching each other, and
others receding. This apparent change of position is called
their proper motion.
CL. The first astronomer to whom the idea of a proper motion of the
stars (that is, a motion of the stars themselves, independent of annual
parallax) occurred was Ilalley. Comparing the anciently recorded places
of Sirius, Arcturus, and Aldebaran with their positions as observed by
QUESTIONS. c. Dimensions of the Galactic System ? 352. What is the proper mo-
tion of the stars? a. How found ?
250 THE STAKS.
himself in 1717, and making every allowance for the variation in the
obliquity of the ecliptic, he still found differences of latitude amount-
ing to 37', 42', and 33', respectively, for which he could not account,
except on the supposition that the stars themselves had changed their
positions. This was confirmed by Cassini in 1738, who ascertained
that Arcturus had apparently moved 5' in 152 years, while the neigh-
boring star rj Bootis had been nearly if not quite stationary. The star
61 Cygni has a considerable proper motion, having changed its position
in fifty years nearly 4'.
b. Motion of the Solar System in Space. In 1783 Herschel
undertook the investigation of this interesting subject ; and finding
that in one part of the heavens the stars approached each other, while in
the opposite part their relative distances seemed to increase, he arrived
at the conclusion that this apparent change in the stars is caused by a
real motion of the solar system in space. For, evidently, if we are
in motion, the stars toward which we are moving will open out, while
those from which we are receding will appear to come together ; and
as it was observed by Herschel that the stars in the constellation
Hercules are gradually becoming wider and wider apart, he inferred
that the motion of the sun and its attendant planets is in that direc-
tion. The mean result of the observations of Herschel, and several
distinguished astronomers who in more recent times have investigated
the subject, is that the point toward which the solar system is moving
is in 260 20' of right ascension, and 33 33' of north declination,
which agrees very nearly with that reached by Herschel himself. The
annual angular displacement of a star situated at right angles to the
direction of the sun's motion and at the mean distance of stars of the
first magnitude, is computed at about V' ; and therefore the velocity
of the motion is estimated at about 160 millions of miles in a year.
. Central Sun. The hypothesis that the solar system is revolving
around a central sun was first suggested by Wright in 1750. Madler
supposed that the central sun is the star Alcyone in the Pleiades ; but
it is not thought by astronomers that sufficient evidence exists for this
hypothesis. All that can be said to be established is, that the sun with
its great retinue of revolving; worlds is moving in space toward a point
in the constellation Hercules.
353. MULTIPLE STARS are those which to the naked eye
QUESTIONS. It. What motion has the solar system ? TTow indicated? To what
point is it moving ? c. Central sun ? 853. What are multiple stars ? Double stars?
THE STABS. 251
appear single, but when viewed through a telescope are
separated into two or more stars. Those that consist of two
stars are called double stars.
a. Double stars differ much in their distance from each other ; in
some cases being so near as to be separated only by the most powerful
telescopes ; in others, they are as much as f from each other. These
stars were carefully observed by Sir William Herschel, and have
received much attention from the distinguished astronomers of more
recent times. The list of this class of stars now contains upward of
six thousand, classified according to their angular distances from each
other.
b. The members of a double star are generally quite unequal in
size. The pole-star consists of two stars of the second and ninth mag-
nitude respectively, and about 18" apart ; Rigel has a companion star
about 10" from it, and of the ninth magnitude ; Castor consists of
two stars of the third and Fig. us.
fourth magnitudes about 5 '
apart ; y Virginis (Gamma
of the Virgin) is a very
remarkable star consisting
of two stars each of the
fourth magnitude. (See
Fig. 118.) e Lyrae (Epsilon
of the Lyre) is an example L POLE - 8T AR : 2 - 1UGEL : r> ' CA8TOS ;
of a star consisting of two stars each of which is double, being thus a
double-double star. In 1862, Sirius was discovered, by Mr. Alvan
Clark, of New York, to have a minute companion star situated about
7" from it.
c. Colored Stars. There is considerable diversity in the color of
both the single and double stars. Thus Vega, Altair, and Spica are
white ; Aldebaran, Arcturus, and Betelgeuse, ruddy ; Capella and Pro-
cyon, yellow. Single stars of a fiery red or deep orange are not
uncommon ; but among the conspicuous stars there is only one
instance (/3 Librae) of a green star, and none of a blue one. Many
QUESTIONS. a. Apparent distance of double stars? ft. Comparative size and color ?
Size of the members of double stars ? Examples? r. Difference in the color of single
stars ? Of double stars ? Complementary colors ? Presented by how many stars 't
252 THE STARS.
double stars exhibit the beautiful and curious phenomena of comple-
mentary colors,* the larger star being usually of a ruddy or orange
hue, and the smaller one, green or blue. In some cases, this is found
to be the effect of contrast ; since, when a very bright object of a par-
ticular color is viewed with another less brilliant, the latter, although
in reality white, appears to have the complementary color of the former.
In this way a large and bright yellow object will cause other objects
to seem violet ; and crimson, produce the effect of green. In many
cases, however, there seems to be a real difference in the color of the
constituents of double stars ; for when one of them is concealed by
introducing a slide in the telescope, the other still retains its color.
Of 596 bright double stars contained in Struve's catalogue, 120 pairs
are of totally different hues. The number of reddish stars is double
that of the bluish stars ; and that of the white stars 2 times as great as
that of the red ones.
d. That some stars have changed in color is an established fact.
Ptolemy and Seneca expressly declare that Sirius was of a reddish hue ;
whereas now it is of a brilliant white. Stars described by Flamstead
were found by Herschel to have changed in this respect ; and y Leonis
and 7 Delphini have changed since his time.
354. BINARY STARS are double stars one of which revolves
around the other, or both revolve around their common cen-
tre of gravity.
a. History of the Discovery, The discovery of this connection
between the constituents of double stars was, perhaps, the grandest of
Sir William Herschel's achievements. It was announced by him in
1803, after twenty-five years of patient observation, which he com-
menced with the view to discover the stellar parallax by noticing
whether any annual change in the relative positions of double stars
existed. To his astonishment, he found from year to year a regular
progressive movement of some of these bodies, indicating that they
actually revolve one round the other in regular orbits, and thus that
* Complementary colors are those which being blended produce white.
They are red, yellow, and Hue. The complementary color of any one of
these is a combination of the other two. Thus orange is complementary of
blue ; and green, of red.
QUESTIONS. d. Change of color in stars? 854. What are binary stars? a. How
discovered ?
THE STARS.
253
the law of gravitation extends to the stars. These stars are called
Binary* Stars, or Systems, to distinguish them from other double stars
which, although perhaps at immense distances from each other, ap-
pear in close proximity, because, as viewed from the earth, they are
very nearly in the same visual line, and therefore are said to be
optically double.
355. The observations of Herschel resulted in the dis-
covery of about 50 binary stars; but since his time the
number has been, according to Madler, increased to 600.
Most of the double stars are believed to be binary systems.
356. ORBITS AND PERIODS OF BINARY STARS. A very
careful scrutiny of these bodies and their changes in posi-
tion has shown that they revolve in elliptical orbits of con-
siderable eccentricity and in periods greatly varying in length.
The following is a list of the most remarkable of these bodies, with
their periods, and the semi-axes and eccentricities of their orbits :
NAME.
PERIOD.
SEMI-AXIS
MAJO?.
ECCENTRICITY.
Yuars.
C Herculis,
36.3 1.25
0.44
rj Coronae Borealis.
43.6
0.95
0.28
Sirius,
49.
7.05
Cancri,
58.9
1.29
0.23
Ursae Majoris,
63.1
2.45
0.39
" Centauri,
753
30.
0.96
Leonis,
84.5
0.85
0.64
70 Ophiuchi,
92.8
4.19
0.44
7 Coronas Austral is,
100.8
2.54
0.60
f Bootis,
117.1
12.56
0.59
(5 Cygni,
178.7
1.81
0.60
TJ Cassiopeise,
181.
10.33
0.77
7 Virginis,
182.1
3.58
0.87
o Coronas Borealis,
195.1
2.71
0.30
Castor,
252.6
8.08
0.75
61 Cygni,
452.
15.4
p Bootis,
649.7
3.21
0.84
7 Leonis,
1200.
From the Latin word bini, meaning two by two.
QUESTIONS. 855. How many discovered ? 356. Their orbits and periods ?
254
THE STARS.
It will be observed from the preceding table that the eccentricities of
these orbits are as great as those of the comets.
b. Dimensions of Stellar Orbits. In this table the semi-axis is
given as seen perpendicularly from the earth ; but to find the actual
dimensions of the orbit, the parallax must be ascertained. The
problem is then a simple one. Thus, the semi-axis of a Centauri is
30" ; but since its parallax is 0.9187", 1" must at that distance sub-
tend more than the semi-axis of the earth's orbit in the proportion
of .9187 to 1 ; that is, it must be 1.088 ; and CO" must subtend
1.088 X 30 = 32.64 times the semi-axis of the earth's orbit, which
is equal to about 3,000 millions of miles. Now, the eccentricity
is .96 ; and therefore the nearest distance to the central star is only .04,
or 120 millions, while the farthest distance is 5,880 millions. In the case
of 61 Cygni, the semi-axis is 15.4", while the parallax is 0.3638" ; hence,
1" subtends at its distance 1 -r-.3638 2.75 (nearly) ; therefore the
semi-axis 2.75 X 15.4 = 42.35 times the semi-axis of the earth's orbit,
which is equal to 3,875 millions of miles.
c. The following list contains all the stars whose parallax has been
found :
NAME.
PARALLAX
NAME.
PAKALLAX
a Centauri,
0.9187
a Lyrse,
0.155
61 Cygni,
0.5638
Sirius,
0.150
21258 Lalande,
0.2709
i Ursee Majoris,
0.133
17415 Oeltzen,
.247
Arcturus,
0.127
1830 Groombridge,
.226
Polaris,
0.067
70 Ophiuchi,
.16
Capella,
0.046
d Masses of the Stars. The joint mass, and in some cases the
separate masses, of each pair of revolving stars can be ascertained,
when we know their period and distance from each other. Thus, taking
Sirius for example, we find its distance from its companion star to be
47 times the earth's distance from the sun, while its period is 49 times
as great as the earth's. Hence, by the law stated in Art. 306, a, the
QTTESTIONS. b. Size of orbits how found? The calculation? c. What is the
nearest fixed star? Parallax of Sirius ? What distance does it denote? Capella?
d. Masses of the stars how calculated ?
THE STARS. 255
mass of the sun being 1, that of Sirius and its companion is 47 3 -f-49*
= 43.25. Now, it has been discovered* that Sirius is situated at a dis-
tance from the centre of gravity of both revolving stars equal to 16
times the earth's distance from the sun ; and therefore the companion
star is 47 16^ = 30 J that distance ; and as their masses are in inverse
proportion to their distances from the centre of gravity, the mass of
Sirius is to that of its satellite as 30| to 16|, or as 123 to 65. Conse-
quently, the mass of Sirius is iff X 43^ 28.3 times the jnass of the
sun ; and, if the densities are the same, its diameter is V28.3, or a lit-
tle more than three times that of the sun, and its disc 9 times as great.
But photometric measurements have shown that its light is 400 times
as great as that of the sun would be if the latter were removed to the
distance of Sirius ; so that the materials of this star must be much
less dense, or its light intrinsically far more brilliant, than that of the
solar orb.
e. The Sun a Small Star. By certain photometric comparisons
recently made by Messrs. Clark and Bond between the star Vega
(a Lyrae) and the sun, it has been shown that if the latter body were
removed to 133,500 times its present distance, it would send us the
same quantity of light as the star. But the nearest star (a Centauri)
is more than 200,000 times as far from us as the sun ; and Vega, about
six times as far as a Centauri. Hence the sun, if removed to the dis-
tance of the nearest star, would shine only as a star of the second
magnitude ; and if removed to the mean distance of stars of the first
magnitude, would appear as a star of the sixth magnitude, and be just
visible to the naked eye. It would seem therefore that the sun, mag-
nificent luminary as it appears to us, is only one of the smallest or
least brilliant of the stars.
357. PHYSICAL CONSTITUTION OF THE STABS. An analy-
sis of the light of the stars indicates that they consist of
solid incandescent matter surrounded with an atmosphere
containing the vapor of some of the elementary substances
existing on the earth ; such as mercury, antimony, sodium,
hydrogen, etc.
a. Spectrum Analysis. The band of rainbow colors, called the
* By Mr. Safford, of Chicago.
QUESTIONS. e. Is the sun a large or a small star ? 357. Physical constitution of the
stars ? How indicated ? a. Spectrum analysis what is it ? How was the method
discovered ?
256 THE STAKS.
solar spectrum, produced by causing the sun's rays to pass through a
piece of triangular glass called a prism, was noticed as early as 1802,
by Wollaston, to be crossed by dark bands or lines ; and in 1815,
Fraunhofer, by examining the spectrum with a telescope, discovered
as many as 500 of such lines, and since then the number perceived has
increased to thousands. Now, it has also been observed that, when
the light of any inflamed vapor passes through a prism, its spectrum
consists of one or more bright-colored bands, differing in number,
relative position, and color, according to the substance from which the
vapor proceeds ; but that when the light of any incandescent but not
vaporized substance is made to pass through the inflamed vapor, the
bright-colored lines are immediately changed to dark lines, the vapors
absorbing from the light the same kind of rays which they themselves
emit. Hence it is inferred that the substances whose peculiar lines are
found in the solar spectrum are contained in a vaporous condition in
the solar atmosphere, and as many as fourteen have been already iden-
tified. The stellar spectra also exhibit similar dark lines, each star
having a peculiar series of them ; and some are recognized as produced
by the burning of substances found on the earth. Thus, some of the
metals are found in some of the stars, and others in other stars ; and
this is thought to account for the different colors which the stars pre-
sent. Sirius has been discovered to have five of our elements ; and
Aldebaran, nine.
358. Stars that appear double when viewed through an
ordinary telescope are often separated by more powerful
instruments, into triple, quadruple, or other multiple stars.
Fig. 119. a. Examples are furnished by
the following stars: e Lyrae, already
referred to, which consists of two
stars, each of which is double ;
C Cancri (Zeta of the Crab), com-
posed of three stars, two large and
one small ; 6 Orionis (Theta of
Orion), a very remarkable star,
consisting of four bright stars,
two of which have small compan-
OBIOMS. TBAPKZIUM OF ORION. ion stars, thus forming a sextuple
QUESTIONS. 363. What are triple stars, etc. a. Examples? Trapezium of Orion?
THE STABS. 257
star. From the configuration of the four principal stars this is
sometimes called the trapezium of Orion. (See Fig. 119.) As all these
stars have the same proper motion, they are believed to constitute
one system. It is said that a seventh star belonging to this system
has been discovered by Mr. Lassell.
359. VARIABLE STARS are those which exhibit periodical
changes of brightness. The number of such stars discov-
ered up to the present time (1867) is about 120. They are
sometimes called Periodic Stars.
a. Examples. One of the most remarkable of these stars, and the
first noticed (by Fabricius in 1596), is Mira the wonderful in the
Whale (o Ceti). It appears about 12 times in 11 years ; remains at its
greatest brightness about a fortnight, being equal to a star of the 2d
magnitude ; decreases for about 3 months, and then becomes invisible,
remaining so 5 months, after which it recovers its brillancy ; the period
of all its changes being about 331^ days.
Algol (13 Persei) is another remarkable variable star of a very short
period, it being only 2 d 20 h 49". It is commonly of the 2d magnitude,
from which it descends to the 4th magnitude in about 3 hours, and
so remains about 20 minutes, after which in 3 hours, it returns to the
2d magnitude and so continues 2 d 13 b , when similar changes recur.
Observation shows that the period of Algol is less than it was in for-
mer years. Its variability was first noticed in 1669. 6 Cephei is
remarkable for the regularity of its period, which is 5 d 8 h 47 111 . Betel-
geuse, one of the four stars in the great quadrangle of Orion, has a period
of 200 days. There is a star in Cygnus the variations of which are
effected in 406 days. Three of the seven stars of the Great Dipper in
Ursa Major are variable stars, their periods extending over several
years. The double star y Virginis is also variable, its two component
stars having changed in brightness, the most brilliant becoming infe-
rior to the other, a Cassiopese is also variable as well as double ; and
there are several others. According to Mr. Hind, the color of most
variable stars is ruddy.
b. Cause of Variable Stars. Several hypotheses have been sug-
gested to account for these interesting phenomena. One is that these
bodies rotate and thus present sides differing in brightness, or obscured
QUESTIONS. 359. What are variable stars? How many discovered? a. Mira?
Algol ? Other examples ? 6. Cause of variable stars ?
258
THE STABS.
by spots similar to those which are seen on the solar disc ; another, that
their light is obscured by planets revolving around them ; and a third,
that their light is diminished by the interposition of nebulous masses,
since it has been observed that during their minimum brightness they
are often surrounded by a kind of cloud or mist. No one of these
hypotheses is entirely satisfactory, and hence we may conclude that
the true cause of the variability of these stars is unknown.
c. The following is a list of the most interesting of these bodies :
NAME.
PERIOD.
CHANGES
OF MAGN.
NAME.
PERIOD
CHANGES
OF MAGN.
Days.
From to
Days.
From to
ft Persei,
2.86
a* 4
a Herculis,
88^
3 4
already mentioned, that clusters and nebulae are invariably abundant
where stars are rare, and as invariably wanting where stars abound,
affords presumptive evidence that all these bodies are physically con
nected with the same great system of the universe of which the galaxy
itself is a portion.
b. What other creations occupy the infinitude of space beyond the
reach of human vision aided by the utmost efforts of optical and me-
chanical skill, we can neither know nor perhaps conceive. There is
reason for believing that light itself is gradually absorbed and thus
extinguished in its journey ings from those remote regions of the uni-
verse, long before it could reach our little orb and give us intelligence
of the worlds from which it spedi But that the works of God are
infinite in extent as they are in perfection and beneficent design, we
can not but believe ; nor as we contemplate the wonders and glories
of the starry heavens those unfathomable abysses lit up by millions
of suns, can we refrain from bowing in adoration and gratitude to
Him who has endowed us with the intellectual power (far more won-
drous than even these worlds themselves) to discover and survey
their vastness and magnificence, and with those moral and spiritual
capacities, by the due cultivation of which we may prepare ourselves
for an existence in that future world where we shall be enabled, in a
far higher degree, to contemplate His power and to understand His
infinite wisdom and beneficence.
QTJTSTIONB. ft. Other creations in thp infinitude of space ? Why not discoverable?
Feelings excited by a contemplation of the starry heavdns ?
APPENDIX.
Cl 02 % g H
> a P 5
sips
?> . * : :
to oc o I s >s n -
as. o
^ o
Mean Diam-
eter.
3-
Oblateness.
.
os to p
Sr a
p Of OS M-
OS OO CO rf^.
s* ^ SP,
OS rf*. tO
fe
tO M- M. CO
OS CO M- Of
H O O H^
CO CO CO
OS -3 Of tO
ol
Mass,
being 1.
Density com-
pared with
water.
Mean Dis-
tance in
Millions.
Eccentricity
of Orbit.
Inclination
of Orbit.
Sidereal
Period.
Ul
Synodic
Period.
333
o oo
3 P ?
Time of Ro-
tation.
o
Inclination
of Axis.
276
APPENDIX.
TABLE II. ELEMENTS OF THE MINOR PLANETS.
NAME.
Number.
Mean Dis-
tance.
_>
i
a
Inclination
of Orbit.
Sidereal
Period.
Discoverer.
2
C3
p
FLORA.
8
43
71
40
18
80
12
27
4
30
52
84
7
9
62
63
25
20
67
44
6
83
21
42
19
79
11
17
46
89
29
13
5
14
32
91
47
70
54
78
23
37
15
51
66
85
26
73
3
75
77
e'a=i
2.2014
2.2034
2.2661
2.2677
2.2956
2.2963
2.3344
2.3467
2.3733
2.8655
2.3657
2.3675
2 386'^
2.3866
2.893
2.395
2.4008
2.4097
2.4217
2.422
2.4259
2.4287
24354
2.44
2.4411
2.4431
2.4519
2.4735
2.5265
2.5498
2.554
2.5766
2.5771
2.586
2.5873
2.5958
2.5959
2.6133
2.6197
2.6228
2.6271
2.6414
2.6437
2.6491
2.6512
2.6536
2.6561
2.6666
2.6684
2.6698
2.6719
.157
.168
.12
.046
.217
.2
.219
.173
.09
.126
.066
.238
.231
.123
.185
.126
.254
.144
.185
.151
.203
.084
.162
.225
.158
.195
.099
.128
.164
.18
.074
.087
.187
.166
.083
.287
.183
.204
.205
.232
.177
.187
.287
.158
.191
.(i87
.043
.257
.307
.136
/
5 58
8 28
5 24
4 16
10 9
8 87
8 23
1 35
7 8
2 6
9 57
9 22
5 28
5 36
3 34
5 47
21 35
41
5 59
8 42
14 47
5 2
8 5
8 34
1 33
4 87
4 37
5 36
2 18
16 11
6 8
16 31
5 19
9 8
5 29
s""i
11 38
5 7
8 38
10 13
3 7
11 44
2 48
8 4
11 53
3 36
2 25
13 1
5
2 28
Yrs. dys.
3 97
8 99
3 150
8 151
8 174
3 175
3 207
3 217
3 229
3 223
8 223
8 225
3 240
8 251
8 256
3 258
3 263
8 270
8 280
3 281
3 284
8 287
3 292
3 296
3 297
8 299
3 806
3 325
4 6
4 26
4 30
4 50
4 51
4 58
4 59
i" '67
4 82
4 88
4 90
4 94
4 107
4 109
4 114
4 116
4 118
4 120
4 129
4 131
4 133
4 134
Hind
1847
1857
1861
1856
1852
1864
1850
1858
1807
1854
1858
1865
1847
1848
I860
1861
1853
1852
1861
1857
1847
1865
1852
1856
1852
1863
1850
1852
1857
1866
1854
1850
1845
1851
1854
1S66
1857
1S61
1858
1863
1S52
1855
1851
1857
1861
1865
1853
18(i2
1S04
1862
ARIADNE
FERONIA .
Poison
C. H. F. Peters.
Goldschmidt...
Hind
HAKMONIA
MKLPOMENE
SAPPHO
VICTORIA
Pogson
Hind
EUTERPE
Hind
VESTA
URANIA
Olbers
Hind
NEMAUSA. . . .
Laurent
Lnther
Hind
CLIO
IRIS
METIS
ECHO
Ferguson
De Gusparis
Chitcornac
De Gasparis
Poison
AUSONIA
PHOCEA
M A6SILIA
ASIA
NYSA
Goldschmidt...
Hencke .
HKHE. . . . .
BEATRIX
De Gasparis
Goldschmidt...
Pogson
Hind
LUTETIA.
Isis
FORTUNA
KURYNOME . .
Watson
De Gasparis
Luther
PAKTHENOPE
THETIS
HESTIA.
Stephan
Marth
AMPHITRITE
EGERIA
ASTR.EA
IRENK
POMONA
De Gasparis
Hencke
Hind ..
Goldschmidt. .
Stephan
Goldschmidt. . .
Luther
MELKTK
PANOPEA
CALYPSO
DIANA
Hind
Luther
De Gasparis
Ferguson
H. P. Tuttle . . .
Peters
THALIA
FlUKS
KUNOMIA
VIRGINIA
MAIA
lo.
PROSERPINE
Luther
Tuttle
JlTNO. ... .
Harding
Peters .
EuRvnicK
FRIGGA
APPENDIX
277
ELEMENTS OF THE MINOR PLANETS CONTINUED.
NAME.
Number.
ji
Eccentricity.
Id
c
1?
Sidereal
Period.
Discoverer.
I
ANGELINA
64
e's=i.
2.681.9
.128
o /
1 20
T dys.
142
Tempel
1S61
CIRCE
84
2.6863
in
5 26
147
Chacornac . . .
1855
CONCOBDIA
58
2.7008
.042
5 2
160
Luther
18CO
ALKXANORA
OLYMPIA
EUGENIA
55
60
<\*>
2.7123
2.7181
2.7212
.197
.117
08
11 47
8 87
6 85
171
172
179
Goldtchumlt.. .
Ihucornnc
Goldschiuidt
36t8
IfCO
1K7
LEDA
88
2.7401
.155
6 58
196
Chacorn:;c ....
16tG
ATAI.ANTA
NIOBE
86
79
2.7461
2.7564
.301
.174
18 42
23 19
201
219
Goldschmidt.. .
Luther
1K5
1861
PANDORA.. .
56
2.7591
.145
7 14
218
Searle
1858
ALCMENE
82
2.7608
226
2 51
214
Luther
164
CURES
1
2.7667
.08
10 86
4 2iO
Piazzi ....
1801
L^ETITIA
39
27671
.115
10 '22
4 221
1856
DAPHNE
41
2.7691
.266
15 ,'9
4 223
Goldschiuidt . .
PALLAS.
2
2.7696
24
84 43
4 228
Olbers ...
1S02
TlIISBE
88
2 7702
165
5 15
4 224
Peters
U66
GALATEA
BKLLONA
74
28
2.7777
2 7785
.238
15
8 59
9 21
4 231
4 232
Tempel
IS 62
1854
LET(
69
2 7804
188
7 57
4 288
1861
TERPIBCHORE
POLYHYMNIA
AGLAIA
81
S3
48
2.8568
2.8641
2.8812
.212
.839
.182
7 5
1 16
ft (
4 802
4 8C9
4 825
Tempel
Chticornac
Luther
18C4
18.*4
1857
CALLIOPE.
22
2 9107
.088
13 44
4 853
Hind
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1861
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6 193
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18C6
MINERVA
Eccentricity, 14.
of planets' orbits, 34
of stellar orbite, 253.
Eclipse, first recorded* 141.
Eclipses, 131.
annular, 139.
central, 138.
cycle of, 139.
number in a year, 135.
phenomena of, 140.
total and partial, 138.
Ecliptic, 64.
obliquity variable, 92 k
Ecliptic limits, 132, 133.
Elements of a planet's orbit, 205
of a comet's, 211.
Ellipse, defined, 14.
major and minor axes of, 14.
Elliptic comets, 211.
nebulae, 265.
Elongation, 44.
extreme, 150.
of planets at Neptune* 192.
Encke's comet, 218.
Epicycle, 31.
Equation of the centre, 35.
of time, 95.
Equator, 50.
Equinoctial, 64.
spring tides, 146.
Equinoxes, 64, 66.
Establishment of the port, 147.
Evection, 129.
Evening and morning star, 47, 163.
FACULJS, 105.
Faye's comet, 211.
Fire balls, 225.
Fixed stars, 18. (See Stars.)
Fizeau's experiments on light, 182.
Foci, 14
Force, centrifugal, 29, 30.
centripetal, 29.
impulsive and continuous, 29.
GALACTIC circle and poles, 248.
Galaxy, 246.
Galileo, 18, 104.
Galle, Dr., finds Neptune, 186.
Geocentric place, 205.
Georgium Sidus, 192.
Gravitation, law of, 29.
how discovered, 30.
Great inequality of Jupiter and Saturn, 206.
Greek alphabet, 232.
HALLEY'S comet, 216, 217.
Harvest moon, 117.
Heliocentric place, 205.
Herschel, Sir W., 183, 185, 190, 248, 250,
253, 264.
theory of solar spots, 107.
nebular theory, 264.
Herschel, Sir J., 34, 109, 153, 174, 177, 271.
Horizon, 54.
dip of, 55.
rational, 55.
Horizontal parallax, 60.
Horrox, 163.
Hour angle, 67.
circle, 67.
Hourly motions of the planets, 40.
Humboldt, 110,223.
Hunter's moon, 118.
Hyperbola, 210.
INCLINATION of orbit, 36, 37.
of axis, 41.
Inequalities, 204.
Inequality of Jupiter and Saturn, 206,
Inertia, 146.
Inferior planets, 149.
~JUNO, discovery of, 199.
Jupiler, 174.
Jupiter's satellites, 178.
eclipses of, 18<>.
libration of, 181.
KEPLEB'S laws, 30, 33.
INDEX
281
Kepler's 3d law, applied, 158, 163.
Kepler's star, 269.
LAPLACE, 130, 148, 181, 206.
Lassell, 23, 186, 188, 197, 251.
Latitude and longitude, 49.
Law, Bode's 39, 196.
of oblateness, 175.
Laws, Kepler's, 30, 33.
Lexell's comet, 220.
Librations of the moon, 121.
Light and heat at Jupiter, 177,
Mercury, 154.
Neptune, 197
Saturn, 184.
Light, aberration of, 245.
extinction of, in space, 274.
intensity of, at different planets, 109.
solar, comparative intensity of, lOtf.
Telocity of, 182.
Limits, ecliptic, 132, 133.
transit, 155.
Longest day and night, 76.
Longitude, 49.
how found, 182.
Lost or missing stars, 260.
Lunar axis, position of, 122.
inclination of, 122.
Lunar day and night, 123.
Lunar mountains, 126.
height of, l. : 7.
eclipses, 135.
Lunar irregularities, 128.
theory, 130.
Lunation, 116.
M ABLER' s chart of Mars, 173,
of the moon, 125,
Magellanic clouds, 272.
Major and minor axes, 14.
Mars, 168.
distance found by phases, 169.
parallax of, how found, 171.
ruddy color of, 174,
polar hemispheres of, 178.
Mass, 25.
of earth and sun, 102.
of the planets, 27.
of sun and planets, how to find, 207.
of Sirius, 254.
Mean and true place, 35.
Mercury, 149.
mass of, 151, 219.
mountains in, 153.
transits of, 155.
Meridian of a place, 56.
Meridian circles, 50.
length of a degree of, 89.
Meridian altitude of the sun, 66.
Meteoric dust, 227.
epochs, 224
rings or streams, 224.
satellites of the earth, 226.
transits, 227.
theory of sun's heat, 111.
Meteoric theory of minor planets, 228.
Meteors, 223.
August, 224.
cosmical origin of, 225.
November, 227.
number of, 2'25.
physical origin of, 2'?8.
Milky Way, 246. (Sec Galaxy.)
Million, idea of, S8.
Minor planets, 199.
magnitude of, 26, 201.
origin of, 202.
principal discoverers of, 200.
Mira, the wonderful star, 26J.
Moon, 112.
harvest, llf.
hbrations of, 121,
phases of, 114.
synodic and sidereal periods of, 116.
kloonlight, in winter, 118.
in polar regions, 118.
horning and evening star, 217.
Motion, laws of, 28.
curvilinear, 29.
resultant, 29.
Mutual attractions of the planets, 202.
tf ADIB, 56.
Nasmyth's " Willow Leaves," 107.
Nebular hypothesis, 202.
theory of Herschel, 264.
Nebula in Andromeda, 265.
in Argo, 271.
in Lyra, 266.
in Orion, 271.
(Jr. b, zTl.
Dumb-bell, 271,
Nebulse, 263.
annular, 266.
cometary, 269.
double, 272.
elliptic, 265.
irregular, 270.
planetary, 267.
resolvable and irresolvable, 26*
spiral, 266.
stellar, 268.
variable, iT2.
gaseous nature of, 264.
where abundant, 265.
Nebulous stars, 269.
Neptune, 194
discovery of, 195.
satellite of, 197
supposed ring, 197.
Newton, 30, 34, 144.
Nocturnal arc, 59.
Nodes, 36,.
November meteors, 227.
Nutation, 244
how discovered, 245.
solar and lunar, 245.
OBLATENESS, of the earth, 90.
law of, 175
INDEX.
Oblique sphere, 53.
Obliquity of the ecliptic, 66.
variation in, 92.
Occultation, 141.
Olbers, 199, 200
theory as to asteroids, 202.
Opposition, 43.
Orbits, planetary, 28-3T.
eccentricity of, 34.
inclination of, ilG.
of comets, 20, 210.
of meteors, 22T.
of satellites, 180, 190.
of stars, 253, 254.
PALI. AS, 199.
Parabola, 210
Parallactic inequality, lunar, 130
Parallax, 59.
of the moon, 60, 112.
of the sun, 164, 171.
of the stars, 229, 254.
Parallel sphere, 53.
Parallels of latitude, 51.
Pendulum, a measure of gravity, 88.
Penumbra, 131.
Perigee, 112.
Periodic comets, 211.
meteors, 223.
stars, 253.
times of the planets, 39.
Perpetual apparition, circle of, 58.
ocoultation, circle of, 59.
Perturbations, 204.
Phases of Mars, 168.
of the moo i, 114.
of Venus, 156.
Phenomena of the heavenly bodies, 17.
Photosphere of the sun, 107.
Plane, defined, 10.
Planetary nebulae, 267.
Planets, 20.
comparative densities, 26.
elements of orbits, 205,
major and terrestrial, 25.
masses of, 27.
mutual attractions of, 204.
orbital eccentricities, 34.
orbital inclinations, 37.
orbital velocities, 40.
relative distances, 38.
rotations, 41.
Pleiades, 243.
Polar circles, 76.
Polaris (see Pole-star),
Poles, of a circle, 15.
galactic, 248.
terrestrial, 50.
P.)le-star, 244.
Positions of the sphere, 58.
Praesepe, 261.
Precession of the equinoxes, 70.
cause of, fiO.
effect of, 91, 24 1.
lunar, 122.
Prime meridian, 50.
vertical, 57.
Priming and lagging of the tides, 14T.
Primitive tides, 147.
Problem of Three Bodies, 204.
Problems for the globe, 52, 70, 79, 06, 24L
Ptolemaic system, 18.
Ptolemy, 18, 129, 238.
Pythagoras, 18.
QUADBATUBE, 144.
Quartile, 45.
Questions for exercise, 48.
RADIATING streaks on the lunar disc, 127.
Radius- vector, 32.
Refraction, 61.
amount at different altitudes, 63
effect of, 62.
effect in a lunar eclipse, 141.
Resisting medium, 217.
Resolvable nebulas. 264.
Retrogradation, arc of, 169.
duration of, 169.
Retrograde motion. 163.
Right ascension, 67.
sphere, 58.
Ring mountains, lunar, 12T.
Rings, meteoric, 224.
of Saturn, 185.
Roemer, 182.
Rotation of nebulae 266.
planets, 42.
Saturn's rings, 187.
satellites. 190.
stars, 257.
sun, 42.
SATELLITE of Neptune, 197.
of Sirins, 251, 255.
Satellites of Jupiter, 178.
Saturn, 183.
Uranus, 23, 194.
Saturn, 182.
belts of, 185.
celestial phenomena at, 190.
density, 184.
equatorial velocity of, 184.
mass, 184.
oblateness, 183.
rings, 1S5-189.
satellites, 189, 190,
telescopic view of, 187.
Schroeter, 153, 159.
Sehwabe's researches on solar spots, 106.
Secondary circles, 50.
planets (see Satellites).
Secular acceleration, lunar, 130.
perturbations, 204.
variations, 205.
length of, unequal, 84.
variable, 86.
Selenograpy, 124
Sextile, 45.
INDEX.
283
Shadow, earth's, 181.
moon's 1ST.
Shooting stars (see Afeteora).
Sidereal day, 92.
month, 11(5.
year, 96.
period of Jupiter, 175.
Mars, 172.
Mercury, 154.
moon, 116.
Neptune, 196.
Saturn, 183.
Uranus, 193.
Venus, 162.
Signs of the ecliptic, 68.
of planets (see each).
Sine of an angle, 101.
Snow and ice at Mars, 173.
Solar day, 93.
eclipses, 135.
heat, theory of, 111.
light, intensity of, 109.
parallax, 163, 171.
spots, 103-108.
system, 18.
motion of, 250.
Solstices, 64.
Spectrum analysis, 255.
Sphere, defined, 14.
positions of, 58.
Spheroid, oblate and prolate, 16.
Stability of Saturn's rings, 1ST.
solar system, 207.
apparent places of, 244.
binary, 252.
colored, 251.
double, 251.
distance of, 230.
list of principal, 240.
lost or missing, 260.
magnitudes of, 230.
multiple, 250, 256
names of, 232, 240.
nebulous, 269.
new, 258.
parallax of, 229.
physical constitution of, 255.
proper motion of, 249.
scintillation of, 229.
shooting or falling, 223.
temporary, 260.
variable, 257.
Star clusters, 260.
conflagration of a, 259.
figures, 241
groups, 261.
Kepler's, 253.
names, 240.
showers, 228.
TychoX 258.
Stationary points, 167-169
Structure of the universe, 273.
Sun, 100.
a small star, 255.
Sun, a nebulous star, 270.
apparent and real diameters of, 101.
apparent motions of, 68, 64
apparent magnitude, 209.
distance from the earth, 99.
inclination of axis, 104.
mass, 102, 207.
meridian altitude, 66.
motion of, in space, 109, 250.
photosphere of, 107.
physical constitution of, 107.
surface and volume, 102.
Sun's heat and light, 111.
Superficial gravity at Jupiter, 176.
Mercury, 153.
Saturn, 184.
Venus, 159.
Superior planets, 168.
Synodic period, 45.
Syzygies, 1 15.
TELESCOPE, invention of, 20.
Telescopic views of Jupiter, 178.
of the moon, 125.
of Saturn, 187.
Temporary stars, 260.
Thales, 140.
Theory, meteoric. Ill, 229.
of nebulae, 264.
of solar spots, 107.
of zodiacal light, 111.
Theta ( Hionis, 256.
Three Bodies, problem of, 204.
Tidal force of sun and moon, 143.
Tides, cause of, 142.
equinoctial spring, 144.
flood and ebb, 142.
height of, 145, 148.
highest, 148.
how retarded, 146.
of rivers and lakes, 148.
priming and lagging, 147.
primitive and derivative, 147.
why they rise later, 146.
Tide waves, 146.
velocity of, 148.
Time, 92.
equation of, 95.
Transits, meteoric, 227.
of Jupiter's satellites, 180.
of Mercury, 155.
of Titan, 190.
of Venus, 163.
Trapezium of Orion, 256.
Triangle, defined, 13.
Trine, 45.
Tropics, 74.
Twilight, 77.
Twinkling of the stars, 229.
Tycho Brahe, 258, 264.
Tycho, a lunar mountain, 127.
UMBBA, 131.
Uranus, 191.
elongation of planets at, 192.
284
INDEX.
Uranus, existence predicted by Clairaut,
218.
satelites of, 23, 194.
sunrise and sunset at, 192.
VARIABLE nebulae, 272.
stars, 257.
Variation, lunar, 120.
of obliquity of ecliptic, 92.
in length of seasons, 86.
Velocity of solar system, 110, 250.
Velocities of planets, 40.
Venus, 156.
atmosphere of, 160.
mountains in, 159.
when most brilliant, 158
Vertical circles, 56.
sun, 74.
Vesta, 119.
Visual angle, 11.
Volumes of sun and planets, 24.
Vulcan, 22, 149.
WILSON'S theory of sun's spots, 107.
Winnecke's comet, 211.
Wolfs researches on sun's spots, 106.
Wollaston's estimate of sun's light, 109.
discovery of lines in solar spectrum,
256.
Wright's theory of the Universe, 5:48.
YEAB, anomalistic, 97.
civil, 96.
equinoctial or solar, 96.
sidereal, 96.
tropical, 96.
ZENITH, 56.
Zenith distance, 57.
Zodiac, 68.
constellations of, 233.
Zodiacal light, 1 10.
cause of. 111.
theory of Chaplain Jones, 110.
theory of Prof. Norton, 111.
Zones, 87.
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