в
* `** **** *** .. '*
76
ARTES
LIBRARY
1817
VERITAS
SCIENTIA
OF THE
UNIVERSITY OF MICHIGAN
UNUN
TUEBOR
SIQUERIS PENINSULAM·AMŒNAM
CIRCUMSPICE
W

Engraved by W Nuller from a Miniature of the
same ze
flainted by
Sam
Shelley
MRS BRYAN and CHILDREN.
A COMPENDIOUS SYSTEM
OF
ASTRONOMY,
IN A COURSE OF
FAMILIAR LECTURES,
In which the Principles of that Science are clearly elucidated, so as to be intelli-
gible to those who have not studied the Mathematics :
ALSO
TRIGONOMETRICAL AND CELESTIAL
PROBLEMS,
WITH A
KEY TO THE EPHEMERIS,
AND A
VOCABULARY of the TERMS of SCIENCE
USED IN THE LECTURES,
Which latter are explained agreeably to their Application in them.
BY MARGARET BRYAN.
These are thy glorious Works, PARENT OF GOOD,
ALMIGHTY! thine this universal Frame,
Thus wond'rous fair; THYSELF how wond'rous then!
Unspeakable! who sit'st above these Heav'ns,
To us invisible, or dimly seen
In these thy lowest Works; yet these declare
Thy Goodness beyond Thought and Pow'r Divine. MILTON.
SECOND EDITION.
LONDON:
PRINTED, BY H. L. GALABIN, INGRAM-COURT, FENCHURCH-STREET,
FOR J. WALLIS, NO. 46, AND WYNNE AND SCHOLEY,
NO. 45, PATERNOSTER-ROW.
1799.
[ iii ]
]
DEDICATION.
To MY PUPILS.
ASTRONOMY
STRONOMY being the most im-
portant science I have had the pleasure
of introducing to your acquaintance, I
think, by publishing my Lectures on
that subject, I shall afford you a plea-
sing retrospect of the sublime ideas it
conveys. And, as I know the recol-
lection of the friend who delivered them
will not be unpleasing to you, agreeably
to your wishes, I have prefixed my por-
trait to these Lectures, together with
those of my two dear children; hoping
A 2
by
iv
DEDICATION.
by the former to make a more lasting
impression on your minds; as, believe
me, to be forgotten by you, would in-
flict a severe pang on that heart which
feels for you almost parental tenderness ;
the truth of which, I trust, you cannot
doubt, as your own breasts bear testi-
mony to the probability, and must na-
turally infer the certainty, of this asser-
tion. Could it be possible to receive
the repeated proofs of your affection
which I have received, and not love
you? No! can I ever forget the
gra-
tulations you have annually offered me,
when each countenance, glowing with
affection or dissolving in tenderness, ac-
cording as the grateful ideas flowed in
your breasts, expressed more than your
words? Believe
Believe me, at those moments
I have felt the most sensible sympathy
thrill
DEDICATION.
V
thrill at my heart; such emanations
as I then received glowed too warmly in
my bosom ever to be extinguished.
How I have returned your affection
you best know. I had but one way of
evincing my sincerity; which was, by
an industrious application to such studies
as would most benefit you, in which
employment I was animated by the
hope of a reward, and such a reward
as deserved all my assiduity to attain,
- no less than the present and future
happiness of my dear Pupils
dear Pupils; which that
they may all enjoy, is the ardent wish of
their faithful and affectionate
MARGARET BRYAN.
August, 1797.
A 3
PRE-
[vii]
PREFACE.
I AM well aware, that, to write on subjects
which have been so extensively considered,
and fully delineated, by the ablest Mathema-
ticians and by Philosophers of the most pene-
trating genius, will not procure me any ho-
nour on the score of originality; yet, I trust,
I shall not incur censure by publishing a Com-
pendium, which, according to my ideas, will
render subjects, generally thought obscure,
clear to the understanding of young people.
If I have failed in the attempt through the
imbecility of my judgement, I hope the mo-
tive may be my apology.
A 4
I
viii
PREFACE.
I crave the indulgence of a discriminating
public to a Work, the result of much thought
and close reasoning; and, as the ideas, formed
of subjects confessedly among the loftiest to
the human comprehension, must be imperfect,
that my remarks on, and manner of digesting,
those which are the most popular may meet
a candid reception.
I know that I have no claim to the public
suffrage, only on account of the clearness of
my illustrations, which, as well as the dia-
grams, are principally original. As to the
phraseology, I fear it is too deficient in orna-
ment to procure me any credit; yet, I hope
the clearness of the elucidations may gloss over
the imperfections of the style in which they
are delivered. Had I copied that of other
authors, I might perhaps have rendered these
Lectures more pleasing, although less intelli-
gible, to my pupils, who, being familiar with
my diction, understand my illustrations much
better, as I have thence been able to deliver
them more naturally and forcibly.
For
PREFACE.
ix
For the minuteness of my descriptions, the
inferences I have taken the liberty to make,
and the digressions I have indulged in by way
of reflection, — I hope to be excused by those
whose superior learning does not need the first,
whose judgement would lead them to make
better than the second, and whose mature rea-
son renders the last unnecessary to them; beg-
ging them to observe that these Lectures were
written for my pupils, and not originally de-
signed for public inspection.
The most tender claims upon my exertions,
(the nature of which may be understood from
the frontispiece,) seconded by the encourage-
ment of my friends, having tempted me to
risk the decision of the public, with diffidence
I submit to its fiat; not wishing to procure
one devoid of judgement, but such as the
light of the understanding, mingling with the
feelings of sentiment without obscuring them,
may justify.
I have not presumptuously offered opinions,
without having previously digested those of
the best writers on the subject; or attempted
to
X
PREFACE.
to elucidate without due observation of the
principles of this science. For this mental
exertion, I expect some countenance from
those whose extensive learning and liberality
lead them to judge impartially; for, they, ri-
sing superior to the false and vulgar prejudices
of many, who suppose these subjects too su-
blime for female introspection, (ascribing to
mental powers the feebleness which charac-
terizes the constitution,) invalidate the idea
by affording all laudable exertions their avowed
patronage, acknowledging truth, although
enfeebled by female attire.
At the tribunal of public and just criticism,
I bow with humble confidence; acknowled-
ging its discriminating judgement, admiring its
general impartiality, yet, conscious of my de-
merits, dreading its award. Therefore, whilst
I invoke its pruning aid to lop off all redun-
dances, I implore its saving influence to pre-
serve unhurt this first shoot of a plant, which,
if, by its fostering mandate, benevolently in-
troduced into the mild, the invigorating, soil
of public esteem, may improve; but, should
the
PREFACE.
xi
the rude breath of censure blow on its present
weak and humble state, striking at the root
of its vitality, it would repress its faint but sa-
lutary odour.
Thus far I have expressed my thoughts as
nearly as possible to convey my ideas, and
with ease to myself; but a harder task remains
to be performed, to express my sense of the
goodness of those numerous friends who have
graced my subscription by their suffrage! If
they can conceive the emotions of joy and
gratitude at this moment vibrating in unison
in my bosom, they will know them to be
such as humanity glories in, all glowing
and felicitating, yet tributary and softened to
the most grateful sense of obligation. To the
sensibility of those who have on this occasion
manifested their sympathy and friendship for
me, I must appeal, to fill up my deficiency of
expression, words being too feeble convey-
ancers for the mind's energies.
One gentleman in particular claims my
warmest emotions of gratitude, as to him I
am indebted for all the advantages procured
me
xii
PREFACE.
me by this publication, by his having kindly
undertaken to peruse the MS.; and, after pe-
rusal, affording it his avowed sanction and pa-
tronage; without which distinction, I could
not have ventured to offer a work of science
to the public, from the presumption it would
have implied, as well as from the apprehen-
sion that the imperfection of my judgement
might have misled me. This friend I am
proud to acknowledge in the learned Dr.
Charles Hutton, F. R. S. of London and Edin-
burgh, and of the Philosophical Societies of
Haerlem and America, and Professor of Ma-
thematics in the Royal Military Academy,
Woolwich. My introduction to this gentle-
man I estcem one of the happiest circumstan-
ces of my life; an epoch I shall ever recur to
with extreme satisfaction. Although our ac-
quaintance has been very short, yet have his
active services, benevolently exerted to pro-
cure me extensive benefit and suffrage, af-
forded me never-ceasing cause of congratula-
tion on the acquisition of so valuable a friend,
whose kindness is the more distinguishing, as
I
PREFACE.
Xili
I had no claims of friendship, or even perso-
nal acquaintance, to entitle me to his notice,
previous to the submitting my MS. to his pe-
rusal. How sensibly do I feel my obligations
to him, they are such as bind me his debtor
for ever.
I hope the candid public will not accuse
me of vanity in publishing a paragraph from
the letter my worthy friend sent me on re-
turning my MS.* as I am induced to do so by
the advantage it may procure me.
* (COPY.)
Woolwich, January 6, 1797.
"Madam,
I herewith return the ingenious MS. of Astrono-
mical Lectures you favoured me with the sight of, which I
have read over with great pleasure; and the more so, to find
that even the learned and more difficult sciences are thus be-
ginning to be successfully cultivated by the extraordinary and
elegant talents of the female writers of the present day.
Should you, madam, give to your friends and to the public
to benefit by the publication of these your learned and useful
labours, I beg to have the honour of being considered one of
the encouragers of so useful a work:
And am, with great respect,
Madam,
Your most obedient and most humble servant,
CHARLES HUTTON."
Having
xiv
PREFACE.
Having premised all I think necessary to
the justification of this undertaking, to excuse
its faults, and to enforce its precepts, with
extreme sensibility, I subscribe myself my
Friends and Patrons most grateful, and the
Public's
Most obedient, humble Servant,
MARGARET BRYAN.
SUBSCRI-
[ xv ]
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Luke Walford, Esq. London.
Mr. W. Walker, London.
Wakeland Welch, Esq.
Mrs. Welch, Maryland-point.
Mr. Were, Margate.
Whitby, Esq. B. A. Trinity-college, Cambridge.
Whatman, Esq. Trinity-college, Cambridge.
Mrs. Whitehead, Margate.
Lieutenant-Colonel Wilson.
Miss White, Jeffries-square.
Reverend Samuel Wix, A. B. Christ-college, Cambridge.
William Wilcox, Esq. Hodsdon, Harts.
Edmund Wilcox, Esq. Hodsdon, Harts.
Mrs. A. Wilcox, Hodsdon, Harts.
Miss Wilkins, London.
Mrs. Witherdon, Ramsgate.
Colonel Wrench.
Mrs. Wyatt, Bocking.
Y.
SUBSCRIBERS.
xxix
Y.
John Yenn, Esq. R. A. Kensington.
Miss York, Ely-place.
Miss Zurhurst, London.
Z.
TABLE
[ xxxi ]
TABLE
OF
CONTENT S
TO THE
SECOND EDITION.
ON Optics
LECTURE I.
On the progressive Motion of Light and its Velo-
city
The Nature of Light. Of Refraction and Reflec-
tion
The Laws of Refraction and Reflection
Of the Nature of Lenses
Of Gravity
Of Pendulums
1
1
1
1
1
1
Of the Increase of Matter about the Equator, and
that it is occasioned by the centrifugal Force ari-
sing from the Motion of our Earth round its
Axis
Page.
5
6
9
13
17
22
24
27
LEC-
xxxii
CONTENTS.
LECTURE II.
Origin of Astronomy
First Measure of Times and Seasons
Symbolical Writing the Origin of Idolatry
History of the Improvements in Astronomy.
1
31
36
41
Of
the Advantages resulting from the Investigation
of this Subject
-
The Appropriation of the Letters of the Greek Al-
phabet to express the different Sizes of the fixed
Stars
Of the Reformation of the Calendar by Julius Cæ-
sar
The old Calendar abrogated, and a new one esta-
blished by Pope Gregory XII.
Of the Dominical or Sunday Letter
Of the Introduction of Telescopes
!
42
56
57
59
60
64
LECTURE III.
Introductory Address -
68
Of the Figure and Affections of the Globe we inha-
bit, and of the Appearances of the Heavens and
heavenly Bodies in consequence of the latter
69
Of the Atmosphere
74
Of the Magnet
75
Of the Horizon
78
Of the Meridian of the Zenith and the Nadir
79
Of the Equator. — Of the sensible and the rational
Horizon -
80
The Celestial Globe and Armillary Sphere explained,
with their Uscs in referring to celestial and terres-
trial Phenomena
82
Of
CONTENTS.
xxxiii
-
Of the longest and of the shortest Days in both nor-
thern and southern Latitudes
Of the Latitude and Longitude of the fixed Stars,
also of the Planets. The Difference between
the Longitude and Latitude of Places on our Earth
and those of the Stars
Of Declination.
The Tropics, why so called.
Of the Sun's apparent Motion North and South
Of the Zones, and the different lengths of the Days
and Nights at each of them
Of the Climates, and the Length of the natural Day
at each of the twenty-four Circles parallel to the
Equator
Of a right, a parallel, and an oblique, Sphere
Of the arctic and antarctic Circles
Of the Precession of the Equinoxes
Of the Inequality of the Sun's apparent Motion.
The Effects of the Sun's Rays falling with greater
or less Obliquity on our Earth
LECTURE
IV.
The Copernican System explained. Of the sup-
posed Nature of the Sun
Of Mercury
Of Venus
Of the Earth.
Of Mars
1
I
1
}
1
87
88
89
90
93
95
97
99
ΙΟΙ
109
113
115
116
!
1
Of Jupiter
Of Saturn
Of the Georgium Sidus
Of the Comets
-
Of the Quadrant and its Uses
}
Of the Adjustment of the Quadrant
b
}
1
118
121
}
#
125
126
134
136
LEC-
xxxiv
CONTENTS.
LECTURE V.
Of the Manner in which Mathematicians and Astro-
nomers estimate the real Sizes and Distances of the
heavenly Bodies belonging to the Solar System.
Of the Diminution of Heat and Light. — Of the
apparent Diameters of Bodies according to their
Distances
Of the true and apparent Places of the heavenly
Bodies
I4I
146
Of Aurora and Twilight.
The Effects of the dif
ferent States of the Atmosphere
147
The Sun and Moon both seen before they rise above
the Horizon
Of Parallax
}
148
149
Of the different Parallaxes
Parallax not referable to the fixed Stars
Of the Transit of Venus
1
Of the apparent Size of the Sun and Moon
Of the Aberration of Light
LECTURE VI.
}
1
1
1
I
t
}
i
Of the fixed Stars, and a View of that sublime Field
of Investigation, the Universe. — Why we sup-
the Stars to be fixed in a concave Sphere
pose
Of the Aurora Borealis
Changes in the fixed Stars
Of Motion and Gravity -
I
1
LECTURE
VII.
1
The Terms Gravity, Weight, Attraction, and cen-
tripetal Force, how applied to express the same
Thing
150
152
155
159
161
172
179
182
185
198
Of
CONTENTS.
XXXV
Of the Orbits of the Planets
Of the Nature of an Ellipse
1
1
199
200
Why the Planets revolve in elliptical Orbits
How the Motions of the Planets are perpetuated.
Of accelerated and retarded Motion -
Of the centrifugal and centripetal Forces. Of the
Motions of the Satellites
201
202
203
Of the longer Axis of an Ellipse, or the Line of the
Apses
205
Why the Motion of a Planet is swiftest when it is at
Perihelion and slowest when at Aphelion
Of the mean Distances of the Planets from the Sun.
The annual Motions of the Planets how as-
certained
-
207
208
Of the apparent diurnal Motion of the heavenly Bo-
dies. Of their apparent retrograde Motion
A Description of the Eye and its Capacities, also
its Effects explained
209
>>
212
LECTURE
VIII.
A Description of the Orrery in its divisible State, and
of the Motions of the Planets of our System, elu-
cidated by the Application of the Planetarium-Part
of it; also by Diagrams, and the known Laws of
projectile and centripetal Forces
The diurnal Motion of the Planets how ascertained.
Why all loose, globular, Bodies, turning on
their Axes, must be oblate Spheroids. Why all
the heavenly Bodies appear equi-distant from us
The Order in which the Stars appear after Sun-
227
232
set
234
How Sir Isaac Newton estimated the Heat and Light
received by each Planet of the Solar System
b 2
236
The
xxxvi
CONTENTS.
The relative Bulks of the Sun and Planets. Why
the Sun appears to pass through all the Signs of
the Zodiac in one Year
Of the true or direct Motion of the Planets, or in
Consequentia. Of their apparent or retrograde
Motion, or in Antecedentia. The Times of the
Retrogression of a superior and of an inferior
Planet different. The Times of each Planet
being retrograde
When a Planet is said to be in Conjunction with the
Of their relative Situations to each other
Sun.
in different Parts of their Orbits
Of the Aspects of the Planets, and how expressed.
Of the inferior and of the superior Conjunction
of Venus and Mercury, and of their greatest Elon-
gations
Of the direct and retrograde Motion of Venus.
When the Motion of an inferior Planet is direct and
when retrograde. -The Absurdity of the Ptole-
mean System evinced
Of the Phases of the Planets
The Time of a superior Planet being retrograde
The Truth of the Copernican System demonstrated
238
241
242
243
244
245
250
252
154
LECTURE IX.
-
Of the Obliquity of the Axis of the Earth to the
Plane of its Orbit
Mr. Norwood's Mode of ascertaining the Number
of Miles contained in a Degree of the Earth, and
the Improvements made since his Time in this
Calculation, by a Knowledge of the true Form of
the Earth on the Principles of Gravity
The Nutation of the Earth's Axis accounted for -
259
262
264
Of
CONTENTS.
xxxvii
Of Solar and Sidereal Time, and of the Inequalities
of the Solar Days amongst themselves
Of the Tropical or Civil Years
Of the Vicissitude of the Seasons, and of the diffe-
rent Lengths of Day and Night throughout the
Year
Of the Motions of the Moon, her different Phases,
and the Inclination of her Orbit to the Ecliptic
Of the Variety in the Moon's Affections
267
274
275
-
281
282
Of the telliscopic Appearance of the Moon
286
Of the Lunar Synodical, and the Lunar Periodical,
Month
290
LECTURE X.
Of the Laws of Shadow
Of Eclipses of the Moon
Of Solar Eclipses
Of the Moon's Atmosphere
Of the Periods of Eclipses
-
1
}
་
1
1
1
1
1
The Phenomena of the Tides considered, and how
produced
301
303
305
307
308
311
Of Winds, particularly that called the Trade- Wind - 320
Elements of Trigonometry
1
1
325
Trigonometrical Problems
334
The general Principles of a celestial Globe ex-
plained
345
Celestial Problems
349
Explanation of the Tables used in White's Ephe-
meris
Characters of Bodies belonging to the Solar System,
and of the Constellations of the Zodiac. - Cha-
racters of the Affections of the Planets, and their
Significations;
369
xxxviii
CONTENTS.
Significations; also other Characters explained that
are used in the Ephemeris
376
A View of the Solar System; referred to Plate 6
Catalogue of the Constellations in the Northern He-
378
misphere; referred to Plate 4
Names of the Stars of the first Class in the Constel-
380
lations; referred to Plate 4
382
Catalogue of the Constellations in the Southern He-
misphere; referred to Plate 5
Names of the Spots in the Moon; referred to Plate
384
13
A Vocabulary of Terms
386
1
}
387
F
A
COMPENDIOUS SYSTEM
OF
ASTRONOMY.
LECTURE I.
GENERAL
INTRODUCTORY REFLECTIONS ON
VARIOUS SUBJECTS. ON OPTICS.—THE EYE.
LIGHT.—REFRACTION.REFLECTION.
GRAVITATION. - PENDULUMS, &C.
NATURAL objects, when properly contem-
plated, continually admonish us in the important
science of Divine Wisdom, leading us to consider
our situation in this sublunary state, our connec-
tions and dependencies; from which we learn the
duties required of us, and the exertions we are
capable of making.
From the consideration of our mental faculties,
we infer the exalted idea of a future state of ex-
istence, so naturally rising in the intelligent mind,
which reflects on the never-ceasing energy of the
mental
B
1
2
LECTURES ON ASTRONOMY.
mental power, and its independency of all mortal
circumstances.
Thus perceiving what is the purer essence of
our nature, and what the grosser, we are conscious
that our present existence was not the primary or
principal intention of our Creator: yet, as it is al-
lotted us preparatory to that for which we were
created, it claims our particular attention; be-
coming either advantageous to us or otherwise, ac-
cordingly as we deal with the objects which sur-
round us.
Our superiority in the scale of beings gives us
the power of applying, to our own use, the gifts
of Providence, by which we are surrounded, with
the greatest advantage, not only so as to supply the
necessities of our mortal nature, but also to de-
rive considerable mental gratification from them.
Shall we then neglect rightly to use the gift of
reason, and thereby become unworthy of such a
boon, as well as lose all the benefits to be derived
from it? Certainly not. Let us rather, on the con-
trary, so exercise and improve our understanding,
as to form a right judgement of the value of things,
by which alone we can be enabled to conduct
ourselves according to the proper circumstances of
the state in which we are placed: a business
which requires more caution in the investigation
than young minds are apt to imagine; ;-imply-
ing a thorough knowledge of the human mind,
which can be obtained only by a careful examina-
tion of its capacities and infirmities.
Before
LECTURE I,
3
Before entering upon this important investiga-
tion, my duty prompts me to offer some reflections
on that Hand which formed us; that Divine Mind
which directs all our involuntary operations; and
that Benevolence which renders these operations
instrumental to the comfort and happiness of all its
creatures.
Yet, how can I presume to recount the works
of the Almighty, or shew the wisdom of his coun-
sels! Far above the narrow scale of human in-
quiry, far out of the reach of the feeble efforts of
human comprehension, are such investigations:
yet are his attributes discoverable in his wise ad-
ministration, made evident to us through the me-
dium of our senses. Let us, then, receive these
emanations of the Divine Mind, shed down upon
us, with as much joy and thankfulness as we do
the rays of the sun when falling upon our crops of
corn, making them yield forth their abundance.
This world is by no means barren of comforts to
those who cultivate a relish for the delights it of-
fers, avoiding satiety; for, by a proper application
of the objects of sense, we shall learn how to ren-
der the things of this life not only serviceable but
delightful to us.
If we attentively regard the wonders of creation,
we shall discover gradations; some rising superior
to others in that excellence, of some kind or other,
which is peculiar to each particular species. In
vegetable and mere animal nature, this is una-
voidable; but, in the higher class of animated na-
B 2
ture,
+
LECTURES ON ASTRONOMY.
ture, in man, much depends on his own exertions,
as is evident from the instances of the learned men
of all ages and all climates; some of whom, though
born under all the disadvantages of superstition
and barbarism, yet, by a right application of their
understanding, they have signalized themselves in
the delightful fields of science and virtue, not ex-
celled even by those who have lived and studied in
the most civilized nations with all the advantage of
instruction and method to regulate their research-
es and this excellence, the former have at-
tained to by a due cultivation of their minds, by
which they have increased in knowledge, by re-
gular gradations, till they have arrived at the
highest pitch of mental improvement.
The operations of the mind, distinguished by
logicians, are four.
The first is perception, from which result our ideas.
The second judgement, which is the assembling
ideas together, and comparing them.
The third is reasoning, which is the exercising
our minds in producing proofs to apply to the dis-
covery of facts.
The fourth, which is the last operation of the
mind, is called method; as we must perceive,
judge, and reason, before we can methodize. The
mind must be stored with the knowledge resulting
from the foregoing operations, before it can be ca-
pable of disposing its intellectual acquirements
into classes, or of uniting them according to their
proper connections and dependencies.
How
LECTURE I.
5
ગ
How delightful is the task of inquiry! How
important the advantages resulting from investiga-
tion! Amply is the searcher into nature rewarded
by the extension of ideas and the strength of judge-
ment acquired; by which the human understanding
is enabled to soar above vulgar prejudices, and to
view the works of God with satisfaction, deriving
consolation from every object in nature.
Suppose we employ the operations of the mind
at present on an object which aptly offers itself;
being so connected with the subjects of these Lec-
tures, that, without it, we could never have con-
templated the wonders of those regions they treat
of; namely, the organ of sight. Do we not per-
ceive its fitness to the office assigned it? and do we
not from thence infer the power and wisdom of
that Being who constructed it? "He that made
the eye, doth not he see?" Thus proceeding,, ac-
cording to the natural operations of the mind, we
discover not only its use, but the necessity of such
an organ to rational beings, as well as to almost all
animated nature capable of self-action; as, with-
out it, how could existence have been continued?
how could the latter have sought their food or the
former have prepared it? From this evidence of
God's preventing goodness we naturally infer that
every part of his creation is replete with the like
instances of benevolence in their several dispensa-
tions.
In order to your understanding the wonderful
contrivance manifested in this little organ, to fit it
B 3
for
6
LECTURES ON ASTRONOMY.
for the rays of light, it will be necessary to con-
template the nature and properties of that subtile
fluid.
The particles of light are inconceivably small,
and their velocity exceeds human conception.
The laws by which they are governed, and by
which other bodies act upon them, by reflections
and refractions, without altering their original pro-
perties, and the facility with which they insinuate
themselves into substances of the compactest tex-
ture, are circumstances which excite astonishment
in the most cultivated minds.
The Sun is the fountain of heat and light,
which are kindred properties, only differently mo-
dified: sometimes they act unitedly, and sometimes
independently of each other.
This fluid is universally diffused, and perpetually
flowing from its source, the Sun. Mixing with our
atmosphere, it supports animal and vegetable ex-
istence, adorns all nature, and is the first natural
principle of motion and vitality.
That light is a material substance has been proved
by its being subject to those laws which characte-
rize materiality; such as decomposition, force;
and being prevented from pursuing its straight
course by the interposition of an opake body. Its
natural motion, like that of all bodies, is uni-
formly progressive, as has been proved by many
experiments; also that its velocity is the same,
whether original, as from the Sun, or reflected, as
by the planets.
From
LECTURE I.
7
From observations of the eclipses of the sa-
tellites of Jupiter, it has been discovered that
light is propagated from the Sun to our Earth
in 8 minutes, 12 seconds. These eclipses, when
they happen at the time the Earth is interposed
between the Sun and Jupiter, are observed a-
bout 8 minutes, 12 seconds, sooner than they
should do by the tables; and, when the Sun
is between the Earth and Jupiter, they happen
8 minutes, 12 seconds, later than they are cal-
culated for. These circumstances are owing to
the light of the satellites having farther to come
in one case than in the other, by the whole diame-
ter of the Earth's orbit.
These observations clearly prove the progres-
sive motion of light, and ascertain its velocity,
as these inequalities are certainly occasioned by
the time which the light takes in traversing that
quantity of space, which is equal to the diameter
of the Earth's orbit, and not to any inequality in
the motions of the satellites in their orbits; for, the
same happens in all parts of their revolutions.
Although it is impossible to convey an adequate
idea of the amazing velocity of light, yet, that we
may form some conception of it, I shall just ob-
serve, that it moves at the rate of twelve millions
of miles in a minute, as is known by comparing
the Earth's mean distance from the Sun with the
foregoing phenomenon.
The unlearned in the sciences are astonished at
the minute calculations made by mathematicians
B 4
of
8
LECTURES ON ASTRONOMY.
of the distances, sizes, &c. of the heavenly bo-
dies and of our Earth, because they are not ac-
quainted with the principles of this science. I
hope, in its proper place, to convince my pupils
that such calculations may be accurately made by
thosc versed in the mathematical sciences.
I shall not enlarge on the subject of optics, or
the nature and properties of light, in these Lec-
tures, more than will be necessary to your con-
ceiving the nature and extent of celestial observa-
tions, after having recalled the attention of my
dear pupils to a retrospect of those clear evidences
they have perceived of this admirable subject in
my lectures on optics: -The wonderful organiza-
tion of the eye, the uses of its different parts, and
the delight it affords!
The rapture with which we have contemplated
the separated rays of light, in all their distinct and
glowing colours, when, charmed with the vari-
egated hues, we have almost forgotten what they
were to authenticate, till, anxious for convic-
tion, we have returned to the theory, when, on
comparing the admirable experiments of Sir Isaac
Newton with his inferences, we have been doubly
gratified by truths so clearly elucidated.
Then, on comparing the properties of light
with the mechanism of the eye, we have perceived
that the eye was formed for the rays of light; that
it had the power, in a great degree, of adjusting
itself to their strongest and weakest impressions;
that its humours were adapted, by their powers of
uniting,
LECTURE 1.
9
uniting, refracting, and reuniting, to answer, in the
most perfect manner, the purposes of vision.
Then, considering the powers employed exter-
nally to aid this delicate machinery, (such as the
muscles, by which all its motions are regulated,)
and that each of these has its particular office as-
signed it, (one raising and supporting the eye, ano-
ther lowering it; one drawing it towards the nose,
another towards the temple; another making it roll
about with ease, and the last moderating the
movements of all the rest, so that they should not
exceed certain limits,) how has the prescient and
preventing providence of God, thus manifested to
us, filled our hearts with love and admiration!
How sensibly have we felt this conviction of an
all-wise, all-seeing, and all-bountiful Creator!
In proceeding with the subject which occasioned
this digression, I shall endeavour to be as concise
and intelligible as possible, avoiding all superfluous
illustration and abstruse terms of science.
By a ray of light is meant the least particle of
light that can be separately impelled.
By a pencil of rays, a parcel of rays issuing
from a point or proceeding towards one.
When an object is illuminated by the sun or a
candle, every physical point on the surface of that
object which is turned towards the light sends
forth rays in all directions, by which power it is
that it becomes visible to us.
That side of the object which is turned from the
light may also be seen; but it appears dimmer,
that
10
LECTURES ON ASTRONOMY.
that part not receiving the direct influence of the
light, but receiving it by reflection only from sur-
rounding objects. All objects would be invisible
on the side turned from the radiant point, if it
were not for that property of light which causeth
it to be reflected.
Before the admirable Newton, by his judicious
and well-conducted experiments, discovered that
the particles of light were turned back before they
touched the reflecting surface, it was generally
supposed that the rays of light were reflected by
striking against the impervious parts of solids, as
other bodies are; but that great and penetrating
genius discovered the error of this supposition,
and has taught us, that the matter of light, co-
ming in contact with some unknown subtile me-
dium, which is equally diffused over the whole
surfaces of those substances, and striking it with a
determined force, is thrown back by the re-action
of this fluid-medium, which fluid he conceives to
be subtiler than air or light, and an intermediate
agent.
<< were re-
"If light,” says this great man,
flected by striking on the solid parts of bodies,
their reflections would not be so regular as they
are found to be; as, however polished the smooth-
est surface may appear to our sight or feel to our
touch, yet is it an assemblage of inequalities; for,
in polishing glass with sand, it is not otherwise
polished than by bringing its surface to a very fine
grain, and, from such a surface, the small particles
of
LECTURE I.
11
of light would be as much scattered as from the
roughest."
This conclusion is so convincing, that, although
we cannot discover the invisible agent which causes
reflection, yet we must admit the probability of its
existence.
That there is such an active medium, whose a-
gency cannot be perceived but by its effects, we
are certain, as, without allowing that there is,
how can we account for all the effects we call gra-
vity? of which I shall say more hereafter.
That the rays of the sun or a candle proceed in
straight lines, whilst moving in the same medium, is
evident by the shadows cast by opake bodies; but
that, in falling obliquely from one medium on to
another of a different density, they are refracted, is
proved by experiments.
By a medium is meant any transparent body
which suffers light to pass through it, as air, glass,
water, &c. These mediums differ in density;
therefore, the light, in passing from one to the
other, is refracted; and the deviation is in some
proportion to the difference of density of the two
mediums.
The rays of the sun, in passing out of the
ethereal region into our gross atmosphere, are re-
fracted, so that we see that luminary before it has
risen above our horizon of a morning and after it
has sunk below it of an evening; so that, by this
refractive power of our atmosphere, we enjoy the
light of the sun a considerable time longer than
we
12
LECTURES ON ASTRONOMY.
•
we otherwise should do, and escape the disagreea-
bleness of a sudden transition from one extreme to
another.
The rays of light, which fall perpendicularly on
a different medium, are not refracted, as when
they fall obliquely; and, when the sun is in the
zenith of any place, that spot to which it is verti-
cal receives its direct influence and suffers the
extremest heat, receiving a greater quantity of the
sun's rays in proportion to the space.
The refraction which light is subject to is easily
seen in a familar instance, by placing any object
at the bottom of a bason, and withdrawing your-
self from it, till it is lost to your view, when, if
another person pours water into the bȧson, it will
become visible to you even in the very situation
which before rendered it invisible. This is the
consequence of the rays of light being refracted,
which causes the image of the object to appear
higher in the bason.
I think it proper to acquaint you with the na-
ture and limitations of the laws of refraction and
reflection, although it is not necessary to these
Lectures to go into a close investigation of those
laws.
Sir Isaac Newton's Theory, as I comprehend it,
supposes all bodies to be filled with a subtile fluid,
and that its action extends all over, and to some
distance from, their surfaces; and that it is the
action of this fluid which causeth refraction, and
the re-action of it, when it receives a given in-
pulse,
LECTURE I.
13
pulse, that causeth reflection. Thus the same
fluid, by its different mode of action, is supposed
to transmit and reflect light, and the latter appa-
rently from the substances themselves.
This subtile fluid that great man conceives also
to be the cause of gravity or attraction, and that it
exists in all space; that this medium is condensed
in our atmosphere, and still more so in the sub-
stances on our earth; and that its density is in pro-
portion to the number of particles in the substances
it penetrates. That, if we admit such a fluid to
be diffused through imaginary space, it must be,
in its natural state, more rare than we can con-
ceive; otherwise it would resist the motions of the
planets very considerably; whereas, the contrary
being the case, as is evident by the regularity of
their motions, we may be certain that this fluid
must be very rare; so rare, indeed, that it freely
penetrates the pores of glass and the densest bo-
dies.
Refraction and reflection are distinct properties;
yet are they analogous, as being the operations of
the same agent, this subtile medium.
The general laws of refraction are, that a ray of
light, in passing out of a rarer into a denser me-
dium, is refracted towards the perpendicular, that
is, towards the axis of refraction, and hence the
angle of refraction is less than the angle of inci-
dence; whereas those two angles would have been
equal had the ray not been refracted. The physi-
cal cause of this may be, that the attraction of the
denser
14
LECTURES ON ASTRONOMY.
denser medium, acting perpendicularly to the ob-
lique direction of the incident ray, diverts the ray
out of its course, in proportion to the superior
force it excrts. But, when a perpendicular ray
falls upon a denser medium, in that case it suffers
no refraction, because (we may still suppose) the
attracting power, acting in the same direction with
the ray, cannot cause it to deviate from its straight
course.
On the other hand, when a ray of light passes
obliquely from a denser to a rarer medium, it is
refracted from the perpendicular; so that the an-
gle of incidence is less than the angle of refrac-
tion.
I shall endeavour to explain the laws of refrac-
tion, upon Sir Isaac Newton's principles of attrac-
tion, referring to Dia. fig. 1, plate 1.— Suppose
the line HI to be the boundary of two mediums,
air and water, N and O; the upper one, N, the
rarer, as the air; the lower one, O, the denser,
as water; which latter is included between the
lines RT, KL. The attractions of the mediums
will be in proportion to their densities; that is, the
compacter or heavier medium possesses a greater
quantity of attracting particles, or, rather, suffers
a greater accumulation on its surface, of that sub-
tile medium which causes gravity or attraction.
Suppose PS to be the distance to which the at-
tracting force of the denser medium extends itself
within the rarer. Suppose the line from A to re-
present a ray of light falling obliquely on the boun-
dary
Plate I.
Fig. 1.
IM
S
N
P
H
R
B
N
S
I
T
nt
M
K
D
Fig. 3.
E
Zenith
F
North Pole
Zenith
Northern
Hanisphere
D
Equator
B
IG
Southern
Hemisphere
South Pole
H
Nadir
M.Bryan delin?
Nadir
E
K
D
Fig. 2.
F
E
A
B
Fig. 4.
I
Fig. 5.
F
m
G
K
F
T Conder sculp
LECTURE 1.
15
dary of the mediums, which is represented by the
line HI, or rather upon the line PS, as it is there
that the denser medium begins to act. As all at-
tractions are performed in lines perpendicular to
the attracting body, when the ray arrives at A, it
will begin to be turned out of its straight course by
the superior force by which it is attracted by the
medium O, more than by the medium N, which
force draws it towards the perpendicular of the
surface O. The ray is bent from its straight course
continually all the way in every point of its passage
between PS and RT, within which distance the
attraction acts. Between these lines it describes
an arch; but, beyond RT, being out of the
sphere of the attraction of the medium N, it pro-
ceeds, uniformly, in a right line from the point W
to C.
Now let us reverse the experiment, by supposing
N the denser and more attracting medium, and O
the rarer; also HI the boundary of those two me-
diums, as before, and RT the distance to which
the upper, and now the denser, medium exerts
its attraction within the rarer; even when the ray
has passed the point B, it will be within the sphere
of the superior attraction of the upper and denser
medium. Now, as the attraction acts in lines per-
pendicular to the surface of the upper medium,
the ray will be continually drawn upwards, toward
the denser medium, and from the perpendicular of
the lower or rarer medium; that is, from its straight
course BK, towards III, in the direction BV.
The
16
LECTURES ON ASTRONOMY.
The two forces, acting upon it, cause it to have a
compound motion, whereby it describes a curve
from B to V. When it has arrived at V, being
out of the influence of the medium N, it will
again go on, in a right line, from the end of the
curve to M.
The attraction of the medium N diminishes con-
tinually, as the ray proceeds from B towards the li-
mit of superior attraction RT, because fewer and
fewer parts continue to act with superiority. In
this diagram, when the ray of light is supposed to
fall out of a rarer on a denser medium, being re-
fracted towards the perpendicular of the denser
medium, the angle of refraction CBE is less than
the angle of incidence ABD. When we suppose
N to be the denser medium, and O the rarer, and
the ray to be passing out of the denser medium N
into the rarer medium O, the refraction being still
towards the denser medium, the ray is turned from
the perpendicular of the rarer medium, and there-
fore the angle of refraction EBM is greater than
the angle of incidence A BD, as may be seen by
transferring the angles to the correspondent letters
on the circle.
All the rays of light which proceed from a large
body at a very great distance may be considered as
parallel rays, as, the greater the distance, the near-
er they approach to a parallel direction.
As a luminous body may be seen from all points.
to which a straight line can be drawn, a luminous
object must, by some unknown power, return
rays
LECTURE I.
17
rays in all directions: the effect of this power is
called reflection.
The reflexibility of light, or the manner in
which it is thrown back into the same medium
through which it is transmitted, is subject to the
same mechanical law as regulates the reflections of
all bodies, the angle of reflection being always
equal to the angle of incidence. This is easily
, seen by letting a ray of light fall upon a mir-
ror; when we shall perceive, that the inclination
of the reflected beam will be exactly equal to that
of the incident one; and, consequently, the angles
made by each will be the same.
Suppose AB, fig. 2, plate 1, to be a mirror,
which receives a ray of light DC; this being the
incident ray, and CE the reflected one. By com-
paring the degrees cut on the semicircle by the
two rays, you will perceive them to be the same;
and, therefore, the angle which the reflected ray
makes with the perpendicular CF is equal to the
angle made with CF by the incident ray; that is,
the angle DCF equal to the angle ECF.
Having informed you of the general laws of re-
flection and refraction, and explained, as well as I
am able, the cause of those effects we perceive of
them, I shall next proceed to inform you of the
degrees of the power of light, under different cir-
cumstances and modifications.
Light, radiating from a centre, diminishes as it
diverges; because, there are fewer particles in a
given space. Thus it is easy to calculate the inten-
C
sity
18
LECTURES ON ASTRONOMY.
sity of heat or light from a centre, if we know
what the degree of heat or light is at that central
spot, or comparatively to judge of its diminution
according to its distance from the centre; light
and heat diminishing as the squares of the dis-
tances increase. Thus, at two rods distance, the
heat or light is four times less intense than at one
rod.
The particles of light are not all of the same
size, and, therefore, are not all refracted in the
same degree by the same power applied; the
largest particles, by the momentum of their mo-
tion, being the least liable to be turned from their
straight course, and the smallest the most easily ;
as all bodies require to be acted upon by forces
proportioned to their magnitude, in order to give
them a determined direction. The different sizes
of the particles of light occasion, by their impres-
sions, those diversities of tints exhibited by the
prism. This instrument, by its peculiar construc-
tion, is calculated to divide or separate the rays
light from each other, according to their grada-
tions of colour and size: the smallest, or most re-
fracted, rays exhibit violet colour; the next in size,
being less refrangible, exhibit indigo; the next,
blue; the next, green; the nexi, yellow; the next,
orange; and the next, red; which last consists of
the largest particles of light, and, of course, the
least refrangible.
of
If, in the rays of light separated by the prism,
we place a double convex lens, they reunite at its
focus,
LECTURE 1.
19
focus, forming a spot of perfectly white light. If
we stop one of the separated rays, and prevent its
uniting with the others, the spot at the focus of the
lens will not be quite white, but made up of a
mixture of all the other colouring particles, exhi-
biting that hue which such a combination is known
to produce. Thus clear and casy are all the ex-
periments of Sir Isaac Newton. Could any means
have been contrived to convince us more fully of
the white appearance of light being the effect of a
due mixture of all these colouring particles?
In order to your understanding the effects of the
glasses, which are used for the purpose of astrono-
mical observation, I shall explain all that is neces-
sary for that purpose concerning the nature and
properties of lenses.
A lens is a transparent substance of a different
density from the surrounding medium, and termi-
nates in two surfaces, either both spherical, or one
spherical and the other plain, or both plain. A
plain glass will refract the rays of light that fall
obliquely on it, but will not collect them into a
point.
A plano-convex is flat on one side and a por-
tion of a sphere on the other, like AB, fig. 3,
plate 1. When parallel rays fall perpendicularly
upon it, they pass through and are refracted, so as
to meet in a point on the other side of the lens,
called its focus; which spot is as far behind the
lens as is equal to the diameter of the sphere of
which the convexity of the lens is an arc; as at C,
which
C 2
20
LECTURES ON ASTRONOMY.
which is at the extremity of the diameter of the
sphere ABCDE. Convex lenses are called burn-
ing-glasses; because, the intensity of the matter
of light from the sun, collected at the focus of a
large convex lens, will burn or consume almost
any substance subjected to its influence.
If the rays of light are not stopped at the focus
of a convex lens, as at C, but are suffered to pro-
ceed, they will, after crossing each other at the
focus, diverge as from C to F and G, all but the
middle ray HI, which, falling perpendicularly on
the axis of the lens, will not deviate; and their
divergence will be exactly equal to the conver-
gence towards the focus. But if, when they have
diverged to the same distance from the focus (as
at KL) as they converged to it, they are not
stopped, they will go on diverging continually, as
from L to G, and from K to F.
If an object, as the Sun, be at an infinite dis-
tance, and its light pass through a convex lens, all
the rays proceeding from it may be considered as
parallel rays; and, all these rays meeting in a
point, called its focus, the object will be transferred
to that spot; so that, by this property of convex
lenses, objects the most remote are brought, as it
were, close to our eye.
Suppose S, between M and N, to be the Sun
at an immense distance, his rays will then appear
parallel at the lens AB, as represented by the lines
between MN and AB. After the rays have passed
through the lens, they will meet at the focus C.
If
LECTURE I.
21
If this lens be placed in an instrument properly
constructed, the image of the sun will be trans-
ferred to the spot C, in its diminished state, and
will then be brought near to the eye of a specta-
tor, notwithstanding its great distance from our
Earth: then, by the aid of other glasses, called
eye-glasses, from their assisting the eye to view
the object as near to it as possible, the angle un-
der which the object is seen may be larger than
the angle the object itself would subtend in the
same situation; as objects appear larger in propor-
tion to the angles under which they are seen.
There are two kinds of telescopes; the refract-
ing and reflecting: the former do very well for
terrestrial objects, but the latter are better adapted
to celestial observations,
A reflector is furnished with a speculum, from
which the image of the object is reflected to the
eye, after being brought to a focus by the mirror,
from which it passes to the eye by means of an
eye-glass, which refracts the pencils of rays, so
that they are brought to their several foci by the
humours of the eye; and, according to their
nearness to that organ, the greater does the object
appear. The end of the telescope, which is al-
ways turned towards the object to be viewed, con-
tains the object-glass, and the other end contains
the eye-glass. According to the different convex-
ities of these two glasses, the object is magnified;
that is, its image, as seen by the eye through these
glasses, is so much larger than the object itself ap-
C 3
pears
22
LECTURES ON ASTRONOMY.
pears to us without the aid of glasses. For a fuller
illustration of this subject, I shall refer the curious
to Dr. Hutton's Mathematical and Philosophical
Dictionary.
Having contemplated one great agent, another
offers itself to our consideration; not less impor-
tant, but of whose essential principles we know
still less than we do of Light. The effect of this
agent is called Gravity, of which I have already
mentioned some particulars, but shall now consider
its general characteristics.
How important is this general principle by
which the mighty fabric of the universe is ce-
mented together, and yet its various elementary
parts separated from each other! Thus at once
uniting and disjoining, its operations are carried
on dependently and independently of each o-
ther.
When we consider this power retaining the pla-
nets within their orbits, and making them observe
their proper distances from each other, and from
the Sun, and causing them to perform their regular
returns of periods, how do we admire the wise
adjustment of this complicated, yet simple, ma-
chinery, and bless that Power who formed and di-
rects this invisible agent, the influence of which,
were it one moment to cease or be diminished,
would produce universal chaos.
As the great Newton could not define the cause
of gravity, it is not likely that we shall be able
to
LECTURE I.
23
to discover what that penetrating genius could not
fathom: let us, then, be satisfied with the bene-
fits we derive from it, and with the knowledge he
has afforded us of its nature, without attempting
to penetrate its essence: 66 For, who can, by
searching, find out God."
The effects of gravity were never sufficiently
considered, till Newton, (to whom no effect in na-
ture was barren of instruction,) by comparing its
effects in substances on our Earth, extended his
speculations to every known part of the uni-
verse.
It is said that a very trifling circumstance first
led Newton to reflect on the effects of gravity, in
falling bodies in particular.—Sitting under a tree,
an apple fell upon his head: we may suppose that
the force with which it struck him roused his at-
tention, on account of the increase of pressure
perceived from so trifling a substance to what it
exerted when held in his hand.
The result of his meditations on this circum-
stance terminated in inferring, that the force,
which falling bodies exerted, was, in some mea-
sure, independent of the body, and external;
which principle being settled, he proceeded to
investigate the effects of gravity in the most distant
bodies in the universe; so that, by a very trifling
circumstance indeed, the greatest discoveries were
produced.
The ancients were not acquainted with the
universality of this property or force. They ima-
C 4
gined
24
LECTURES ON ASTRONOMY.
gined that there were some substances which,
by nature, were light, and therefore ascended;
which opinion is now entirely disproved; as, in
what is called an exhausted receiver, all substan-
ces fall towards the Earth, and with equal ve-
locity.
That gravity acts towards the centre of our
Earth, is well known, by observations taken of
the weight of bodies on different parts of the
Earth's surface. At all parts of it which are equi-
distant from its centre, their weight or force of
gravity is equal; but, as all places on the surface
of the Earth are not at an equal distance from its
centre, being more distant at the equatorial parts
than at the poles, bodies weigh heavier at the
poles than at the equator; and, at every interme-
diate part of the Earth's surface, the weight has
been found to be in proportion to its distance from
the Earth's centre. This has been ascertained, by
first observing the vibrations of pendulums of e-
qual lengths, at London and under the equator,
and then at different distances from both situa-
tions.
For the uses of the pendulum, we are chiefly
indebted to Galileo, who, observing the vibrations
of a lamp suspended from the roof of a house,
discovered that they were performed sensibly in
the same time, whether great or small; that their
extent continually diminished, till the motion en-
tirely ceased; and that the vibrations were slower
in proportion to the lamp's distance from the point
of
LECTURE I.
25
of suspension. This discovery delighted him ex-
ceedingly, as, by it, he perceived that he was fur-
nished with a true measure of time.
As all circumstances which serve to illustrate the
subject of motion are intimately connected with
the Science of Astronomy, we shall contemplate a
little the laws which govern the motions of pendu-
lums, and the forces they are subject to.
Pendulums of the same length vibrate in the
same time, whatever be the proportion of their
weights. If one pendulum be four times as long
as another, the shorter will vibrate in half the
time, performing two vibrations in the same time
that the longer performs one; so that it is the
length of pendulums that determines the time of
their oscillations.
A pendulum is a heavy body, suspended by an
inflexible line from a fulcrum or prop, and is
moveable round it; moving backwards and for-
wards to the same limits on cach side of it. There
is one point within every pendulum, into which, if
all the matter that composes the pendulum were
condensed, the time in which the vibrations were
performed would not be altered by such condensa-
tion this point is called the centre of oscillation.
The point round which the pendulum vibrates is
called its centre of motion.
Huygens was the first who demonstrated the
properties of pendulums. He asserted, that if the
point to which a pendulum is suspended were
perfectly fixed, and all manner of friction and re-
sistance
26
LECTURES ON ASTRONOMY.
sistance removed, then a pendulum, once set in
motion, would for ever continue to vibrate with-
out diminution. But as this is not the case in
practice, a pendulum, which has received a cer-
tain impulse, will, unless that impulse be conti-
nually renewed, (as in the swing wheel of a clock,)
describe less and less arcs every time, till its mo-
tion is totally lost.
The motion of a pendulum being accelerated by
gravity, like that of all falling bodies, proves, that in
those parts of our globe, where the same pendu-
lum moves slower than it does at other parts of it,
the force of gravity must be less in those parts;
and, as gravity always draws towards the centre of
our Earth, those parts must be farther from that
centre.
The time of each vibration of a pendulum is in
proportion to the square root of its length; that of
ten inches in length making its vibration in half the
time that one of forty inches makes its vibration in.
Thus, the shorter the pendulum, the swifter it moves,
according to the above ratio; for, as a pendulum
oscillates always the same arc of a circle, the
longer pendulum must be a longer time in de-
scribing the arc of its circle, because that circle is
larger. The time in which the same pendulum
performs its oscillations, depends upon its length,
as well as upon the force which impels or draws it
towards the Earth; if the force be diminished, its
motion will be retarded, and, when this is the case,
the pendulum-rod must be shortened, to supply the
diminution
LECTURE I.
27
diminution of force. By the application of the
principles of motion in this instrument was the
quantity of the increase of matter about the equa-
tor ascertained.
Sir Isaac Newton thus accounts for the increase
of matter at the equator.
The diurnal motion of
our Earth being performed round an imaginary
line which passes through it, the surface of our
Earth at the equator, or part in the midst between
the poles, must be farther from this centre of mo-
tion than any other circle parallel to it; and con-
sequently those parts must move with greater ve-
locity than any other, and have a greater tendency
to fly off from the centre. All bodies in motion
have a tendency to fly off from the centre round
which they move, which is evident by a very sim-
ple experiment: Take a tassel of thread, and
tie it to the end of a stick; then roll the stick
quickly round in your hands, and the threads
will endeavour to recede from the centre; and, the
quicker the motion, the greater will be the force
they exert to fly off from the centre. Thus it is
with the equatorial parts of our Earth, as the
Earth is continually turning round a line within it-
self, called its axis.
As gravity or attraction acts on all parts of our
Earth, and the centrifugal force is greatest at the
equator, it is evident that that additional force
must, in some degree, diminish the power of gra-
vity; therefore it is that bodies weigh less at the
equator, not being impelled with so much force,
on
28
LECTURES ON ASTRONOMY.
on account of the re-action of the centrifugal force.
Mathematicians have compared these two forces,
and have found the centripetal force to be about
290 times greater than the centrifugal, or that
which is caused by the motion of the Earth on its
axis; and that the Earth is of a figure resulting
from the difference of those two forces; which idea
has been confirmed by bodies weighing only 289
pounds at the equator, which weigh 290 near the
poles.
The scientific Newton instructed mankind in
those laws, by which these effects in nature are
now ascertained, although the great efficient cause
of them cannot be understood. His assertions
have been proved by subsequent inquiries, and
are established by experience, as will be seen
when we come to treat of the mensuration of the
Earth.
Thus much I thought it necessary to premise,
before entering upon the more immediate subjects
of Astronomy; as, without these leading principles
of this stupendous Science, separately and pre-
viously impressed on our minds, we might have
found the aggregate too mighty for us, including
too many ideas to be digested together, and im-
plying more than could well be comprehended by
young minds. Ah! what is there in Nature which
does not, with all our pains, with all our scrutiny,
contain much more than we can comprehend?
Nothing is perfectly revealed to us. What is light?
Who can investigate its essence, or determine its
essential
LECTURE 1.
29
essential properties? Yet much has been ascer-
tained of it by the incomparable Newton, whose
well-conducted experiments and conjectures, found-
ed on similar effects perceived of things we do
understand, are inferences not to be rejected, be-
ing the result of sound reasoning and steady appli-
cation. Such are all the truths advanced and hy-
potheses framed by this excellent, man! His re-
searches were not made in a detached or desultory
way; but each new subject referred to what went
before; and no wandering ideas had room to enter,
so closely was the firm texture of his philosophical
inquiries woven together.
Having advanced sufficiently on the subjects of
light and gravity for our present purpose, I shall
not extend them farther at this time, but beg leave
only to conclude them with reflections which the
sense I entertain of the weakness of human rea-
son, when employed to understand the energies of
the Divine Mind, aptly prompt me to make. Of
nothing can we speak with certainty; we cannot
account for all the operations of those senses which
we continually perceive the effects of, or compre-
hend in what manner they make us perceive the
effects of causes more remote. Who can say how
the organs of vision convey to our minds the idea
of visible objects? What is our mind, our under-
standing? Who can explain those things?
mortal can. Then why, when we acknowledge
ourselves so totally ignorant of our own nature,
why should we expect to understand the sublimer
No
energies
30
LECTURES ON ASTRONOMY.
energies of divine truths, or to comprehend the
nature of spiritual existences? or why withhold
our assent to evidences which, when we compare
them with the necessities of our nature, we find as
fitting to them as the organs of our bodies to their
functions.
END OF THE FIRST LECTURE.
[ 31 ]
LECTURE II.
TORS. CHALDEANS. EGYPTIANS.
ORIGIN OF ASTRONOMY.
ITS FIRST CULTIVA-
FIRST
ORI-
MEASURE OF TIMES AND SEASONS.
GIN AND SYMBOLICAL EXPLANATION OF THE
ZODIAC.
CONSTELLATIONS; THEIR USE
IN NAVIGATION.
OF THIS ART.
ORIGIN AND PROGRESS
HISTORY OF ASTRONOMY.
THE CALENDAR.
THE descendants of Noah, by their numerous
progeny, being obliged to extend themselves for
the purpose of supplying their families with ne-
cessary food, formed a numerous nation in the
wilderness of Shinar; where, the cultivation of the
land becoming their principal object, it was natural
for them to endeavour to ascertain the return of
particular seasons, in order to provide for the exi-
gencies of each.
The human mind has always been found capable
of providing for the emergencies of our present
state, when called into action; although, by the
feeble efforts observable in some minds, one would
be led to consider it as a poor resource: however,
this imbecility must not be accounted the natural,
but rather the infirm and accidental, state of the
mind, produced by inactivity.
No
32
LECTURES ON ASTRONOMY.
•
No doubt, when the importance of the observa-
tion first caused the Chaldeans to reflect on the
motions of the heavenly bodies, they were sur-
prised that curiosity had not previously led them to
observe what necessity then compelled them to in-
vestigate.
The Chaldeans saw, that, at some periods, the
Sun afforded them more of his influence than at
others; and perceived, that, according to these
circumstances, their corn in ripening was either be-
nefited or otherwise, so as to produce full ears or
scanty and imperfect grain. But how were they
to enjoy the benefit of the former effect, or to
avoid the disadvantage of the latter, unless they
could foresee the returns of these periods? To
obtain the desirable purpose of knowing when
particular seasons would return, the Chaldeans
found the courses of the Moon particularly well
calculated: perceiving her to rise and set to their
horizon, to change her places of rising and setting
each time, and to vary her form, they took notice
of the time in which she performed all her changes;
and they observed, that, after one course was ac-
complished, all the same circumstances were re-
newed and repeated as before. By remarking how
often the Moon performed her changes from one
state of the Sun, in respect to that part of the
globe, to another, they furnished themselves with
regular periods, and were thus enabled to avail
themselves of the advantages offered them by each
season.
Deriving
LECTURE II.
33
Deriving such great advantages from the Moon,
it would not have been surprising if they had paid
that adoration to her which is ascribed to them by
some historians, although apparently without just
grounds for such an assertion. Why should their
festivals, at the time of the new Moon, be ad-
dressed to her as their object of adoration? It is
more rational to suppose it as the period fixed upon
to offer their public thanks to the Deity for so great
a gift; and the new Moons, which renewed the
seasons, being kept the most solemn of all, serves
to strengthen this latter opinion, as it proves that
the benefit derived from the Moon, by the infor-
mation it conveyed, was what excited their praise
and thankfulness.
As they had not at this period classed the stars in
constellations, they could not note the progress of
the Moon by their aid, but only by her different
appearances and situation in respect to the horizon,
to observe which they assembled on high places or
in deserts.
Their periodical sacrifices always ended in a re-
past, at which, what had been sacrificed was eaten
with gratitude by the whole company. These de-
votional and convivial meetings tended, no doubt,
to harmonize their minds and conciliate their mu-
tual good-will.
The festival of the new Moon continued for a
considerable time, and was observed in many na-
tions; we read of its being a custom among the
Hebrews, the Egyptians, the Persians, the Turks,
D
the
34
LECTURES ON ASTRONOMY.
the Greeks, and the Romans, down to the time of
the Gauls.
After the restitution of the observation of times
and seasons by the Moon, the next thing which
appears to have excited the attention of astrono-
mers was the dividing time into years; for which
purpose they began to group the stars, that they
observed the Sun to pass by in his apparent revolu-
tion, into constellations, under some familiar figure
emblematical of the respective seasons in which
the Sun was in those signs.
This improvement is ascribed by some authors to
the Egyptians, by others to the Chaldeans, which
latter I have ventured to adopt, as the arguments
in favour of that decision I think incontrovertible;
which are, that, admitting the character ascribed
to each constellation in the Zodiac to be symboli-
cal of the seasons, as no doubt they were, they
having no other types of their ideas but what were
expressed in this hieroglyphical manner, the ap-
plication of them to the seasons in which the Sun
passed through those signs answered exactly to
their Shinar, but by no means to Egypt, which, at
the season represented by Virgo, or the Gleaner, is
inundated by the overflowing of the Nile. The
waters not withdrawing till the latter end of Octo-
ber, the time of harvest in Egypt is not till March
and April, as the grain cannot be sown till Novem-
ber.
This circumstance, doubtless, entirely invalidates
the idea of the Egyptians being the dividers of
the
LECTURE II.
35
the Zodiac; and to suppose that names were given
to those constellations, and that they should include
such a certain portion of that circle in the heavens
without its being previously divided, is an incon-
gruous idea, and not to be admitted; therefore we
may allow, with many others, the division of the
Zodiac to be more ancient than the Egyptian co-
lony. Have we not good reason, then, to ascribe it
to the Chaldeans? They being the first people af-
ter the flood, and being compelled to investigate
some of the celestial phenomena, it is most pro-
bable, that, after they had advanced so far as to
calculate the periods of the Moon, they did not
stop there; but that, finding the advantages re-
sulting from the consideration of one of the hea-
venly bodies, they prosecuted their researches, in or-
der to ascertain that period in which all the circum-
stances of the seasons had been passed through.
And how could they effect this but by distinguish-
ing the situation. of the Sun in respect of the hori-
zon and particular stars?
Another argument in favour of the Chaldeans
being the dividers of the Zodiac offers itself. They
never could have ascertained the returns of the
seasons by the observation of the Moon alone; as,
although, in twelve revolutions of that body, the
Sun would have nearly performed his apparent re-
volution, yet not entirely so; therefore, if they
had been guided by observation of the Moon's
riod alone, compared with the annual period of
the Sun, they would have made great mistakes,
D 2
pe-
and
36
LECTURES ON ASTRONOMY.
and could never have calculated the returns of the
seasons with accuracy.
The method said to have been pursued by these
astronomers, in the infancy of science, in order to
ascertain the important epocha in which all the
circumstances of the seasons had been passed
through, and afterwards of dividing the Zodiac
into twelve parts, was as follows: They prepared
a couple of vessels; piercing a hole in the bottom
of one of them, they placed it over the other ves-
sel; after putting a plug into the orifice, they filled
the upper vessel with water, and left them in that
situation. Observing the time a particular star, in
that circle of stars which the Sun appeared to pass
through, transited the horizon, they instantly with-
drew the plug, and suffered the water to run into
the lower vessel, which it did gradually and almost
regularly; letting the operation continue till the
same star again passed the horizon the next eve-
ning, when withdrawing the under vessel, they
provided themselves with the measure of time of
one entire revolution of the heavens.
The way this ingenious people prosecuted their
researches on this subject was, by procuring two
vessels, each of which would contain one-twelfth
part of the whole quantity of water employed in
the foregoing operation. Placing one of these ves-
sels under the large one with the hole in it, they
poured the whole quantity of water before em-
ployed into that vessel, and waited for the appear-
ance of that remarkable star at the horizon which
they
LECTURE II.
37
they had before started from;
when they with-
drew the plug, and let the water run into the small
vessel; which, when full, they removed, and
placed the other of the same size in its place, let-
ting it be filled in the same way; and thus al-
ternately they filled the vessels three times each,
observing, at the beginning and end of each o-
peration, what particular star was at the horizon.
Thus did they perform six divisions of the Zo-
diac ;
for the other six, they were obliged to
wait till a proper season for the observation of
fered.
Those acquainted with the science of Hydrosta-
tics and Hydraulics, or to whom I have had the
pleasure of delivering my lectures on those sub-
jects, know, that the velocity with which water
flows from a given aperture is in a certain propor-
tion to the height of the fluid. Whether the Chal-
deans were acquainted with this circumstance I
know not. To the first part of the knowledge to
be derived from the operation alluded to, it cer-
tainly was not essential, but to the subsequent
part, in the way they performed it, it undoubtedly
was; from which we may infer, even supposing
them to have been unacquainted with the law be-
fore-mentioned, they must have observed the diffe-
rent velocity with which the water flowed, and,
consequently, that they made some allowance for
it; otherwise, their divisions and subdivisions could
not have been so exact: and, admitting the ne-
cessity of this observation, it is most probable that
D 3
their
38
LECTURES ON ASTRONOMY.
their manner of conducting this experiment, al-
though, in some respects, properly described, may
not be so in every part of it.
I imagine that the notion of the Ægyptians being
the dividers of the Zodiac might originate in the
symbolical writing continuing, and being much
extended, in their time, as they certainly added
other figures, adapted to the circumstances of their
peculiar situation.
The overflowing of the Nile being to them an
epoch of great importance, they were led to make
observations on those stars, which, when in a cer-
tain situation in respect to their horizon, foretold
the approach of that inundation. The star which
by its magnitude presented itself most particularly
was that which they afterwards called the Dog-
star, from the affinity the service it rendered them
had to that which the house-dog affords his master,
by warning him of approaching danger; - this
star always appearing in the morning, before dawn,
immediately preceding the overflowing of the Nile;
- on discovering which, when in a certain situa
tion, they retired to the higher lands, first provi-
ding themselves with every thing necessary for their
temporary retreat.
They included that remarkable star under the
figure of a dog's head, to which they affixed a hu-
man body, with a kettle on its arm, and wings on
its feet, thus describing the circumstances of
their temporary retreat; which continued whilst
the Sun was in the signs Leo and Virgo; to ex-
press
LECTURE II.
39
press which, they placed, on the edges of terraces,
the figure of a sphinx, made up of a female face
and the body of a lion couching.
Having spoken of the overflowing of the Nile, it
may not be unpleasing, to those who are not ac-
quainted with the cause of that inundation, to in-
form them to what it is ascribed.
The Nile flows through the middle of Ægypt,
and falls into the Mediterranean-Sea by seven out-
lets. The overflowing of its banks is owing to the
heavy rains which regularly fall in Ethiopia (which
is situated south of Ægypt) in the months of April
and May; the waters of which, rushing down
upon the low country of Ægypt, lay great part of
it under water; which, although it occasions some
inconvenience to the inhabitants, yet repays them
by the fertility it produces. And thus may we per-
ceive, in all the dispensations of Providence, tem-
porary evils more than alleviated by permanent good.
In referring to that part of the symbolical writing
of the ancients, which is connected with the sci-
ence of Astronomy, we may first examine the infe-
rences deducible from the figures of the Zodiac, in
respect to the seasons, as handed down to us by
historians,
The Spring is distinguished by Aries, or the
Ram; Taurus, or the Bull; and Gemini, or the
Twins; which latter were formerly represented by
Kids; and, as these animals are produced at this
season, it is supposed that circumstance is meant
to be thus expressed.
D 4
The
40
LECTURES ON ASTRONOMY.
The first month of the next quarter, being re-
presented by the Crab, admits but of one solu-
tion:
their having perceived that, after the Sun
had arrived at a certain height above the horizon,
he returned back again declining from that height,
they meant to express this retrogression of that
luminary by an animal which walks backwards.
When the Sun was passing under the next con-
stellation, they felt extreme heat, and therefore
they introduced the figure of a Lion, denoting the
raging sensations at that time.
The character given to the next constellation
seems equally appropriate, denoting that season in
which the gleaner gathers the refuse of the harvest-
fields.
The equality of the days and nights, when the
Sun enters Libra, is naturally represented by the
Balance; as are also diseases, which follow the
great heat, by the Scorpion.
The next constellation is symbolical of the sport-
ing season. The next is characterized by a Goat;
that animal, climbing rocks, being supposed em-
blematical of the Sun again ascending towards its
highest situation.
The circumstances of the rainy season are ex-
pressed in the figures of Aquarius and Pisces.
The circle which includes these figures is called
the Zodiac, because it is a circle of animals.
Thus did men, by a little use of their reason,
fix a standard for regulating all the affairs of life.
How rich a gift is reason, and how all-sufficient
for
LECTURE II.
41
for our necessities, when properly exercised! but
how base, as well as inconvenient, is the abuse
of it!
Symbolical writing was most probably produced
by Astronomy, and was, no doubt, found greatly
useful in acquainting people with events that would
happen at certain seasons. Yet the multiplicity of
figures necessary to express all ideas by this mode
must have rendered it very irksome; which caused
man's invention to construct other characters,
which, by their different combinations, might
serve to express all the different emotions of the
mind, and record all circumstances; and, when
this great object was accomplished, it became the
popular mode, and symbols were totally laid a-
side.
Symbolical writing was productive of one great
evil to after-ages: being misconceived, it pro-
duced that hydra-mischief called idolatry. These
symbols remaining in places of public worship,
where they had been placed in reference to those
seasons when festivals were held, their significa-
tion not being known, false ideas were annexed to
them, by which the people became gross idola-
tors.
It is recorded that the Ægyptians, having placed
a symbolical representation of the Sun, under the
figure of a man with a sceptre in one hand and a
whip in the other, denoting his rule over the day,
and his regulating the course of nature, succeed-
ing ages supposed that this figure represented the
man
42
LECTURES ON ASTRONOMY.
man who ruled the heavens; that he lived in the
Sun, having been translated from earth to heaven;
that he watched over Egypt, and had a particular
affection for it. They called this supposititious de-
ity God, Jove, Ammon.
Thus, not being able to comprehend the proper
attributes of these figures, they invented circum-
stances to account for the attributes themselves;
and this, we may naturally suppose, was the origin
of idolatry.
The feasts of the Chaldeans and Egyptians,
thus perverted, were communicated to the neigh-
bouring nations, and proved the origin of fables,
metaphors, and a variety of deities, which pro-
duced that mixture of truth and falsehood found in
the fabulous history of those times.
It is also imagined that the figures of the Zodiac
gave rise to the worship of animals, and to the doc-
trine of transmigration.
Omens were also much used in those times, such
as the flight of birds; which ridiculous custom origi-
nated in those figures which were intended to re-
present the winds. In short, the figures of men
and animals, contrary to their original signification,
were converted into celestial and infernal powers,
and the whole world was filled with superstition
and idolatry.
But let us now leave this barren retrospect, and
return to the progress of astronomical knowledge,
and to the uses to which it was applied in ancient
times.
As
LECTURE II.
43
As the people became divided into different na-
tions, the exigencies of trade and navigation led
them to consider the stars more attentively; and
they observed some stars which never set below the
horizon, and which were seen constantly very
nearly in the same place. These served them,
though not accurately, as a guide to steer their
course by.
The group of stars thus distinguishable by their
brilliancy and peculiar situation was that we now
call the Great Bear, but which the Phoenician pi-
lots called Parrasis, which signified the Rule, the
Guide, and sometimes Doube, signifying that
which gives advice, and also, in the Phoenician
language, the Bear. In this latter sense it was not
intended to be understood; yet, being received
according to that idea by the Greeks, they repre-
sented it under the figure of a bear, which was
quite foreign to the meaning, though it remains the
same to this day.
The Phoenician navigators finding that this con-
stellation, now called Ursa Major, or the Great
Bear, occupied a large space, and that it made a
very extensive revolution, which subjected them to
considerable deviations from the true course, they
sought for some constellation less variable in the
situation of its parts; when they discovered one of
the same form, but of less dimensions, and nearer
to the pole, and, of course, less liable to change
of situation. This was the constellation we now
call Ursa Minor, or the Little Bear.
One
44
LECTURES ON ASTRONOMY.
One star, in this constellation, by its situation,
which is very near the axis of the apparent motion
of the heavens, served them for an accurate guide,
when it was not obscured by clouds: by this dis-
covery, navigation was much benefited and ex-
tended.
The observation of the polar star afforded the
Phoenicians the opportunity of becoming a wealthy
and respectable people. Their territory, although
but a border of Syria, became opulent, in conse-
quence of their extensive commerce to all the
coasts of the Mediterranean: they possessed them-
selves of very useful ports in Spain, especially the
modern Andalusia, which at that time went by
the name of Tarsis: the fruitfulness of the vines,
the vast quantity of timber, corn, and cattle, and
the mines of gold, silver, and tin, made this coun-
try the principal object of their attention.
On account of the extent of this voyage, they
were obliged to build large ships; from which
circumstance, all ships of large dimensions were
called ships of Tarsish. Possessing an enterprizing
disposition, they were not content with this boun-
dary, but after a time they ventured to pass the
Streights; which undertaking, we are informed,
proved very advantageous to them, as by that
means they procured a safe asylum for all the riches
they brought from other countries, in the island of
Cadiz, which was then called Gadir; other na-
tions not being sufficiently skilled in the art of na-
vigation, to approach them in that harbour,
The
LECTURE II.
45
The success of this enterprize made them bold
in forming new ones, which they prosecuted with
the same ardour and with the like success; so that
finally they insured to themselves an advantageous
commerce, not only to all the coasts of the Me-
diterranean, but also to Asia and Africa, through
the gulph of the Red Sea. Thus, by the obser-
vation of only one star, the Phoenicians became
the richest people in the world; and they appear
to have been the first who extended navigation to
any considerable length.
This science was communicated to the Hebrews
by the pilots of Hiram, king of Tyre, about 1000
years before Christ, which was before the time
that the Greeks had any knowledge of it.
History acquaints us, that the cause of the pros-
perous and happy state of the Tyrians did not es-
cape the attention of the wise prince Solomon,
who, perceiving that navigation was the parent of
opulence, and an extensive marine establishment
the dispeller of idleness, obtained the service of
the pilots of King Hiram to conduct his fleets,
which he had established in Elah and Ezien-Geber:
That the Tyrians and Hebrews went together to
Ophir, and brought from thence immense quanti-
ties of gold, jewels, valuable woods, and ivory;
and that they were three years in performing this
voyage.
A considerable trade is at this day carried on
with Africa, where this Ophir was, for gold-dust,
which the torrents of rain scatter on the coasts,
after
46
LECTURES ON ASTRONOMY.
after having washed it from the mines, which are
very numerous in that country, especially in the
mountains of Manica, from whence descends the
river Saphara.
These voyages were discontinued about two
thousand years, after which the Portuguese re-
newed them, about three centuries ago; and it is
said, that they ascribed to themselves the first at-
tempt at this navigation.
The commerce which was carried on so long by
the Phoenicians and Hebrews was destroyed by the
kings of Babylon; yet, although their long voyages
to Cadiz were interrupted by the conquests of
these ambitious monarchs, they did not lose the
recollection of them.
Herodotus informs us, that Neaco, king of Æ-
gypt, who reigned 600 years before Christ, wishing
to restore the ancient splendor of that kingdom,
found he could not succeed without navigation, and
therefore appointed an extensive marine establish-
ment. Among other projects, it is said that he
attempted a junction of the Mediterranean-Sea
with the Indian-Ocean, but was obliged to aban-
don that project.
The Phoenicians, although not at that time in
the practice, yet were well informed in the theory,
of the navigation of the Red Sea, by the accounts
handed down to them from their ancestors; they
therefore readily undertook to conduct the fleets of
Neaco along the coasts of Africa, in their voyage
to the parts through the Red Sea.
It
LECTURE II.
47
It was Thales the Milesian, who about this
time (600 years before Christ) taught the Greeks
of Ionia the use of the pole-star. Travelling into
Ægypt, Crete, and Phonice, in search of know-
ledge, he became acquainted with the advantages
resulting from the observations of this star, and
communicated them to the Greeks of Ionia at his
return, from whence, in process of time, the
knowledge of the stars was conveyed to all parts
of Greece.
Before this communication of the use of the po-
lar star, the navigation of the Greeks was very
circumscribed, as may be inferred from the man-
ner in which the ancients celebrated the expedi-
tion of the Argonauts, which was made across the
Propontis, now the sea called Marmora, on ac-
count of the great distance they ventured from
shore, though it is only three hundred miles in cir-
cumference, lying between the Streights of the
Dardanelles and that of Constantinople.
To express their admiration of this bold enter-
prize, as it was thought to be at that period, they
made a constellation of the ship which had passed
from Colchis to the mouth of the Phase. Thus we
perceive the difficulty of navigation before the
siege of Troy.
Virgil has expressed the timidity of the ancient
navigators, by making his Grecian hero coast a-
long from place to place, agreeably to that pro-
priety which characterizes all his descriptions,
which in date and locality perfectly accord with
the
48
LECTURES ON ASTRONOMY.
the time and circumstance he relates, and, in this
instance, is the more remarkable, because in his
time navigation had been much improved, and
therefore it required the greater degree of judge-
ment to keep exactly to those circumstances which
preceded it.
Those who are not acquainted with the expedi-
tion of the Argonauts, previously referred to, will
find a full account of it in Lempriere's Bibliotheca
Classica, or Classical Dictionary; and a map of
the country I have been adverting to, with both
the ancient and modern names of places, &c. in
D'Anville's Atlas, or Body of ancient Geogra-
phy.
Thales was justly called one of the wise men of
Greece, as his extensive knowledge in geometry,
astronomy, and philosophy, testifies.
It was this great man who discovered the solsti-
ces and equinoxes, and divided the sphere into
five zones. He also divided the year into 365
days. He died at the age of 95, about 548 years
before Christ.
In Thales we have an example of the utility of
observation, judiciously taken, and how a mind,
prone to study, rises progressively from one truth
to another, and the extension the mental power is
capable of, which ought to excite in us the like
application in all we attempt to investigate.
I love to trace the gradual progressive elevation
of ideas, from their first dawn, in those minds that
have indicated such a sublimity of sentiment and
clearness
Я
LECTURE II.
49
clearness of intellect as are not common; I cannot
help participating in the satisfaction they must
have felt, who, by a due cultivation of their un-
derstanding, have rendered their fellow-creatures
such essential services; and I honour them from
my heart.
The manner in which the great philosopher
Thales determined those phenomena, the discovery
of which was ascribed to him, was by due obser-
vation of the stars under which the Sun passed in
its apparent revolution, and those passed by the
Moon. He perceived that they did not both pass
exactly under the same, but that the orbit of the
Moon cut that of the Sun in two points, deviating
a little from it on each side, and that it did not al-
ways cut the orbit of the Sun exactly in the same
place each month, but that these variations re-
turned nearly in the same order after a certain
number of revolutions of the Moon.
Whether this great man was sensible of the be-
nevolent design of our Creator in this arrangement
of the nodes of the Moon, is not said, but it
seems an impeachment of his judgement, deroga-
tory to his character, to suppose him ignorant of
the advantages accruing to all the inhabitants of
the Earth from this wise ordination of Providence,
who, but for it, would, once a fortnight, be de-
prived of necessary illumination.
As we are certain that he understood the con-
sequence of their being in a direct line, by his cal-
culating the time of the eclipses, it must have
E
been
30-
LECTURES ON ASTRONOMY.
been impossible for the utility arising from the de-
viations from a right line to have escaped his ob-
servation.
This discovery of the cause of eclipses relieved
the people from the dreadful apprehensions for-
merly attendant on those temporary deprivations of
the Sun's light, which they had supposed to be oc-
casioned by the wrath of God.
How ignorant the Medes and Lydians were of the
cause of these phenomena, is evident from the effect
a total eclipse of the Sun had on them in the time of
a battle, in the heat of which the Sun being sud-
denly obscured to the place at which they fought,
they desisted from all hostilities, and all animosity
subsiding on the evidence, as they thought, of di-
vine indignation, in which they were mutually in-
volved, as recorded by Herodotus.
Geography was also much benefited by this dis-
covery, particularly by the observation of lunar
eclipses, which served to give juster ideas of the
distances of countries.
Thus, suppose two spectators placed at different
parts of the globe, and each prepared to notice
the instant of the Moon's entering into the shadow
of our Earth; also the time of its total obscura-
tion, and of its emersion. Then, on comparing the
two times noted by each observer, they were en-
abled to judge of the comparative distances of the
places from each other, east and west, even sup-
posing them only acquainted with the apparent mo-
tion
LECTURE II.
51
tion of the heavens. Lunar eclipses also served
to ascertain the rotundity of the Earth.
Before this time, the Earth was often supposed
to be a flat surface surrounded with water; which
opinion was strengthened by the writings of the
poets, who always expressed the Sun's rising
above the ocean, and setting in it to cool him-
self.
This vulgar prejudice was shaken off by those
of the Ionian school, who, becoming acquainted
with the circumstances of the Moon shining by
borrowed light, perceived, by the form of the
Earth's shadow projected on it, that it must be
globular.
The Ionians seem to have been an ingenious and
sagacious people, and to have possessed great stea-
diness of character; probably the salubrity of the
climate might contribute to these advantages, as
we know that soundness of constitution is gene-
rally accompanied by strength of understanding
and perseverance in all the mind seeks after.
Thales was so happy as to find in his disciple
Anaximander the same disposition for knowledge,
and ardent spirit of inquiry, as he himself pos-
sessed; so that the congeniality of their tempers
made them firm friends and allies.
How great was the advantage of thus being
enabled to compare their ideas together! for,
however penetrating a genius individuals may pos-
sess, their advancement in knowledge will be
much retarded without the aid of another of simi-
E 2
lar
52
LECTURES ON ASTRONOMY.
lar talents; as it is by comparing their opinions,
that they can establish them with facility and as-
sert them with confidence. If the understanding
does not rise above mediocrity, I can assert from
experience the disadvantage of not having a se-
cond person to consult on its opinions; as I have
felt the impediment it has been to the prosecution
of my present study, by being obliged to digest
the opinions of all writers on the subjects of these
Lectures without any assisting friend to strengthen
or confute my ideas as they arose.
Although Astronomy was much advanced in the
time of Thales the Milesian, yet Geography must
have been very imperfect, as it was not till the
time of Newton and Huygens that the true figure
of the Earth was discovered.
Before their time, all the calculations of the
distances of places, &c. were made on the suppo-
sition that the Earth was a perfect sphere; but
these great men, by the known laws of gravitation,
discovered that the true figure of the Earth was
that of an oblate spheriod.
Notwithstanding the imperfection of Geography
in the time of Thales, it was sufficient to enable
the scientific Greeks to enlarge their territories,
and keep the command of the ocean, in spite of
the formidable fleets of Persia, whose empire they
at last destroyed; and, for this victory over a pow-
erful enemy, it is said they were indebted to their
extensive learning, not to their forces, which were
by no means equal to those of the Asiatic monarch.
After
LECTURE II.
53
After the death of Thales, Pythagoras taught
the Europeans that the Earth and Planets turned
round the Sun, which luminary was, in respect to
them, at rest in the centre of the system; and
therefore that the diurnal motion of the Sun and
Stars was not real, but occasioned by the motion
of our Earth on its axis in a contrary direction;
and this idea is ascribed wholly to him. He stu-
died Astronomy in Ægypt, where he went for that
purpose, and he remained there a considerable
time, consulting with the priests and Magi on all
the subjects of Astronomy. The instruction they
afforded him he communicated to the Grecians at
his return, together with his own improvements of
that science.
After Pythagoras, Astronomy was neglected for
about two hundred years; most of the celestial
observations brought from Babylon, we are in-
formed, were lost, few only being revived by the
Ptolemys, who renewed the study, and sought ea-
gerly after the works of the ancient astronomers,
thinking no knowledge comparable to that of the
system of the world; by which means Alexandria
became the school of that science.
The ideas they formed were totally different
from those of Pythagoras, for which their judge-
ment ought not to be impeached, as most proba-
bly they were not possessed of any vestiges of
that more natural system; because, after such a
lapse of time since the science has been cultivated,
E 3
many
54
LECTURES ON ASTRONOMY.
many remnants of it could not be expected, at
least of the speculative part.
Eratosthenes, keeper of the library of Alexan-
dria in the time of Ptolemy Evergetes, undertook
to calculate the number of stades* that might
make up the circumference of our Earth; and, as
he arrived somewhat near the truth, even in the
infancy of this science, it may not be thought im-
proper or intrusive, if I describe the method by
which he ascertained it: and I shall have pleasure
in acquainting you with the ingenuity of the mode,
as I always feel great delight in communicating
circumstances expressive of the sagacity of that
active principle, the human understanding.
Eratosthenes observed, that in the summer sol-
stice the Sun passed through the vertical point of
the city of Sienna, which was situated on the con-
fines of Ægypt and Ethiopia, under the tropic of
Cancer. In the situation to which the Sun would
be vertical on that day, he had a well dug, which
at twelve o'clock on the day of the summer sol-
stice would be wholly enlightened within side by
that luminary. At the distance of 150 stades
round this well, posts raised perpendicularly cast
no shadows. He had a concave hemisphere made,
which he placed in the city of Alexandria; raising
a post perpendicularly in the centre of it, the top
of this post or needle was exactly at the centre of
a sphere of which that was the radius. Remarking
* A stade contains 925 paces; a pace 5 feet.
on
1
LECTURE II.
55
on the appointed day, at the instant of noon, the
distance of the Sun from the vertical point, by the
shadow of this post, he found, at that time, on
that day at which the Sun was vertical to the city
of Sienna, it wanted one-fiftieth part of the whole
circle to be so at Alexandria. This he disco-
vered by the distance of the shadow of the top of
the post from the foot of the needle; from which
observation he naturally inferred, that the city of
Alexandria must be one-fiftieth part of the whole
circumference of the Earth distant from Sienna.
The distance between those two cities was ea-
sily measured; and, when ascertained, he multi-
plied it by 50, and thus discovered that the Earth
was 250,000 stades in circumference, the distance
between Sienna and Alexandria being 5000 stades.
Although this was not an accurate measurement,
yet it was as nearly so as could be made by those
unacquainted with the laws of gravity, or the more
elevated principles of the mathematics.
Hipparchus, who lived at this time, distin-
guished 1022 stars, by giving names to them, and
placing them in their true situations in respect to
latitude and longitude,
Succeeding astronomers have added considerably
to the catalogue; Dr. Halley, Mr. Flamsteed, and
others, having augmented the number to near 5000,
and ascertained their situations with the greatest
accuracy.
Although the stars have each a name, those
names are, for the most part, expressed only by
E 4
the
56
LECTURES ON ASTRONOMY.
the letters of the Greek alphabet; those, which
are the most conspicuous in each constellation, be-
ing marked with the first letter, a; the next with
ß, the second letter in that alphabet; and so on.
Yet there is one exception to this rule, which is,
that any stars which require particular notice, al-
though they are not the most conspicuous in the
constellations to which they belong, are distin-
guished by that character used to denote one of
the first class.
We are told that our ancestors, at least the
Druids, were not inattentive to the phenomena of
the heavens; but the Romans were by no means a
scientific people; military discipline and politics
seem to have engaged their whole attention, while
physics and astronomy were overlooked by them;
and that necessity, rather than inclination, (as we
may naturally suppose from the character of the
people,) rendered Cicero, Pompey, and Julius Cæ-
sar, favourers of this admirable science.
Always occupied in ambitious projects, which
could not be effected without the aid of navigation,
it became necessary to them to be acquainted with
times and seasons, places and distances. Julius
Cæsar, by his perpetual and far-extended con-
quests, became one of the most eminent geogra-
phers of his time; this he could not have been
without some attention to Astronomy; we there-
fore naturally conclude, that, notwithstanding his
active and enterprising spirit led him to martial
exploits, yet he sometimes relaxed himself in the
harmonizing
LECTURE II.
57
harmonizing and calm delights of astronomical ob-
servations; and that he did so is evident from his
manner of addressing one of the priests, on his
reformation of the Calendar, viz. "I expect that
Eudoxus will not, in future, be more famous for
the Ephemerides which he gave to Greece, on his
return from Ægypt, than I shall be by the order to
which I have reduced the course of the year."
Which prediction was verified.
I do not think that it could afford you either en-
tertainment or useful instruction were I to relate
all the different subdivisions of time, or variations
in the Calendar, since the course of the year was
established; I shall therefore only mention such
circumstances of it as may serve the purpose of
necessary information, and justify my assertions re-
specting it.
The month called July derives its name from
Julius Cæsar, he having rendered the mode of
computing the year more conformable to the ap-
parent annual course of the Sun; which caused
his name to be given to the most delightful month
in the year, in compliment to his abilities. Al-
though he reformed the Calendar very considerably
from what it was in the time of the Greeks, yet,
as his computation was made on the supposition
that the Sun performed his apparent annual revolu-
tion in exactly 365 days and 6 hours; which is
contrary to the fact, as it is performed in 365 days,
5 hours, 48 minutes, and 49 seconds; therefore,
according to his computation, the civil year must
have
58
LECTURES ON ASTRONOMY.
have exceeded the solar by 11 minutes 11 seconds,
which, in 130 years, amounted to one revolution
of the Earth on its axis; a space of time that al-
tered the times of the Sun's situation one whole.
day; which, in the course of 47,450 years, would
have entirely changed the seasons, from the time
they were first calculated for.
Notwithstanding this incorrectness in the Julian
Calendar it was adopted by all the states of Eu-
rope, being considered at that period a perfect com-
putation of time.
Julius Cæsar's reformation of the Calendar arose
from his having imagined that the Sun completed
his apparent revolution in 365 days 6 hours;
whereas, amongst the Greeks, it was computed
to be performed in 354 days, which must have
rendered their Calendar very imperfect and embar-
rassing.
In order to allow for the odd six hours in each
year, Julius Cæsar introduced an additional day
every fourth year, and omitted the six hours in the
three intervening years, making each of them to
consist of only 365 days. He made the first Ju-
lian year to consist of 444 days, which caused
great confusion: his motive for this was, to allow
for the 90 days which had been lost by the former
mode of computation. In order that the courses
of the Moon might agree with the seasons in his
Calendar, he divided some of the months into a
greater number of days than others.
The
LECTURE II.
59
The first who began to discover the imperfection
of the Julian Calendar were Bede, Sacro Bosco,
and Roger Bacon. Perceiving that the true equi-
nox preceded the civil, they set about rectifying
this error; and, having found the cause of it, they
calculated what must have been the difference from
the time that the vernal equinox was fixed by the
council of Nice, in the year 325, and they found
that it had differed, from that time to the year
1582, about ten days.
Although these great men discovered this error,
yet it was not reformed by them, this being ef
fected by Aloisius Luilius; as, in the very year
those had made the discovery, Pope Gregory XIII.
had the old Calendar abrogated and the new one
established, under the appellation of the Grego-
rian Account, or New Stile, which is the one now
in use in most parts of Europe.
The first step that was taken, to render the cir-
cumstances attending the Sun's apparent motion
conformable to calculation, was, lopping off those
ten days which had been gained, and which had
displaced the equinoxes, so as to bring them to
correspond nearly with the 21st of March and the
22d of September. A similar alteration in the
Calendar was made by the parliament of England
in the year 1752, when the difference had amount-
ed to eleven days, which eleven days were taken
from the month of September; and then, by call-
ing the 3d of September the 14th, they brought
the autumnal equinox to the proper place, which
it
60
LECTURES ON ASTRONOMY.
it was in at the time the council was held in
1752. In order to retain the equinoxes in their
proper situation, it was ordered that three days,
every 400 years, should be omitted, in the follow-
ing manner : the years 1800 and 1900, which
should have been leap-years, were to be computed
as common years, containing only 365 days each;
that the year 2000, and every fourth hundred year
after that, should be a leap-year, containing 366
days, the intermediate hundreds being only com-
mon years: and, by this judicious arrangement,
our reckoning will not vary a whole day from the
true time in less than eight or ten thousand years;
a difference so small, as not to be at all mate-
rial.
Our times and seasons now correspond with
those settled by the first Christian council, in the
time of Constantine the Great, when the festivals.
of the church were fixed by his order, in the year
of our Lord 325.
Having explained the Calendar sufficiently for
my purpose, those who wish for a farther elucida-
tion of the subject, or mathematical definition of
it, I beg leave to refer to that useful oracle, the
Mathematical and Philosophical Dictionary of Dr.
Charles Hutton.
The first seven letters of the alphabet (A, B,
C, D, E, F, G) are set to the days of every week,
and repeated over and over again from the begin-
ning to the end of the year, viz. A to the 1st day
of the year, B to the 2d, C to the 3d, and so on
till
LECTURE II.
61
till G on the 7th; then, over again, A to the 8th
day, B to the 9th, &c. So that the same letter
falls upon the same day of every week in the year;
and the letter which falls on the first Sunday, and
every other Sunday after, in the same year, is called
the Dominical or the Sunday letter for that year.
But as the 365 days of an ordinary year contain
one day over the exact 52 weeks, the Sunday-let-
ters will fall back one place every year; so that if
the Sunday-letter be G for some year, it will be F
the year after that, and E the second year after,
&c.
As the intercalary day introduced into the calen-
dar by Julius Cæsar, and which still continues in
use, being allowed for in February of the leap-
year, might otherwise have caused some confusion,
these first seven letters of the alphabet are used in
the following manner: the 28th and 29th of Fe-
bruary in the Bissextile have but one letter as-
signed them, so that the following Sunday goes
back a letter, and so on for the rest of the year.
As thus-
Suppose the Dominical letter in leap-year to be
C: then, after the 29th of February, the Sunday-
letter will be B; and, if in leap-year the 1st of Ja-
nuary be on a Friday, the first Sunday will be on
the 3d of January, therefore the Dominical letter
will be C; and the first Sunday, the year after,
falling on the 1st of January, the Sunday-letter
will be A. In a common year, all the Sundays in
it have the same letter; but, in leap-year, the ad-
ditional
62
LECTURES ON ASTRONOMY.
ditional day displaces the letters; therefore, if the
first day in a common year fall on a Sunday, the
next year it will happen on a Monday, and the
next on a Tuesday, and so on; and, to prevent all
the letters being displaced in a leap-year, the Sun-
day-letter alone is altered.
Having mentioned the circumstance which oc-
casioned one of the months to be named after Ju-
lius Cæsar; in justice to the abilities of Augustus,
I cannot refrain from mentioning the circumstance
which procured from him the like distinction,
which was, his having ascertained the several ele-
vations of the Sun above the horizon at different
times of the year.
This he effected by means of
the shadow of an obelisk 111 feet high, which he
caused to be erected in the Field of Mars for the
purpose of this observation.
Ptolemy's astronomy, though founded on an er-
roneous system, served to give the observers of that
age an idea of the apparent course of the heavenly
bodies, as also to foretel natural events, and to
bring geography to certain rules.
After the death of Ptolemy, speculative astrono-
my again began to decline, and at last was totally
laid aside.
Historians inform us, that, in the first ages of
Christianity, the most learned Christians were
wholly occupied in the important mission of in-
structing nations in the revealed religion, and in
repelling innovators; which, added to the frequent
changes of rulers, laws, and language, kept na-
tions
LECTURE II.
63
tions in a tumult unfavourable to science: that,
about the middle ages, the knowledge of our
globe, history, and eloquence, were neglected;
and that part alone of philosophy, which belonged
to logic and metaphysics, was in vogue: that, ne-
gligent of the graces of elocution, they became
rude in their manners and speech, and that their
arguments were calculated rather to disgust and
perplex than to convince. The latter of these as-
sertions we may easily conceive must have been
the consequence of the former, as, by experience,
we know, that to confute without politeness and
gentleness is not the way to make our tenets re-
spected or adopted.
It is said that these supercilious Arabian philo-
sophers were shunned by all the world, and were
considered as a public nuisance; as the doctrines
they taught tended not to the service of either God
or man, being subversive of all harmony and civi-
lization.
Philosophy thus transformed, and stripped of all
her fine embellishments, was rescued from total
degradation in 1214, by some very few learned
men, particularly by Roger Bacon, our countryman,
who, about that time, restored it to its native im-
portance, clothing it with all that could render it
lovely and respectable; so that it became an object
of public esteem and suffrage.
In this century the Emperor Frederic the Se-
cond caused Ptolemy's construction of the Universe
to be translated from the Arabian into Latin.
In
64
LECTURES ON ASTRONOMY.
In the year 1270, Alphonso, king of Castile,
employed several learned men in the business of
reforming Astronomy; and became himself an able
astronomer. Charles, surnamed the Wise, gave
great encouragement to this science. Copernicus,
in the 15th century, re-established the ancient Py-
thagorean system, which admitted that the Earth
might move round the Sun, by which the consti-
tution of the heavens was again brought to natural
and certain principles.
It was Gallileo who chiefly introduced teles-
copes into the use of Astronomy, in the year
1610, and by that means discovered the satel-
lites of Jupiter, the phases of Saturn, the moun-
tains of the Moon, the spots on the Sun, and the
revolution of the latter on his axis; discoveries
which opened a wide field of inquiry and specu-
lation.
The immortal Newton was the first who demon-
strated, from physical considerations, the laws that
regulate all the motions of the heavenly bodies, as
well as of our Earth; which set bounds to the pla-
nets' orbits, and determine their greatest excursions
from, and nearest approach to, the Sun, their
grand vivifying principle.
He taught the cause of that constant and regu-
lar proportion observed by both primary and secon-
dary planets, in their circulation round their cen-
tral bodies, and their distances compared with
their periods: he also introduced a new theory of
the
LECTURE II.
65
the Moon, which accurately answers to all her irre-
gularities, and accounts for them.
Doctor Halley favoured us with the Astronomy
of Comets, and, as I before mentioned, with a
Catalogue of the Stars, together with astronomical
tables.
Mr. Flamsteed, after observing the motions of
all the stars for upwards of forty years, gave some
curious information on that subject, with a large
catalogue of them.
Lastly, Dr. Herschel, whose opinion of the con-
struction of the universe I shall give in the course
of these Lectures, has very judiciously extended
this field of science, and has discovered another
planet belonging to our system. This gentleman's
application to the science, and the liberal manner
in which he has transmitted his observations, de-
serve great commendation.
I trust this short sketch of the origin and pro-
gress of Astronomy, and of the advantages it has
procured for us, has not been unpleasing or use-
less, as the human mind must always feel satisfac-
tion in tracing such things from their source to
their utmost range; and no doubt but the important
inferences, deducible from this epitome of ancient
knowledge, must tend to enlarge the minds of those
who have not been previously acquainted with these
circumstances.
To preclude criticism, I must beg the historian
to observe, that I did not think it necessary to my
plan to introduce any thing of those times in which
F
this
66
LECTURES ON ASTRONOMY.
this science was not cultivated or improved; as
to have related all the false systems that prevailed
at different times would have afforded but a morti-
fying retrospect, not tending to promote my grand
design, in recording the speculations and works of
past ages, which was, to excite in my dear pupils
a spirit of inquiry from the instances I produced of
the advantages resulting from investigation; which
rule of selection has occasioned that want of con-
nection necessary in writing the history of past
ages, but not, I presume, in relating the history of
the rise and advancement of astronomical know-
ledge, as it must necessarily have included matter
foreign to the subject of these Lectures.
END OF THE SECOND LECTURE.
[ 67 ]
LECTURE III.
INTRODUCTORY ADDRESS.
OF THE FIGURE
AND AFFECTIONS OF THE GLOBE WE INHA-
BIT, AND OF THE APPEARANCES OF THE
HEAVENS AND HEAVENLY BODIES IN CONSE-
QUENCE OF THE LATTER.
THE CELESTIAL
GLOBE AND ARMILLARY SPHERE EXPLAINED,
WITH THEIR USES IN REFERRING TO CELES-
TIAL AND TERRESTRIAL
ZONES.
CLIMATES.
PHENOMENA.
GEOGRAPHICAL DE-
FINITIONS, &c. THE CAUSES OF THE VI-
CISSITUDE OF SEASONS AND CLIMATES.
A PHYSICAL DEFINITION OF THE PRECES-
SION OF THE EQUINOXES; AND THE EF-
FECTS OF THE SUN'S RAYS FALLING
WITH
GREATER OR LESS OBLIQUITY ON OUR EARTH.
MORAL REFLECTIONS AND INFERENCES.
- O Spirit! that dost prefer
Before all temples th' upright heart and pure,
Instruct me; for, thou know'st! Thou, from the first,
Wast present; and, with mighty wings outspread,
(Dove-like,) sat'st brooding on the vast abyss,
And mad'st it pregnant! What in me is dark,
Illumine; what is low, raise and support;
That, to the height of this great argument,
F 2
I may
68
LECTURES ON ASTRONOMY.
I may assert Eternal Providence,
And justify the ways of God to man.
MILTON.
Do not your breasts glow with the ardour of
this divine poet, when you reflect on the wonders
which present themselves in heaven above and on
the earth beneath? They surely must.
That mind must be devoid of all sensibility that
can behold the resplendent glories of the heavens,
- feel the vivifying power of the Sun,
reflect
on the advantages derived from transmitted and
reflected light, examine into the diffusive excel-
lence of the work of creation, compare its ge-
neral connections, inferring from thence the con-
solatory conviction of an all-wise, all-powerful,
and all-merciful Creator, whose superintending
and preventing goodness is never ceasing, is never
diminished, and will endure for ever, without
the warmest emotions of joy, gratitude, love, and
admiration!
Cherish, my dear friends, this transport! It will
elevate your minds above those low pleasures of
sense, which debase human nature, and will ani-
mate you to an imitation of those graces and bene-
volent emanations, so conspicuous in the dispensa-
tions of Providence, which the contemplation of
such sublime and interesting subjects must natu-
rally tend to excite in your breasts.
Having, in the two foregoing Lectures, taken a
review of such parts of the Astronomy of past
times
LECTURE III.
69
times as was adapted to our purpose, I shall, in
the following ones, endeavour to inform you of the
principles of this noble science, and lead you on to
consider the phenomena which, in its present im-
proved state, it so clearly elucidates.
The part of the creation which claims our first
attention, being immediately connected with us, is
the globe we inhabit.
Our Earth is richly endowed with all things ne-
cessary to our temporal existence, both for the sup-
port of our animal nature, and also for the gratifi-
cation of those senses we are furnished with. By
its compound motion, we enjoy the grateful re-
turns of day and night for the purposes of labour
and rest, and the pleasing vicissitude of seasons.
The former motion is rotary, and is called the diur-
nal motion, being that of the Earth round its axis,
which is performed from west to east in twenty-
four hours, occasioning the apparent motion of the
Sun and the whole heavens, from east to west, in
that time.
By the motion of the Earth on its axis, or rather
on that imaginary line passing through the centre
of the Earth round which it revolves, all the celes-
tial bodies are alternately presented to our view,
and hid from it, being disposed, in respect to the
appearances of things to us, in a concave sphere
(though not actually so) which seems to encircle
our Earth.
The other motion of our Earth is progressive,
being performed round the Sun, and is called the
F 3
annual,
70
LECTURES ON ASTRONOMY.
annual, as the time it takes in performing its
entire revolution round that luminary is called a
year.
We have reason to suppose that our Sun, with
its planets, forms only one link of the great chain
of the universe, and that all those beautiful lumi-
naries, the fixed stars, are equal in size and glory
with our Sun, each serving to enlighten a system
of planets in the same manner that our Sun does
those of his system.
The distance of the fixed stars from our Earth
must be very great, as there is no visible alteration
in their positions, with respect to each other, when
viewed from different parts of the Earth's orbit,
that can be referred to their distance from us; so
that the diameter of the Earth's orbit, though e-
qual to 192 millions of miles, is but a point in
comparison of their distance from us.
What an enlarged idea does this convey to us of
the majesty of the great Creator!
Well might the enraptured poet exclaim,
When all thy wonders, O my God!
My rising soul surveys,
Transported with the view, I'm lost
In wonder, love, and praise.
ADDISON.
I have informed you, that the figure of our Earth
is globular, although not a perfect sphere; and
have accounted for its deviation from that form.
The Earth being nearly spherical, and being im-
pelled forwards, must move round a line within it-
self,
LECTURE III.
71
self, as we observe all bodies of that form to do,
when impelled forwards. The extremities of this
imaginary axis are called the poles of the Earth;
that pointing towards the part of the heavens, deno-
minated the north, is called the north pole, and that
directed towards the opposite point is called the
south pole.
The change observed in the appearance of the
visible starry hemisphere, I have before informed
you, led to the discovery of the star now called the
pole-star, from its being situated near the point an-
swering to one extremity of the axis of the diurnal
motion: this point is considered as stationary in re-
ferring to the diurnal motion of our Earth; and,
when we transfer it to the heavens, it is equally so,
on account of the immense distance of the polar
star from us.
The elevation of this star above the horizon
differs according to the latitude of the place it is
viewed from. The farther we travel north, the
higher will this star appear above the horizon; if
we proceed southerly, it will become less elevated,
till we shall at last lose sight of it, and another
star will present itself in the south, near the other
extremity of the axis of our Earth; but there is
no star so near the line of motion in the south
as in the north.
Although I am not fond of adverting to erro-
neous opinions, yet Ptolemy's system of the uni-
verse must not escape observation, as, in refuting
the errors of it, we establish the present known
F 4
system
72
LECTURES ON ASTRONOMY.
system of the world, and manifest the absurdity of
his.
The falsity of the Ptolemiac system will be best
understood, by comparing it with the known phe-
nomena of the heavens.
He supposed that our Earth was fixed in the
centre of the universe; and that the Sun, with the
other heavenly bodies, revolved round it once in
twenty-four hours from east to west; also that they
had different periodical times, which latter he
was obliged to admit, in order to account, as he
imagined, for their annual changes and various ap-
pearances.
This mistaken notion of things does not seem
extraordinary in one, who considered appearances
only, without mathematical aid; by which we
have been brought to form just ideas of things so
remote, and without which, united with the known
laws of gravity and attraction, we never could
have attained to such sublime truths, our senses
alone being very inadequate to judge of the real
motions of the heavenly bodies, or of our
Earth.
When a ship leaves the shore, if the sea be
calm, the passengers in the vessel do not perceive
its progressive motion, but the objects on land ap-
pear to them to move: thus, reasoning by analogy,
we can conceive, that our Earth moving through
the subtile etherial medium, where it meets with
no sensible resistance, if it has a motion, that mo-
tion cannot be perceived by us. Again, when we
consider
LECTURE III.
73
consider that there is no such thing in nature as a
larger body revolving round a less, as its centre of
motion; we are convinced, that, as the Sun is
known to be so much larger than our Earth and all
the other planets of our system, it must be the
body included within the orbits of all the rest, ha-
ving a less motion, or describing a less circle round
the centre of gravity of the whole system, than any
other body belonging to it.
It has been suggested by those who would not
be convinced to the contrary, either by reason or
experience, that, if our Earth had a progressive
motion, a stone, dropped from any considerable
elevation, would not fall directly perpendicularly,
as the body over which it was dropped must have
advanced considerably in the time of its fall; not
reflecting that a body, when impelled by another
body in motion, partakes of the motion of that
body.
The annual progressive motion of our earth is e-
qually deducible from observation of the heavenly
bodies; for, as its diurnal motion is referred to the
apparent motion of the Sun from east to west, so
is its annual revolution referable to that motion of
this luminary, discoverable from its rising and set-
ting at different parts of our horizon, and traver-
sing a certain space, called the Zodiac, in a
year.
That circle which terminates our view, on what-
ever part of the Earth we are placed, is called the
horizon. This appears to divide the great expanse
into
74
LECTURES ON ASTRONOMY.
into two hemispheres; that above our horizon at
the time is called the visible hemisphere; and that
hid from our view the invisible.
Before the Sun rises above our horizon, a faint
light proclaims his approach, which advantage we
derive from our atmosphere, as I have previously
informed you, by its reflecting the rays of light to
our eyes long before we feel their direct influence.
Were it not for this property of the atmosphere,
we should not only lose the advantage of the mild
approaches of this luminary, by which our sight
would be impaired; but likewise, when he was vi-
sible to us, all objects would be dark, excepting
those which received the direct impulse of his rays.
The density of the atmosphere decrcases with its
height, as has been proved by experiments. A ba-
rometer, being placed at the foot of a mountain,
has stood, suppose at 29 inches, by the great pres-
sure of the air, which must have been occasioned
by its density and pressure; but, taken to the top
of the mountain, it has sunk to 25 inches, and that
by a progressive gradation in its ascent. On com-
paring the diminution with the distance, in the
foregoing observation, it has been computed that
the height of the atmosphere is about 20 leagues
above our Earth; but, as the atmosphere seems to
be indefinitely extensible, I think that its real
height above our Earth cannot be accurately ascer-
tained.
This fluid, which surrounds our Earth and re-
volves with it about the Sun, is what we call sky;
which,
LECTURE III.
75
which, although of considerable density, yet it
transmits the light of the Sun to us, and allows us
to view the glories of the heavens in all their splen-
dor and harmony, unless obscured by the gross
vapours of our Earth.
The effects of the accumulation I am speaking
of was a great impediment to navigation, whilst
the polar star was the only guide to mariners; as,
when it was thus obscured, they had no other by
which they could steer their wandering vessels. —
At length it pleased the Almighty, by one of those
circumstances miscalled casualties, to afford them
a more constant guide, by imparting to mankind
the knowledge of that property of the magnet by
which it points to the pole of the world.
The essential properties which cause this pheno-
menon have not been ascertained. It is thought
to be produced by a subtile fluid, which fluid is
considered as being composed of two kinds of ele-
ments united by affinity; and that these elements
have a greater tendency to each other than those of
the same kind. Excepting the afore-mentioned
tendency, their attractions follow the laws of gra-
vity, and this fluid has affinity with the particles of
iron.
After having engaged the attention of the most
celebrated philosophers, the essential properties of
this subtile fluid, like those of light, gravity, and
electricity, remain undefined; from which we may
conclude, that we are let to know no more than is
necessary for our comfort and convenience in this
life,
76
LECTURES ON ASTRONOMY.
life, and that there is a boundary we shall not be
permitted to pass, till we are translated into that
pure state in which we shall be able to behold the
works of Providence as they really are- and be
made to understand those holy mysteries, which,
for wise purposes, are now hid from us; for, as
the excellent Dr. Blair remarked, in a sermon I
once had the pleasure of reading to you,
"This
obscurity is our happiness; as, were we permitted
to see the beauties of the celestial regions, and to
comprehend the excellence of divine things, we
should disrelish our present enjoyments." Let us
then be satisfied with the usefulness of the effects,
and in tracing the benevolence of the works of
God, as we have good reason to be, although
we cannot develope the glories of the heavens, or
understand all the energies of the Divine Mind.-
But to return to the magnet and its use in naviga-
tion.
The north pole of this curious and important
phenomenon points nearly to that spot which is
supposed to represent the northern extremity of
the axis of the Earth's motion; yet it very seldom
points exactly to it; so that the magnetic meri-
dian seldom answers exactly to the meridian of any
place on our globe.
The meridian of a place is that circle which
passes over it and through the poles of the world.
The Sun is on this line at twelve o'clock at noon.
each day, which, with astronomers, is called the
beginning of the first hour of the day; but, by o-
thers,
LECTURE III.
77
thers, the middle hour of the twenty-four. The
variation of the needle from this line is different at
different places on our Earth, both by sea and
land; it is also continually varying at the same
place; so that, although in the year 1580 it was
11 degrees east at London, it is now 23 degrees
and a half west at that city. The variation is al-
ways reckoned from the north pole, east or
west.
The directive power of the magnet was applied
to the purposes of navigation in the fourteenth
century, yet its variation was not discovered till
the latter end of the fifteenth century; prior to
which it was supposed always to point due north
and south.
Columbus, who discovered the deviation, did
not perceive the extent of it, imagining it to be
invariably the same at the same places; and it was
not discovered till the year 1625 to be different, at
different times, at the same place.
Various are the theories advanced to account for
these irregularities; but, all being mere conjecture,
they are by no means satisfactory. However, I
shall state some of the most popular ideas concern-
ing them, although it is impossible for me to ascer-
tain their authenticity.
Supposing our Earth to be encompassed by a
magnetic fluid, magnetic needles, placed on its
surface, freely suspended, would have different di-
rections at different places; which is conformable
to experience; and the apparent irregularities in
the
78
LECTURES ON ASTRONOMY.
the variation of the needle must be occasioned by
the situation of the magnetic poles.
If the magnetic poles agreed with the poles of
the world, there would be no variation; so that
the magnetic needle would point due north and
south continually.
If the axis of the magnetic poles passed through
the centre of the Earth, it would be easy to assign
the quantity of variation at each place: but this is
not the case; therefore, to account regularly for
the variation, it is necessary to know the exact si-
tuation of the magnetic poles, their number and
force, also their distance from the real poles; whe-
ther they shift their places; and, if they do, the
quantity of motion every year, - circumstances
which philosophers have in vain endeavoured to
discover,- - an uncertainty which is some impedi-
ment in navigation.
The dip of the needle, or its depression below
the horizon, is also subject to a variation, and is
said to be not less than 72 degrees now at Lon-
don.
The ancient astronomers divided the horizon
into four parts, and distinguished only four points
by names, which they called the cardinal points,
as being the principal: these were placed at the
intersections of the meridian and prime vertical
circles with the horizon. Those of the meridian
with the horizon they called north and south; and
the other two, at right angles to the former, the
east and west. These four are still called the
cardinal
LECTURE III.
79
cardinal points, and the intermediate the colla-
teral.
The compass, or the boundary of our view on
all sides horizontally, is now divided into thirty-
two parts, or points, and their distances from their
primaries are expressed by degrees.
The point immediately over our heads is called
our zenith, and refers to the highest point of the
apparent celestial sphere: it is equi-distant from
every part of the horizon, and is reckoned 90
degrees, or a quarter of a circle, every way from
it.
The nadir is the lowest point of the celestial
sphere, and is hid from us, being that point di-
rectly opposed to our zenith.
Every circle, large or small, is, by mathemati-
cians, divided into 360 parts, which they call de-
grees; 90 degrees, or a quarter of a circle, is u-
sually employed to measure all angles formed be-
tween a line perpendicular to the horizon which
goes up to our zenith, and all other lines that are
not below our horizon.
Our Earth being a spherical body, the limit of
our view must change at every change of our situ-
ation on this globe. A spectator on the Earth at
A, fig. 4, plate 1, has his view bounded by the line
from B to C; if he travels to D, his visible horizon
will be at E F.
That circle which we suppose situated directly
between the north and south points of the com-
pass, and passing through the east and west, is
called
80
LECTURES ON ASTRONOMY.
called the equator of our Earth; because it equates
or divides the globe into two equal parts: that on
the north side of this circle is called the northern
hemisphere, and that on the south side of it is
called the southern hemisphere.
The poles of the world are the poles of the e-
quator, and the zenith and nadir may be called the
poles of the horizon; as the poles of every circle of
a sphere are those two points which are at the
greatest distance from the plane of that circle; and
the poles are always 90 degrees from the circle
every way.
The highest point in which the Sun appears
above the horizon of any place, and at which
he arrives nearly at twelve o'clock each day, is
on the meridian: if from this spot we describe a
circle through the north and south points of the
compass, and passing through our zenith, we shall
call that the meridian of the place of observation.
Every place on our Earth has its particular meri-
dian passing over its zenith, and through the north
and south points of the compass, or from the north
and south poles of the world.
We do not change our meridian by travelling
north or south, but only our zenith; if we travel
east or west, our meridian is changed by every re-
moval; all the meridians intersect each other at
the poles, as shewn fig. 4, plate 1.— The equator
being every where equi-distant from the poles of
the world, it divides every meridian into two equal
parts.
The
LECTURE III.
81
The poles of the heavens are formed by a conti-
nuation of the axis of our Earth; and, in like
manner, the circles I have been describing are
transferred to the celestial concave; so that when
I am describing celestial phenomena, and speak of
the equatorial, horizontal, and meridional circles, I
transfer those of our Earth to the heavens; which,
although imaginary, serve as fixed points for ob-
servation, as it is to them, together with the e-
cliptic, that we refer all the motions, &c. of the
heavenly bodies.
As the horizon of a place distinguishes night
and day at that place, the length of the day and
night must differ at every place; for, as each has a
different zenith-point over it, the horizon must also
be different.
The apparent rising and setting of all the hea-
venly bodies are referred to the horizon; and, the
higher they are elevated above it, the longer they
stay with us.
Mathematicians denominate all those circles
great, the diameter of which passes through the
centre of the sphere, and the planes of which di-
vide the globe into two equal parts.
The equator, the meridian, and horizon, are
great circles of our globe, and, together with the
ecliptic, the great circles of the celestial sphere.
Small circles divide the globe into two unequal
parts; such are the parallels to the equator of a
terrestrial globe, and the parallels to the elliptic of
a celestial sphere.
Ꮐ
In
82
LECTURES ON ASTRONOMY.
In referring our horizon, or the boundary of our
view, to the heavens, we regard only our sensible
horizon; our rational horizon, or that which, if
our globe were of sufficient magnitude in com-
parison of the great expanse, would, as it were, cut
our globe in halves, would differ from our sensible
one.
Let A B C D, fig. 5, plate 1, represent our Earth,
and EFG the heavens, which is near enough to
the body ABCD to form an angle with it, mea-
sured by mn, when we compare the line drawn
from its centre, and the one from its surface, as
from A to m; but, if we compare the lines drawn
through the middle of the Earth to the supposed
heavens at O, in their more distant situation, as re-
presented by the semi-circle HIK, with the other
line drawn from the top of the Earth to O, we
shall perceive that these lines, on account of the
great distance, terminate the same, meeting in a
point at O: this is the case in fact, our Earth being
but a point in comparison of the distance of the
fixed stars; as is evident by our always seeing the
polar star in the same point of the heavens, not-
withstanding the annual motion of our Earth.
I will now endeavour to explain some of the
phenomena of the heavens by means of the celes-
tial globe, represented fig. 1, plate 2. It is called
the celestial sphere, because on it are delineated
those stars we see, and those circles we imagine,
in the concave sphere of the heavens. But, being
on a convex surface, they appear in a reverse or-
der,

Plate II.
E
Fig. 2.
Tropic of Cancer
Ecliptic
Equator
Horizon
B
NEARY
90 13 12 12 18
London
30
30
20
D
D
Sonth
Zenith
70
Ofe
Fig. 3.
Nth Pole
70
Do go 80 B
Trigid Zone
Polar
Circle
Temperate
Zone
Trepie
Torrid
Zone
Equator
Torrid
Zone
Tropic
Temperate
Zone
G
Polar
Circle
Frigid Zone
Sth Pole
North
не
B
sees Aries
APRIL
Fig. 1.
M
T.Conder Sculp
UNIV
OF

NIK
OF
106
Fig: 4.
Right Sphere.
Fig: 5.
Parallel Sphere.
Fig: 6.
Plate III.
Oblique Sphere.
Trapic
of
Capricorn
Polar
Holar
Tropic of Cancer
Ecliptic
Hordon
Aqualo
Meridians
Fig: 1.
Antarctic
Pole
Tropic of Cancer
Equator
Ecliptic
Horizon
10 20
MERIDIAN
Equinoc
Zenith
o 30 00
Solstice Colure
Meridians
Arstic
Axis of
Un Selphe
Tropic of
Cancer
DIAC or ECLIPTIC
THE
EARTH
ricorn
36 36 HORIZON
quinoctial
80
20 10
Tropic of Cancer
Taliptic
Equator
ropic
Horizon
Meridians
retic Circ
09
Nadir
Climates
Pole
Polar
Circle
Fig: 2
D
Fig: 7.
L
Sun's rays
in Summa
Sun's rays
in Winter
m
B
H
Horizon of London
Southern
Polar Circle
Tropic
Cancer
Equator
Tropic
Capricor
South Pole
D
Atmosphere
North Pole
Northern
Polar Girele
Polar
Pole
Circle
Fig: 3.
C
Pole
Circle
Polar
Equator
Gircle
H
Pol
Polar
YK
D
B
T.Conder sculp
LECTURE III.
83
der, and therefore, in transferring them to the hea-
vens, we must suppose ourselves situated within
the centre of it; as is represented by the armillary
sphere, fig. 1, plate 3, in which our Earth is in
its proper situation in respect to those circles
of the heavens represented by the armillary part
of it. I shall refer you to each occasionally.
When speaking of the imaginary circles of the
celestial expanse, the armillary sphere will ex-
hibit these phenomena most clearly, when re-
ferring to other celestial circumstances, the ce-
lestial globe will best answer our purpose. And
by their several uses I hope to make you un-
derstand all the apparent motions and changes
of the heavens, so far as relate to the circles
of the sphere, and to the
urnal motion of our Earth.
I will explain the rationale of the celestial globe.
This globe, being duly balanced, turns with fa-
cility round a pin, which serves it for an axis, as
our Earth does on its axis, or line of gravity;
which motion exhibits the apparent motion of the
heavens, occasioned by the diurnal motion of our
Earth.
real annual and di-
Preparatory to which,
The broad circle CD of a celestial globe al-
ways is used to represent the horizon of any
place on our Earth, when the latitude of the
place is brought to cut the edge of the hori-
zon. This I shall explain more fully to you
hereafter.
G 2
The
84
LECTURES ON ASTRONOMY.
The horizon of this globe has four separate cir-
cular spaces delineated on its surface, the inner-
most of which is divided into 360 degrees, and
four quadrants; the numbers on the latter begin
at the east and west points of the compass, being
counted each way to 90 degrees, which is at the
north and south points.
The next circular space contains the 32 points of
the mariner's compass; the next, the 12 signs of
the zodiac, which are divided into 30 degrees
each; and these are characterized by the names,
signs, and figures, belonging to them. The outer
circle of the horizon contains the months and
days; the former are divided from each other, and
the latter numbered.
The brass graduated circle which crosses the
globe, north and south, is called the general me-
ridian, because it serves to shew the meridian and
zenith of every place on our Earth.
This circle is divided into quadrants, each of
which you know must contain 90 degrees. The
numbers on two of the quadrants begin at the
circle on the globe which represents the equa-
tor, and increase towards the poles; being used
to shew the distance of any star or circle of
this globe from that imaginary circle of the hea-
vens which it represents. The other two qua-
drants have their numbers counted from the poles
towards the equator, being used for the purpose
of fixing the globe to the latitude of any place,
which
LECTURE III.
85
Į
which is always estimated by the elevation of the
pole above the horizon of the place.
The Sun's geocentric place for 12 o'clock every
day in the year is known by reference to the
days of the month, and signs of the zodiac, on
the horizon of this globe: but, as his splendor
at that time prevents our seeing those signs in
which he is, we are obliged to defer the ob-
servation till that luminary has withdrawn his
beams, when we shall perceive the sign directly
opposite to that in which he was at 12 o'clock at
noon of our day, at 12 o'clock at night on our me-
ridian.
The graduated side of the brass meridian of a
celestial globe should face the east, as the globe
should always be turned from east to west, to re-
present the apparent diurnal motion of the Sun and
heavens.
In Adams's globe, which is the one represented,
fig. 1, plate 2, the equator is used for the hour-cir-
cle, which is, I think, very proper; as the time
that the apparent revolution of the heavens is per-
formed in is 24 hours, which you know is occa-
sioned by the real motion of our earth on its axis
in that time, in a contrary direction, or from west
to east,
Over this circle on this globe, which serves for
an hour-circle, is placed a semi-circular wire that
carries two indices, which serve to shew how
long any planet is in performing any part of its
revolution, and when it will be fit for observation;
G 3
also
86
LECTURES ON ASTRONOMY.
also the same of the apparent motion of the stars,
and the time of their being above our horizon, as
I shall explain in the problems. The hours are
placed below the degrees of the equator of this
globe.
The equator of our Earth is called the Line by
mariners; and, when they pass over it, they say
they have crossed the line.
The Sun moves in this imaginary circle of the
heavens on two days only in the year; the one in
spring, and the other in autumn; at which times
the day and night of each parallel are equal a-
mongst themselves; and hence these intersections
of the ecliptic, or Sun's path, with the equatorial,
are called the equinoctial points.
The ecliptic, or apparent path of the Sun in the
heavens, forms with the equatorial (or imaginary
circle, which is supposed to be exactly between
the north and south pole of the world) an angle of
23 degrees and a half.
The ecliptic on the globe is divided into twelve
equal parts, each of which contains 30 degrees,
corresponding to the space occupied by each sign
of the Zodiac in the heavens. The Sun always
appears among the stars described on this zone, and
to advance among them easterly, a space nearly
equal to a degree each day, going through all the
signs exactly in a year.
The equinoctial points, or intersections of the
ecliptic and equator, are at the beginning of Aries
and Libra. The first of Cancer and the first of
Capricorn
LECTURE III.
87
Capricorn are called the solstitial points, because,
when the Sun arrives at either of them, he appears
to be stationary for several days, or to arrive nearly
at the same elevation in the heavens above the ho-
rizon. When he is in one solstice, which is at that
circle parallel to the equator called the tropic of
Cancer, he makes the largest angle with the hori-
zon in northern latitudes, which, at that of Lon-
don, being 51 degrees and a half north, makes the
longest day happen on the 21st of June. When he
is at the other solstice, which is at the tropic of
Capricorn, he makes the least angle with the hori-
zon of London, having the least elevation above it,
and the shortest day is on the 21st of December at
that city.
In southern latitudes it happens in a reverse or-
der, their longest day being when the Sun is at
the tropic of Capricorn, and their shortest when
he is at the tropic of Cancer. In both cases,
the length of the day must increase with the
degree of latitude; as, the higher the Sun rises a-
bove the horizon of a place, the longer will he
remain above it, and therefore the length of the
longest day, and of the shortest, at every place,
will differ from those of every other place, accord-
ing to the latitude of each,
The 24 circles on the celestial globe, which
intersect each other at the poles of the ecliptic,
are used to shew the latitude of the fixed stars,
which is reckoned by their distances from the e-
cliptic.
G 4
The
88
LECTURES ON ASTRONOMY.
The latitude of the stars is counted from the
ecliptic, the most important circle of the heavens,
being that in which the Sun always appears in
glorious majesty ; — and in reference to his ap-
parent motion we speak of the poles of the eclip-
tic.
The Sun has no latitude, being always in the
ecliptic; and to speak of his longitude is not so
proper as his place in the ecliptic, because his mo-
tion is only apparent.
The eight circles drawn parallel to the ecliptic
on this globe are to shew the latitude of the pla-
nets, those never deviating from the ecliptic more
than the space included within the exterior of these
eight circles on each side of it.
The longitudes of the planets are reckoned on
the ecliptic, and eight parallel lines on each side of
it, beginning at the first degree of Aries, and count-
ing eastward.
The longitude of the stars is also counted on the
ecliptic, and all the parallels to it.
The difference between the longitude and la-
titude of places on our Earth, on a terrestrial
globe, and those of the heavenly bodies on a
celestial sphere, are these: The longitudes of the
heavenly bodies are counted on the ecliptic and
parallels to it, beginning from that part of it, dis-
tinguished by the sign Aries; but the longitude
of places on our Earth are counted on the equa-
tor and parallels to it; and the first degree, or
where we begin to count from, in England, is
at
LECTURE III.
89
at London, or at Greenwich; so that the celestial
and terrestrial longitude differ from each other, the
former being settled at the first degree of Aries,
and the latter at London, which is not in the same
spot. The latitude of the heavenly bodies also dif-
fers from that of terrestrial places; the first being
counted from the ecliptic, but the second from the
equator.
The distance of any heavenly body from the
equator, measured upon the meridian, is called
its declination, which answers to the terrestrial la-
titude.
The brass semi-circle fixed to the poles of the
globe (as represented by GI, fig. 1, plate 2) ren-
ders the working of problems of declination more
convenient than by the general meridian, it having
a sliding piece of brass (H) on it, which may be
fixed to any spot on the globe.
The Sun's declination, as seen on the celestial
sphere, is the same as the latitude of the place to
which he is then vertical, as seen by a terrestrial
globe; from which you perceive, that parallels of
declination on the celestial sphere are the same as
parallels of latitude on the terrestrial globe, both
being parallel to the equator.
Those two parallels to the equator, called the tro-
pics, (ED and CF, fig. 2, plate 2,) are 23 degrees
and a half distant from it on each side, being situ-
ated at the Sun's greatest deviations from it, north
and south.
As
90
LECTURES ON ASTRONOMY.
As the Sun is advancing towards Cancer from
Aries, he appears more and more northerly every
day above our horizon, when he arrives at the
meridian; so that he is more and more eleva-
ted above it each day till he is arrived at Can-
cer, which is his most northern situation. Af
ter arriving at his highest situation, he descends
from it in the same manner, appearing lower or
nearer to the horizon each day at noon, till he
arrives at Capricorn, his most southern situa-
tion.
This apparent motion of the Sun backwards
and forwards, north and south, has occasioned the
parallels at which he arrives to be called tropics,
with the additional name of the sign of the Zo-
diac which touches those parallels in which the
Sun appears at the time, one being called the
tropic of Cancer, and the other that of Capri-
corn.
The surface of our Earth is divided into five
zones, which are denominated according to the
degrees of heat or cold felt at those parts, fig. 3,
plate 2.
The spaces between the tropics and polar circles
are called temperate zones; the breadth of each is
43 degrees 4 minutes.
The torrid zone is all the space between the tro-
pics, the breadth of which is 46 degrees 56 mi-
nutes. The equator divides it into two equal
parts, containing 23 degrees 28 minutes each.
By the ancients, this zone was thought not ha-
bitable,
LECTURE III.
91
bitable, on account of the great power of the
Sun on those parts. They did not reflect on
that part of the constitution of animal nature,
which is provided by the Deity, to moderate the
heat of all climates, or to accommodate itself to
them.
The spaces between the poles and the polar
circles are called frigid zones; the breadth of each
segment between them is 46 degrees 56 minutes,
as from A to B, or 23 degrees 28 minutes every
way from the pole.
The inhabitants of the torrid zone have the Sun
pass through their zenith twice a year, at which
time the heat is excessive, by reason of the great
quantity of the Sun's rays they receive at that time.
The people inhabiting the parallels to the equator,
as CD, fig.3, plate 2, within the torrid zone, are
called Amphiscians, from Amphiscii, which signi-
fies about and shadow, because these people have
their shadow at noon on opposite sides of them at
different times of the year.
Those who live immediately on that part of the
torrid zone, described by the equator, or on the
centre of it,. are called Ascii or Ascians, because
at certain times of the year they have no shadow.
In the torrid zone, the Sun rises and sets every na-
tural day, because the distance of the Sun from the
pole always exceeds the height of the pole in those
latitudes.
In the temperate zones, also, the Sun rises and
sets every natural day, because the height of the
pole
92
LECTURES ON ASTRONOMY.
pole is less than the distance of the Sun from the
pole.
In the temperate zones, the least height of the
pole exceeds the greatest distance of the Sun from
the equatorial, and therefore the Sun never passes
through the zenith of the inhabitants of these
zones. Where the temperate zones join the frigid,
the height of the pole being equal to the Sun's
distance from it, when the Sun is in either of these
tropics, the inhabitants of those circles see the
Sun perform an entire revolution above their ho-
rizon, so that they have perpetual day; and, when
he is arrived at either, the other has perpetual
night.
The people inhabiting the temperate zones are
said to be Heteroscii, which signifies that during
the whole year they have their shadows at noon
projected different ways from each other. We,
who inhabit the northern temperate zone, as at F,
fig. 3, plate 2, are Heteroscii to those who inhabit
the southern temperate zone, as at G, and they
are said to be the same in respect to us.
In the frigid zone, the least height of the pole
exceeds the greatest distance of the Sun from the
equator, the same as happens in the temperate
zone, and therefore the Sun never passes through
the zenith of the inhabitants of these zones. Every
where, in a frigid zone, the height of the pole is
greater than the least distance of the Sun from the
pole, so that, in some parts of the Earth's annual
revolution, it is at a less distance from the pole
than
LECTURE III.
93
than the pole's height above the horizon, at which
times it does not set below the horizon, or even
touch it, in a frigid zone.
At such parts of the Earth's orbit, where the
Sun's distance from the pole exceeds the height of
it, or the latitude of the place, the Sun rises and
sets every day.
The people who live at the poles are called Pe-
riscians, from Periscii, because their shadows go
quite round them in the same day, when the Sun
does not set to them.
Astronomers and geographers divide the Earth
into 24 climates of half-hours, and six of months.
-The surface of our Earth, between the equa-
tor and the polar circles, they divide into 24 parts,
on each side of the equator, which are distin-
guished on a terrestrial globe by circles drawn pa-
rallel to the equator; and may be seen, fig.2, plate
3.There is the difference of half an hour in
the time when the Sun is above the horizon on the
longest day at one parallel, and the next to it;
therefore the days are longer by half an hour on
one parallel than on the former, throughout the
whole 24 parallels from the equator to the polar
circles.
As the longest natural day at the equator is 12
hours long, at the polar circles it must be 24.
In the latitude of London, which is on the ninth
parallel from the equator, as at CD, fig. 2, plate
3, the longest day contains 16 hours and a
half.
Between
94
LECTURES ON ASTRONOMY.
Between the polar circles and the poles, six pa-
rallels are drawn on the first parallel, the day is
one month long, and it increases one month at
each, so that at the poles the day is six months
long.
We may consider our Earth, in respect to its dif-
ferent inhabitants, as we do a ball of magnet,
which, by its power of attraction, when rolled in
steel filings, supports them in all possible direc-
tions, even when turned with the greatest celerity,
as it is thus that the Earth by its attraction
draws every body on its surface towards its centre,
and by its great attractive power retains them on
its surface, notwithstanding the velocity of its mo-
tion on its axis.
Those people are called Antipodes, who are si-
tuated in direct opposition to each other on the
Earth. Their hours, seasons, and days, are also
in a direct opposite order, it being day with one
when night with the other. They are at the same
distance from the equator, but on opposite meri-
dians, as at A and B, C and D, E and F, fig. 3,
plate 3.
The Antcecians are those who, inhabiting the
same parallel and the same portion of the meridian,
(only one north and the other south,) have their
hours the same, but their seasons different, as G
and H, fig. 3, plate 3.
Those who are situated on the same paral-
lel of latitude, only differing by half-circles of
the meridian, as at G and I, or H and K,
have
LECTURE TII.
95
have their seasons the same; and it is mid-
night with one, whilst noon with the other Pe-
riceci.
There are three situations of the celestial sphere
in regard to our Earth, which are easily shewn by
either the globe or armillary sphere, and may be
seen by fig. 4, 5, 6, plate 3.
All those who live under the equator are situated
in a right sphere, because the poles are in their ho-
rizon, and their zenith-point is in the equator.
In which situation, the heavenly bodies rise and
set right or perpendicularly to the horizon, and
the Sun's apparent path is cut into two equal parts
by it; which makes the days and nights equal in
length to the inhabitants of the equator all the
year through; the Sun being twelve hours above
and twelve below the horizon, during each re-
volution of the Earth on its axis. See fig. 1,
plate 3.
A parallel situation, or sphere, is the situation
of those people who inhabit the poles. - These
have the equator in their horizon, one of the poles
being in their zenith and the other in their nadir.
In this position the stars never rise or set to their
horizon, because the apparent motion of those lu-
minaries is parallel to it; so that they have but
one day and one night all the year, each six
months long. Those of the north pole have per-
petual day for the six months that the Sun is on
the northern side of the equator, and those of
the
96
LECTURES ON ASTRONOMY.
1
the south pole for the six months that the Sun
is on the southern side of the equator. See fig. 5,
plate 3.
In our island, we are situated in an oblique
sphere, and so are all those who do not live un-
der the poles or the equator: as to us and them,
all the circles parallel to the equator make ob-
lique angles with the horizon; so that there are
as many oblique positions of the globe as there
are positions from the equator to the poles. Sec
fig. 6, plate 3.
In an oblique situation of the globe, the orbits
of all the heavenly bodies make oblique angles
with the horizon; which make the days and
nights unequal, excepting at the equinoctial points,
or intersections of the equatorial and ecliptic. At
all other times of the year the daily circles of the
Sun are unequally divided by the horizon of those
who live in an oblique sphere; but when the
Sun is in the equator, that circle being divided
into two equal parts by the horizon, it is equal
day and night, - which happens about the 23d
of March and September. All the rest of the
year the days are longer or shorter than the
nights, to the inhabitants of an oblique sphere.
When the Sun is on the northern side of the
equator, those situated in the northern part of our
globe have their days longer than their nights,
while those in the southern have theirs shorter.
When the Sun is on the southern side of the equa-
tor, those inhabiting that part have their days long-
er
LECTURE III.
97
er than their nights; whilst those on the northern
have theirs shorter.
The polar circles have been called the arctic and
antarctic, and have those terms always affixed to
them on globes and planispheres, though not with
strict propriety, unlimitedly; as by an arctic cir-
cle is meant the largest parallel, that is always
above the horizon of any place in the northern
hemisphere, including all those stars which ne-
ver set to the horizon, but make a complete circle
above it, and which is also called the circle of
petual apparition, being never hid from our view.
By the antarctic circle is meant the largest pa-
rallel that is entirely hid below the horizon of any
place, and which is the circle of perpetual occul-
tation, never rising above the horizon of the inha-
bitants of the northern hemisphere.
per-
All arctic circles touch the horizon in the nor-
thern point of the compass; and all antarctics
touch the horizon in the southern point of the
compass.
The polar circles do not answer for the arctic
and antarctic to any of the inhabitants of our
Earth, but to those who live under either of the
tropics. This is easily seen by fixing either of
the tropics on a sphere to the zenith-point, and
then placing it in any other situation; as then you
will perceive that the polar circles are the arctic
and antarctic to the polar regions only, every other
place having its arctic and antarctic circle in diffe-
rent parallels.
II
The
98
LECTURES ON ASTRONOMY.
i
!
The cause of the groups of stars on the ce-
lestial sphere being included within familiar fi-
gures, you are already acquainted with; of which
constellations you know there are twelve on that
path or circle which the Sun appears to pass
through, and to every part of which he is actually
transferred by our observations, on account of the
annual motion of our Earth. All the constel-
lations on the north side of the zodiac are called
northern, and those on the south side of it are
called southern.
I have annexed to the plates of the celestial he-
misphere a catalogue of the constellations, and re-
marked the principal stars in them by their names
at full length.
The constellations are said to increase their lon-
gitude continually from west to east; contrary to
the apparent motion of the heavens, by which the
first star in the constellation Aries, which 1900
years ago was at the vernal equinoctial point, is
now removed about thirty degrees from it, which
is the whole constellation, or one-twelfth part of
the zodiac; to conform to which circumstance, de-
lineators of celestial spheres have placed the cha-
racter or sign only of the constellation at that point,
having removed the star that used to occupy that
station thirty degrees from it; so that if we want
to find the place of a particular star in any of the
constellations of the zodiac, we look for it within
the figure of it; but if we wish to compare the
circles of the sphere with any circumstance rela-
tive
LECTURE III.
99
tive to the planets, we look for the character only,
which is called the sign, on the ecliptic circle, and
not at the figure or constellation itself.
This change of the longitude of the stars, or the
retrograde motion of the intersection of the eclip-
tic with the equator, is called the precession of
the equinoxes, which motion is found to be about
50 seconds in a year, and is said to be owing to
the attraction of the Sun and Moon on the protu-
berant matter about the equator.
The opinion of Sir Isaac Newton, touching the
physical cause of the precession of the equinoxes,
is, that it arises from the broad spheroidical figure
of the Earth; which is a natural inference, as the
accumulated matter about those parts must occa-
sion a greater degree of attraction both by the Sun
and Moon.
The variation which has been discovered by Dr.
Bradley in the quantity of the change of the equi-
noctial points, one year with another, is ascribed
to the variation in the attraction of the Moon, as
the plane of her orbit is sometimes above 10 de-
grees more inclined to the plane of the equator
than at another; therefore that part of the whole
annual motion, which depends on the action of the
Moon, must vary in its quantity, although that
which depends on the attraction of the Sun con-
tinues the same, that luminary keeping nearly
the same inclination to the equator every year.
Therefore, although the mean annual precession,
proceeding from the united. influence of the Sun
H 2
and
100
LECTURES ON ASTRONOMY.
and Moon, is 50 seconds, yet the apparent an-
nual precession sometimes exceeds that mean
quantity, according to the various situations of the
Moon's nodes.
The idea, of the obliquity of the ecliptic to the
equator being variable, seems to have arisen from
the change observed in the latitude of the fixed
stars, as well as from the actual diminution of
the angles they form between them, discoverable
by observation with good instruments, and is also
admissible on the principles of attraction referred
to the variable inclination of the Moon's orbit,
which must affect its action on the redundant mat-
ter about the equator, both as to its longitude and
latitude.
The precession of the equinoxes is performed
in a contrary order from the apparent annual mo-
tion of the fixed stars, being from west to east, so
that the places of those luminaries, although im-
moveable, are transferred to a more eastern situa-
tion.
As great changes have happened in the situ-
ation of things on our Earth, some have imagined
that the position of it, in respect to the fixed
stars, may also have been variable; but this lat-
ter idea I do not think admissible, there being
no good grounds for such a conjecture; because,
in old records, ancient historians, as Herodotus,
in relating the events which happened in the
time of the Egyptian Astronomy, have made
some inferences totally inconsistent with our bet-
ter
LECTURE III.
101
ter knowledge of the physical principles of that
science.
It was impossible for Herodotus, or any of his
contemporaries, to form accurate ideas of circum-
stances preceding their time, having no better
authority for the events they related than that
of the hieroglyphical traditions of the Egyptians;
and how liable those were to be misconceived, I
have already informed you. It requires strong
judgement and deep reasoning to digest the wri-
tings of Herodotus, as, in the events he relates,
fiction and truth are so blended, that human com-
prehension is scarcely equal to the task of se-
parating them; and for this his veracity is not
to be impeached, as it originated in the materials
from which his work was composed. — The fault
was in their ambiguity, not in his skill in com-
piling and uniting; in both of which he evinces
great discernment and deep crudition. He has
great merit as an historian, by not attempting
to mislead; as, on the contrary, he frequently
intimates a doubt of the probability of those cir-
cumstances, which, as a faithful historian, he is
obliged to relate.
The Sun's apparent motion is unequal; i. e. the
motion of our Earth in its orbit is sometimes swift-
er than at others, on account of the elliptic form
of its orbit, which causes it to be nearer to the Sun
in one part of it than in others; the former hap-
pens in winter, so that there are eight days more
from the vernal to the autumnal equinox than from
H 3
the
102
LECTURES ON ASTRONOMY.
the autumnal to the vernal. The summer's heat
and the winter's cold are occasioned by the diffc-
rent obliquity of the Sun's rays falling upon our
Earth, and the different duration of that luminary
above the horizon. In the former season, they
fall with less obliquity, and therefore more of his
rays are received on particular parts of our globe :
in the latter season, they fall with greater obli-
quity, therefore less of his influence is received,
and he continues a less time above the horizon
also.
Fig. 7, plate 3, will convey a clear idea of what
I have been asserting. Suppose ABCD to repre-
sent our Earth, and HI the horizon of a spectator
at the latitude of London; K to be the elevated
place of the Sun above the horizon in summer,
and L that above it in winter. You observe that
the rays of the Sun in the former case fall with less
obliquity, and therefore the same quantity fall in
the small space of our globe, mn, as do from
the Sun in the latter case on the large space of
it, on, on account of their greater obliquity in
the latter case. You also observe that they pass
through a greater quantity of dense atmosphere
in the winter, by which also we may suppose
their power is somewhat diminished or weakened
by the reflective and refractive power of that me-
dium.
We observe that the Sun rises at different points
of the compass, or at different parts of the ho-
rizon of any place we live at, at different sea-
sons
LECTURE III.
103
sons of the year: this occasions him to make
sometimes a larger angle with it than at others;
of course he must be longer above our horizon,
making a larger circuit above it; and his rays
are less oblique than when he makes a less angle
with it.
From December till June he is continually in-
creasing his diurnal range northerly, and of course
rises higher each day than the preceding one: thus
the days increase in length during that time.
From June till December he appears to return
towards the south, making continually less and
less stay above the horizon, and of course the days
then decrease.
You now perceive the cause of the pleasing
vicissitude of seasons; - that, when the Sun rises.
high above our horizon, by the continuance of
his influence, and the less obliquity of his rays,
the fruits of the Earth are ripened; and that,
after performing this salutary office, he retircs
from us by degrees, and bestows the like be-
nign influence on other countries. At our time
of need he returns again, and thus is continually
and abundantly aiding every part of the habitable
world.
How grand the design, and how perfect the ac-
complishment of as much as we have already ex-
plored! Then what must be your admiration, as-
tonishment, and gratitude, as we advance in the
scrutiny of the wise administration of Providence?
It will exceed all that we can form an idea
H 4
of,
104
LECTURES ON ASTRONOMY.
of, and contain more than we ever can compre-
hend; for, the ways of the Almighty are unsearch-
able, although his attributes are as clear as noon-
day.
Religion being the firmest support of happi-
ness, I wish to fix your attention on subjects
that will lead you to the attainment of it; and
shall therefore occasionally display the attributes
of the Deity, deducible from the subjects of
these Lectures, by which I shall fortify your minds
against the shock of accident and the terror of
calamity; raising your hopes on that solid basis,
which neither time nor circumstance can ever
shake.
Irreligion amongst the unreflecting is so pre-
valent, that both my duty and affection prompt
me to enlighten your minds, that you may not
be blinded by passion or ignorance; but, by ha-
ving your understandings cleared from those mists,
which hide so many things from common obser-
vation, you may be established in faith and good-
ness.
I regret that these subjects* are not more ge-
nerally understood; but as you, my dear young
friends, will sensibly feel the great advantage re-
sulting from the instruction they convey, you will,
I hope, endeavour to use them for the benefit of
* By these subjects, I mean all those included in my Course of
Lectures on Natural Philosophy, as well as the present under con-
sideration, as they are all delivered for the same beneficial purpo-
ses to my pupils, whom I am now particularly addressing.
others,
LECTURE III.
105
rather
others, but without vanity or ostentation,
recommending these studies for the delight they
afford, than as being indispensably necessary;
unless you perceive any of your fellow-creatures
doubtful of an over-ruling Providence, or devia-
ting from the paths of moral rectitude; then in-
deed the conviction such subjects as these bring
with them renders them indispensable; and it be-
comes your duty (if you have the opportunity)
thus to convince them of their error, and to re-
claim them the arguments these studies furnish
you with being more likely to effect that desi-
rable purpose than all the remonstrances you could
advance, being truths which cannot be confuted
by the most subtle arguer; for, like gold in the
furnace, the more they are tried, the brighter and
more beautiful their intrinsic worth will appear.
Yet disgrace not, as some do, the cause you mean
to serve, by a pharisaical conduct, by a display
of
your own merits or deserts: such is the in-
firmity of human nature, that none are exempt
from error; all we can do is to strive against it;
and although we may, by the advantages afforded
us, avoid the more flagrant faults, or perhaps mis-
conceptions, of our neighbours, yet we can deserve
no praise, although we should the severest blame,
if we shut our hearts against conviction, and
acted contrary to our more enlightened judgement.
The most uncultivated may be as good in intention
as the most learned; although, for want of due
cultivation, the good seed planted by our Creator
may
106
LECTURES ON ASTRONOMY.
may not have produced that plenitude, which, if
the emanation of divine instruction had been shed
on their minds, no doubt it would have done.
The unreflecting are likewise objects of pity:
then let us not condemn but sympathize with them,
and endeavour their reformation, by convincing
them of their error, and that in the tenderest man-
ner, not wounding deeper than the case requires;
and let our words be like balm to heal that wound.
Let us reflect on the infirmities of human na-
ture; reflect that perfection is not the lot of huma-
nity; that this life is a state of trial, in which the
best of us find many things to combat with; and
that all we can do is to endeavour to fortify our
minds against the temptations of sense, by che-
rishing those ideas most likely to enable us to es-
cape from their allurements: this, which is our
duty, will by habit become our inclination, so
that we shall derive the highest gratification, as
well as the amplest sources of consolation, from ra-
tional amusements, in whose train follow health,
cheerfulness, and joy.
That thou art happy, owe to God;
That thou continuest such, owe to thyself,
That is, to thy obedience: therein stand.
MILTON.
END OF THE THIRD LECTURE.
[107]
}
LECTURE IV.
THE SOLAR SYSTEM EXPLAINED, AND THE NA-
APPEARANCES OF THE BODIES
TURE AND
WHICH COMPOSE IT PARTICULARLY DIS-
CUSSED. - OF THE QUADRANT AND ITS
USES.
THAT most admirable logician Locke, in his
Essay on the Human Understanding, very justly
observes, that -"Though God has given no in-
nate idea of himself, though he has stamped no
original characters on our minds wherein we may
read his Being, yet, having furnished us with
those faculties our minds are endowed with, he
has not left himself without witness, since we have
sense, perception, and reason, and therefore can-
not want a clear proof of him as long as we carry
ourselves about us."
It is not sufficient to our happiness to know that
there is an all-powerful, all-wise, and ever-endu-
ring Providence; to perfect our felicity, we wish
to discover his attributes; - for which desirable
and essential knowledge we need only make use
of that reason he has blessed us with, by ap-
plying it to understanding the truths of Christia-
nity, and comparing them with the natural affec-
tions of things, all of which contain the most per-
fect
108
LECTURES ON ASTRONOMY.
fect evidence of the tender mercy, the universal
love, and over-ruling providence of the Almighty.
What is it but these assurances that animate us to
the scrutiny of the wonders of his hands and to
the observance of his laws? - Without them, our
exertions would become languid, we should tire
in an occupation from which we could derive
no advantage to ourselves or others. But, the re-
verse being the fact, we pursue our investigations,
both of the natural and spiritual affections of
things, with avidity, deriving from them ne-
ver-failing sources of delight and satisfaction. Our
hearts are humanized and softened,
all gloomy
ideas are banished from our minds,
more is required of us than what contributes to
our happiness, even in this life; - no unnecessary
restraints, -no austerity of manners;-but, on the
contrary, that our thankfulness will be best ex-
pressed by a cheerful enjoyment of the gifts be-
stowed on us,
we find no
Providence has kindly planted in every human
breast a proper sense of right and wrong; there-
fore, if we apply our reason to define the mean-
ing of these intimations, we cannot be misled ;
but shall find that the service of God is pleasant
in the performance, as well as joyful in the end.→
For,
Know thou this truth (enough for man to know),
"Virtue alone is happiness below:"
The only point where human bliss stands still,
And tastes the good without the fall to ill;
Where
LECTURE IV,
109
Where only merit constant pay receives,
Is blest in what it takes and what it gives;
The joy unequall'd if its end it gain,
And, if it lose, attended with no pain;
Without satiety, though e'er so bless'd,
And but more relish'd as the more distress'd.
The broadest mirth unfeeling Folly wears,
Less pleasing far than Virtue's very tears:
Good, from each object, from each place, acquir'd,
For ever exercis'd, yet never tir'd;
Never elated while one man's oppress'd,
Never dejected while another's bless'd;
And where no wants, no wishes, can remain,
Since but to wish more virtue is to gain.
POPE.
I have informed you that the first thing ob-
served by the ancient Astronomers was the ap-
parent diurnal motion of the whole heavens; after
which, the periodical revolutions of the Sun and
Moon excited their attention, -to ascertain which
required minute observation of the celestial bo-
dies;
these led to the discovery of the present
system of planets, 'the peculiar motions of these
bodies not escaping the scrutiny of minute obser-
vations.
The discovery of the planets did not immediately
serve to establish our present system upon just
principles, as I have pre-acquainted you; it being
thought that the Sun moved round the planets, in-
stead of these moving round him, as their centre of
motion.
The Solar system, or that which was revived by
Copernicus, is now too firmly fixed ever to be
doubted, unless the science of Astronomy should
again
110
LECTURES ON ASTRONOMY.
again be neglected; and even then, without all
writings are expunged, it will not be possible for
the present theory to be misconstrued, as the am-
biguous legends of the ancients were.
In the Copernican system, which is represented
plate 6, the Sun is supposed to be at rest in respect
of us, in the centre of it, and immoveable; al-
though in fact he has a motion on his axis, that is
performed in 25 days 6 hours, which has been
discovered by the spots on his disk; as also ano-
ther motion round the centre of gravity of the
whole system, which is occasioned by the various
attractions of all the planets.
The Sun is conceived to be seven hundred
and sixty-three thousand miles in diameter, and
his surface is continually emitting pure light or
fire.
The popular opinion of the nature of the Sun
is, that it is composed of heterogeneous particles
capable of combustion, and not of entirely pure
fire; because, when viewed through a telescope,
less bright spots are perceived on his surface, the
shape of which is variable, as well as the situation
and number of them. These appearances are first
obscure, and then become brighter by degrees, so
that at last they exceed the other parts of the Sun
in brilliancy. Their obscurity is supposed to be
produced by the smoke of the volcanoes previous
to the combustion.
Whatever be the substance of that glorious lu-
minary, the Sun, the matter it diffuses is well
known,

Plate VI.
View of the Proportional Magnitudes of the PLANETARY ORBITS
Fig.1.
ENE
ESE
Orbit of the Georgium Sidus.
Proportional
Magnitudes of the
Primary Planets.
Saturn
Apparent
Magnitudes of the
Sun
seen from each Planet
Jupiter 2
Georgium Sidus.
Mars o
Earth.
Venus
Mercury
05
from
SSE
Mer
cury
from
Venus
from the
Earth
from Mars
fromo Jupiter
from Saturn
from-
Georgium Sidus
CNB. The Proportional Magnitude of the Sun,
with respect to the Figure of the Planets here
given is represented by the Circle of Saturn's
Orbit. Markd
MANO
MSM
m.
D
Fig. 2.
C
G
233
T.Conder sculp
M
OF
M
LECTURE IV.
111
known, and its uses to mankind strike the mind
with sensations like those its influence imparts to
vivifying and expanding.
all nature,
Those bodies which move round the Sun, re-
garding him as their centre of motion, are called
planets; of which there are now seven disco-
vered. The nearest to the Sun is called Mer-
cury; the next, Venus; then, our Earth; the
next, Mars; then, Jupiter; then, Saturn; and
the most remote from the Sun is called the Geor-
gium Sidus, or Herschel. All these bodies shine
by reflecting the light of the Sun; therefore, when
they are deprived of his beams, they become to-
tally obscure.
In order to your understanding the construction
of the Solar system, and the laws by which it is
regulated, I shall endeavour to explain both by
figures, accompanied by the theory, preparatory
to my illustrating them by the instruments I use ;
as in doing so I hope to afford all who may do me
the honour of perusing this Treatise a clear eluci-
dation of these subjects, as well as my pupils an
useful theorical retrospect. Fig. 1, plate 6, repre-
sents the situation of the planets in respect to the
Sun and to each other, the character of each being
placed on its orbit.
Beside the planets, there are other bodies be-
longing to our system, called comets, which, in
one part of their orbit, go off too far to be seen
by us.
The
112
LECTURES ON ASTRONOMY.
The periods, magnitudes, circumference of the
orbits, distances from the Sun, diurnal rotations,
and other circumstances of the planets, are exhi-
bited on tables in a subsequent part of these Lec-
tures, containing the representation of the Solar
system, which I have copied from those of Dr.
Hutton, by that gentleman's kind permission.
It is well known, that all the other planets, (as
well as our Earth,) of which we are able to disco-
ver the spots on their surfaces, have a motion on
their axis, by the regular change of situation
observed of those spots, from which we may in-
fer, that those of which we cannot perceive these
effects have the same.
By the irregular appearance of the motions of
the planets in their orbits, as seen from our Earth,
sometimes moving backward or retrograde, at
others appearing stationary, at others moving di-
rect, being the result of their having a progres-
sive motion round the Sun, like that of our Earth,
we do not hesitate to acknowledge these clear evi-
dences of their doing so, and also that they re-
spect the same central body as the centre of their
motion.
Perceiving the planets to be regulated by the
same laws as our Earth, we naturally conclude that
they also are the residences of rational creatures,
like ourselves, endowed with the like sensibilities,
capable of enjoying an equal portion of the gifts
of Providence, as they receive an equal share of
heavenly influence.
Mercury
LECTURE IV.
113
Mercury is the nearest planet to the Sun, being
only thirty-seven million of miles distant from him,
which, compared with the remoteness of the other
planets, may be termed near, although in fact it is
an immense distance; yet such is the density of
the Sun's light at that distance from him, that
Mercury is seldom seen, being lost in the splen-
dor of his rays, by which we are prevented from
ascertaining this planet's motion on its axis, no
spots being discoverable, so highly is its surface il-
luminated.
As Mercury is never so far removed from the
Sun as Venus, or the other planets of our system,
we know that his orbit must be included within
those of all the rest: another circumstance corro-
borates this opinion ;
- when a number of bodies
move round another as their centre of motion, the
squares of their periodic times are proportional to
the cubes of their distances from the central
body.*
Mercury performs his revolution round the Sun
in about 87 days 23 hours, which is a much short-
er time than any other planet performs its annual
revolution in, the length of his year being not
quite three months of ours. His diameter is sup-
* Any number which is multiplied by itself is called the square
of that number; as suppose z be multiplied by itself, the square of
that number is 4, and 2 is called the root of 4, or the square-root.
If a square number be multiplied by its root, as 4 by 2, the pro-
duct 8 is called the cube, or third power of 2, which, in respect
to the 8, is called the cube-root.
I
posed
114
LECTURES ON ASTRONOMY.
posed to be equal to three thousand two hundred
miles; but, on account of his nearness to the Sun,
his motion is so quick, as not to admit of accurate
mensuration, being at the mean rate of one hun-
dred and five thousand miles an hour.
Mercury exhibits phases like the Moon, which
proves that he shines only by reflected light, not-
withstanding his peculiar brilliancy. The times for
the observation of this planet are a little after sun-
set, and a little before sun-rise.
Venus, the next in order, appears the most
beautiful star of the heavens, as viewed from our
Earth; she is denominated the morning and even-
ing star, and is the next planct to Mercury in our
.system. Her distance from the Sun is computed
at sixty-eight million of miles, and her mean mo-
tion in her orbit at the rate of seventy-six thousand
miles an hour. The circumference of her orbit
being four hundred and thirty-three million of
miles, and her annual revolution being performed
in 224 of our days and 17 hours, which is the
length of her year, not quite two-thirds of ours.
The diameter of Venus is computed at seven
thousand seven hundred English miles; her rota-
tion on her axis is performed in 23 of our hours
and 22 minutes.
That the Earth is not within the orbits of Venus
and Mercury is evident, by these planets never
being visible when in conjunction with the Sun, or
in opposition to that luminary, i. c. we never see
these stars shine when they are in the same sign
with
LECTURE IV.
115
When
with the Sun, or in the opposite sign to it.
Venus is in the same sign with the Sun, and di-
rectly in a line between us and that luminary, she
appears only a dark spot on the Sun's disk; and,
when she passes over the disk of the Sun, her pas-
sage over it is called the transit of Venus.
Venus and Mercury are called inferior planets,
because their orbits are included within that of the
Earth. These planets are never seen in the east-
ern point of the heavens when the Sun is in the
western, on account of their near approach to that
luminary, following close after him in the even-
ing, when he retires from our view, and imme-
diately preceding him in the morning, announcing
his returning influence, which gladdens the face of
nature by dissipating the incumbent gloom.
Whilst Venus is performing her apparent office
of attendance, she is called Hesperus, or Vesper,
the evening-star, in which she continues 290 days;
when that of Harbinger, announcing the Sun's ap-
proach to gladden the Earth, Phosphorus, the
morning-star; in which office she remains the
same time as in the former.
This planet exhibits phases like the Moon; and
spots similar to those perceived on that satellite
have been discovered on her surface, by which her
rotation on her axis has been ascertained.
Our Earth is the next planet in the system. Of
this planet I have already said much, and shall say
a great deal more; but, in placing it in its situa-
tion in regard to the other planets, I shall only
I 2
treat
116
LECTURES ON ASTRONOMY.
treat of it in those respects in which I have the
others. Its diameter is seven thousand nine hun-
dred miles, the circumference of its orbit five hun-
dred ninety-eight millions, and its mean annual
motion fifty-eight thousand miles an hour, by which
it performs its period in 365 days, 5 hours, and 19
minutes. Its mean distance from the Sun is nine-
ty-five million of miles, therefore its motion in its
orbit is not much more than half as swift as that of
Mercury in his. The Earth is accompanied in its
annual progress by one Moon, for the most bene-
ficial purposes.
Mars is the next planet in the system, and his
orbit is consequently exterior to that of our Earth,
his motion in which is computed, at a mean rate,
fifty-five thousand miles an hour; its circumference
being nine hundred and twelve million of miles,
through which he revolves in 686 of our days and
23 hours. His diameter is near four thousand two
hundred miles; his distance from the Sun one
hundred and forty-four million of miles; and he
performs his diurnal rotation in 24 of our hours.
and 39 minutes. The light reflected from this
planet appears of a reddish dusky colour; which ap-
pearance, added to the deficiency of reflected light,
(this planet not having a Moon,) gives the idea of
its atmosphere being more dense than ours, and
that thus, by its greater refractive power, it sup-
plies the place of a Moon to that planet, refracting
and reflecting the light of the Sun for a considera-
ble length of time before that luminary rises above
the
LECTURE IV.
117
the horizon of places on that globe, and after he
has set below it. That excellent astronomer,
Dr. Herschel, has discovered two white circles
round the poles of this planet, which he thinks
originate from the snow lying about those parts.
The diurnal rotation of this planet is discoverable
by the spots on its surface.
Mars, when in that part of his orbit in which
the Sun is between us and him, is five times far-
ther removed from our Earth than when our Earth
is interposed between the Sun and that planet. In
the former situation he is said to be in conjunc-
tion, and when in the latter in opposition, in refe-
rence to his situation in respect to the Sun as seen
from our Earth. According to his distance from
us and the Sun at any time, such will be and ap-
pear his illumination; and, according to the for-
mer, his apparent size. In the quadratures he ap-
pears like a half-moon, but never horned like Ve-
nus, which convinces us that his orbit is exterior
to ours. This you will perfectly understand by the
planetarium. This planet being nearly twice the
distance from the Sun that our Earth is, his dia-
meter, as seen by the inhabitants of Mars, must
appear about half as large as it does to us; and
the heat and light be not more than one-fourth
part so great as at our globe: their year is nearly
twice as long as ours.
*Heat diminishing in proportion to the squares of the distances,
and the apparent diameters of objects in proportion to the distances
themselves inversely.
I 3
It
118
LECTURES ON ASTRONOMY.
It is perceived by the revolution of the spots on
the disk of Mars, that his axis is nearly at right
angles to the plane of his orbit; which must cause
the days and nights to be nearly equal to every
part of this globe.
Jupiter, the next planet in the system, affords
great scope for speculation, many things being ob-
servable of it not exhibited by any other planet of
it such as the variety of its lustre on different
parts of its surface, some parts appearing of a
duller and fainter illumination, and these latter oc-
cupying spaces on the planet similar to zones or
belts, that run parallel to each other and to the
plane of its orbit, to which its axis inclines but
very little indeed; on which account the days and
nights must be nearly equal to each other; and all
over this globe it is the same as with Mars, a per-
petual equinox.
The belts are not always discoverable on the
face of Jupiter; sometimes eight of them are per-
ceived, sometimes not more than one; if the chan-
ges in their appearances are observed, they seem
to be occasioned by the flowing of one belt into
another, as while one is decreasing another is in-
creasing; and what farther corroborates this opi-
nion is, there is lying between the belts obliquely,
at the time of these changes, a stratum of the
same hue with themselves.
Bright spots also appear on the face of this planet,
one of which is so remarkable, that the time of the
rotation of Jupiter on his axis is ascertained by it.
After
LECTURE IV.
119
After the discovery of this remarkable and sta-
tionary spot on the face of Jupiter, it disappeared,
and did not re-appear till fourteen years afterwards,
and then it was exactly in the same place, where
also it has continued to appear every fourteenth
year since the discovery, which was made in 1694,
by which his period is also determined.
This planet is the largest in the system, his di-
ameter being computed at eighty-nine thousand
miles, which is eleven times as much as that of
our Earth; and yet such is the amazing velocity of
his motion on his axis, that he revolves round it in
9 hours 56 minutes. The circumference of his or-
bit is estimated at three thousand one hundred mil-
lions of miles, and his motion in it twenty-nine
thousand miles an hour; so that he performs his
annual revolution in 4332 days 9 hours. His mean
distance from the Sun is four hundred and ninety
million of miles. Jupiter is attended constantly
by four Moons, which revolve round him, or ra-
ther round the centre of gravity between the pla-
net and themselves; these must afford Jupiter a
great portion of reflected light.
This planet is also nearer to our Earth when in
opposition than when in conjunction with the
Sun; and, his mean distance from that luminary
being a little more than five times farther than that
of our Earth, the inhabitants of that planet must
feel but one twenty-fifth part of the influences of the
Sun felt by us; and to them his apparent diameter
must be only one-fifth part of what it appears to us.
I 4
The
120
LECTURES ON ASTRONOMY.
The four satellites of Jupiter occasion that pla-
net to have four different months, according to the
period of each. It is supposed that the shortest
of these months contains only 4 days, and the
longest 41 days; the second about 8, and the
third 17 days.
The distances of Jupiter's satellites from each
other render them very distinguishable, and the
shadow they cast on his disk, when interposed be:
tween him and the Sun, as well as their eclipses in
passing through his shadow, prove them to be
opake bodies, and that they serve to afford reflect-
ed light to Jupiter in the absence of the Sun, as
the Moon of our Earth affords us.
The discovery of the satellites of Jupiter has
proved of some aid to navigators, the eclipses of
which have afforded them the opportunity of com-
puting their longitude at sea. As thus, having
noted the time in White's Ephemeris, or the Nau-
tical Almanac, in which a satellite will be im-
mersed in the shadow of its primary, in the longi-
tude of Greenwich, suppose it is at 7 o'clock in
the evening of such a day; and, being at sea, if
we do not perceive this circumstance till 9 o'clock
at night, the difference of time being two hours,
by allowing the number of degrees of the equator
equal to that space, which is known to be 15 de-
grees to an hour, we discover that we are in 30
degrees of longitude, which is west, because the
time is later than at London or Greenwich: - if
it happens two hours sooner, then we know that
we
LECTURE IV.
121
we are so many degrees east of London or Green-
wich. In practice, the observation is taken with
greater accuracy, allowing for the difference of
time-pieces; but the motion of our Earth on its
axis being uniformly performed in the same time,
15 degrees of the equator or circle of our globe,
directly situated between the two poles of the axis
of motion, must always be equal to one twenty-
fourth part of the time in which it performs its re-
volution.
The velocity of light, I have previously inform-
ed you, was also ascertained by these eclipses; so
that we may readily admit that many important
truths have been sanctioned by this admirable in-
vestigation, for the idea of which we are indebted
to Gallileo.
Saturn, the next in the system beyond Jupiter,
is so far removed from us and the Sun, that inves-
tigations of his phenomena are not so attainable as
those of Mars or Jupiter.
His distance from the Sun is nine hundred mil-
lion of miles; and he performs his annual revolu-
tion in rather more than 29 of our years. His dia-
meter is supposed to be seventy-nine thousand
miles. He is encircled by a luminous ring, which
is nearly as bright as the planet, which phenome-
non has occasioned various conjectures, but has
produced nothing decisive. It appears detached
from the planet, as in some situations a star has
been seen between the ring and its primary; for
such I conceive it most natural to call the planet,
on
122
LECTURES ON ASTRONOMY.
on whose affections it must I think be dependant;
as on no other grounds can we account for its con-
stant attendance on it, or the changes of its ap-
pearances; although some philosophers have form-
ed a different idea of their connection, in the in-
fancy of the observation, which subsequent obser-
vations seem to invalidate: they have supposed
this white appearance exterior to the planet to be
produced by the vapours which issue from its sur-
face, forming a sort of continuous white cloud; -
others, that it is occasioned by a vast number of
satellites disposed in the same plane, which, by
their affinity, blend their lights together, and so
form the appearance of one luminous body, which
affords an abundant quantity of reflected light to
that remote planet of the solar system. This, if
necessary, would consistently account for it; but
Saturn, being attended by seven moons, precludes
that idea, as those must be quite sufficient to make
up for the deficiency of intrinsic light, at the dis-
tance of those Moons from the Sun, by which
their illumination must be fainter than that of the
Moon which illumines our nights.
Yet, as nothing is created in vain, we natu-
rally wish to find out the use of this extraordi-
nary light, which we may suppose essential to the
comfort of the inhabitants of that planet; which
desire prompts me to offer my conjecture on that
subject, and will, I trust, be an excuse for my te-
merity.
On
LECTURE IV.
123
On account of the immense distance of the Sun
from this planet, may it not be necessary that it
should be encompassed by a peculiar fluid mass,
exterior to its atmosphere, to collect the rays of
light before they fall into the region of the atmos-
phere, by which they may acquire additional bril-
liancy and force; and thus compensate to the in-
habitants for the distance at which they are placed
from their grand vivifying principle, by transmit-
ting and reflecting the light, with such due lustre
and heat as may be essential to the circumstances
of that planet? This opinion I offer with ex-
treme diffidence; as, probably, in endeavouring to
throw additional light on the subject, I may only
evince the necessity of additional light to my un-
derstanding, in order to supply the deficiency of
my judgement.
When our eye is in the plane of Saturn's ring, it
becomes almost invisible to us, appearing only as a
dark band or line across the body of the planet.
It disappears twice in every revolution of that pla-
net round the Sun; at other times it appears more
or less inclined to the planet, and sometimes sur-
rounds the outward circle of its illuminated face,
so that we can distinguish it clearly from the
planet. When the eye of an observer is raised
above the plane of the ring, a shadow is per-
ceived above it on the planet. Besides this
ring, Saturn has two luminous belts, which are
permanent.
Saturn
124
LECTURES ON ASTRONOMY.
Saturn is about one thousand times as big as our
Earth, and three-quarters the size of Jupiter. He
always shews a full round face, but his light ap-
pears dull to us on account of his immense dis-
tance; from which latter circumstance his revolu-
tion on his axis cannot be ascertained by an ob
server on our Earth. His Moons all move round
his equator, which is inclined to the plane of his
orbit in about 30 degrees.
Saturn's ring appears to us quite distinct from
his disk when the planet is in 20 degrees of
Sagitarius, and then the northern parts of the pla-
net are turned towards the Sun, when it must
be summer to those places situated north of his
equator.
When he is in 20 degrees of Pisces, the ring
is quite shut, appearing only as a line upon the
equator; and, the equator being turned towards
the Sun, the days and nights must be equal to
all the inhabitants of that planet at that time. —
When the planet is in 20 degrees of Gemini,
the southern parts of it are turned towards the
Sun, and the ring again appears luminous and dis-
tinct; this is the time of summer with the in-
habitants of those parts.
When he arrives at
Libra, the Sun again being over his equator makes
the days and nights equal, and the ring again ap-
pears only like a line across the planet.
These positions seem to sanction my idea of the
ring being a peculiar region, adapted to the pur-
pose of affecting the intrinsic light in its approach
to
LECTURE IV.
125
to this planet; as it does not appear luminous but
in those parts which receive the direct influence of
the Sun's beams.
The last discovered planet, and most remote in
the system, is the Georgium Sidus, which was
discovered by Dr. Herschel. It is not discernible
without the aid of glasses of considerable power,
on account of its immense distance from the Sun
and from our Earth. It was first discovered near
one of the feet of Gemini. Its distance from
the Sun being twice that of Saturn, many of its
phenomena have not been discovered. Only two
Moons have as yet been perceived to attend
on this planet, though doubtless, on account of
its remote situation in respect to the Sun, it has
more. The regularity of its motion correspond-
ing to that of the other planets, and its moving in
the same direction, prove it to be one of our sys-
tem. Its mean distance from the Sun is nineteen
times greater than that of our Earth from it. By
observation of its progress in different parts of its
orbit, it has been found that it moves through it in
about 82 years, and that it is ninety times larger
than our Earth.
From the different phases they exhibit, it is
evident that all the satellites of the planets are
opake bodies, shining only by reflecting the light
of the Sun; and that they revolve round their
* Since this was written, I find Dr. Herschel has discovered six
of the Moons belonging to the Georgium Sidus.
primaries
126-
LECTURES ON ASTRONOMY.
primaries as those revolve round that grand vi-
vifying principle, situated in the centre of all their
motions by the kind and all-wise ordination of Pro-
vidence, by which they are compelled to accom-
pany their respective planets through the whole of
their annual revolutions.
Mars, Jupiter, Saturn, and the Georgium Si-
dus, include the orbit of our Earth, which is
made evident to us by their elongations and dif-
ferent appearances, as I shall hereafter illustrate.
Also, that the Sun is the central body round
which they must revolve, and that their orbits are
situated, in respect to each other, as I have de-
scribed.
The comets of our system remain to be ex-
plained; the astronomy of which, although im-
perfect, approaches nearer to certainty than that
of those who, living in remote ages, were unac-
quainted with the laws of gravity, and of those
also which regulate the subtile effluvia of the Sun,
&c.
These extraordinary bodies are found, by their
reflective power, to be opake. The matter of
heat and light darts from them like fiery tails; -
as when an insulated jar is receiving a full charge
from the electrical machine, it throws off its re-
dudancy, so do the comets emit a stream of fire
from their bodies on the side opposed to the Sun,
from which they receive their superabundant fire;
— therefore, if I may be allowed to reason from
analogy, I should suppose that by this mode do
the
LECTURE IV.
127
the comets throw off the redundant heat which
they must receive from the Sun, at the times of
their nearest approaches to him; and, conscious
of the happy equilibrium sought after by all na-
tural bodies, which is happily attainable by the
constitutional construction of their parts, I ven-
ture to intimate the possibility of this being the
cause of the effect we perceive of these motions
called fiery tails; - that the additional heat thus
issuing from these bodies prevents an accumula-
tion unfavourable to animal existence, supposing
these bodies to be inhabited, as we have great
reason to do, seeing that God has created nothing
in vain.
If my opinion of the appearances I have been
adverting to is futile, or any arguments can be
produced to invalidate it, I am open to convic-
tion; but till then I shall retain it, and think
myself excusable in advancing my ideas on the
subject, till the physical causes of these appear-
ances can be ascertained, all that has hitherto
been said of them, like my observation, amount-
ing to no more than mere hypothesis.
The other circumstances of the comets have
been pretty accurately ascertained by the admi-
rable and sublime Newton, such as the degrees of
heat, light, and motion, communicated to them.
Estimating the degree of heat each must receive
from the Sun on its nearest approach to that lu-
minary, he supposed the one seen in 1680 might
have retained its heat for twenty thousand years,
supposing
128
LECTURES ON ASTRONOMY.
supposing it were necessary that it should, which
we may conclude not to be the case, and that
therefore such an accumulation never actually
takes place. In this supposition I do not pre-
sumptuously mean to confute his assertion, as I
conceive that great man by no means intended
to convey an erroneous opinion, but that he meant
merely to shew us the immensity of that power
which could suffer such extremes of heat and
cold, without altering the happy indispensable
harmony of nature; and I am the more assured
of this, as, although the heat, he estimated might
be received by the comet which appeared in 1680,
was so intense and profuse as, by his calculation,
it would have been sufficient for the animation
of that planet for twenty thousand years, yet,
as he immediately after discovered that its pe-
riod was not more than five hundred and seventy-
five years, we may conclude so great a natura-
list as this great man could not admit that the
comet actually did retain so superabundant a
quantity of heat; therefore I conceive that I am
justified in asserting, that, such an inference not
being deducible from his calculation of the period
of this comet, or from the universal laws of na-
ture, although he advanced the postulatum, he
meant not to convey such an idea as that they
actually would retain such a superabundant quan-
tity of heat.
But it is unnecessary for me to
perplex you with speculations which all nature so
clearly determines upon.
The
LECTURE IV.
129
The comets all revolve round the Sun in el-
liptical orbits; but the cause why all the bo-
dies of our system do so I shall inform you of,
(when treating more particularly of their periods,)
and why those of the comets are peculiarly long
ellipses.
These bodies disappear from our view, and
again become visible, according to their situa-
tion in respect to the orbit of our Earth; as, in
revolving in very long ellipses, they are sometimes
too remote for our inspection, their greatest dis-
tance from the Sun being far beyond the orbit
of the Georgium Sidus: these bodies are not
much larger than our Moon. When they are in
those parts of their orbits in which we can see
them, some things may be observed of them,
which seem to corroborate my ideas.
That the tail, or fiery matter, exhaled from these
bodies, is always in the direction of the Sun's
beams, and on the opposite side of the comet
from the Sun; and, the nearer they are to that
luminary, the longer is the stream of fire emitted
from them. This luminous tract appears diffe-
rently formed, according to the situation of it in
respect of an observer on our Earth.
In fig. 2, plate 6, let S represent our Sun, M the
orbit of Mercury, V that of Venus, T that of our
Earth, M of Mars, J of Jupiter, S of Saturn, and
ABCD that of a comet; A at its greatest distance
from the Sun, and B its least. You observe, that
in the former it is far beyond all the orbits of the
K
planets,
130
LECTURES ON ASTRONOMY.
;.
planets, and in the latter it is almost as near
to the Sun as within one-sixth part of the Sun's
diameter from it. When the comet arrives at
F, which is near the orbit of Mars, it emits
but a small quantity of fire; as it approaches
nearer to the Sun, as at E, the tail becomes
longer; when at B, it appears longest of all,
being its nearest situation to the Sun; as it re-
volves from B to D, receding from the Sun by
degrees, the tail becomes less and less; and when
it arrives at G, the orbit of Jupiter, it is not
seen without a telescope of great power. The
length of this tail is sometimes as much as 40
degrees of the heavens; a space equal to about
eighty million miles. The periods of the comets,
although they may be, and have been, pretty
accurately ascertained, yet, on account of the
length of that part of their orbits in which they
are hid from our view, and the time taken up
to perform it in, also their similar appearances,
no great accuracy in this part of Astronomy can
be expected, as their motion in some parts of
.their orbits may be slower than is calculated for;
and, when we do see a comet, we can no other-
wise assert its identity, that it is the one ex-
pected to appear at the time, but by compa-
ring its direction through the great expanse with
the track pursued in the other case; in which
latter also we are subject to be deceived, as there
are an innumerable multitude of comets, and the
orbits of some of them may be performed so
nearly
LECTURE IV.
131
nearly in the same plane as to baffle our discrimi-
nation.
That their periods have not been fixed upon im-
mutable principles is evident by those which, ha-
ving been expected at stated times, at one time
appearing agreeably to the prediction, at another
within a certain short space of time after the
period previously anticipated, and at another not
at all. The two former circumstances were ob-
served of the one which was first seen in 1456,
the time of which was calculated at 75½ years,
and which was actually seen, or supposed to be
seen, as a comet did appear at the several pe-
riods, i. e. in 1531, 1607, and 1682; but in 1758,
when it was again expected, it did not appear;
but one was visible in 1759, about six months
after the predicted time, which was supposed
to be the same. The latter circumstance, of a
comet appearing, as supposed, exactly at the pe-
riod fixed, at one time, and not appearing again
at or near its expected return, was experienced re-
specting the one which was seen in 1661, which,
being 129 years from its former appearance, occa-
sioned great expectation of its return in 1789, but
no comet then appeared, or has since been per-
ceived of any note.
These bodies revolve round the Sun in all direc-
tions, some moving easterly, some westerly, some
northerly, some southerly, some obliquely, and
some perpendicularly, to the plane of the planet's
orbits. These circumstances must render it still
K 2
more
132
LECTURES ON ASTRONOMY.
more difficult to ascertain their identity and affec-
tions. Indeed I think the greatest philosophers
and ablest mathematicians must confess, that the
nature and affections of these bodies are far be-
yond their scrutiny and calculations.
Three of the comets have had their periods set-
tled, as near the truth as could be expected, yet
not, I think, permanently so. The first of these
is that which appeared in 1532, 1607, 1682, and
1759, which I have before-mentioned; the latter
appearance of which did not exactly answer to the
foregoing periods. Should it, in future, conform
to either, its period being supposed about 75 years,
we may expect its return in 1834.
The second appeared in 1532, 1661, and was
expected in 1789, but has not yet appeared;
therefore we cannot suppose the period of this yet
fixed.
The third is the one Sir Isaac Newton estimated
the heat of in 1680, and the period of which he
settled at 575 years; the accuracy of which calcu-
lation cannot be decided till the year 2255. The
velocity of the latter comet's motion, when it was
nearest to the Sun, was computed at eight hun-
dred and eighty thousand miles an hour.
•
When these motions were first discovered, it
was supposed they were the repositories of the
wicked, where they received punishment for their
crimes, and that their torments were occasioned
by the extremes of heat and cold; which ideas
originated in the opinion of the impossibility of
animal
LECTURE IV.
133
animal existence being supported under such vicis-
situdes; but (thanks to science and investigation)
these dreadful ideas are removed: we can view
these glories of the heavens without horror; and,
though we are not certain of their being made for
human beings in their rational state, yet we are
conscious that God can accommodate the animal
body to any degree of heat or cold, if he pleases;
supposing that these extremes are experienced by
the inhabitants of those bodies, which I do not
think is the case, as I imagine that the superabun-
dant heat is thrown off from those globes in the
manner I have been describing, and only a suffi-
cient quantity retained for all the circumstances of
these planets.
Let stupid Atheists boast the Atomic dance,
And call these beauteous worlds the work of chance;
But nobler minds, from guilt and passion free,
Where truth unclouded darts her heav'nly ray,
Or on the Earth, or in th' etherial road,
Surveys the footsteps of a ruling God!
Whose single fiat form'd th' amazing whole,
And taught the new-born planets where to roll;
With wise direction curv'd their steady course,
Imprest the central and projectile force ;
Lest in one mass their orbs confus'd should run,
Drawn by th' attractive virtue of the Sun,
Or quit th' harmonious round, and wildly stray
Beyond the limits of his genial ray.
Mrs. ELIZ. CARTER.
Ilaving dwelt sufficiently on the circumstances.
of the size, distances,
&c. of the planets of our
K 3
system,
134
LECTURES ON ASTRONOMY.
system, it must naturally have excited
your curio-
sity to know how these have been ascertained of
objects so remote, and that are not accessible. ·
I shall therefore endeavour to convey to you
some idea of the mode by which mathematicians
acquire their knowledge of the comparative size
and distances of the heavenly bodies of our sys-
tem, and of their distances from each other; by
the application of which observation to the science
of mixed mathematics their real size and distances
are known, The instrument thus employed is
called a quadrant; by which the relative size and
distances of the bodies of our system are ascer-
tained, and a just idea of their comparative mo-
tions is formed, which renders it extensively useful
in practical Astronomy.
Every circle, great or small, being by mathema-
ticians divided into 360 parts, which they call de-
grees; ninety degrees, or a quarter of a circle, is
sufficient to measure all angles formed between the
horizon of any place on our Earth and the line per-
pendicular to it, which goes up to the zenith, as
in fig. 1, plate 7, where the line BC represents the
plane of the horizon, and ABC the quadrant,
AC the perpendicular to the horizon, and A the
zenith-point.
An angle is the opening between any two lines
which touch each other in a point; and the width
of the opening determines the portion of the circle
* A degree, when used in relation to the circumference of our
Earth, includes a space of 69 Engliſh miles.
included

Plate VII.
D
Fig. 1.
Fig. 2.
F
Fig. 5.
E
G
E
B
の
​D
H
I
Fig. 3.
H
E
S
Fig. 4.
E
H
K
G
B
R
F
M.Bryan delin
T.Conder sculpt
OF
LECTURE IV.
135
included within the angle, the length of the lines
not being in the least considered.
Let the lines CA and CB, fig. 1, plate 7, re-
present a pair of compasses, and the curved lines
AB, DE, and FG, the quarter of so many cir-
cles of different sizes. You perceive, that al-
though each of these differs from the others in size,
yet that each contains the same portion, or a
quarter, of a circle; and thus it would be from
the smallest to the largest that could be formed,
they would all contain exactly 90 degrees
each; by which simple observation, the compa-
rative measure of angles may be extended to an
indefinite distance.
The altitude of a star above our horizon, and
its situation in respect to the points of the com-
pass, may also be known by the application of
this instrument. The one represented fig. 2, plate
7, is called a quadrant of altitude, from that use
of it.
It is mounted on a pedestal, and is moveable.
round an axis at D, which affords the opportunity
of placing the quadrant in any vertical position,
inclining it more or less to the horizon, as occasion
requires.
The circle EF of this instrument is intended to
represent the plane of the horizon; and on it the
points of the compass are graduated,
In the centre of this plane, the pedestal moves
in a socket, so that the quadrant may be directed
towards any point of the horizon. Upon the ra-
K 4
dias
136
LECTURES ON ASTRONOMY.
dius CB of the quadrant, two sights are perfora-
ted; on the point B a dark glass is placed, to use
for the inspection of the Sun. The end C has a
large hole, with cross-wires, by which we may
perceive the ascent or descent of the Sun, or any
other object, through the opposite sight. There is
also below it a small hole, which is used to take
the Sun's altitude on the opposite sight. The arm
E shews the point of the compass in which a ce-
lestial object appears.
The screws, GHI, are to adjust the plane of
the quadrant to the exact level of the horizon,
which is the first part of the adjustment of this
instrument, and which is ascertained by placing
the plane of the quadrant in different situations of
it, in respect to the points of the compass, till the
line of sight is, in all of them, perpendicular to
the plate of the quadrant, or plane of the hori-
zon, which may be effected by placing the line of
sight only in two opposite situations of the hori-
zon, and observing that the plumb-line touches
the plane of the quadrant in both of them:
thus:
Bring the index to 0°, and mark the degree cut
by the plumb-line on the plane of the quadrant;
then move the index to 180°, which is exactly op-
posite to 0°, and observe the degree cut by the
plumb-line; if it is the same as in the former ad-
justment, then there will be no occasion to alter
the screws; but, if it is not, one or both of the
screws between 60° and 70° must be turned, till
the
LECTURE IV.
137
the plumb-line intersects the middle degree, or
part, between the two foregoing degrees marked:
then, observing what that degrce is, the index
must be turned to both the 90°, being at right an,
gles to the former part of the operation; and the
adjustment of the plumb-line to the last observa-
tion, or middle degree, must be made by turning
the screw at 180°, observing not to alter the other
screws. After one or both of these adjustments,
the quadrant will be ready for use, and will shew
you the distance of any celestial object from the
zenith-point; that is, how much it wants of being
perpendicular to you; also its height above your
horizon. Having found the object, direct the line
of sight towards it; and count the number of de-
grees from the plumb-line to the end of the qua-
drant next your eye, and that will shew the dis-
tance of the object from the zenith; and the de-
grees on the quadrant, from the plumb-line to the
end of the quadrant farthest from your eye, will
shew you its height, or altitude, above your hori-
zon. Lastly, to know what point of the compass
it is on, look at the degree on the plate of the ho-
rizon to which the quadrant is directed, allowing
for the variation of the compass, which you should
always fix the horizon of the quadrant to, previous
to making your observation, which is now 23°
west at London.
By a quadrant, and similar instruments, (the
principles of which are so simple that any person
may understand them,) we are able to obtain an
accurate
138
LECTURES ON ASTRONOMY.
accurate relative measurement of the circles of the
heavens, and the distances of the heavenly bodies
from each other, which enable us to authenticate
the observations of the learned, although we are
not able to pursue their mode of investigation, in
ascertaining the real sizes and distances of those
sublime objects; and thus we reap the advantage
of abler heads, without the trouble and applica-
tion by which they procure that information they
so liberally afford us. Surely we are much indebt-
ed to those great men, who, by unwearied assidu-
ity, have supplied us with such useful knowledge,
whereby we are enabled to apply their calculations
without any great mental exertion, and are as cer-
tain of their validity as if we were to fathom the
depth of that sublime science which furnishes us
with such valuable truths, by the observation of
those circumstances which corroborate their pre-
vious intimation.
Modern astronómers and mathematicians de-
serve our highest esteem and commendation, who,
by a communicable spirit, liberally extend the
province of science, and thereby confer a lasting
benefit on society: not like the ancients, who,
contracted in their ideas, and wishing to be consi-
dered as superior beings, hoarded up their scienti-
fic principles for the purpose of ostentation:
and what was the consequence of their selfish and
mysterious conduct? Nothing less than, in some
cases, the total subversion of all their knowledge;
which dying with them, the succeeding genera-
tions,
LECTURE IV.
139
tions, uninstructed in their theories and investiga-
tions, and perhaps not possessing the same spi-
rit of inquiry, the science became neglected or
perverted; and thus all the advantages which
had been procured were lost to mankind.
Such conduct is, like the folly of the avaricious
man, who hoards up that which, at his death,
cannot profit him; and which devolves to those
who, having been circumscribed by his parsimony,
are unacquainted with the use of riches; there-
fore, setting no value upon the means they pos-
sess of communicable kindness and rational a-
musements, too frequently run into excesses, and
squander their time in useless, if not dangerous,
pursuits; by which the intention of their prede-
cessor is frustrated: whereas, when both the
philosopher and the rich man give glory to God by
a free communication of their gifts, and a proper
application of them, the science of the former is
extended, and the riches of the latter usefully em-
ployed.
What Armstrong has pointed out, as the pro-
per use of riches, is equally applicable to the
extensive communication of intellectual acquire-
ments; and, therefore, in agreement with my
comparison between them, I shall conclude this
Lecture in his words:
But for one end, one much-neglected use,
Are riches worth your care (for, Nature's wants
Are few, and without opulence supply'd):
This noble end is, to produce the soul,
Τα
140
LECTURES ON ASTRONOMY.
To shew the virtues in their fairest light,
To make Humanity the minister
Of bounteous Providence, and teach the breast
That gen'rous luxury the gods enjoy.
ARMSTRONG.
END OF THE FOURTH LECTURE.
[ 141 ]
LECTURE V.
THE MANNER IN WHICH ASTRONOMERS AND
MATHEMATICIANS ESTIMATE THE REAL SI-
ZES AND DISTANCES OF THE BODIES BELONG-
ING TO THE SOLAR SYSTEM.
ABERRATION OF LIGHT.
AND OF THE
Of heav'n my strain's begun! From heav'n descends
The flame of genius to the human breast!
But not alike to ev'ry mortal eye
Is this great scene unveil'd: for, since the claims
Of social life to diff'rent labours urge
The active pow'rs of man, with wise intent
The hand of Nature on peculiar minds.
Imprints a diff'rent bias, and to each
Decrees its province in the common toil.
AXENSIDE.
MATHEMATICIANS and astronomers acquire
their knowledge of the real sizes, distances, and
situations, of the heavenly bodies of our system,
by means of plane and spherical trigonometry, pa-
rallax and refraction, the apparent diameters
of bodies at certain distances from our Earth,-
the diminution and velocity of light; investiga-
tions minutely and deeply entered into by them;
but which studies, extensively considered, do not
come within the sphere of knowledge I wish to
conduct my pupils into, being unnecessary to their
peculiar
142
LECTURES ON ASTRONOMY.
peculiar province in life to comprehend all the
phenomena they prove; more especially as we
are furnished with the result of them all, which
we are enabled to apply to our entire satisfaction.
The study of mathematics would be a misappli-
cation of your time, which might be justly at-
tributed to vanity and ostentation, and be consi-
dered unbecoming your character as females, by
employing that time which is more usefully oc-
cupied in pursuits adapted to your situation in so-
ciety, and as the validity of astronomical compu-
tation may be proved by those instruments I have
provided, aided by your reason.
For the foregoing reasons, I shall also avoid
introducing into this work astronomical tables for
computation; although I might do so from those
authors who have published them; but, as you
would not understand the principles upon which
they are constructed, they could afford you no
more satisfaction than you can derive from merely
examining the result of them in an Ephemeris, as,
being unacquainted with the sublimer branches of
the mathematics, you could only derive a superfi-
cial knowledge of them. Nor could I, for the
same reasons, define them properly; and, there-
fore, to attempt it would be deviating from my
settled rule of conduct in all I instruct you in, by
communicating that which I did not fully compre-
hend; a folly of all others the most inexcusable in
those who teach, and one which I trust will never
be imputed to me.
To
LECTURE V.
143
To those who, being acquainted with the elements
of mathematics, wish to understand the construc-
tion of astronomical tables, I recommend Dr. Hut-
ton's Mathematical Dictionary, in which they will
find ample scope for their abilities, as well as the
most clear elucidations, which are calculated to in-
Struct, not confound, the student.
Having premised so much, I shall content my-
self with bringing you acquainted with the nature
of those things mathematicians apply to the sci-
ences they cultivate, in order to ascertain the real
sizes, distances, &c. of the heavenly bodies, .with-
out perplexing you with theories too profound for
your contemplation.
What I have already related of the general na-
ture and properties of light will render the postu-
lata, I am about advancing, intelligible; and the
theorems in trigonometry, subjoined to these Lec-
tures, will assist you in comprehending the practi-
cal part of the subject.
When light falls obliquely on a medium of a
different density, you know it is refracted; you
are also acquainted with the laws of refraction,
and that heat and light diminish as the squares of
the distances increase from the object which emits
them; also that the apparent diameters of bodies
decrease in proportion as we are farther removed
from them, directly as the distances themselves;
i. e. at twice a given distance they appear half as
large, and at four times that distance a quarter as
large, and at five times the distance only a fifth
part
144
LECTURES ON ASTRONOMY.
part as large, and so on.
But heat and light di-
minish as the squares of the distances: as thus;
at twice the distance they are four times less hot
and light; at three times the distance nine times
less, and so on. The bulk or solid contents of
the heavenly bodies are computed by their diame-
ters, and their comparative bulks by the cubes o
their diameters; i. e. if the diameter of one body
be double that of another, then its bulk is eight
times larger than that of the smaller; if the dia-
meter be three times greater, then it is twenty-se-
ven times bigger, being calculated thus: twice 2
is 4, and twice 4 is 8,also, 3 times 3 is 9, and
3 times 9 is 27. Let us now apply these general
laws to particulars.
As the quantity of heat and light thrown off
from the surface of the Sun must become thinner
and thinner as it recedes from him, on account of
its divergence, those planets of our system, which
are most remote from that luminary, must have a
less portion of his influence impressed on them
than those which are situated nearer to him; and
this force must be inversely in proportion to the
squares of their distances, throughout the whole
system of planets; which positions the observa-
tions of astronomers upon the affections of the
planets serve to authenticate.
The direct influence of the Sun's rays can never
be received on any part of our globe but that to
which he is vertical, so that he is never seen in
his right place by any but those to whom he ap-
pears
LECTURE V.
145
pears in their zenith-point; at the time of his be-
ing in which, they see him in his true situation; at
other times, and at other places, his rays falling
obliquely, they are refracted, and therefore he is
not seen in his proper place.
The same happens in regard to all the heavenly
bodies shining either by intrinsic or reflected light;
for, when that light falls obliquely upon our dense
atmosphere, it is refracted; therefore we never see
any celestial object in its true place but when it is
in our zenith-point.
To estimate the deviations of the rays of light,
in order to ascertain the true place of a celestial
object, is one of the most difficult parts of astro-
nomical calculation.
The more we consider the intricacies of the su-
blime sciences of Astronomy and Mathematics,
the more do we admire the superior sagacity and
perseverance of those who have gone extensively
into those investigations; it requiring most asto-
nishing strength of mind to bear such continual
exertion of the mental powers, and a disposition
the most tranquil to endure it.
It will be impossible in this part of my subject
to avoid repeating occasionally what I have before
advanced; for which unavoidable circumstance I
hope to be excused.
You know that the refractive power of our at-
mosphere occasions that faint light, which in the
morning we call Aurora, and in the evening twi-
light. Astronomers have estimated the degrees
L
of
146
LECTURES ON ASTRONOMY.
of refraction at every degree of altitude; and have
found that they diminish in their degrees as the
Sun approaches the zenith-point. The latter part
of this hypothesis is undeniable; but the former
cannot surely be settled for all seasons at the same
ratio, as it must depend on the state of the atmos-
phere.
In illustrating the effects of the refractive power
of the atmosphere, I must refer you to fig. 3,
plate 7, in which ABCD represent our Earth,
EFGH its atmosphere, which decreases in den-
sity as it is more distant from the surface of the
Earth, as has been discovered by the barometer;
the mode of applying which to this observation I
have previously communicated.
Suppose A, fig. 3, plate 7, to be the place of a
spectator on our Earth, who is viewing the hea-
vens; let S be supposed the Sun, which is not yet
risen above the horizon IK of the spectator at
A. When the Sun's beam, represented by the
line from S to L, touches the atmosphere at M, it
will be turned from its straight course, and be so
refracted, that, to the observer at A, the image of
the Sun will appear at s, in the direction s A; by
which means he will see that luminary before he
has risen above his horizon I K.
Again, when the
Sun is above the horizon IK of the spectator at
A, in the direction s N, the rays of light falling
upon the atmosphere at N, and being refracted,
are drawn towards the perpendicular A P, and ap-
pear to the observer at A in the direction Q A.
When
LECTURE V.
147
When the sun-beam becomes a tangent to the at-
mosphere, as at R, then twilight ends; because
the light does not fall upon any part of our atmos-
phere. Refraction sensibly takes place when the
Sun is about 18 degrees below our horizon. The
circumstance of the Sun being about 18 degrees
below our horizon, at the beginning of Aurora in
the morning, and at the ending of twilight in the
evening, has enabled mathematicians to calculate
the sensible height of our atmosphere, but with
certain limitations, I imagine, allowing for the
state of it, as it must sometimes be more strongly
refractive than at others.
The state of the atmosphere is often very im-
properly expressed by those unacquainted with its
nature, who, when their spirits are depressed, as-
cribe that effect to the heaviness of the air;
whereas, on the contrary, it is produced by its
rarity or lightness; which rendering its impres-
sions weaker on our bodies, not being sufficient
to counteract the spring of the air within them,
the blood-vessels and nerves become relaxed; but
when the air is more dense, (as is always the case
when we see the clouds and vapours buoyed up by
it,) its weight and elasticity, balancing the internal
air, braces our whole system, making us feel light
and sprightly. The barometer evinces this very
clearly, the quicksilver falling in it when the sky is
obscured by clouds and vapour, and rising when
these are dispersed and the blue canopy of heaven
encircles us.
L 2
As
148
LECTURES ON ASTRONOMY,
As the state of the atmosphere must determine
its power of refraction, the length of the time we
have the image of the Sun refracted to our view,
before he actually rises above our horizon, must
be variable. When the sky is clear, by the greater
density of the atmosphere, we see the Sun about
ten minutes before he transits the horizon; but
when it is cloudy, sometimes not above six mi-
nutes, the time differing according to the density;
which difference, from the most dense to the most
rare state, is found to be about four minutes.
We also see the image of the Moon before she
transits our horizon, which, in the state of the
densest atmosphere, is not more than two minutes
the orbit of the Moon making but a small angle
with that of our Earth.
s;
The duration of the Aurora and twilight de-
pends on the obliquity of the ecliptic circle, or
Sun's apparent path with the horizon, in the par-
ticular part where the Sun is, on account of the
length of time he is passing through the 18 de-
grees below the horizon, which are counted per-
pendicular to it; and therefore the more oblique
the direction of the Sun's path to the horizon is,
the longer must it be in passing through that space.
On the latter, the duration chiefly depends, and is
always calculated in proportion to, allowing some-
thing, I should suppose, for the difference of re-
fraction in reference to the different state of the at-
mosphere at different seasons.
Reflecting
LECTURE V.
149
Reflecting on the laws of refraction, that when
the light falls from a rare on a denser medium, it
is refracted towards the perpendicular of the den-
ser medium, we are sensible that the object, by
this law, must always appcar higher than it really
is; yet not actually so high as if refraction alone
caused the deviation of the object from its true
place; for, parallax, (the nature of which I shall
explain to you,) acting in a different direction, di-
minishes the height of the object.
It is not only refraction and parallax which
cause our senses to be deceived in respect to the
real situation of the heavenly bodies, - the aber-
ration or motion of light assists in the delusion, if
not allowed for.
Let us first consider what relates to parallax,
and the meaning of the term.
The arch of the heavens, intercepted between
the true and apparent place of a celestial object,
(independant of refraction) is called its paral-
lax.
The true place of a star is referred to the obser-
vation of it, as if taken from the centre of our
Earth, which not being practicable, in order to
ascertain its true place, the difference must be al-
lowed for, as thus:-
Let ABCD, fig. 4, plate 7, represent our
Earth, and T the centre of it. Suppose A the
situation of a spectator on it,
and EFG the
orb or sphere of the fixed stars, also eƒ g
that of Jupiter, or any other planet.
L 3
If the
spectator,
150
LECTURES ON ASTRONOMY.
spectator, on the surface of the Earth at A, be
supposed looking at the Sun, Moon, or a planet
at f, it will appear at G, which is its apparent
place; whereas that in which it would be seen
from the centre of our Earth, at T, is the point F,
which is its true place. The difference of place is
called the parallax of altitude, and is the difference
of the angles formed between two visual rays and
the perpendicular AE; one of the former being
directed to the centre, and the other to the surface,
of the Earth.
The parallax of altitude is measured on the
arch of the great circle, which is between the true
place F, and the apparent place G. It is also
called the diurnal parallax, as it depends on the
diurnal motion of our Earth.
The parallaxes used by astronomers are many;
and which they are obliged to allow for, when ta-
king the declination, right ascension and descen-
sion, longitude and latitude, of the heavenly bo-
dies; all of which differ in respect to the parallax.
To define all of these by diagrams would be tedious,
and is unnecessary to you, as reference to them is
not requisite to any but those who study the ab-
struse mathematical demonstrations of these truths,
who will not need a definition of them in this
place; therefore, having given you an idea of
what is meant by parallax, I shall only define the
meaning of its different applications in Astronomy.
Parallax of declination means the diminution of
the declination of an object by the parallax of al-
titude.
LECTURE V.
151
titude. The parallax of altitude I have fully ex-
plained, to which you must transfer your idea, in
respect to the meaning of parallax of declination,
right ascension and descension, longitude and la-
titude.
Parallax of right ascension is reckoned on an
arch of the equatorial, as you will perceive, when
working the celestial problems annexed to these
Lectures; the parallax of altitude increases the
ascension and diminishes the descension; these are
both counted on the equatorial circle.
Parallax of longitude is an arch of the ecliptic,
shewing how much the parallax of altitude in-
creases or diminishes the longitude.
Parallax of latitude is the arch of a circle of lati-
tude, whereby the parallax of altitude increases or
diminishes the latitude.
There are also other parallaxes, one of which
is the angle formed by two right lines, drawn
from the Sun to the Earth, and from the Sun to
the Moon, at either of their quadratures.
Another is called the parallax of the annual or
bit of the Earth, which is the difference between
the place of a planet, as viewed from the Earth
and the Sun.
The parallax of altitude decreases the altitude of
the object, as you may see by fig. 4, plate 7; in
which F is the true place, being referred to the
centre of the Earth at T, and G its apparent
place, at which it appears to a spectator on the
surface of the Earth at A, the true place being
higher
Im 4
152
LECTURES ON ASTRONOMY.
higher than the apparent; which effect of the pa-
rallax of altitude being contrary to that of refrac-
tion, (which elevates the object's apparent situa-
tion,) in some cases makes the effect of refraction
very inconsiderable.
The parallax, as well as the refraction, being
greater in proportion to the greater obliquity of
the object to the horizon, they must both diminish
in proportion as the object rises towards the ze-
nith, where it is nothing; therefore neither paral-
lax nor refraction have any effect on objects in our
zenith.
Parallax does not affect our observations of the
fixed stars, as viewed from our Earth, on account
of their immense distance from it; the Earth being
but like a point, its diameter is as nothing, as well
as that of the Earth's annual orbit; from which
cause it is that astronomers cannot estimate the
sizes or distances of the fixed stars, not being able
to form an angle with any of them, either by the
semi-diameter of our Earth, or by that of its orbit.
A parallactic angle, or parallax, which means
the same, is the angle formed in the centre of the
Sun or a planet, by two right lines drawn, the one
from the centre of the Earth, and the other from
its surface.
The parallaxes chiefly used by astronomers are
those, which arise from viewing the object from the
centre of the Earth; and considering it as viewed
from the centre of the Sun, and also from the sur-
faces of the Earth and Sun, and from all com-
pounded ;
LECTURE V.
153
pounded; these are used to discover the sizes and
distances of the planets of our system, both in re-
spect to the Sun and our Earth. The difference
between the place of a planet, as seen from the
Earth and Sun, is called the parallax of the Earth's
annual orbit. The nearer a planet is to the
Earth, the greater is its parallactic angle.
Suppose, in fig. 5, plute 7, T to be the centre
of our Earth, and ABC its surface, DEFG part
of the orbit of Jupiter, and HIK the same por-
tion of the orbit of Mars.
The angle BET, made by the more distant
planet with our Earth, is less than BIT, that
made with the nearer, as may be seen by the
portions of the semi-circle ABC between each.
In regard to the parallax of the Moon, several
things are to be allowed for, her meridian altitude,
the equation of time, her longitude, latitude, de-
clination, &c.
The Sun, although an immense body, yet being
so far removed from our Earth, has but a small
parallax with it; and therefore astronomers have
recourse to the parallaxes of the planets nearest
to our Earth, Venus and Mars, from which that
of the Sun is deducible, as by knowing the mo-
tions of the Earth and planets, they are able to as-
certain the distance between them and our Earth,
for any part of their orbits, and also between them
and the Sun; by which they are enabled to find
that of the planet from the Sun, at the time of its
conjunction with, or opposition to, that luminary;
in
154
LECTURES ON ASTRONOMY.
in the former case, by adding the distance of the
planet from our Earth at that time, to its distance
from the Sun in that part of its orbit, the sum
shewing the distance of the Sun from the Earth,
when the Earth is in that part of its orbit; also by
observing the apparent diameter of the Sun at that
time, and knowing the diminution of objects ac-
cording to their distances from the place of obser-
vation, they discover the size of the Sun; as they do
that of all the planets by the foregoing observations.
When Mars is in opposition to the Sun, know-
ing that he is twice as near to our Earth as the Sun
is, by observing his parallax with our Earth,
which must be twice as much as the Sun's, they
discover the parallax of the Sun, and are able to
make the same inferences as in the former case.
Cassini, by observation of Venus, when in her
inferior conjunction, (at which time he knew how
much nearer she was to our Earth than the Sun,
and consequently that her parallax must be so
much larger with our Earth than with the Sun,)
he found the Sun's parallax with our Earth was
10 seconds, and that his mean distance from it
was equal to twenty-two thousand semi-diameters
of the Earth, or eighty-one million of miles; the
semi-diameter of the Earth, at the equator, being
computed at three thousand nine hundred and se-
venty-eight miles.
The distance of Venus from the Earth, at the
time of her being in a direct line between it and
the Sun, is less than her distance from the Sun;
and
LECTURE V.
155
and her distance from the centre of the Sun is
found by her passage over the Sun's disk, which is
called the transit of Venus.
The transit of Venus has excited the particular
attention of astronomers. That of Mercury, at
the time of his inferior conjunction, might also be
observed, as, at that time, he appears like a dark
spot on the Sun's disk; but, on account of his
nearness to that luminary, the difference of the pa-
rallax between him and our Earth and the Sun and
the Earth is so little as not to answer the purpose,
not being sufficient to make any deduction from.
But the parallax of Venus being nearly four times
as great as the solar parallax, on account of her
being so much nearer to the Earth than Mer-
cury, and farther from the Sun, it causes great
difference in the time in which he is seen to be
passing over the Sun's disk from different parts of
the Earth.
It was Dr. Halley who was so particularly
anxious to engage the attention of astronomers
to this mode of determining the Sun's parallax,
and for which purpose he furnished the Royal
Society, in the year 1691, with an account of the
particular periods when such transits would hap-
pen, assuming the position, that, if the interval
in time, between two central transits of Venus
over the Sun, (Venus not always passing over the
centre of the Sun's disk in every passage, on ac-
count of the obliquity of her orbit to the cen-
tral solar ray,) could be calculated to a second in
two
156
LECTURES ON ASTRONOMY.
two places of different degrees of longitude, the
Sun's parallax might be calculated pretty accu-
rately, allowing for the difference of time at which
it should appear at each, on account of the di-
urnal motion of the Earth: as thus. Suppose
one observer is situated 90 degrees west of the
other, it will be six o'clock in the morning at the
former situation when it is noon at the latter; in
agreement with which local circumstances, that
allowance must be made. Then let us suppose
that Venus transits the centre of the Sun at the
former place at 7 minutes past 6 o'clock, and at
the latter at 12 o'clock at noon. Deduct 6 hours
for the difference of longitude, and the remainder
will be 7 minutes of time; which time, being
converted into parts of a degree of the equator, is
called Venus's horizontal parallax with the Sun. I
shall illustrate this part of the subject of Astro-
nomy in the manner of Ferguson, who has fami-
liarly explained the mode by which those grand
objects of the size and distance of the Sun have
been ascertained, and which will give you a good
general idea of parallax. It is called taking the
horizontal parallaxes of the Sun and Venus, be-
cause it refers only to those bodies and the Earth
in a horizontal position, and is the mode by which
all the parallaxes of the heavenly bodies of our
system are worked, in order to discover their real
distances from each other; which being thus
known, their sizes are estimated by the apparent
diameters at those distances.
The
Plate VIII.
Fig. 1.
F
G
72339
H
h
G
3
H
!
Fig. 5.
M.Bryan del
10
20
Fig. 2.
7.8333
Fig. 3.
30
W/
T
W
-27067
B
F
D
E
37667 B EM
Fig. 4.
G
T.Conder sculpt
LECTURE V.
157
The Sun, on account of his immense distance
from our Earth, when viewed from two places on
its surface, will appear nearly in the same point of
the heavens; but Venus, being less than the Sun,
and almost four times nearer to the Earth, when
she passes over the Sun's disk, will appear at the
same time to be on different parts of his surface, to
two spectators placed on different parts of the
Earth.
In fig. 1, plate 8, S is intended to represent
the Sun, V Venus, and ABDE the Earth. Sup-
pose one observer to be at A, another at B,
and a third at D, viewing Venus at the same
instant. To the observer at A, Venus will ap-
pear upon the Sun at F, as she will be seen by
him in the right line AVF. To the observer at
B, she will appear upon the Sun at G, in the line
BVG: and, to the observer at D, she will appear
on the Sun at H, in the direction DVH.
positions are very clear, as the lines represent
the visual rays of the spectators, observing the
phenomenon from different parts of the Earth's sur-
face.
These
The elliptical form of the planets' orbits causing
them to be at different distances from the Sun,
and from each other, in different parts of them
to know their mean distance from the Sun, it be-
comes necessary to compare their least and great-
est distances, and take a mean between them; in
order to which, observation must be taken of the
transit of Venus at two different distances from the
Sun,
158
LECTURES ON ASTRONOMY.
Sun, as well as when the Earth is in different parts
of her orbit; and, when the mean distance of one
planet is known, all the rest may be discovered by
that standard.
Ferguson has shewn what the difference of the
parallaxes is, in two different parts of the orbits
of Venus and our Earth; we will, therefore, pur-
sue his explanations, referring to the diagrams by
which he illustrated them. Fig. 2, plate 8, has
the Earth, abde, placed nearer to the Sun, S,
than in fig. 1, plate 8, consequently Venus is near-
er to the Earth; and the arc, a d, intercepted be-
tween the two observers placed on the Earth's sur-
face at a and d, bears a greater proportion to the
distance of Venus from the Earth, than it does in
fig. 1, plate 8; i. e. the angle formed between
them is larger, because their distance from each
other is less.
As the space, f g h, in fig. 2, over which Venus
passes, is longer than FGH, fig. 1, the planet
will be longer in passing over the former than over
the latter; for, the nearer the Earth is to the Sun,
the greater will be the space through which Venus
will appear to move on the Sun's disk; which is
occasioned by the real motion of the Earth on its
axis, on which the observer is placed, and, of
course, by which motion he is carried along
therefore, you perceive, that the nearer the Earth
is to the Sun, the greater will be the space that
Venus will appear to us to describe on its surface,
and consequently the longer will she be in passing
over
LECTURE V.
159
over it. The real motion of Venus in her or-
bit, compared with the time she takes in passing
over the Sun's disk, gives her parallax, as I have
previously informed you.
These positions we are able to authenticate by a
quadrant to our entire satisfaction. - Having ex-
plained the principles on which the sizes and dis-
tances of the bodies of our system are known, I
shall next treat of the mode of computing their
motions in their orbits.
By the laws of motion it is discovered, that the
velocity of a body moving round a centre, will
be in proportion to the squares of its distance
from its centre of motion compared with its size;
therefore, the real size of the planets of our sys-
tem being known by their apparent size at known
distances, and those distances being also ascer-
tained, their velocities have also been calculated,
and which have answered accurately to their
known periods.
Let us consider the effect of the apparent dia-
meter of objects, at different distances, by re-
curring to those of the Sun and Moon. These
appear nearly of the same magnitude as viewed
from our Earth, although their real sizes are very
different; this apparent equality of size is occa-
sioned by their different distances from the Earth.
The Moon being only two hundred and forty
thousand miles from us, whereas the Sun is nine-
ty-five million of miles removed from our Earth;
and the bulk of the latter exceeding that of the
former,
160
LECTURES ON ASTRONOMY.
former, in the due proportion, makes them at that
difference of distance both appear of the same
size; the apparent diameters of objects diminish-
ing exactly as their distances increase.
Although we have not entered along with those
great men (who have applied these known laws
to the grand objects which caused the investigation)
into all their complicated and tedious processes,
yet we are able to form a sufficient idea of their
mode of calculation, to give our assent to the
practicability of ascertaining the sizes, distances,
and motions of those heavenly bodics which are
not too remote for their scrutiny. Their indefa-
tigable zeal and accuracy in prosecuting their spe-
culations is evident, by the correctness with which
they calculate and foretel the appearances of ce-
lestial phenomena for different periods.
Those who wish to amuse themselves with ap-
plying the previous intimations of astronomers, in
order to satisfy themselves of their authenticity,
and to examine into the wonders of the celestial
regions, I recommend the use of White's Ephe-
meris, or the Nautical Almanac, which contain
every thing necessary for observation; and the
time being equated for every day in the year ren-
der them particularly useful. I purpose annexing
to these Lectures a Key to the Ephemeris, in
order that its use and application may be properly
understood by those not pre-acquainted with the
information it is intended to convey.
Having
LECTURE V.
161
Having explained two of the causes of our not
seeing celestial objects in their true place, ex-
cepting when they are in our zenith, - parallax
and refraction, — the remaining one must not pass
quite unnoticed, although not very essential to us,
being but trifling in its effects, and therefore
scarcely sensible.
This, which is called the aberration of light, is
occasioned by the motion of that fluid compared
with that of our Earth, and is referred to the
fixed stars more particularly. It was discovered
by that great Astronomer, Dr. Bradley, in the year
1725.
That there was an apparent difference in the
places of the fixed stars, when observed at the
same time for many nights together, had been
previously noticed by Dr. Hook; but the cause
which produced this change was not discovered
till Dr. Bradley unveiled the mystery. It was
long before this gentleman could ascertain the
fact he wished to discover, as it required instru-
ments and time-pieces of peculiar accuracy to
make the observations necessary for determining
it. The particulars of this subject are related
nearly in the following manner by Dr. Hutton in
his Dictionary:
Dr. Bradley was accompanied and aided in his
researches on this subject by Mr. Molineux. The
instruments they used were constructed by Mr.
M
Graham,
162
LECTURES ON ASTRONOMY.
Graham, on the accuracy of which was their chief
dependence.
On the 3d of December, 1725, they remarked
the bright star on the head of Draco, as it passed
near their zenith, and carefully took its situation
by the instrument, noting the time of observation:
they repeated this process on the 5th, 11th, and
12th, days of that month, at the same hour,
when there appeared no essential difference in its
situation.
On the 17th of December, amusing themselves
with the instruments, they again viewed this star,
not expecting to see any difference in its place;
but were much surprised to find that it passed a
little more southerly than before.
They knew that this change of place could not
proceed from the nutation of the Earth's axis,
(which motion I shall have a better opportunity of
explaining to you than the present offers,) there-
fore they suspected the accuracy of their instru-
ments; but on the 20th of December they repeat-
ed their observations of this star, and perceived
that it was removed still more southerly. This
dissipated their former fears, and animated them
to a farther scrutiny. Perceiving that the depar-
ture of this star from the pole was gradual, they
became very anxious to discover by what regular
cause this was produced; for which purpose they
observed how far it was removed at each observa-
tion, till it arrived at its most southern limit,
which it reached in March, 1726, and where it
was
LECTURE V.
163
was removed from the place of their first obser-
vation of it, December 3d, 20 seconds more sou-
therly.
In this situation it remained till the middle of
April, when they first perceived its return towards
the north. The beginning of June, it had arri-
ved at the same point in which they noticed it in
December; and from that time it pursued its nor-
thern direction till September; when, on its be-
coming stationary, they perceived that it had ad-
vanced 20 seconds nearer to the pole than it was
in December and March.
From September it returned towards the south,
till it had regained the same situation that it was
in on the day they first made observation on it, al-
lowing something for its difference of declina-
tion on account of the precession of the equi-
noxes.
Without following the learned Doctor through
all his observations, I shall just give you the result
of them.
After comparing all their observations, with va-
rious conjectures respecting the cause of those re-
gular deviations they had perceived, at last it occur-
red to Dr. Bradley, that it might proceed from the
progressive motion of light, referred to the Earth's
annual motion in its orbit. If, says he, light be pro-
pagated in time, the apparent place of a fixed object
would not be the same when a person is moving
any other direction than that of the line passing
through the eye, as it would be if the eye were
in
M 2
also
161
LECTURES ON ASTRONOMY.
also at rest, but would appear in different directions,
according to that motion of the spectator.
This is too evident a position to be doubted;
and therefore we have now two observations by
which we are assured of the velocity of light, and
that its motion is progressive like that of all other
bodies in motion.
Thus, having found that the apparent places of
the fixed stars, by the velocity of light, differed a-
bout 20 seconds from their true places, Dr. Brad-
ley, by trigonometry and calculation, proved that
the velocity of light is about ten thousand times
greater than the velocity of the Earth in its orbit;
for, knowing the mean velocity of the Earth's an-
nual motion, and comparing it with the apparent
changes in the places of a fixed star, he could
compute what were the relative velocities of light
and the Earth in its orbit; as the difference be-
tween the apparent places of the stars would be in
proportion to the two velocities.
These inferences making the velocity of light to
be the same as it was before estimated by obser-
vation of the eclipses of Jupiter's satellites, -
who will venture to confute the validity of as
clear a fact as ever was demonstrated?
Having conducted you thus far, I shall close
my Lecture, that your imaginations, not being too
crowded, may have room to exercise themselves,
by reflecting with due attention on the wonderful
and benevolent laws which govern all those pro-
cesses of nature, with which you are already ac-
quainted,
LECTURE V.
165
quainted, before I introduce you to the other won-
ders and beauties of the creation; so preparing
you by degrees to contemplate such a glorious as-
semblage of divine things as you will have exhi-
bited to your understanding in the course of these
Lectures.
By what I have already delivered, you must per-
ceive the advantages of investigation, and of pro-
perly examining into the effects of the minutest
subject; by which you have heard what great and
useful truths have been discovered.
These exercises of the mind produce reflections
the most enlivening; hence also the judgement
is strengthened, and ample sources of amusement
and instruction procured, and by which you will
avoid the languor attendant on an inattentive ob-
server of nature, who may be said to vegetate ra-
ther than live; for, what is life without know-
ledge, or understanding the things by which we
are surrounded, and from which such inferences
are deducible, as alone can elevate the mind, and
make us feel the important rank we hold in crea-
tion, with the certainty of a future state of more
glorious existence,
If any one deny a vacuum, let him look into
the mind of an unreflecting person, and he will
find one; not indeed exactly what he may be look-
ing for, but figuratively so; and, to pursue the
metaphor, the stone which has been so long sought
for may be found in the bosom of the natural
philosopher, whose mind, constantly exercised on
subjects
M 3
166
LECTURES ON ASTRONOMY.
subjects the most interesting by the ideas they
convey of divine things, feels a tranquillity un-
known to the uncultivated in the sciences.
The mind has a constitutional activity, which
cannot be totally suppressed; but sometimes it is
exerted on subjects which disgrace its inherent ca-
pacity, such as examining into the affairs of our
neighbours, for no other purpose but to gratify an
impertinent curiosity; such activity bespeaks a
mean understanding, to say no worse. I do not
mean that the good or bad actions of our neigh-
bours should be indifferent to us, or that the one
should not receive our commendation, and the
other our censure; as such passiveness may sub-
ject us, in the former case, to the imputation of
indiscrimination, and in the latter imply our sanc-
tion. Were these discriminations more generally
acknowledged, I believe the world would be
much better than we find it; for, whilst riches
shield a vicious person from public contempt, I
fear virtue will not entirely triumph-except in its
own consciousness.
Do then, my dear pupils, shew your superiority,
independency, and purity of mind, by shunning
the vicious, however exalted or aggrandized, and
by countenancing virtue under all circumstances:
but do not mistake the meaning I wish to convey
by the word independency, and imagine that those
whose superior rank renders them deserving of
particular respect, by including the advantages re-
sulting from a polished, rational, and religious,
education,
LECTURE V.
167
education, are not entitled to it: that is not to be
implied as to distinguish such persons, by particu-
lar attention, and to cultivate their acquaintance and
friendship, is but a just tribute to their merits and
our judgement; whereas the withholding them,
and affecting to disregard their opinion, implies
gross ignorance, and want of cultivation in our-
selves; for, sure every person of sense and good
breeding will, with pleasure, subscribe to the
forms of society, to procure the advantages result-
ing from the friendship and conversation of a po-
lished and well-informed person, which they must
so greatly prefer to those of a rude and illiterate
one.
Besides the advantages just mentioned, you will
also in general find more true religion and virtue
in the higher walks of life than in the lower, as
vice is the growth of a foul and neglected soil,
and virtue of the purest and most highly culti-
vated; for, look into the minds of those who are
vicious, either in high or low life, and you will
find them equally gross and unenlightened. There-
fore, do not confound the means with the end,
but only regard the means when the end is ob-
tained.
As you all must, I am sure, admire virtue in
others, you will, I hope, practise it yourselves,
and as well for its own loveliness, as for the ad-
vantages it affords.
And if you pant for glory, build your fame
On that foundation, which the secret shock
M 4
Defies
168
LECTURES ON ASTRONOMY.
•
Defies of envy and all-sapping time.
The gaudy gloss of fortune only strikes.
The vulgar eye; the suffrage of the wise,
The praise that's worth ambition, is attain'd
By sense alone, and dignity of mind.`
Virtue and sense are one; and, truft me, he
Who has not virtue is not truly wiſe.
ARMSTRONG.
END OF THE FIFTH LECTURE.
[ 169 ]
LECTURE VI.
OF THE FIXED STARS; AND A VIEW OF THAT
SUBLIME FIELD OF INVESTIGATION, THE
UNIVERSE.
THE NORTHERN LIGHT, OR
AURORA BOREALIS.
FIXED STARS.
CHANGES IN THE
OF MOTION AND GRAVITY.
FROM Astronomy we learn the immensity of
that Being, who could thus perfect his work in
wisdom, and control its various operations by his
power.
Our wonder and admiration is naturally extend-
ed beyond all bounds by the sublime objects of
our present consideration; yet if we examine
through all nature, from the minutest object to the
most enlarged, we shall find equal cause for asto-
nishment.
In the survey of our system, we perceive the
order and influences even of those we cannot ex-
amine into; and, reasoning analogically, we ac-
knowledge the idea of worlds on worlds innume-
rable, dispersed through the vast extended uni-
verse; ideas too large for finite conception,
which must be governed by finite laws, — laws
which are totally inadequate to the real aggregated
conception of this conflux of systems on systems
impelled
170
LECTURES ON ASTRONOMY.
impelled by divine command, and immerged in
the bosom of immensity.
To comprehend the real excellency of the de-
sign, we must examine its parts distinctly, by
which alone we can form a right notion of it:
as thus, When we consider all those bright
luminaries, the fixed stars, cach as belonging to
a particular system; - that it has worlds circula-
ting round it, as that of our system has; and that
they are kept in their proper stations, receiving a
due proportion of the influences of this great cen-
tral body; that each system is kept from infringing
on its neighbouring system; so that they suffer no
impediment from each other in their various in-
dependent affections; and, lastly, that these worlds
are probably peopled with creatures whose ne-
cessities must be amply provided for, if they exist
at all, by that great and good Providence, who
has created all things, how does our admiration
of the whole design increase! Even by diminishing
the object, we enlarge its importance: for, as the
investigation of the organs of the minutest insect
but serves to increase our astonishment by the
skill displayed in them, - so does the usefulness
we discover in each part of the universe, when se-
parately considered, raise our ideas of that great
and good Being, who, in exhibiting the sublimest
spectacle of his power, has not neglected the mi-
nutest want of all his creatures.
Smart has beautifully portrayed the sufficiency
of the smallest creatures to supply the exigencies
of
LECTURE VI.
171
of their existence, not only by the construction of
their organs, but also by the instinctive fore-know-
ledge they are endowed with; which he has ex-
emplified in the little ant.
"Conscious that December's on the march,
Pointing with icy hand to want and woe,
She waits his due approach, and undismay'd
Receives him as a welcome guest, prepar'd
Against the churlish Winter's fiercest blow.
For when as yet the favourable Sun
Gives to the genial Earth th' enliv'ning ray,
All her subterraneous avenues
And storm-proof cells, with management most meet
And unexampled housewifery, she forms:
Then to the field she hies, and on her back,
Burthen immense ! she bears the cumb'rous corn.
Nor rests she here her providence, but nips
With subtile tooth the grain, lest from her garner
In mischievous fertility it steal,
And back to day-light vegetate its way."
SMART.
Thus we see that the attributes of the Almighty
are as evident in the smallest as in the largest
portion of his works; and, like the particles of
light, the more they are separately considered,
the brighter do their native beauties appear.
The sublime imagery of the universe, usually
presented to us by writers on this subject, al-
though extremely beautiful and noble, becomes
more valuable, and creates more love and admi-
ration of the Creator, when analyzed, than when
considered
172
LECTURES ON ASTRONOMY.
considered only in the mass, without reference
to its divisible excellence,
Dr. Herschel, a gentleman of great abilities,
which he employs most gloriously, and for which
application of them he deserves more praise than
I can bestow, has furnished us with many curious
observations, which may with propriety be ad-
mitted, as his indefatigable exertions, and asto-
nishing instruments, aided by the most penetrating
discernment, validate all his assertions, and render
his inferences worthy attention.
This great man, like all superior geniuses, ad-
vances his opinions with great caution, and never
asserts any thing positively but what he is assured
of.
He conjectures that the numerous hosts of sys-
tems, dispersed throughout the wide extended fir-
mament, are connected together by the mutual
contact of their circumambient atmospheres, alto-
gether forming one great sphere; in the manner I
suppose he means, as we observe of a large drop
of water, which is composed of a number of
smaller globules, kept together by the mutual co-
hesion of their external parts, occasioned by
their centripetal forces, which are equal to each
other in cach, and exerted in every possible di-
rection; so that, by counterbalancing each other,
an equilibrium prevails, which assimilates them,
and connects them together, forming one perfect
sphere of immense magnitude. Knowing that the
fixed stars shine by their own light, and not by
reflecting
LECTURE VI.
173
reflecting the light of our Sun, we with reason
conclude that they are each of them of the same
nature with our central body; which being ad-
mitted, we naturally infer that they give light and
life to other systems of planets, as that of our Sun
does to its circumfluent worlds.
From the known divergence of light from a
centre, it is that we know that the fixed stars can-
not shine by reflecting the light of our Sun, as, at
their great distance from it, the Sun's rays cannot
reach them, being all dissipated long before they
could arrive at those remote regions, and therefore
none of their effects can be experienced by those
bodies. Again, we are sure that the fixed stars
are of no use to our Earth, or the other planets of
our system, and therefore with propriety we con-
clude they are intended to answer the same be-
neficial purposes with our Sun to other worlds.
As what is there in nature which does not evince
usefulness as well as beauty?
would it not be contrary to common sense, and
common observation, could we weakly suppose
that God has created such immense bodies with-
out that great design, which we perceive evinced
in all he does, - of connecting beauty, harmony,
and the most extensive usefulness, with the most
unbounded benevolence; so that we cannot say
which of these is the most prominent characteristic
of his works. This must convince every sensible.
mind of the real nature and appointment of the
innumerable hosts of fixed stars; and raise in us
Nothing. Then
the
174
LECTURES ON ASTRONOMY.
the most profound love, gratitude, and adoration,
of a Being, so wise, so good, possessed of pow-
er so unlimited, of glory so resplendent, of bene-
volence so universal, and which are never cea-
I am so animated by the
sing, never ending.
subject, that I could go on for ever enumerating
those impressions of an all-wise and bountiful
Creator. I know not how the Almighty performs
all the wonders I behold, nor do I vainly attempt
to dive into what is, I know, far above human
comprehension, never being intended for the in-
trospection of earthly existences. A time will
come, when we shall behold the works of God as
they really are, resplendent in truth and glory.
In the mean time we must endeavour, by purify-
ing our minds, to fit them for the participation of
the joys which such divine contemplations and
participations afford those who are partakers of
them.
Had the Almighty blessed us with every thing
fitting for our earthly existence only, we should
have been certain that this state was to terminate
it; but he has not been less provident in supply-
ing us with all that is requisite for a future state of
exaltation; and, in order to our attaining this per-
fection, he has furnished us with a strong sense of
right and wrong, even so strong, that those who
act the most basely acknowledge it, although they
act in contradiction to its intimations. Why
should we have this instinctive knowledge infused
into us, if we were not intended for a better state
than
LECTURE VI.
175
than this? or why were we created at all? and,
above all, why furnished with a soul, that active
principle, whose energies are never ceasing, ne-
ver suspended?-These intimations can never be
mistaken.
The brute creation is not sensible of good and
evil, excepting as far as respects their corporeal
necessities; therefore we conclude that they are
not designed for a future state of reward or pu-
nishment, but were created for our use, though
not for our abuse; which latter is a perversion too
common, and on no account justifiable, and for
which, like all abuses of the dispensations of Pro-
vidence, no doubt we shall one day be called to
account.
Some people doubt of a reward of good and
evil deeds, because they wish there may be none.
If there were to be no reward, wherefore should
we be placed on this stage of existence at all?
We might at once have entered on our perfect
state, had we been fitted for it; and why, if all
our deeds are equally good, were we furnished
with an inward sense of right and wrong? Ad-
mitting the necessity for such a monitor, we also
must admit that there is a cause for it; and that
the Almighty, who has so fully evinced his super-
intending and preventing goodness, in the natural
world, would not leave us destitute of what con-
cerned our spiritual well-being.
The Almighty has perfected us in all that is ne-
cessary to our obtaining everlasting happiness, by
having
176
LECTURES ON ASTRONOMY.
having sent us his only Son, to redeem us from
death; and also to teach us how we ought to act
in this life, in order to attain a better. No means.
could so fully have confirmed us in the belief of a
future state, or in the practice of virtue, as the
appearance and divine character of our Saviour.
He was encumbered with a fleshly body, yet kept
it in subjection; no malignant passions had exis-
tence in his mind, yet he suffered the most cruel
tortures of both body and mind; and all this to
show us how we ought to conduct ourselves. He
not only took upon him our flesh, but patiently
endured the pains of mortality, the greatest bodily
sufferings. Let us then endeavour to copy this
bright original; being assured, that by conducting
ourselves according to his example, we can alone
be happy in this life, and obtain the joys of futu-
rity. I recommend those, who doubt, to peruse
Payler's Truths of Christianity, in which they will
find ample sources of consolation and conviction.
I will not invade the clerical province, by endea-
vouring to establish true, and confuting erroneous,
opinions of religion; but conclude the subject by
exhorting you to examine the truths of Christiani-
ty, which will be your surest guard against errors.
This exercise of your minds is necessary to your
eternal happiness; for, when we begin to forsake
God, he will forsake us; therefore we should
guard against schism, not only for its own sake,
but also because it too frequently leads to, and
terminates
LECTURE VI.
177
terminates in, the most deplorable of all evils,
skepticism.
But to return to the contemplation of those
objects, from which such delightful evidences are
deduced, and of which we can only judge by
analogy. That effect of the light of the fixed
stars, which is called twinkling, proceeds from
the vibration in the particles of light, produced
by the particles of the atmosphere which interpose
between us and them, and is peculiar to intrinsic
light; as, when light is reflected in the mass as it
were, its parts are not so divided from each other,
and therefore the atmosphere does not communi-
cate to them that undulating motion. The stars
appearing colourific, when viewed through certain
telescopes, is owing to the light being refracted by
the glasses; and, as all the particles of light are
not equally refrangible, some of them will not
unite at the focus of the glass, but remain in their
separated state. The quantity of light not being
augmented by glasses, as the surface of the body
is, may occasion the light of the stars to appear
duller through them than when viewed by the
naked eye the refraction I have mentioned may
also contribute to the diminution of lustre, want-
ing something of that due mixture which consti-
tutes a bright light. The former is a long-esta-
blished position, the latter my conjecture; the pro-
priety of which, those acquainted with the nature
and properties of light and the effect of glasses can
best judge.
N
The
178
LECTURES ON ASTRONOMY.
The fixed stars, as the name indicates, are per-
fectly at rest in respect to each other, as may be
known by observing the relative position between
any two stars in respect to any part of the heavens;
as they always appear in the same situation, where-
ver observed from.
The reason of our supposing the stars to be set
in a concave sphere arises from the indefinite ex-
tension of the universe, and our viewing them from
a sphere of light, as it were, which is formed with-
in our eye. The fixed stars are not supposed to be
equidistant from us, but to be placed at different
degrees of remoteness, which occasions some of
them to appear larger, as viewed from our Earth,
than others; those which are nearest, of course,
appearing largest; and those, most remote, the
most minute; therefore, although we apply the
terms expressive of different degrees of magnitude
to them, yet they refer to appearances only, as they
may be of the same magnitude for ought we can
know to the contrary.
Dr. Herschel, by means of glasses of immense
power, has discovered that the galaxy, or milky
way, as it is called, and which runs irregularly
and obliquely to the zodiac, and crosses it in Can-
cer and Capricorn, always keeping the same situa-
tion, passing through Cassiopeia, Cygnus, Aquila,
Perseus, Andromeda, Ophiucus, and Gemini, nor-
therly, and by Scorpio, Sagittarius, Centaurus, the
Argonautis, and the Ara, southerly,
an innumerable quantity of fixed stars.
consists of
This gen-
tleman
LECTURE VI.
179
•
tleman conceives our Sun to be one of this exten-
sive stratum of luminaries. These Suns of the
universe may, or may not, all be of the same size,
as the Almighty could proportion the planets to an
animating body of any dimension.
The Doctor says, that, although the Sun, which
regulates our system, is in the centre of it, in re-
spect of us, yet that we should not consider him as
in the centre of the universe, as most probably our
system is composed of not one hundred-thousandth
part of the whole creation; for, in the most crowd-
ed parts of the milky way, he has seen 588 stars
pass through the field of his large telescope in the
space of one minute.
The Aurora Borealis is a meteor only seen occa-
sionally, but then mostly in the northern part of
our horizon, in the northern hemisphere. It ap-
pears chiefly in spring and autumn.
The opinions of astronomers concerning it are
various, and differ so widely, that it is difficult to
conjecture which is right, as they may all be wrong;
yet, as I think one has the preference, on account
of its being deducible from known principles, I
shall venture to advance those circumstances which
appear to validate it; but at the same time will not
attempt to decide for others, and therefore I will
give them the opportunity of making their own
inferences of some of the most feasible ideas.
entertained of this phenomenon, circumstantially
relating the varieties observed in its
N 2
appearance.
The
180
LECTURES ON ASTRONOMY.
C
The Aurora Borealis has by some been ascribed
to a subtile effluvia, which, entering at one pole, is
ejected at the other with violence, in order to re-
store an equilibrium; by others, to the effects of
the Sun's atmosphere.
Various other hypotheses have been formed, but
nothing certain is ever likely to be understood of
this extraordinary and partial illumination. - We
may amuse ourselves as much as we please on this
subject, but we must be satisfied with conjecture
after the greatest stretch of our sagacity.
This light sometimes takes a horizontal direc-
tion, like the break of day; at others, like fine lu-
minous beams, well defined, and of dense light,
accompanied by a quick motion, which is always
succeeded by sudden flashes pointing upwards in
the same direction with the beams; this, in my
opinion, gives some degree of sanction to the idea
of their being the electric fluid passing off at the
north pole, particularly as other circumstances
tend to identify them, such as these appear-
ances happening indeterminately, which bespeaks
accumulation; for, although particular circum-
stances may cause them to happen in some re-
spects periodically, yet not entirely so, the trans-
mission not happening till a certain quantity is ac-
cumulated, and, when redundant, its being af-
fected in the same way as the charge of an electric
jar is when too replete, by bursting from the
substance which contains it, thereby restoring its
equilibrium.
All
LECTURE VI.
181
All the testimonies we bring to authenticate this
opinion invalidate that theory which ascribes these
appearances to the atmosphere of the Sun; for,
if they proceeded from that, they would be more
constantly seen, and not liable to such irregu-
larities in their form and in their manner of act-
ing.
The flashes which succeed the beams of the
Aurora Borealis emit a fainter light, and are much
broader, than the beams themselves. These flash-
ings often continue for hours with intermission,
but gradually grow weaker and weaker till they
totally disappear. Their flashing only at inter-
vals seems to imply their exchanging powers
with each new cloud, which the revolution of
our Earth on its axis brings them in contact with.
All these effects are similar with those that would
actually ensue from the electric fluid, yet it is
impossible to assert positively that it is the
same.
Sometimes the Aurora appears like arches, near-
ly in the form of a rainbow, reaching from one
point of the horizon to another. The arches al-
ways cross the magnetic meridian at right an-
gles, tending to the east and west points of the
compass.
Those beams which are perpendicular to the
horizon are so in respect to the magnetical me-
ridian, and therefore we may suppose that this
meteor has some affinity with the magnetic fluid;
that the electric fluid, and that which causes mag-
netism,
N 3
182
LECTURES ON ASTRONOMY.
netism, have affinity, we know by experience,
passing the electric charge of a battery, i. e. (of
a number of charged jars connected together,)
through a magnet, inverts the poles, and po-
larity may be given to a piece of steel by electri-
city.
The circular direction taken by the beams at
times has not been accounted for, but most likely it
depends on the known laws of motion.
The light of this meteor being differently con-
densed in its appearance, at different times, may
be occasioned by the different state of that part
of the atmosphere through which it passes, and
that by which its light is transmitted to us.
The sudden disappearance of certain stars, and
the appearance of new ones, have excited the at-
tention, and exercised the genius, of some of the
most celebrated astronomers both ancient and mo-
dern; as has also the apparent periodical changes
of brightness in some of them.
Most of the theories advanced of these pheno-
mena are deduced from considering the stars, or
Suns of the universe, of the same nature with ours,
and made up of heterogencous particles, which
are capable of combustion at the surface of the
body they compose. Some have supposed the ab-
sence of these luminaries to be occasioned by the
inflammable matter being decomposed, by which
the ignition of course ceasing, there can no longer
be any luminous appearance: and also, that, as
combustion must continue some time before igni-
tion
LECTURE VI.
183
tion takes place, this causes the appearance of
new stars.
The former part of this theory I think defec-
tive, and the disappearance of certain stars more
naturally accounted for by those who imagine
their absence to be occasioned by a planet of the
system that star illumines eclipsing it in its revɔ-
lution, at a particular time of the nodes, and
thereby hiding them from our view, than by
those who attribute this obscuration to a default
in the constitutional allotment of the essential pro-
perties which cause combustion. — I give you
the former opinion as well as the latter, because
it is equally popular; but still I think it impro-
bable, not being consistent with the never-ceasing
influence of the Sun, which illumines our system;
and, were this circumstance of defection to take
place, what would become of that system which
that Sun used to animate? It must be totally
annihilated. I do not say that this is impossi-
ble,
by the will of God it might so happen;
but I cannot with satisfaction subscribe to its
being a natural and inevitable consequence, or by
any means deducible from what we observe of the
combustion of substances on our Earth, to which
it may have no analogy; as I think we cannot
with propricty explain the operations of infinite
power upon principles deduced from finite circum-
stances.
The brightness of the fixed stars being some-
times greater than at others, most probably is oc-
casioned
N
184
LECTURES ON ASTRONOMY.
casioned by the spots on their surfaces, the same
as are observed on the face of our Sun; and these
also may occasion the appearance of what we call
new stars; for, when the surface of one of these
Suns is much obscured by the spots on its disk, the
quantity of light may be so much diminished, that,
on account of the immense distance of that star
from our Earth, we may not see it for a considera-
ble time.
Before entering into a nearer introspection of
our system, it will be necessary to give you some
farther information of the laws of motion and gra-
vity; without which, you would not be able to
give your assent to what I am about to treat of;
but, when informed of the laws of motion, you
will freely and instinctively subscribe to the facts
presented to you of the motions of the planets
round the Sun; and other motions referable to the
Sun, the planets, and the satellites. And, by the
observation of the wise allotment of powers to
each included in this instruction, you will be dou-
bly gratified; as, by comprehending the laws by
which the great machine is actuated, you will
discover the nice adjustment which nothing but
infinite wisdom could ordain; and thus, by be-
ing able to estimate the effects, instead of di-
minishing the importance of the plan, you will
deduce from it the most consolatory and eleva-
ting ideas of the influence, the glory, and the
goodness of God; who, if he were to withhold
his
LECTURE VI.
185
his continual supply of animating matter, could in
an instant check the planets in their courses, and
produce universal disorder in a system, the order
and influences of which are now so harmoniously
beautiful.
The Almighty has been pleased to appoint mo-
tion his chief agent in all his operations, as is evi-
dent by all the phenomena of nature, which uni-
versally obey the laws of motion, and are perfected
by them.
It becomes therefore essential to those, who
wish to comprehend the changes and operations
perceived in that part of the great system of the
universe exhibited to them, to understand the
known laws of motion; and the importance of
this knowledge is evident in the advantages which
have been procured, by attending to those laws,
as well as by reference to the deficiency in the an-
cient Astronomy, from the universal ignorance of
those laws which then prevailed.
The laws of motion are called laws of nature,
because they are rules observed by all natural bo-
dies.
Sir Isaac Newton has defined the laws of mo-
tion, and confined them to three states of de-
pendency. His first law is, that every body per-
severes in the same state, either of rest, or, if im-
pelled forward by one force only, in an uniform
rectilineal motion; unless in the first case it be
compelled to move by some power acting on
it; or, in the latter case, by a force in a contrary
direction
186
LECTURES ON ASTRONOMY.
direction from the projectile, which it has re-
ceived.
Thus we perceive, that a body receiving a cer-
tain impulse, in a line straight forward, would
pursue that course for ever, were it not for some
other power retarding that motion.
In regard to substances on our Earth, they are
retarded by two powers; one, the resistance they
meet with from the air, and the other, gra-
vity: the first opposing the progress of a body
which has been impelled forward, and the other
drawing it from its straight course downwards,
by which motion its course is altered. But in
the etherial regions, where there is no sensible
resistance, the planets perpetually revolve in
their orbits, only the direction of their motion
is continually changing from the force of gravity
or attraction, which, in one part of their orbits,
accelerates their motion, and in the other retards
it.
Sir Isaac Newton's second law is, that the mo-
tion, or change of motion, in a moving body, is
always in proportion to the force impressed on it,
to cause it to change its motion, and in the same
direction of the received impulse. Thus, we un-
derstand that a double force impressed on a body,
to cause it to move, will make it move with a dou-
ble velocity, and so on.
All change of motion will retard the direct
motion of a body in proportion to the force ex-
erted to turn it from its straight course; i. e. ac-
cording
LECTURE VI.
187
cording to the difference of the force exerted in
the two directions. If I impel a body forward
into the air with a certain force, the power of
gravity will be continually drawing it from its
straight course; and, as the power of gravity in
this case is to my strength in projecting the body,
so much will it retard the motion of the body,
and draw it out of its straight course, indepen-
dent of the resistance of the air, which will also
act in opposition to my strength, and likewise re-
tard the velocity of the body.
All motion in a straight line is called projec-
tile; therefore, if I throw a ball up in the air,
the law of motion is equally observed as when
I project it in a straight line horizontally, as the
ball, in the former case, will ascend with a mo-
tion proportioned to the advantage which the
force I exert has over gravity, and the resistance
of the air. We will suppose that the force I
exert in throwing up a ball to be such as would
cause it to describe 60 feet in one second of
time, did not gravity and the resistance of the
air act in opposition to its ascent: but, as the
force of gravity, independent of the resistance of
the air, causes all bodies to fall to the Earth at
the rate of 16 feet nearly in the first second of
time, my ball would not rise above 44 feet in
the first second. Nor will it rise those 44 feet in
the next second of time; because, in the next
second, the power of gravity increasing on the pro-
jectile as the body approaches the Earth in the pro-
portion
188
LECTURES ON ASTRONOMY.
portion of three to one, it will fall 48 feet; so
that it will not actually rise above 12 feet. And
as, in the third second, gravity will have the ad-
vantage over the projectile force, it will return
and fall to the ground. Let us suppose the ball
as being projected from a piece of ordnance, in a
horizontal position, although this is not the fact in
practice; for, were cannon planted in that direc-
tion, they never could discharge a ball to effect,
as the whole force of the charge would be coun-
teracted by gravity, as you will understand by the
examples I am going to give you of projectiles;
not that I propose instructing you in the ballistic
art, that being foreign to my purpose; but, having
spoken of a ball being projected from a cannon in
a horizontal direction, I fear, if I were not to un-
deceive you, you might suppose that to be the
usual mode of placing cannon.
In continuing my illustration of the effects of
motion and gravity, by a piece of ordnance, you
are to suppose A, fig. 3, plate 8, to be a ball just
discharged from a cannon, with a force capable of
carrying it to G, in a straight line, if gravity did
not act on it, which is an unnatural supposition :
then we must explain how its activity is exerted,
and in what degree it will retard as well as pre-
vent the ball from pursuing the straight line F G.
The line from F to G is divided into four parts,
which are to answer to four seconds of time; by
which you will understand the curve that the ball
will describe in each second of its motion.
In
the
LECTURE VI.
189
the first second, by the force impressed on it, it
would describe the space from F to B; but gra-
vity, acting in a perpendicular direction, will
bring it down to C. In the next second of time,
(in which, if it had pursued its straight course, it
would have arrived at Q,) the effect of gravity in-
creasing in each second by the odd numbers, as
the body approaches the Earth, will bring it down
to D, which is three times as low as it was brought
down by the same power, in the time of the first
second of time. In the third second, it will be
brought down five times as low as in the first se-
cond, as to E. And, in the fourth second, it will
fall down to H.
These points form a curve, as the ball is gra-
dually descending through the spaces FC, CD,
DE, EH. This curve is called a parabola, and
in this direction all bodies fall, unless they are pro-
jected perpendicularly upwards or directly down-
wards.
The curvilineal course of a falling body projected
straight forwards is caused by the combined mo-
tion communicated to it in a horizontal and per-
pendicular direction; the latter being the effect of
gravity, which is uniformly accelerated; by which
the former is uniformly counteracted.
In defining the theory of projectiles, by circum-
stances observed of things on our Earth, in order
to your comprehending the motions of the heaven-
ly bodies, I have not allowed for the resistance of
the air, which, in practice on our Earth, makes
the
190
LECTURES ON ASTRONOMY.
the theory of projectiles more difficult, as, in fact,
they do not agree with what I have advanced
when the resistance of the air is taken in to the
computation, the deviations from a parabola being
in that case very considerable; but which are in-
applicable to the motions of the heavenly bodies,
which move in an unresisting medium; therefore
the idea of the parabola perfectly accords with
their motions, when the directions of gravity are
considered as parallel to each other, but of an el-
lipse when the attraction tends always to one com-
mon centre.
Having observed to you, that bodies projected
perpendicularly fall in the same line of direction,
you must perceive by the foregoing illustration,
that their doing so, is occasioned by the projectile
and gravitating force acting in the same line of
direction.
Sir Isaac Newton's third law is, that re-action is
always equal, and in a contrary direction, to ac-
tion; and that this happens when both bodies are
in motion, as well as when only one of them is
impelled. From which we infer, that, if one body
presses another, either at rest or in motion, it is
equally pressed by it; and, if a body strikes ano-
ther in motion, in a contrary direction, it commu-
nicates such part of its motion to that body, in the
same direction with itself, as it loses; and the ve-
locity of each depends on the proportion of the
bulk of the bodies; that which contains the great-
er quantity of matter, having less velocity than
that
LECTURE VI.
191
that which contains less. These, being equally
applicable to the laws of attractions, are adapted
to the explanation of the motions of the heavenly
bodies.
Motion has a variety of dependencies, which
are duly estimated, according as they are equable,
accelerated, or retarded. Equable motion is also
resolved into simple and compound; compound
motion into rectilinear and curvilinear. - - Equa-
ble motion is that by which a body describes
equal spaces in equal times. Accelerated mo-
tion is that which is continually impelled, and
thereby receives a continual augmentation of its
velocity, which is the same as is effected by gra-
vity. Retarded motion is continually decrea-
sing, in the same way that accelerated motion
is continually increasing; and both are the effects
of gravity, or attraction, which, in the former,
acting in opposition to the rectilineal motion, re-
tards it; whereas, in the latter, by conspiring with
that motion, it accelerates it. Simple motion
is that which is given by one force only; but
compound motion is produced by more than one
force, which act upon the body in various direc-
tions.
Sir Isaac Newton, upon the principles of the
motions of natural bodies, discovered that matter
could not move itself, and therefore that a body
in motion could not of itself change either its ve-
locity or its direction; from which he was led to
examine into the causes of those effects when
produced.
192
LECTURES ON ASTRONOMY.
produced. In order to estimate the proportion
of those powers, it became necessary to measure
them, which he was able to do by a due obser-
vation of their effects. That which makes a body
heavy, when at rest, accelerates its motion in
falling, and bends its course into a curve. The
force which causes a moving body to recede from
a centre, or from the body round which it re-
volves, is called centrifugal force; and that which
occasions it to approach a centre is called centri-
petal.
The former is occasioned by the natural endea-
vour of the moving body to continue in its state
of rectilineal motion, which, but for the latter,
would carry it off in a tangent from the centre
round which it revolves; and the latter, which
urges a body towards a centre, and makes it re-
volve in a curve round it, is occasioned by gravity
or attraction.
The centrifugal and centripetal forces require
particular attention, being intimately connected
with the motions of the heavenly bodies.
When a body describes an exact circle round a
centre, we know that the centrifugal and centri-
petal forces are equal to each other, their action
being always performed in a direct opposite order
to each other. But, if we perceive a revolving
body to recede farther from, and approach nearer
to, the central body at one time than at another,
we are certain that in neither case can they be
equal to each other; as, in the former, the cen-
trifugal
LECTURE VI.
193
trifugal force must prevail, and, in the latter, the
centripetal. These positions you must bear in
mind against I recall your attention to them, when
treating of the planets orbits, the form of which
depends on these circumstances.
I have informed you that the Sun is the largest
body in the system, and that it is situated in the
centre of all the other bodies of it; also, that
those bodies, being of different sizes, revolve in
orbits exterior to the Sun, at different distances.
from this great central body. The certainty of
this position will be evident to you, on considering
the laws which govern the motions of revolving
bodies.
First, Let us suppose two equal weights to be
fixed to the two ends of a piece of wire, and the
wire to be suspended on a point so as to turn
round on it, when impelled forward: this circular
motion could not be effected but by the point of
suspension being placed at an equal distance from
each weight; for, the weights being equal to each
other, the centre of gravity must fall directly
at an equal distance from each, and round which
alone it could revolve.
If, instead of two equal weights, two unequal
ones were fixed to a wire, the point of suspension,
or centre of gravity, will be removed nearer to the
large weight than to the small one; and, there-
fore, when placed in a revolving situation, the
smaller weight will describe a circle exterior to
the larger one, because the centre of gravity will
Q
be
194
LECTURES ON ASTRONOMY.
be farther removed from it. The greater the dis-
proportion of the weights, the nearer will the cen-
tre of gravity be to one, and the farther removed
from the other; the centre of gravity being at
that distance from each weight, which is in pro-
portion to the difference of their gravity or at-
traction.
The Sun being the largest body of the solar sys-
tem, it must be nearer the centre of gravity than
any other body belonging to it.
The Sun and the planets are connected together
by attraction, and therefore are all actuated by the
same impulse, only in a different degree. The
motion of the Sun is very slow, and he describes
but a very small circle round the centre of gra-
vity: his motion being so very slow, and his bulk
very considerable, we do not perceive that he
moves. His motion on his axis is discoverable by
the spots on his disk, and it is occasioned by his
globular form and progressive motion.
I shall postpone farther illustration till another
opportunity, as I have furnished you with much
to reflect upon; and, as my future elucidations
will be better understood by giving you time to
exercise your minds, in establishing the principles
I have already laid down; that being absolutely
essential to your perfectly comprehending the af-
fections of the heavenly bodies, which are all the
result of the laws we have been considering; and
which I have endeavoured to communicate in a
familiar manner, and so as to fatigue you as little
as
LECTURE VI.
195
as possible, considering the dryness.of the subject;
which, however unpleasing to you in description,
will be found intrinsically valuable, by affording you
much real satisfaction; as, without these previous
intimations, you could not understand one-half of
the phenomena I shall describe to you; but, by a
proper application of them, all will
appear rational
and easy, and you will be delighted by having the
laws, by which the Almighty conducts the affairs
of the universe, thus rendered as familiarly plea-
sing to you as they are infinitely sublime.
END OF THE SIXTH LECTURE.
[ 197 ]
LECTURE VII.
OF THE ORBITS OF THE PLANETS. THE LAWS
BY WHICH THE PLANETARY MOTIONS ARE
REGULATED.
OF THE NATURE OF VISION,
AND THE ORGANIZATION OF THE EYE.
How charming is divine philosophy!
Not harsh and crabbed, as dull fools suppose,
But musical as is Apollo's lute,
And a perpetual flow of nectar'd sweets.
MILTON.
How beautifully, how justly, has the sacred
bard described the delights of philosophy! You
have already tasted the sweet pleasures flowing
from that never-failing spring; you will acquire a
greater relish at every draught; drink deep, and
fear not,
its freshness prevents surfeiting, and
its variety precludes satiety.
Having examined gravity in general, I shall now
apply it to the consideration of particular subjects,
comprehended in its effects on the planets of our
system.
The terms weight, gravity, attraction, and cen-
tripetal force, denote the same thing, only they
are differently applied. In order to your un-
derstanding their proper application, I shall in-
form you how they are used, so as to be expres- ·
03
sive
198
LECTURES ON ASTRONOMY.
sive of the different circumstances of the same
thing.
When a body is impelled towards the Earth,
the power by which it is drawn downwards is
called gravity.
When this power is considered as tending to-
wards the centre of the Earth, it is called centri-
petal.
When a substance is supported in its way to the
Earth, it is called weight; but, when we refer it
to the Earth or planets motions in their orbits, we
call it attraction.
Newton discovered that it was this power which
retains the heavenly bodies in their orbits, and in
their respective situations in regard to the Sun, and
other bodies of the same system, according to their
relative powers of attraction, as they all mutually
attract each other.
By the aid of mathematics, the incomparable
Newton ascertained the quantity of attraction ne-
cessary to make the planets revolve at certain dis-
tances from the Sun, and from each other, as also
the satellites from their primaries.
We are certain that the planets must be retained
in their orbits by some power which is continually
acting upon them; that this power draws them
towards the centre of their orbits; and that its
effect increases as they approach the centre, and
is diminished as they recede from it, in a certain
proportion to the distances. The laws of this
power have been found to be the same as those
observed
LECTURE VII.
199
observed of gravity; and therefore we may be-
lieve their identity, which has been settled by
imagining a line drawn from the Sun to either
of the planets, when, on observing the time taken
by a planet in passing over an arch of the ellipsis,
circumstances accorded exactly with what would
happen in bodies falling towards our Earth by the
power of gravity; i. e. the nearer the body was
to the attracting power, or centre of the Sun, the
quicker was its motion, and its motion was uniform-
ly accelerated in approaching the Sun. The same
has also been discovered of the Moon in respect to
the Earth; the Earth gravitating towards the Moon,
and the Moon towards the Earth, in proportion to
their different powers of attraction, which occasion
them to revolve round a centre of gravity between
them, and to cause the Earth to be nearer to that
centre than the Moon, because the Earth is the
larger body.
The centripetal power of the primary planets is
directed towards the centre of the Sun, and that
of the satellites towards the centre of their prima-
ries; which power is exerted in proportion to the
distances of those bodies from their central bodies,
being reciprocally as the squares of their distances
from them. This evidently proves that it must be
the same power actuating them all, and that this
power is gravity, or attraction, as the effects are
the same with those observed in respect to bodies
on our Earth.
O 4
The
200
LECTURES ON ASTRONOMY.
The planets perform their revolutions round the
Sun in elliptical orbits. Before I inform you why
they do so, I shall explain the nature of an el-
lipse.
Fig. 4, plate 8, is an ellipse; its transverse axis,
or longest diameter, A B; its shortest diameter
CD; the two points F F the foci, which are so si-
tuated, that, if any two right lines were drawn
from them, and made to meet in a point in any
part of the circumference of the ellipse, the sum
of those two lines would be equal to the longer
axis AB; as the two lines drawn from FF to
G, fig. 4, are found to be, by applying a pair of
compasses to the scale A B, fig. 5, plate 8.
You may say, perhaps, of what use is this illus-
tration? as at first view its utility does not appear;
but you will change your opinion when I inform
you, that, without comprehending the foci of an
ellipse, you cannot understand why the Sun, being
placed in the lower focus of every planet's orbit,
should occasion him to be in the centre of gravity
of all their mutual attractions, as at one time he
must be farther from them than at another, and
from all the planets he must be at different dis-
tances; but, by having the nature of the foci of
an ellipse explained to you, all will become clearly
understood.
Perhaps it may not be deemed intrusive if
I introduce in this place the manner of form-
ing an ellipse, by which instruction also my il-
lustration
LECTURE VII.
201
lustration of this part of the subject may be bet-
ter understood.
Fix on a plane two pins, at any distance from
each other; round which tie a loose thread ac-
cording to the size of the ellipse you wish to de-
scribe; then, straining this thread with a pencil,
carry it round with a steady hand, and the pencil
will describe the curve line called an ellipse.
Now, if there were but one fixed pin, the pencil
at the extremity of the thread would, in being
carried on, describe a complete circle; hence you
conceive that the nearer the pins are to each other,
the shorter will be the ellipse, and the nearer it
will approach to the form of a circle.
The distance or space, FH, is called the ec-
centricity, which is different in the orbits of the
different planets; but, in all, it is so small that it
is taken but little notice of. In the orbits of co-
mets the eccentricity is very great, as, on account
of their being very long ellipses, the foci are very
distant from each other.
We are certain that the orbit of the Earth, as
well as those of the other planets of our system,
are ellipses, because the Sun appears of different
sizes at different times of the year. His diameter
in June is about 31', and in December about 32′,
on account of the Sun being nearer to the Earth
in winter than in summer.
The attraction between the Sun and the planeťs,
and between the satellites and their primaries,
must be mutual, and in proportion to their quan-
tities
202
LECTURES ON ASTRONOMY.
tities of matter; for, if it were not so, the Sun,
by his great attraction, would draw all the bodies
of our system into himself.
It is gravity or attraction which gives weight to
bodies, forms all the planets into solid balls,-
circumscribes their orbits, and retains on their
surfaces the beings created to inhabit them, not-
withstanding the amazing velocity of their motions.
on their axes. How great is the power, how
universal the agency, of this invisible principle!
I have informed you, that, if two forces are act-
ing on a body in contrary directions, of unequal
power, the body impelled will move in the di-
rection of the strongest force, and with a velo-
city equal to the difference of the velocities of the
two forces. Thus, in reference to the motions of
the heavenly bodies, we allow that they, being im-
pelled to move by divine command in a straight
line, are brought down from that line by the pow-
er of gravity or attraction, and that they after-
wards move by the velocity gained in their fall;
as we perceive things to do on our Earth.
The motions of the heavenly bodies are perpe-
tual, because they do not move in a resisting me-
dium, or suffer any friction, and because their in-
fluences are perpetual; yet their motions are acce-
lerated and retarded according to the different ef-
fects of gravity acting upon them, as I shall farther
explain to you.
A body moving round the Sun has its motion ac-
celerated in falling towards it, but is kept off from
it
LECTURE VII.
203
it by the centrifugal force acquired in falling, which
force is independent of the Sun, and proceeding
from the progressive motion of the impelled body,
by the direction of which force alone it would go
on in a straight line for ever; but the Sun drawing
it from that line by its attraction or centripetal
force, these two forces being exerted in contrary
directions, instead of the body going off in a tan-
gent to its orbit, by the force it has acquired in
falling, it acquires a curvilinear motion; and it
ascends again to the same height, because the
power of attraction and the projectile force act
upon it, both in its descent and ascent, only the
effects are in a contrary order; but, being in an
equal degree to each other in both cases, the
curve the body describes on each side of the Sun
must be the same.
The Sun is situated in the lower focus of the
elliptic orbit of every planet. The planes of the
orbits of all the planets cut the Sun as it were in
half, and are differently inclined to that of the
Earth. Those two points of the orbits which
cross that of the Earth are called the nodes of the
planets. That by which a planet goes above the
plane of the Earth's orbit is called its ascending
node; and that, by which it descends below the
same, is called its descending node.
Nothing is more easy to be understood than the
motions of the primary planets being deducible
from the known laws of two forces only, namely,
the centrifugal, or force from the centre of an im-
pelled
204
LECTURES ON ASTRONOMY.
pelled body, produced by its natural tendency to
proceed in a straight line, by the progressive im-
pulse; and the centripetal, which causes two or
more bodies in motion, connected together, to re-
volve round a centre; which, when referred to the
motions of the planets, the centrifugal force is
known to perpetuate their motions, and the cen-
tripetal force to cause them to revolve round the
Sun, by the superior attraction of that body. In
regard to the effects of attraction between the
planets, they are very inconsiderable, on account
of their immense distance from each other, and
comparatively small quantity of matter, although
it is something when they are in the same quarter
of the heavens, each attracting the other in pro-
portion to their quantity of matter.
The motions of the satellites round their prima-
ries, compounded with their motions round the
common centre of gravity of the system, occasion
them to be less uniform in their affections than the
primaries in theirs, as you may suppose, on re-
flecting that each of them, although it gravitates
towards its primary, yet it must also be affected by
unequal attractions from the Sun, at different
times, being sometimes nearer to that luminary,
and at others farther removed from it, than its
mean distance.
Although the motions of the primary planets
may be esteemed uniform, as far as respects their
motions in the same parts of their orbits, being
always at the same rate in each; yet are they not
equal

Plate IX.
Fig. 2.
au
West
m
R
69
P
North!!
F
South
15
Virgo
Leo
Libra
M.Bryan delin!
UNIV
OF
Scorpio
East
Fig. 1.
E
Apogee
3Perigee
A
Fig. 3
P
Gemini
Cancer
Taurus
H
Aries
Pisces
Sagittarius
B
T
Capricornus
Fig. 4.
Aquarius
D
T.Conder sculp
LECTURE VII.
205
equal in all parts of them; on account of the Sun
being placed in one of the foci of their elliptical
orbits, and not in the centre.
When they are in that part of their orbits in
which they are approaching the Sun, their motion
becomes quicker and quicker; and, when in that
in which they are retiring from it, their motion is
slower and slower. This I will farther explain by
a diagram.
Let the ellipse ABCD, fig. 1, plate 9, repre-
sent the orbit of a planet; S, the Sun, in the lower
focus of the ellipse. Let AB (which is the longer
axis of the ellipse) be the line of the apses,
point at A the higher apsis, and that at B the
lower.
the
The higher apsis is the place of a planet when
it is at its greatest distance from the Sun, and
which is also called its aphelion; and the lower
apsis is the place of a planet in its nearest ap-
proach to the Sun, and is called its perihelion; al-
so the line of the apses, or apsides, passes through
the centre of the orbit of the planet, as well as
through the centre of the Sun. The extremities
of the line DC, fig. 1, plate 9, are the points of
the planets orbits, at their mean distance from the
Sun.
Suppose the ball at E to be a planet, which is
projected in a straight direction towards F, through
the etherial unresisting medium. If no other than
this projectile force acted on it, it would go on for
eyer in that straight course, and thereby be de-
prived
206
LECTURES ON ASTRONOMY.
prived of its grand vivifying principle, the Sun;
but, the instant of its projection, the attrac-
tion of the Sun begins to affect it with a de-
gree of power proportioned to its distance from it,
and in a direction which acts perpendicularly to
its projectile force it is thereby brought down
more and more from its straight course EF, in the
proportion I have before shewn you by fig. 3,
plate 8. This attraction; acting more and more on
the body as it approaches the Sun, forms the orbits
of the planets into ellipses.
Thus the motion of a planet will be more and
more accelerated in its way from A by C to B,
fig. 1, plate 9, because the attracting power will
be gaining continually on the projectile. But,
when it has arrived at B, it will have gained so
much force from its centre, as to overcome the
Sun's attraction, by which wise allotment of pow-
er the body is prevented approaching so near to
the Sun as to be involved in its conflagration, which
would totally annihilate it.
These two powers being duly weighed, or ba-
lanced, in the scale of Infinite Wisdom, prevents
the projectile force from carrying the body off in
a tangent from its orbit, in the direction BG,
when it has arrived at B, by the Sun's attraction
preserving it within certain limits. These two
powers, always acting on the body, cause it to
describe the same curve, in its departure from the
Sun, that it described in its approach to it, by
the motion of the
which it again arrives at A;
planet
LECTURE VII.
207
planet being as uniformly retarded by the Sun's at-
traction in its departure from that body, as it was
accelerated in its approach to it. When the pla-
net arrives at A, the Sun's attraction brings it
down again in the same manner as before; -and
thus wonderfully are the motions of the planets
perpetuated and circumscribed.
You now know why a planet's motion is swift-
est when it is in its perihelion, and slowest in its
aphelion. When it is at C or D, its motion is
called mean, being between both extremes. These
places of a planet are also called its mean distance
from the Sun. The motion of a planet in these
places of its orbit is such, as, if continued always
at the same rate, would cause it to describe its
orbit exactly in the time it does describe it in, by
means of the different velocities.
What I have advanced of the motions of the
planets in their orbits is applicable to those of the
satellites, only there are some irregularities in the
latter, the consequence of their obeying two cen-
tral forces.
Such are the different causes of irregularity in
the motion of the Moon, that it has but one
strictly uniform, and that is on its axis; by which
we always have nearly the same illuminated face
of this satellite turned towards us, when it is
visible.
I shall not at present speak of the irregularities
and other affections of the Moon, as a better op-
portunity will offer for discussing this part
of our
subject,
208
LECTURES ON ASTRONOMY.
subject, but proceed in applying what we know of
motion and gravity to the primary planets; having
advanced sufficiently of the laws of gravity and pro-
jectiles for your comprehending their effects on the
bodies of our system, of which I am about to treat.
There are, you know, seven planets belonging
to the Sun, depending on his influences, already
discovered, of which I shall speak. There may
be more; but of these only we can treat confi-
dently.
Each of these planets, of which our Earth is
one, is encompassed by an atmosphere, by which
the creatures inhabiting them are able to exist.
We know that animal life cannot be continued
without the impressions of the atmosphere of the
Earth, and that its healthful state also depends on
circumstances of it; therefore, it is natural to sup-
pose, that all those bodies, which are circumfused
by that same fluid element, are supplied with it
for the same beneficial and essential purposes.
The motions of all the planets being also analo-
gous to those of the Earth, we conclude that they
are of the same nature, and thereby capable of
supporting all animal and vegetable life.
Some of the other planets revolve nearer, and
some at a greater distance from, the Sun, than our
Earth does, as I have pre-acquainted you; also
that their periodic times are proportioned to their
distances, and that these are all rationally ac-
counted for on the theories of gravity and cen-
trifugal force, and accord with them.
The
LECTURE VII.
209
The mean distances of the planets are in the
following proportion, which proportion is repre-
sented by the circular orbits of the planets deli-
neated plate 6. The distance of the orbit of the
Georgium Sidus from the Sun is divided into 190
parts, as is exhibited on the scale drawn from the
Sun at A, to the orbit of that planet at B. Saturn
is situated at 95 of those parts, Jupiter at 52,
Mars at 15, the Earth at 10, Venus at 7, and
Mercury at 4.
The annual motions of the planets are ascer-
tained by their change of place in the heavens;
being removed from one place in the zodiac to ano-
ther. Their direct motion is according to the or-
der of the signs, from west to east; and this is
their true motion; their revolution on their axis is
performed in the like direction.
The apparent diurnal motion of all the heavenly
bodies above our horizon, from east to west, is oc-
casioned by the diurnal motion of our Earth,
which corresponds with that of all the other pla-
nets, being performed from west to east.
The planets, as viewed from our Earth, have
another apparent motion, on account of the an-
nual motion of the Earth and them, in the same
direction, with different velocities. This motion
is called retrograde, as it makes them appear to
us to go back again, as it were, by transferring
their places in the heavens to different situations,
in respect to the Sun and us, as from the east to
the west side of that luminary, at particular times.
The
P
210
LECTURES ON ASTRONOMY.
The cause of this deception I shall, in due time,
fully explain to you, both by diagrams and the in-
strument called a planetarium.
All the planets and comets of our system appear
bright, by reflecting the light of the Sun, as is
known by the different phases of those (which are
visible to us) at different parts of their orbits.
Those planets which, in revolving round the
Sun, regard him as the centre of their motions,
are called primary; and those which regard a pri-
mary planet, as the centre of their motion, revol-
ving round the centre of gravity between it and
themselves, are called secondary planets, or satel-
lites.
Comets are primaries, because they regard the
Sun, or centre of gravity between them and the
Sun, as the centre of their motion.
Such of the primaries as are situated most re-
motely from the Sun have their quantity of re-
flected light considerably augmented by the num-
ber of Moons, or satellites, which accompany
them in their revolutions.
The satellites also appear to be habitable worlds,
if we may judge of the rest, by what we perceive
of that which belongs to our Earth, the vicinity of
which to us renders the mountains and cavities.
on its surface visible, by the aid of telescopes.
The Earth not being placed in the centre of the
periodic motions of the planets, they must be
sometimes nearer to us than at others, and of con-
sequence appear larger or smaller, in proportion to
their
LECTURE VII.
211
their distances from us, as the apparent sizes of
bodies diminish according as their distances in-
crease; because it is not their real diameter that
we can judge of by appearances, but the angles
under which they are viewed, which angles will
be greater or less, in proportion to their distances.
For the foregoing reason also, at a given distance,
bodies which differ in size will also differ in appa-
rent magnitude. If a very large body be placed
at as much greater a distance from us, as it ex-
ceeds in size a less body in a nearer situation,
they will both have the same apparent magnitude
or diameter. The position of an object will alter
its apparent diameter, as will also the degree of
light under which it is viewed; - the latter effect
is produced by the different extensions of the pu-
pil of the eye in different degrees of light. If we
look at an object in a very strong light, the pupil
contracts; but, if in a very weak light, it ex-
pands, and of course, in the former case, the an-
gle under which the body is seen, at a given dis-
tance, must be diminished, but in the latter it
must be enlarged; and therefore the apparent size
of the body must agree with these circumstances.
For the above reasons, all objects viewed from our
atmosphere, in a medium more dense or obscure
than it, appear larger than they do in the air.
I feel an irresistible impulse, which I trust I shall
be excused for obeying, to introduce, in this place,
some observations on the wonderful construction
of the eye, the admirable disposition of its parts,
P 2
and
212
LECTURES ON ASTRONOMY.
and the happy and nice powers of adjustment they
are endowed with, to answer all the purposes of
vision.
The eye is the instrument invented by Infinite
Wisdom to convey to our mind the idea of visible
objects. To doubt of the truth of this assertion is
impossible, when we examine its structure, and
the effects produced on it by the rays of light.
The eye is placed in a bony cavity called the
orbit; its form is globular; within this globe arc
contained three different kinds of humours enclosed
in several distinct sorts of teguments, or coats, in
which blood-vessels, nerves, and arteries, are cu-
riously interwoven.
I shall first treat of the external advantages at-
tendant on the mechanism of the eye, and its con-
comitant appendages.
The inside of the orbit, which contains the eye,
is lined with a lubricating and membraneous sub-
stance, which affords the eye a soft bed to perform
its movements in, without injury to its delicate
substance. Those arches of hair, called eye-brows
and eye-lids, are not less useful than beautiful; for,
they defend the eyes from too strong a light, and
prevent dust or other small substances from falling
into them, by being provided with muscles, for the
purpose of projecting or drawing them down, so
as to defend the cyc from a glare of light, and
from incumbent particles of dust.
The eye-lids afford also a perfect and secure
asylum for the eye when we sleep, or have occa-
sion
LECTURE VII.
213
sion to guard against external injury. When we
are awake, and unfearing of external annoyance,
the eye-lids, by their motion, diffuse a fluid over
the eye, which keeps it constantly moist and clear,
by which alone it could answer the purposes of
vision.
These lids join at their two extremities; and,
that they may shut with greater exactness, and
not fall into wrinkles when they are elevated,
each edge is stiffened with a cartilaginous arch,
which is bordered with hair; by the latter the
contour of the eye-lids is softened, the eye pro-
tected from straggling motes, and the light mode-
rated in its approach to the retina. The eye-lids
also assist in these desirable effects, by excluding
a superabundant quantity of light.
The upper part of the orbit of the eye has a
gland placed in it, which constantly furnishes suf-
ficient moisture for keeping the part of the eye
exposed to the air in a proper state of lubricity
and pellucidity; and, that this purpose may be
fully answered without our attention to it, we shut
the eye-lids, or wink our eyes, without the con-
currence of our will or reason.
The corner of the eye, next the nose, is provi-
ded with a curuncle, for the purpose of keeping
that corner of the eye from being perfectly closed,
that any tears, &c. may flow from under the eye-
lids, when we sleep, into two little holes, one of
which is in each eye-lid near the corner, for car-
rying off any superfluous moisture.
P 3
The
214
LECTURES ON ASTRONOMY.
The eye is furnished with six muscles, which
spread their tendons far over the eye, in order to
effect a motion in every direction, excepting an
oblique one towards the nose, which is aided by a
particular auxiliary. The side of the eye next to
the nose not allowing room for a muscle, a small
bone is placed on the side of the nose, with a
hole in it, which serves as a pulley for the tendon
of a muscle to pass through, by which an oblique
direction of the eye is obtained.
The eyes have a parallel or uniform motion, in
which they always coincide: this is extraordinary
to human reason, as the organs of the two eyes
are totally distinct, having no communication with
each other, and yet they appear actuated by the
same force or mechanism. The purposes supposed
to be effected by this union of action and direc-
tion is that of seeing things single which are
viewed double. I shall give you Sir Isaac New-
ton's supposition respecting our seeing things sin-
gle, which are painted double, that is, the two ima-
ges of the object painted on the retina, one in each
eye appearing but as one to the imagination.
"The species of objects seen with both eyes
may unite where the optic nerves meet before they
come into the brain, the fibres of both nerves u-
niting there, and, after union, going thence into
the brain, in the nerve which is on the right side
of the head, and the fibres on the left side of
both nerves uniting in the same place, and after
union going into the brain in the nerve which is on
the
LECTURE VII.
215
the left side of the head; and these two nerves
meeting in the brain in such a manner, that their
fibres make but one entire species or picture, half
of which is on the right side of the sensorium,
and comes from the right side of both eyes,
through the right side of both optic nerves, to the
place where the nerves meet, and from thence to
the right side of the head into the brain; and the
other half on the left side comes in the like man-
ner from the left side of both eyes. The optic
nerves of all animals which look the same way, as
men, horses, dogs, &c. meet before they come in-
to the brain; but the optic nerves of such animals
as do not look the same way with both eyes, as
fishes, do not meet before they go into the
brain."
This conjecture appears reasonable, and may
therefore be admitted; but the effect must after all
be referred to the mind, as well as what causes
that involuntary motion which produces the effect,
or that motion which causes the image to be seen
at all; for, although undoubtedly vision, or the
appearance of objects, is occasioned by the pic-
tures on the retina, yet the eye can see no part of
itself, it is the mind that perceives and judges ;
the eye is only the medium, or instrument, by
which the idea is conveyed to the mind; and for
the operations of the mind upon the body, or the
body upon the mind, we are unable to account.
Considering the eye merely as an instrument,
we need not inquire why, when the pictures of
P 4
objects
216
LECTURES ON ASTRONOMY.
objects are painted in it, in a reverse posture, our
imagination perceives them upright; to solve
which difficulty, anatomists have been unable; nor
can they ever afford us a rational solution of a
circumstance independent of the organization of
the human body. All our senses are aided by the
mechanism of the organs created for their use,
but their impressions are referable only to the spi-
rit, -the understanding; and therefore not defi-
nable by human comprehension.
Having treated of the principal external parts
of the eye, and the advantages procured by their
nice adjustment, I shall venture to speak of its in-
ternal parts, which will be less digressive, as all
the instruments used to aid astronomical investi-
gation have been constructed upon the principles
of refraction, reflection, &c. effected by the va-
rious humours and coats of the eye, and therefore
they will be better understood from a description
of this grand original and its affections.
The globe of the eye consists of several coats,
containing three pellucid liquors, which are so ad-
justed that the rays proceeding from luminous ob-
jects, and admitted at the fore part of the eye,
called the pupil, are brought to a focus on the
back part of it.
The outer coat, or sclerotica, is a hard sub-
stance of a whitish colour, resembling parchment,
the hinder part of which is very thick, and is o-
pake; from whence it becomes gradually thinner
and thinner as it approaches the part in front of
the
LECTURE VII.
217
the eye, where the white terminates; the other
part of this tegument is thin and transparent, and
projects a little, forming the segment of a smaller
sphere: this part is called the cornea, from its
transparency: this quality of it is necessary for the
free admission of the light. This membrane is
composed of several layers, and replenished with
clear water and pellucid vessels.
The second coat of the eye, or the choroides,
is soft and tender, is composed of innumerable
little vessels, and it adheres to the sclerotica; it is
outwardly of a brown colour, and inwardly almost
black. This tegument, like the sclerotica, is dis-
tinguished by two names, the fore part being call-
ed the uvea, and the hind part the choroides.
The fore part, or uvea, commences where the
cornea begins, i. e. at the edge of that dark part
of the eye called the iris. It is attached to the
sclerotica by a narrow circular rim, from which
part the choroides divides from the sclerotica, or
changes its direction, turning inwards to the
axis of the eye, or middle of the globe of the
eye, and thus forms that round hole we call the
pupil. The uvea commences where the cho-
roides divides from the sclerotica, from which part
to where it turns inwards and forms the hole call-
ed the pupil, is called the iris, which is composed
of the dark colour of the choroides, called the
uvea, combined with the reflections of the light
occasioned by the puckering of the membrane on
turning inwards.
The
218
LECTURES ON ASTRONOMY.
The pupil of the eye has no determinate size,
but depends on the action of the membrane which
forms it, which either expands or contracts it, so
as to accommodate the organ of sight to the
strongest or weakest impressions of the particles
of light; as thus: when the light is too intense,
the pupil is contracted, to prevent the admission
of too great a quantity of light, which would in-
jure the sight; but, when the light is weaker, the
pupil is enlarged, and thereby a greater quantity
of the rays of light fall upon the retina, in order
to render it in both cases duly active. The whole
of the choroides is opake, therefore no light can
enter the eye but what passes through the pu-
pil.
The third and last membrane of the eye is called
the retina, because it is spread like a net over the
bottom of the eye. It is a continuation of the op-
tic nerve, and lines the inside of the choroides;
and the concave side of it covers the surface of
the vitreous humour, terminating where the choro-
ides turns inwards, so that it contains the vitreous
humour. On this membrane, within-side the eye,
that is, on its convex surface, are painted the ima-
ges of objects.
The coats contain the humours of the eye; one
humour forms a solid substance, another is soft, and
the other perfectly liquid. The humours are of
such forms and transparency as are best adapted
for transmitting the rays of light, and placing
them in positions favourable to distinct vision. -
They
LECTURE VII.
219
They are all clear like pure water, possessing no
essential colouring particles; therefore the colours
exhibited by them must be derived from the
impressions of the different particles of light.
The most fluid of these humours is called a-
queous; it fills the interstice between the cornea
and the pupil, and also the space between the
latter and the chrystalline humour. Its form is
plano-convex, its quantity is so abundant, that it
swells out the fore part of the eye into the seg-
ment of a small sphere. It is not known from
whence this humour is supplied, yet its source is so
unfailing, that, if the coat which contains it be
wounded, so that the humour all flows out, if the
eye is kept closed a proper time for the wound to
heal, the fluid will be recruited.
The second humour is called the crystalline; it
is as transparent as the aqueous, but less in quan-
tity, and more dense, of the consistency of a stiff
jelly. Its form is doubly convex, but the two
parts are of different convexities; the most convex
part is received into an equal concavity in the vi-
treous humour.
The crystalline is contained in a kind of case,
the fore part of which is thick and elastic, the
hind part thin and soft. This case is suspended in
its place by a muscle, which, together with the crys-
talline, divides the globe of the eye into two une-
qual portions, the smaller and foremost containing
the aqueous humour, the larger and posterior the
vitreous.
The
220
LECTURES ON ASTRONOMY.
The crystalline humour has no visible communi-
cation with its case; for, when it is opened, the hu-
mour slips out.
In old age the crystalline becomes discoloured,
and therefore all objects appear less bright, and
are tinged with yellow, which degeneracy, not
coming on suddenly, prevents old people from
being sensible of this effect of it.
The vitreous is the third and last humour of the
eye, and appears like glass; it is neither so dense
as the crystalline, nor so liquid as the aqueous. It
fills the greatest part of the globe of the eye,
filling all the space between the sclerotica, from
the insertion of the optic nerve to the crystalline
lens.
The optic nerve passes out of the seat of the
brain through a small hole in the bottom of the or-
bit of the eye; it enters the orbit of a form nearly
globular, but compressed, and is inserted into the
globe of the eye nearly in the middle, though not
quite so, but rather higher and nearer to the
nose.
Having said sufficient of the construction of
the organ of sight for your comprehending the
wise and wonderful disposition of its parts, I shall
proceed to instruct you in the mode of its admi-
nistration, and convince you that the cye was made
for the rays of light, so as to enable you to confute
the ignorant and unreflecting.
Fig. 4, plate 9, represents the coats and humours.
of the eye. The outer coat of the eye, called the
sclerotica,
LECTURE VII.
221
sclerotica, is represented by the exterior of the
lighter shaded circles BF B; the more convex part
of which, from B to B, is the cornea.
The choroides is represented by the inner light-
shaded circle BF B.
United with the choroides, and a part of them,
is the uvea, which reaches from B to B.
Between A A is the pupil.
V is the optic nerve which spreads itself within
the choroides, and, in the figure, it is represented
by the dark part of it inclosed in the circles
BFB.
EE is the crystalline humour.
BABC contains the aqueous humour.
And the large space BEDEBF the vitreous.
Vision, as far as the eye is concerned, is ef
fected by such refraction of the rays of light, by
the skins and humours of the eye, as causes distinct
images of exterior objects to be painted therein,
and which purpose they are admirably contrived
for effecting.
All the rays of light, which enter the pupil
from any luminous object, are united closely toge-
ther upon the retina, by which they make a
stronger impression than in their simple state.
The retina is placed at a proper distance from the
refracting substances, in order that each pencil of
rays may be received on it in distinct foci, so that
the images may appear conspicuous.
The degrees of the power of refraction of each
humour of the eye have not been determined for
all
222
LECTURES ON ASTRONOMY.
all states of it; but those of the aqueous and vi-
treous humours, in their sound and perfect state,
are supposed to be much the same with common
water, and that of the crystalline a little more.
The humours of the eye altogether form a convex
lens, the effects of which will be easily understood
by the diagram.
Let P QR, fig. 4, plate 9, be a luminous object.
The pencils of light BPB, BQB, BRB, from
the points P, Q, R, falling upon the cornea B A B,
are refracted so as that they would belong to foci
beyond the eye, at a, b, c; but the surface of the
crystalline humour, C, increasing the degree of the
refraction, would make them meet in foci nearer
to the eye, but yet exterior to it, at h, i, k. But,
lastly, the refraction being still augmented, by
their passing out of the crystalline humour into the
vitreous, they are brought to their proper foci on
the retina, at p, q, r.
You will recollect that the
rays of light, in falling upon a lens of unequal
convexities, are refracted in passing in and out of
that lens, in proportion to the different convexities
of the two surfaces; and in a contrary direction.
Also, that the refracted rays meet in a point, at a
certain distance from the refracting surface they
depart from; and that, as the rays of light, in
passing through a convex lens, are each differently
refracted, they will meet in different points, but
at the same distance from the refracting surface.
This illustration of the nature and effects of vi-
sion will not, I hope, be thought intrusive, as the
subject
LECTURE VII.
223
subject is truly curious and interesting; and as
many who may peruse this book may not have
considered these effects, or even the nature of the
organ of sight, so as to derive the many consola-
tions, the many delights, both of body and mind,
offered in this epitome of Infinite Wisdom and Be-
nevolence.
Thus, whether we soar in contemplation of the
majesty and glory of God displayed in the heavens,
or pursue our scrutiny of the wonders and bene-
volence of his administration and dispensations,
manifested in the organization and effects of things
upon Earth, still we discover new cause for con-
gratulation, new sources of delight and adora-
tion.
Can any thing be more delightful than employ-
ing our understandings in researches, which bring
us nearer in thought to God, and which convey
to us sure testimonies of his love?
When, in contemplating the powers the Al-
mighty employs in regulating the planetary sys-
tem, we perceive that all nature is supported by
two opposite forces, acting upon each other, by
which an harmonious equilibrium universally pre-
vails, — how do we admire the greatness of that
power, the infallibility of that judgement, that
can thus appropriate and adjust properties to the *
effects required !
When we investigate the organization of the ob-
jects of nature, and perceive that all the wisdom
and power of God are employed for the benefit of
his
224
LECTURES ON ASTRONOMY.
his creatures, how do our hearts glow with love
and thankfulness; the sweet sensations it pro-
duces diffuse a serenity, which, like a charm, bu-
ries our cares in oblivion.
Let us endeavour to copy the attributes of this
bright Original, by using our power and abilities,
not to afflict or be useless to our fellow-creatures,
- but to protect and to serve them.
Our understanding was given us in trust, like
all other blessings; for the use and abuse of which,
we must one day give an account. Therefore, in-
dependent of ten thousand inconveniences, which
result from not employing this great boon to the
honour of God, we shall also incur the displeasure
of that Divine Dispenser of good gifts, who ex-
pects that we shall improve every talent committed
to our charge.
If you recur to the numerous instances in his-
tory, of the abuse and neglect I am speaking of,
you will perceive the baneful effects of them in
those who, not using their understanding aright,
or by neglect in the cultivation of it, have become
grossly depraved, and cruel in the extreme; their
minds becoming impure and hardened, they lost all
relish for what was lovely and good, and delighted
only in all that was evil, till at last they became
despised and abhorred of mankind. It is unne-
cessary, in this place, to enumerate those instances
of depravity evinced in the conduct of those who
have neglected the cultivation of virtuous, bene-
volent, and religious sentiments, in order to deter
my
LECTURE VII.
225
my pupils from falling into the same errors, as
they are familiarly acquainted with them in their
course of reading and digesting the history of past
ages; and as they have testified their abhorrence,
by shuddering at the horrid representation of those
crimes, and have gladly turned from such un-
worthy and ungenial subjects of our animadver-
sion, to those, in which the human character has
been delineated with all its attractive charms of
sensibility and integrity, and in which the most
refined and highly cultivated understandings have
been portrayed.
The contrasted effects, of a virtuous and philan-
thropic, to those of a vicious and hardened, dispo-
sition, strike every sensible mind most forcibly.
Let us then endeavour to avoid what leads to the
one, and cherish all that perfects the other, as
no one is wicked or hardened all at once; and as
virtue, like the security of all else that is truly va-
luable, requires vigilance.
No subjects tend more to invite us to the exer-
cises of all religious and social duties, than those
of Astronomy and Natural Philosophy.
Let me entreat you, my dear pupils, to imitate
the harmonious effusions of nature, by being uni-
formly kind to each other, and by conducting
yourselves with innocency and truth, so fulfilling
your appointment upon Earth, and with all sim-
plicity effecting the purposes of your being. Then
shall the virtuous, the benevolent, impressions you
have received be reflected in your actions, in as
Q
charming
226
LECTURES ON ASTRONOMY.
charming a manner as the light of the Sun from
the bosom of the rose; and your virtues be as
communicable, as delightful, in their influences,
as the sweet effluvia of that flower diffused by the
circumfluent atmosphere.
AND OF THE SEVENTH LECTURE.

Plate
H
GEO
H
T
S
L
Fig: 2.
KA
B
P
K
Fig. 1.
S
Φ
H
P
2
Fig: 3
R
Fig: 4.
F
Fig:5
T.Conder sculpt
S
UNIV
OF
[ 227 ]
LECTURE VIII.
A DESCRIPTION OF THE ORRERY IN ITS DI-
VISIBLE STATE, AND THE MOTIONS OF THE
PLANETS OF OUR SYSTEM ELUCIDATED BY
THE APPLICATION OF THE PLANETARIUM
PART OF IT; ALSO BY DIAGRAMS AND THE
KNOWN LAWS OF PROJECTILE AND CEN-
TRIPETAL FORCES.
THIS instrument was constructed by Mr. Mar-
tin, and is now sold by Messrs. Jones, Holborn.
It is called a planetarium, and is represented, to-
gether with its appendages, plate 10. The whole
forms a complete and elegant construction of an
orrery; and which, being divided into its respec-
tive particulars of clucidation, namely, of the pla-
nets, the scasons, and the Moon, renders it pre-
ferable to the largest compound orrery, in which
the whole phenomena are exhibited at the same
time, such an assemblage of movements rather
causing confusion in the spectacle, unfavourable to
accurate and individual observation.
In fig. 1, plate 10, the instrument is furnished
for the purpose of elucidating the planetary phe-
nomena, and is in this arrangement of it called a
planetarium.
Q 2
The
228
LECTURES ON ASTRONOMY.
The seven primary planets are placed in their
proper stations, and accompanied by their respec-
tive satellites. They are all put in motion by
turning the handle H, which communicates with
the wheel-work in the box A.
This machine illustrates the annual motion of
the planets, on which depend many curious phe-
nomena, one of which is the apparent retrogres-
sion, which the parts 4 and 5 are particularly cal-
culated to exhibit.
Fig. 2 represents the appendage, which, when
attached to the plate of the orrery, forms a tellu-
rium, for which purpose the planets must be taken
off the supporting stem in the centre of the in-
strument, and fig. 2 placed on it, and fastened
down by a screw at a. Under the globe of the
Earth, fig. 2, is an index NO, which shews side-
real time, or that in which the Earth performs its
diurnal rotation. At P is another index, which
shews solar time, or that in which the Sun transits
the meridian of any place on our Earth. H and I
is called the terminator, because it divides the
dark from the illuminated part of the Earth. G
is the solar ray, shewing to what part of the
Earth the Sun is vertical, for every day in the
year, as the Earth revolves round the Sun, and on
its axis; also its declination.
The arm, K, rests on the plate of the orrery,
and serves to point out the Sun's place in the
ecliptic circle, (which is represented on the outer
circle of the plate of the orrery,) as transferred by
the
LECTURE VIII.
229
the annual revolution of our Earth in its orbit.
RST are moveable circles, which shew the longi-
tude and latitude of every place on our Earth,
when the circle RS is placed over the equator.
These are sometimes called the moveable ho-
rizon and meridian: the former is used with strict
propriety, but not the latter when referred to this
instrument, in which the terminator HI always
represents the visible horizon, and therefore the
circle RS is then properly a circle of longitude
only.
Fig. 3 represents that part of the orrery which
is adapted to illustrate the phenomena of the
Moon, and, when it is placed on the plate of the
orrery, the instrument is called a lunarium.
Having given you a general description of this
curious orrery, I shall proceed to employ it in its
individual arrangement, and first render it a pla-
netarium.
The planets are placed on the supporting stem,
according to their respective situations in regard to
the Sun, which latter is represented by a large
brass ball, S. The signs of the zodiac are engra-
ven on the planisphere according to their apparent
arrangement in the heavens, to which the places
of the Sun and planets are transferred. The signs
have their respective or correspondent months and
days also engraven on a circle exterior to them; so
that the Sun and planets may be placed in their
proper situation for every day in the year, referring
to White's Ephemeris, which informs us of the si-
Q 3
tuation
230
LECTURES ON ASTRONOMY.
tuation of each, with their aspects in respect to
our Earth and the Sun.
The assumed period and orbits of the three
most remarkable comets are represented on the
plate of the orrery, as well as the known periods
of Jupiter, Saturn, and the Georgium Sidus, and
their orbits.
The planets are represented by ivory balls; the
one half of each of them black, and the other
half white; the white or illuminated sides of the
planets being always turned towards the Sun;
their known phases, as seen by a spectator on the
Earth, is represented by the revolutions of the pla-
nets, which latter is effected by turning the han-
dle of the instrument, which puts each planet in
motion round the Sun, and with the different de-
grees of velocity they actually have in the hea-
vens, so that their aspects, in respect to the Earth,
are seen very clearly; and, as the planets move
independently of each other, they perform their
periods in the same relative time as the real pla-
nets do in their orbits.
On putting the machine in motion, we must
observe the place of any planet in the ecliptic;
and, when it returns to the place from whence it
started, see how many days it has been in per-
forming its revolution, and we shall find that it
corresponds exactly with the known period of that
planet.
To observe their relative velocities, we must
take the Earth as a standard, and we shall find
that
LECTURE VIII.
231
that they all observe the same relative velocities as
they really have in the heavens.
Suppose we place Mercury and our Earth on
the same point of the ecliptic: when Mercury ar-
rives at the same part from which he started, we
shall perceive that the Earth has advanced only
87 days in her annual orbit. In like manner we
may observe the periods and relative velocities of
each planet, by taking our Earth and time as a
standard.
Venus and Mercury are called inferior planets,
because their orbits are included within the Earth's,
and of course their revolutions are performed in
less time; that of Mercury being performed in 87
of our days, and that of Venus in 224.
The revolutions of the planets in this instru-
ment are to be expressed in round numbers, the ni-
cer divisions of time not being allowed for in the
planetarium. In pursuing our observations, we
shall perceive that Mars performs his revolution on
this instrument in 686 days, Jupiter in 4332, Sa-
turn in 10761, and the Georgium Sidus in 30445 ;
all of which accord with their known periods, ex-
cepting the difference of hours and minutes.
Those planets, which describe orbits exterior to
that of the Earth, are called superior; the motion
of the most remote planet is so slow, as scarcely
to be observed, but by its effects, on this instru-
ment.
The little white balls represent the Moons or
satellites which accompany the planets in their
Q 4
revolutions ;
232
LECTURES ON ASTRONOMY.
revolutions; which, being stationary, excepting as
placed by the hand on the instrument, have not
their illuminated sides distinguished from the o-
ther; for, they cannot exhibit their proper phases,
as they do not describe their orbits round their
central bodies, but only round the Sun. Another
part of this machine is adapted to exhibit all the
phenomena of our Moon, which is the most es-
sential to us to be informed of, as the phases of
the others may be inferred from their known posi-
tion, as set down in the Ephemeris, which is all
that is necessary for our observation of them. The
primary planets of this instrument have no diurnal
revolution, those also being unnecessary, as fig. 2,
plate 10, is constructed to illustrate all that re-
spects the diurnal motion of the Earth very clear-
ly; and, of the others, we know that they have
such a motion, which is quite sufficient, as of
most of them we have ocular demonstration, by
the different situation of certain spots on their
disks, these moving from one side of the planet
to another, as seen from our Earth, and disappear-
ing and re-appearing; also the motion of these spots
being always uniformly performed in the same way,
going off from the western edge, and re-appear-
ing on the eastern. The distance between the
spots appearing narrower at the margin than
when at the middle of the disk proves those bo-
dies to be globular, and that they turn on their
axes.
All
LECTURE VIII.
233
All loose or soft bodies, turning on an axis,
must become oblate spheroids, which is found to
be true, in respect to the Earth and several of the
planets. All globes which do not turn on their
axes are perfect spheres, on account of the equa-
lity of weight. The former obtain a spheroidical
form, by their equatorial parts moving quickest,
by which velocity they have a greater tendency to
fly off from the centre in a rectilinear direc-
tion, which raises the middle or equatorial parts
highest.
All the heavenly bodies appear at an equal dis-
tance from us, although their real distances are
very different.
The Moon is nearer to us than any other body
in our system, yet she appears at the same dis-
tance from us as the Sun does, and all the hea-
venly bodies appear as if placed in a concave
sphere; which deception arises from our eye be-
ing in the centre of the sphere of light of their il-
lumination; and therefore we
and therefore we cannot properly
judge of their distance, or that of any object pla-
ced beyond the ordinary reach or circle of our
view, having no means of judging of objects with-
out that sphere, as we cannot compare them with
intervening ones, as we can of objects within
that sphere. That this is the cause of the decep-
tion alluded to is evident, even by luminous ob-
jects on our Earth in a dark night, when we can
see no intervening object, by reason of the natural
sphere of light being lost in obscurity. As thus:
in
234
LECTURES ON ASTRONOMY.
in approaching a town, in which we cannot dis-
cern any thing but the lamps, the buildings or
intervening objects not being discerned by us, we
cannot say which of the lights is nearest to us,
nor can we judge of the real distance of any of
them; and thus it is with celestial objects.
We may conclude that the fixed stars appear
of different magnitudes to us, not so much from
any difference in their sizes, but by being placed
at different distances from our Earth, as their dif-
ferent times of appearing after sun-set seem to
determine; for, after being accustomed to the
bright light of day for many hours, it is most
probable that those stars, which, by their situation,
appear the brightest to us, must be first seen, on
account of their superior brilliancy, occasioned by
their situation in respect to the Sun and Earth,
and not on account of their real size; for, we
know that when a room is first darkened, a small
glimmering light is not perceived, although a
bright light of the same size would be; but,
that, when the eye has been accustomed to the
gloom of the apartment, it becomes sensible to
the least light admitted through the smallest cre-
vice of it.
When the Sun has sunk 12 degrees below the
horizon, the stars denominated of the first magni-
tude appear; and these we may suppose to be the
nearest to us, both on account of their apparent
magnitude, and also by their being first perceived
by us. When the Sun has sunk 13 degrees below
the
LECTURE VIII.
235
the horizon, stars of the second magnitude and
degree of lustre are perceived; when 14 degrees
below it, those of the third degree of both; when
15 degrees, those of the fourth degree; and,
when 18 degrees, those of the fifth and sixth de-
grees of lustre and apparent magnitude; these are
all that are visible without the aid of glasses;
those perceived by their assistance are, on that ac-
count, called telescopic stars.
Those stars, which Astronomers have not redu-
ced to classes or magnitudes, are called nebulæ or
light clouds.
The most remarkable star in each constellation
is marked with the first letter of the Greek alpha-
bet; the next with the second letter in that alpha-
bet, and so on. When there are more stars in
the constellation than there are letters in the Greek
alphabet, the superabundant ones are distinguish-
ed by the Roman characters a, b, c, &c. and,
when these have not been sufficient to express
them all, the numeral figures have been used 1,
2, 3, &c.
Let us now resume the consideration of the
bodies which compose the solar system. You
know that all the planets, and their satellites,
shine by reflecting the light of the Sun; you are
therefore sensible that the side, turned towards
that luminary, must be light; and, as the planets
are opake bodies, the side turned from the Sun
must be involved in darkness, and cast a shadow
from
236
LECTURES ON ASTRONOMY.
from them on the opposite side, by intercepting
the rays of light.
Sir Isaac Newton has calculated the quantity of
heat in the Sun by the bulk of that body, and by
its heat at the surface of the Earth; also its pro-
portional heat at all the other planets, excepting
the Georgium Sidus.
He says, that at Mercury the heat and light
from the Sun must be near seven times as much
as it is with us, on account of the comparative
sizes of the Earth and Sun with that of Mercury
and the Sun, and their respective quantities of
matter and distances from each other.
In like manner he has also determined the de-
grees of heat and light received from the Sun by
each planet belonging to the system: Venus re-
ceiving nearly twice as much as the Earth receives,
Mars not half as much as the Earth, Jupiter not
one-thirtieth part so much as the Earth, and Sa-
turn about one-hundredth part of what is received
by the Earth. His mode of calculation may be
understood, by applying it to one planet only; as
thus: having found the distance of Saturn from the
Earth and the Sun, and its real diameter by its appa-
rent one, as seen from the Earth; by solid geometry
he discovered that the Sun contained 2360 times as
much matter as Saturn, and consequently, by com-
paring the known heat at the distance from the
Sun at which our Earth is placed, he could ascer-
tain the heat at Saturn. Also, by knowing the
size
LECTURE VIII.
237
size of each planet, and the Sun's power on
it, he could estimate the distance of the cen-
tre of gravity between each planet and the Sun;
so that of Jupiter he found to be nearly in the su-
perficies of the Sun; that of Saturn a little within
it; and that the common centre of gravity of all
the planets with the Sun is not farther from that
luminary than his semi-diameter, as I have before
informed you; also, that round this centre the
Sun revolves, by the united attractions of all the
planets combined with his own.
In this instrument, fig. 1, plate 10, the orbits of
all the planets are perfectly round, and in one
plane, which is not exactly according to fact, as
they acquire an eliptical form by the observance
of two motions; they also cross each other and
the plane of the Sun's orbit in different parts of
their orbits, and with different inclinations to it.
But these circumstances, in which this instrument
differs from the true shape and inclination of the
planets orbits, are no impediment to the applica-
tion of it, in regard to the phenomena of the pla-
ces of the planets in their orbits; and, any defi-
ciency respecting the nodes, the Ephemeris will
always supply for any time, or any planet, shew-
ing the place of the nodes; and, if we want to
distinguish the exact point of the heavens in
which any planet will appear at any given time,
we need only make use of a quadrant, or a similar
instrument, with a celestial globe and compass,
which will authenticate each observation anticipa-
ted
238
LECTURES ON ASTRONOMY.
ted by Astronomers, of the situations and bearings
of the planets, &c.
On turning the handle of this machine, if we
imagine ourselves in the Sun, all will appear regu-
lar; but, if we consider the motions of the pla-
nets, as viewed from the Earth, all those irregula-
rities will be perceived that actually take place,
in the observation of them taken from our
Earth.
The relative bulks of the balls are to each other
as those of the real Sun and planets are, only not
exactly in the same proportion; for, the Sun is
877,650 times as large as the Earth; Saturn 586
times as large; Jupiter, which is the largest of all
the planets, is 1049 times as large as our Earth;
Mars is five times less than our Earth; Venus very
little, if any thing, less; and Mercury 27 times
less.
To render the celestial phenomena more gene-
rally and better understood, I shall explain each
by a diagram, as well as by this instrument; and I
hope the repetition will not be found irksome, or
be thought unnecessary: I shall explain them as
concisely as possible, and am certain it will serve
the beneficial purpose of rendering the circum-
stances of the heavenly bodies more universally in-
telligible.
I shall begin with the grand vivifying principle,
the Sun, and shew you why it appears to pass
through all the signs of the zodiac in one year;
and this I shall do, by supposing that we could see
the
LECTURE VIII.
239
the sign which the Sun is in, at the same time
that we see him; which, although contrary to
fact, yet will serve our purpose of illustration, as
we can always know what sign the Sun is in at 12
o'clock each day, by observing what constellation
of the zodiac is on our meridian at 12 o'clock at
night, as the Sun must be in the opposite sign to
that.
These being understood, you must suppose the
exterior circle of fig. 2, plate 9, to represent the
ecliptic, or Sun's apparent path in the heavens ;
the circle ABCD to be the orbit of the Earth;
and E, F, to be the Earth in two different situa-
tions in it; also S the Sun.
When the Earth is at E, the Sun will appear to
a spectator on the Earth to be in Taurus. As the
Earth moves on easterly in its orbit, and arrives at
F, the Sun will be transferred to a more easterly
situation as viewed from it, and appear at Leo.
And thus, by the annual motion of the Earth, the
Sun will be transferred to all the signs of the zo-
diac, and appear to pass through them all in one
year.
This is very evident by the planetarium; for, if
we fix the Earth in any situation in her orbit, and
turn her forward in it to any other, we shall per-
ceive that the Sun's place will be changing con-
stantly in respect to the ecliptic-circle of the pla-
netarium or orrery, and that it will enter a new
sign every month; circumstances which actually
take place in our observations of that body in the
heavens,
1
240
LECTURES ON ASTRONOMY.
heavens, in regard to the constellations, and their
locality also accords with the speculum phenome-
norum.
The annual motion of the Earth is the cause
of another phenomenon, which may be under-
stood from fig. 2, plate 9, or rather the same
phenomenon, only considered in reference to ano-
ther circumstance produced by it; and that is,
we have the opportunity of viewing all the con-
stellations of the zodiac by their being above our
horizon, after sun-set, in the course of twelve
months.
When our Earth is at E, in fig. 2, plate 9, that
part of it which is turned from the Sun, and ap-
pears dark, represents night, and of course the
constellations which are opposite to that dark side
are visible to us at night.
When the Earth is at F, the dark part of it be-
ing turned towards the constellation Aquarius,
that will be on our meridian at 12 o'clock at night.
And thus, by the Earth's progressive motion, all
the stars of the zodiac are presented to our view
in the course of 12 months, a new constellation
appearing on our meridian at 12 o'clock at night
every month.
This is likewise pleasingly exhibited by the pla-
netarium, which, whilst the Earth is performing its
revolution, as it advances, shews all the stars of the
zodiac that are above the horizon for every night in
the year, although it does not shew the other con-
stellations, for which information a celestial globe
must
LECTURE VIII.
241
must be referred to, being adapted for that pur-
pose.
The true motion of the planets, which is ac-
cording to the order of the signs, is called direct,
or in consequentia. The apparent motion is some
times contrary to the order of the signs, which is
called retrograde, or antecedentia.
All the planets sometimes appear to have a re-
trograde motion, contrary to the order of the signs;
or, rather, are supposed to have that motion by
being transferred from one place in the ecliptic
to another more westerly; whereas, in their direct
order, they advance easterly. The apparent re-
trograde motion of a superior planet is occasioned
by the progressive motion of the Earth, but that
of an inferior by its own annual motion; and,
therefore, the places of their retrogression are very
different, the superior appearing retrograde when
in opposition to the Sun, that is, when our Earth is
between them and the Sun; and the inferior about
their inferior conjunction with him, which is, when
they are between our Earth and the Sun. The
times, also, of the apparent retrograde motion of
superior and inferior planets are different; that of
a superior happening oftener to those which move
the slowest, but that of an inferior to those which
have the swiftest motion; therefore Saturn oftener
appears retrograde than Jupiter, and Mercury than
Venus; and because a superior planet appears re-
trograde once in each revolution of our Earth, and
an inferior once in each of its own revolutions.
R
The
242
LECTURES ON ASTRONOMY.
The time of Saturn being retrograde happens at
the intervals of one year and thirteen days of our
time; of Jupiter, one year and forty-three days;
of Mars, two years and fifty-two days; of Venus,
one year and two hundred and twenty days; of
Mercury, one hundred and fifteen days. Saturn
continues in a state of retrogression one hundred
and forty days; Jupiter one hundred and twenty
days; Mars seventy-three days; Venus forty-two;
and Mercury twenty-two; at a mean calcula-
tion.
A planet is said to be in conjunction with our
Earth, or the Sun, or another planet, when it is in
the same point of the ecliptic with either: this is
true conjunction. There is also an apparent
conjunction. These conjunctions are thus distin-
guished from each other: when a line, drawn
through the centre of the Sun and a planet,
passes also through the centre of our Earth, these
bodies are really in conjunction; but when this
does not happen, although to an observer on
the Earth they may appear in conjunction, they
are not so in fact. When an inferior planet is
between us and the Sun, it is said to be in its in-
ferior conjunction; and when the Sun is between
us and a planet, it is said to be in its supe-
rior conjunction. The former happens only to the
inferior planets; and, when they are in it, they
cannot be seen by us, but as a dark spot on the
Sun's disk.
In
LECTURE VIII.
243
In referring to the situation of the superior
planets, when in a right line with our Earth and
the Sun, when they are in the same sign with
the Sun, (at which time we cannot see them,)
the Sun being between them and the Earth, they
are said to be in conjunction; and, when they
are in the opposite sign to that in which the
Sun is, they are said to be in opposition, the
Sun and planet being on opposite sides of our
Earth.
As the planets all revolve round the Sun with
different velocities, they must of course change
their relative situations to each other.
When an inferior planet is in the same sign or
degree of the ecliptic with the Sun, or with the
Earth, it is said to be in conjunction with it; and
when a superior planet is in the same degree of
the ecliptic with the Sun, it is also said to be in
conjunction with it; but when it is in the oppo-
site point of the ecliptic from the Sun, that is, in
the same sign with our Earth, it is said to be in
opposition to the Sun, but in conjunction with the
Earth. Any two planets that are in the same sign
of the ecliptic are said to be in conjunction with
each other.
When the planets are the sixth part of a circle,
or 60 degrees, from each other, their situation is
denominated sextile. When a quarter of a circle,
or 90 degrees, from each other, quartile. When
one-third of a circle, or 120 degrees, from each
other, trine. When half a circle, or 180 de-
R 2
grees,
244
LECTURES ON ASTRONOMY.
grees, from each other, they are said to be in oppo-
sition.
These situations are called the aspects of the
planets; which are expressed in the Ephemeris by
characters: Conjunction by 6, Sextile by *, Quar-
tile by, Trine by A, and Opposition by 8, as
exhibited in page 38 of the Ephemeris.
The motions of the planets, and their places in
the ecliptic, as seen from the Earth, are called
geocentric; their real motions and places in the
ecliptic, which are those in which they would be
seen if viewed from the Sun, are called helio-
centric.
I shall now apply these terms to practice, by
which they will be clearly understood, after ha-
ving explained the different affections and situa-
tions of the planets by diagrams.
Let A BCD, fig. 3, plate 9, represent the eclip-
tic, which is divided into twelve parts, and on
which the twelve signs of the zodiac are deli-
neated; T our Earth in its orbit; and V V Ve-
nus in hers, in two opposite points of it; that at
V 1, in which she is placed in the same situation
or sign with our Earth, is called her inferior con-
junction; and that, at V 2, represents her supe-
rior conjunction. Venus is also represented at
E and F, being the places of her greatest elon-
gations or distance from the Sun, as viewed
from our Earth, which is 48 degrees from it;
which are counted on the arch of the ecliptic that
measures the angle formed between the straight
lines
LECTURE VIII.
245
lines ET FT, or FT ST; one drawn from Venus
to the Earth, and the other from the Earth to the
Sun; as those two lines form the angle of which
the arch GA or AH is the measure, the Sun
and planet both being transferred to the ecliptic
circle. This is the difference also between the
geocentric place of the Sun and the planet.
Venus never appears to go farther from the
Sun, on each side of him, than to those two situ-
ations G and H, or 48°.
Let the circle L m n o represent the orbit of
Mercury, and pq the places of his greatest elon-
gations, which are only 28 degrees distant from
the Sun. On considering the situation of these
two planets, you will perceive that when Venus
is at V 1, and Mercury at m, in their inferior con-
junction, those planets cannot appear but as dark
spots on the Sun's disk; and that, when Venus is
at V 2, and Mercury at L, in their superior con-
junction, they cannot be seen by us, being in the
same sign with the Sun.
When Venus appears west of the Sun, which is
from her inferior to her superior conjunction, she
rises before the Sun in the morning; and, from
her superior to her inferior conjunction, or when
she is east of the Sun, she sets after him in the
evening. She is in each of these situations, alter-
nately, for 290 days.
I shall now explain the foregoing by this instru-
ment, by first placing the Sun, Venus, and our
Earth only, on the supporting stem. When I turn
R 3
the
246
LECTURES ON ASTRONOMY.
the handle, you will perceive that Venus is
nearer to the Earth at one time than at another;
also that she will appear sometimes nearer to
the Sun, as seen from the Earth, at others farther
from him, and at others in conjunction with that
luminary.
When Venus is placed between the Earth and
the Sun, she represents her inferior conjunction,
and her situation when she appears as a dark spot
on the Sun's disk. When on the other side of the
Sun, in which she appears in the same sign with
it on this instrument, she is said to be in her su-
perior conjunction, at which time she connot be
seen in the heavens. The same may be observed
of Mercury.
ray
I shall now take off the balls which represent
Venus and the Earth, and place the socket, fig. 5,
plate 10, on the wire which supported Venus;
and the socket P, fig. 4, plate 10, to which a long
wire is fixed on that part which carries the Earth:
then, by imagining the brass wire to be the visual
of a spectator on our Earth, directed towards
Venus, which is represented by the white ball at
the extremity of the visual ray, and which has
the part of the wire connected with it, supported
in a groove on the top of fig. 5, plate 10. This dis-
position of these parts of the instrument will ena-
ble me to shew you, why the planet does not
seem to us to recede from the place of the Sun
beyond certain limits on each side of him; also
the cause of its apparent retrograde motion, which
is
LECTURE VIII,
247
is not actually seen by us, only known by the situ-
ation of the planets in respect to the Sun and
fixed stars at any time.
L
Placing now Venus in her superior conjunction;
then, as she passes from that to her inferior con-
junction, she will appear, as supposed to be viewed
from our Earth, westerly of the Sun, which is
the time of her being a morning-star; but, as
she is moving from 48 degrees on the other
side of her inferior conjunction to her superior,
she will appear east of the Sun; then is the time
of her being an evening-star.
I have already informed you that Venus appears
retrograde, or to move backward in the ecliptic
westerly, once in each of her revolutions in her
orbit. I beg you to observe, that her time and
place of being retrograde is when she has pass-
ed through her superior conjunction eastward,
which is her direct and true motion, and arri-
ved to a certain point of the ecliptic near her
inferior conjunction, which forms an angle of 48
degrees with the Sun's place as viewed from our
Earth, at which place the visual ray from the
Earth is a tangent to her orbit; then, if you re-
mark the point of the ecliptic of the orrery at
which the planet appears, and observe the mo-
tion of the ivory ball after it has arrived at that
point on the eastern side of the Sun, you will
perceive its motion to be easterly, or direct.
I will remove the brass ball which represents
the Sun, that you may see this more evidently:
R +
the
248
LECTURES ON ASTRONOMY.
the cause of this deception is occasioned by not
having an intervening object to distinguish the
circular motion of the planets.
You now comprehend the cause of the appa-
rent retrogression of the planets; also the cause of
its not exceeding certain limits on each side of
the Sun; that the former arises from our not being
able to judge of the circular motion of those bo-
dies, for want of an intervening object; and the
latter, because in two points of the inferior pla-
nets orbits, the line of sight, or visual ray of a
spectator on our Earth, becomes a tangent to their
orbits; that is, touches the extremities of the di-
ameter of their orbits, and thereby confines their
apparent motions within that diameter.
This is better scen by the shadow of these balls
received on a screen, which shews it very clearly;
the inconvenience arising from the intervention of
the supporting stem being obviated.
The apparent retrograde motion of the planets
may also be understood from fig. 1, plate 11, in
which ABCD represents the ecliptic, S the place
of the Sun, but that luminary invisible; T the
Earth in its orbit, and VGH Venus in hers; also,
at V, the place of her superior conjunction. Let
us suppose her to be moving from that situation
easterly, till she arrives at H, near her inferior
conjunction; then will her place in the ecliptic
appear at E, as seen by a spectator on the
Earth.
Now,
Plate XI.
سلة
CHWest
чи
Virgo
Fig. 1.
A
North
South
Leo
B
E
East D
G
H
Fig. 2.
A
Fig. 3.
KIHGAFED C
Cancer
Worth
Gemini
B West
M
5
Libra
M.Bryan delint
Scorpio
Sagittarius
South
D
K
Capricomus
E
R
B
Taurus
H
D
Aries
East C
Aquarius
Pisces
T.Conder sculpt
LECTURE VIII.
249
ray
Now, suppose the line 1 2 to be the visual
of an observer on the Earth, this ray being a tan-
gent to the orbit of Venus, that is, touching one
of the extremities of its diameter, as she is com-
pleting the other part of her revolution from H to
G, till she arrives at G, where the ray again be-
comes a tangent to her orbit; she will appear to
move amongst the fixed stars backward, or con-
trary to the order of the signs, from east to west,
because there is no intervening object by which to
judge of her circular motion.
When an inferior planet is in the superior part
of its orbit, its motion appears true and direct,
from west to east; when in the inferior, false and
retrograde, from east to west.
In referring to this diagram, I have taken no
notice of the motion of our Earth in its orbit, as it
would only confuse the mind by multiplying ideas,
and as the relative situations of the two bodies
are as well understood without it.
All that we have observed of Venus and our
Earth is equally applicable to Mercury; allowing
that, on account of his distance from the Sun
being less than that of Venus, his change of mo-
tion must happen oftener, as it depends also on
his arriving at the two extremities of the diameter
of his orbit, the same as that of Venus does ; and
therefore, on account of his orbit being less than
that of Venus, and his motion in it quicker, the
circumstance alluded to must occur oftener to
him.
At
250
LECTURES ON ASTRONOMY.
At the points of a planet's orbit, in which it
appears to change the direction of, its motion, it
seems to remain some time stationary, because a
part of the curve is so near the point which the
ray touches, that it cannot be distinguished from
it.
One thing remains to be observed of fig. 3,
plate 9, in which I have considered the Earth as
at rest, and Venus in motion, which serves to con-
vince us of the absurdity of supposing the Earth
to be actually at rest in the centre of our system;
because, if it were so, the planet would appear
to pass through all the signs of the zodiac in its
revolution; or, supposing it to be at rest at all,
even in its situation represented fig. 1, then the
planets would always be seen in the same signs
of the zodiac, as between F and E; whereas they
are seen in all, occasionally, according to the
motion of our Earth compared with their mo-
tions.
This instrument is particularly well calculated
for exhibiting the phases of the planets of our sys-
tem, which shine only by reflecting the light of
the Sun; and, therefore, by fixing them for their
situation at any time, in respect to the Sun and our
Earth, and turning them on in their orbits, their
different phases, as seen from the Earth, will be
exhibited.
We will, if you please, first, make observation
of the phases of Venus; as, on account of her
near situation to our Earth and the Sun, they are
more
LECTURE VIII.
251
more distinguishable than any other. If we place
Venus at either her superior or inferior conjunc-
tion with the Sun, and turn her on in her orbit,
as the Earth and planet revolve round according
to their respective velocities, the ivory ball will
exhibit the phases of Venus as seen from the
Earth. Thus, if we wish to know what phase
that planet will exhibit for any evening on which
she will be visible, we must place the Earth and
Venus in their respective places on the planeta-
rium for that evening, (by the information of an
Ephemeris,) and, after fixing both balls with the
white sides towards the Sun, we shall see the
phase of Venus as it will be actually perceived
by us through a telescope, or very nearly so, al-
lowing something for the inclination of her orbit,
or place of the nodes, this instrument not exhibit-
ing those deviations.
The phases of Venus may also be understood
from fig. 3, plate 9. V1 is Venus with her dark
side turned towards the Earth, which renders her
illuminated side invisible to us. When seen, she
appears as a dark spot on the Sun's disk, which is
called her transit: this does not happen every
time she is in her inferior conjunction, because of
her orbit being inclined to the plane of the eclip-
tic, or central solar ray, and therefore she does not
always pass in a direct line between the Sun and
us; and, when she does not nearly do so, on ac-
count of her distance from the Sun and us, she
does not appear to pass over his disk. When she
is
252
LECTURES ON ASTRONOMY.
is in her superior conjunction, as at V 2, fig. 3,
plate 9, she has the whole of her illuminated sur-
face turned towards the Earth; but, on account of
her nearness to the Sun at that time, if not in a
direct line with the central solar ray, she is not
seen by us in either case; in one, because of her
affinity of situation to that luminary, and in the
other, on account of the solar ray intercepting our
view of her.
When Venus is near to her superior conjunction,
she appears nearly round to us, but small, on ac-
count of her distance from the Earth. When she
is east of the Sun, which happens immediately
after she has passed through her superior con-
junction, she appears larger every day, because
she is approaching nearer to the Earth each
day.
The superior as well as the inferior planets are
sometimes nearer to the Earth than at others, and
consequently appear larger at those times at which
they approach nearest to it. They have also the
appearance of being stationary and retrograde, as
well as the others; yet, by describing an orbit
much larger than ours, and exterior to it, they
constantly turn the greater part of their illuminated
side towards us, and therefore appear almost like
the Moon at full.
The superior planets are retrograde when seen
in opposition to the Sun, that is, when our Earth
is interposed between them and that luminary;
and they are direct when in conjunction with
the
LECTURE VIII.
253
the Sun, that is, when the Sun is between us and
them.
Let A BCD, fig. 2, plate 11, represent the or-
bit of Mars, (as it is immaterial which of the su-
perior planets is nominated to illustrate their ge-
neral motions and appearances,) EFGH the or-
bit of our Earth, and S the Sun. Then, when
Mars is at I in his orbit, and the Earth at K in
hers, the Sun being between the planet and the
Earth, Mars will be in conjunction with it. But
when Mars is at L, and the Earth at K, the Sun
and planet being on contrary sides of the Earth,
the planet is said to be in opposition to the
Sun.
In explaining the retrograde motion of a supe-
rior planet, by fig. 3, plate 11, we must consider
ABCD the ecliptic, NMRS the orbit of Mars,
OPQT the orbit of our Earth, and S the Sun, in
the centre. As the superior planet is much lon-
ger in performing its annual revolution than the
Earth, and, as its apparent retrograde motion de-
pends on the diameter of the orbit of our Earth,
it will be more natural to suppose Mars to be at
rest in this illustration, and the Earth in motion;
therefore, let us suppose Mars to be stationary, as
at N, in opposition to the Sun, and let the Earth
be first considered, as at O, when it is exactly in
a direct line between the Sun and Mars. In this
situation of Mars and our Earth, the former will
appear to us to be in the opposite sign to that in
which the Sun appears; but, if the Earth be sup-
posed,
254
LECTURES ON ASTRONOMY.
posed, as at O, in its orbit, the visual ray to a
spectator on it, as directed to Mars, will be trans-
ferred to A in the ecliptic. If we consider the
Earth at either P or Q, a line drawn from it
through the planet to the ecliptic forms a tangent
to the Earth's orbit. Whilst the Earth is moving
from Q to P, through 12 3 4 5 6, and its conjunction
with the Sun at T, its motion is direct, or from
west to east, in the ecliptic, as may be seen by
the lines drawn through that part of the Earth's
orbit, through Mars to the ecliptic. When he ar-
rives at P, the visual ray is directed to K in the
ecliptic; and, in moving through 6 5 4 3 2 1, and its
opposition N, it will appear to describe the arch
of the ecliptic KIHGAFEDC, and to move
from east to west, or retrograde, through the same
portion of the ecliptic. When the planet is either
at P or Q, it will appear stationary for a few
days.
I hope I have now conveyed to you a clear idea
of the real and apparent motions of the planets.
One thing yet remains to be illustrated by the pla-
netarium, which is, the absurdity of the Ptolemaic
system, and the truth of the Copernican. I will
place the ball which represents our Earth on the
centre stem of this instrument, and a small brass
ball to represent the Sun on the arm, which usu-
ally carries the Earth round in its annual orbit, and
all the other planets in their proper situations.
This disposition of the heavenly bodies is confor-
mable to the Ptolemaic system of the universe;
and,
LECTURE VIII.
255
and, on putting the bodies (thus arranged) in mo-
tion, we shall perceive, that, were our Earth so
situated, the motions of all the planets would ap-
pear regular and direct to us, and that every other
phenomenon observed of them, as their periods,
phases, &c. would be exactly contrary to what is
actually perceived of them. Venus and Mercury
might also be seen in opposition to the Sun or in
the opposite sign to him; and the superior planets
when in the same sign, or in conjunction with the
Sun.
My desire of introducing to my dear pupils
these studies arises from a conviction of their uti-
lity, inasmuch as they elevate the mind by the
communication of ideas naturally tending to refine
and purify the imagination, leading it to reject
frivolous and low pursuits, and to delight only in
such things as exalt and perfect human nature; by
which means they will avoid engaging in the fol-
lies of those thoughtless beings, who waste their
days in baneful pleasures which finally terminate
in mortification and disgust.
That active principle, the imagination, must be
employed on some object or subject; it is there-
fore the duty of those, who undertake to form the
minds of youth, to guard them against those
which are improper: this duty can no way be so
efficaciously performed as by introducing them to
those which are not only proper, but improving
and interesting; and that this is essential, the
many instances we meet with of prostituted abi-
lities,
256
LECTURES ON ASTRONOMY.
lities, both in society and literature, clearly demon-
strate.
How much then have those to answer for, who,
possessing superior sense, not only neglect the
proper use of it, but employ it in such a manner
as to deprave human nature. Never, my dear
young friends, suffer yourselves to read an author,
be his abilities ever so great, who wishes to in-
struct you in what is contrary to virtue, by paint-
ing vice in false colours; for, such is the infirmity
of our nature, that it is not safe to be familiar
with books, or conversation, which have the least
immoral tendency; because the effects of habit
are so powerful, that what at first may disgust us
(by reason of the native dignity of virtue which is
inherent in every uncorrupted breast) may, by the
mind becoming accustomed to it, and losing that
delicacy natural to it, cease to disgust us ;— and,
when the finer impressions are thus injured by the
rough and coarse ideas impressed on the mind,
they are not only deprived of their energy, but too
often no vestige remains.
How important does it appear then, to cherish
all ideas that elevate the mind, and lead to virtue!
It is the only sure barrier against the encroach-
ments of folly and depravity, and is also the most
graceful ornament of our nature; for, if we wish
to please by an engaging exterior, there is no
surer method to obtain that advantage, than by
furnishing our minds with ideas which are beau-
tiful and harmonious, and dignity of charac-
—
ter
LECTURE VIII.
257
ter will always result from elevation of senti-
ment.
We can judge, by the performance of any artist,
whether he has cultivated a good or a bad taste;
and, if we perceive the former, we not only ad-
mire the subject, but the man; but if the latter,
although equally well executed, we are not pleased
with the performance, nor can we esteem the art-
ist; as we suppose, in both cases, that the charac-
ter of the piece is descriptive of the genius or dis-
position of the person who produces the effect.
Thus will you become esteemed and admired, in
proportion as you cultivate a taste for the sublime
and beautiful, which you can only attain by an in-
nate sensibility to each, and which, when pos-
sessed of, will never fail to produce the sweet, the
charming, emanations of inherent excellency.
END OF THE EIGHTH LECTURE.
S
[ 259 ]
LECTURE IX.
OF THE OBLIQUITY OF THE AXIS OF THE EARTH
THE NU-
TO THE PLANE OF ITS ORBIT.
TATION OF THE EARTH'S AXIS ACCOUNTED
FOR. OF MR. NORWOOD'S METHOD OF AS-
CERTAINING THE NUMBER OF MILES CON-
TAINED IN A DEGREE OF THE EARTH; AND
THE IMPROVEMENTS MADE SINCE HIS TIME
IN THIS CALCULATION, BY A KNOWLEDGE
OF THE TRUE FORM OF THE EARTH ON THE
PRINCIPLES OF GRAVITY.-
OF GRAVITY. OF SOLAR AND
SIDEREAL TIME, AND THE INEQUALITIES
OF THE SOLAR DAYS AMONGST THEMSELVES.
OF THE TROPICAL OR CIVIL YEAR.
OF
THE VICISSITUDE OF THE SEASONS, AND THE
DIFFERENT LENGTHS OF
DAY AND NIGHT
THROUGHOUT THE YEAR.
OF THE MO-
TIONS OF THE MOON.
HER DIFFERENT
PHASES.
THE INCLINATION OF HER OR-
BIT TO THE ECLIPTIC.
THE GREAT VA-
RIETY IN HER AFFECTIONS.
OF THE SY-
NODICAL AND PERIODICAL MONTH.
Not content
With ev'ry food of life to nourish man,
S 2
By
260
LECTURES ON ASTRONOMY.
By kind illusions of the wond'ring sense
Thou mak'st all nature beauty to his eye
Or music to his ear.
AKENSIDE.
By removing the planets, and placing fig. 2,
plate 10, on the plate of the orrery, it forms a tel-
lurium, which is constructed to exhibit the phe-
nomena occasioned by the diurnal and annual mo-
tions of the Earth, and the obliquity of its axis to
the ecliptic, with every circumstance in which the
Sun's influence on it is individually considered.
The globe turns on an axis, which is inclined to
the plane of its orbit, as that of our Earth is, in
an angle of 66 degrees, which is the distance of
the north and south extremities of it from the sol-
stitial points, those being the Sun's limits on each
side of the equator, as will be perceived (when the
Earth is turned on in its orbit) by observation of the
solar ray G.
RS represents one half of the circle of longi-
tude, as I have already mentioned, and RST
the moveable meridian: the former should always
lay over the equator of this globe, as the longi-
tude of places on it are referred to the equator;
and the latter will then shew the latitude of all
places on this globe, which is their distance from
the equator. When we want to know the longi-
tude of places, we set the first degree of a circle
RS in a line with London, that being the place
from which longitude is counted in England, and
then all the degrees of longitude will answer to
their
LECTURE IX.
261
their proper places on this globe. If we want to
know, at the same time, the latitude of all the
places on the globe, we must observe the horizon-
tal lines from each degree of latitude, marked on
the semicircle RTS, and the places will each cor-
respond with their respective degrees of latitude :
- or we may, after finding the longitude, move
the globe round, so that the general meridian may
lie over the different meridians of places on the
Earth.
The dial under the globe shews sidereal time,
or that in which the Earth revolves on its axis,
which is always performed in 23 hours, 56 mi-
nutes, and 4 seconds. The dial under the Sun
shews solar time, or that which elapses between
the Sun transiting our meridian one day, and
his return to it the next day: the effects of
these circumstances I shall explain in their proper
place.
When we fix the Earth on any part of the eclip-
tic-plate of the orrery, the Sun's place on it will be
transferred to the opposite sign.
As it is by the Sun's place that we usually set as-
tronomical instruments, in order to observe terres-
trial and celestial phenomena, in using this instru-
ment, I look for the Sun's place, and, letting the
index K point to it, set the Earth to the opposite
sign. On turning the Earth on in its annual orbit,
the index K, moving along at the same time, trans-
fers the situation of the Sun to every point of the
ecliptic-circle, and keeps the Earth and Sun in their
$ 3
respective
262
LECTURES ON ASTRONOMY.
respective situations during the Earth's entire revo
lution in its orbit.
The terminator HI, which divides the enlight-
ened from the dark hemisphere, together with the
solar dial, serve to shew the length of the day and
night of every place on the globe, for any day in
the year, by setting the globe to the situation of
those places for any given time, in respect to the
solar ray; which is easily done, by taking the situ-
ation of the Earth at any time as a standard.
Previous to applying these observations, I have
a few things to acquaint you with respecting the
Earth, which I omitted introducing before, think-
ing it might afford me the opportunity of a neces-
sary revise of a subject much treated of in my pre-
liminary Lecture. I then informed you of a mode
used by the ancients to measure the size of our
Earth, and also pointed out to you the imperfec-
tion of that mode, originating in their ignorance of
gravity and geometry.
We will now examine the accuracy of the mo-
dern mode of estimation, resulting from the know-
ledge of gravity and mathematics.
Many methods have been devised for determi-
ning this fact of the size of the Earth; but I shall
select the one pursued by Mr. Norwood, and prac-
tised in 1635, as it was more successful than any
that had been previously adopted, and is easily un-
derstood, being divested of those niceties of cal-
culation since entered into, which, although im-
provements on the accuracy of his, yet, in descri-
bing
LECTURE IX.
263
bing the mode he pursued, we are less perplexed
and equally gratified, the principles of estimation
being the same in all. Before following Norwood
in his investigation of this subject, I will inform
you, that, by the inferences deduced from his
mode, and from the improvement of others, since
his time, in calculation, who have allowed for the
oblate figure of the Earth, and have used instru-
ments of greater nicety of adjustment, by which
the quantity of a degree has been ascertained with
more precision, it appears that the Earth is about
25,000 miles in circumference, 7,978 in diameter
at the equator, and 7,938 at the poles; also that
its surface contains 198,950,000 square miles.
A
Mr. Norwood's manner of estimating the length
of a degree on the Earth's surface, and its circum-
ference, was this: He took the Sun's altitude
when on the meridian at London, on the day of
the summer-solstice, and then made the same ob-
servation of the Sun's altitude, on the meridian at
York, on the year following. He thus discovered,
by the difference of its altitude at the two places,
that their difference of latitude was 2° 28'. He
likewise measured the distance between the two
cities, or their difference of latitude in miles.
This must have been very tedious, as, at every
curviture of the road, he must have made a draw-
ing, and have calculated the sides of all the angles
and triangles, in order to reduce the whole into an
uniform arch of a circle, allowing also for the as-
cents and declivities in the road. These two pla-
S 4
ces
264
LECTURES ON ASTRONOMY.
ces lying nearly under the same meridian, or ha-
ving nearly the same longitude, when the above-
mentioned circumstances had been allowed for,
also the latitude of the two places, the angle of
the arch of a circle formed on the scale corre-
sponding to the great circle of the heavens, the
relative portion of a whole circle on the scale
was clearly seen; and, of course, by the quan-
tity it contained in English miles within that arch,
compared with the degrees of a circle, it was dis-
covered how many English miles a degree con-
tained.
When this observation was taken, the figure of
the Earth was not considered otherwise than as a
perfect sphere. But, since his time, all impedi-
ments to accurate computation have been over-
come by Picard, Cassini, and other measurers,
who have taken observations at many different de-
grees of latitude between the equator and the
poles. Thus we find that perseverance will sur-
mount all difficulties arising from natural effects.
This globe, you perceive, by the degrees on the
brass semicircle, is inclined to the centre of the
Sun or plane of its orbit, in an angle of almost
66 degrees, which is nearly its constant inclina-
tion to it; although it varies a little, but not more
than 19 seconds of a degree in nine years; and
the motion which causes this variation is called the
nutation of the Earth's axis.
This motion of the axis of our Earth is produ-
ced by the attraction of the Sun and Moon upon
the
LECTURE IX.
265
Al-
the protuberant matter about the equator.
though this motion is dependant, both on the at-
traction of the Sun and Moon, yet it is effected
chiefly by that of the Moon, on account of her
nearness to the Earth, and of her deviating farther
from the equator; by which her action is as it
were perpetual. These two attractions, being un-
equal to each other, cause this motion of the axis
of our Earth to be performed in a conical shape,
the extremity of the axis forming a small elliptic
revolution round the centre of their mutual attrac-
tions, which is completed in 18 years and 7
months, being nearly the same with the period of
the Moon's nodes, which I shall speak of hereaf
ter; upon the motions of which the quantity of
the nutation of the Earth's axis each year princi-
pally depends. The period of its entire revolution,
or time of the axis of our Earth forming exactly
an angle of 66 degrees and a half with the eclip-
tic, or central solar ray, has been fixed by obser-
vation, taken at different times of the declination
of the fixed stars, as well as by calculation on Sir
Isaac Newton's principles of attraction. As the
orbit of the Earth is an ellipse, it is certain that it
must be nearer to the Sun in some parts of it than in
others; also, that as its axis is inclined to the cen-
tre of the Sun, when the Earth is situated in those
parts of its orbit where the equator is in a straight
line with the Sun, which happens in only two
points of it, the action of the Sun cannot affect
the axis of the Earth so as to incline it more or
less
266
LECTURES ON ASTRONOMY.
less from its perpendicular situation, as it acts
equally on the two extremities of the axis; but,
when it is in any other part of its orbit, the Sun
acts obliquely, and unequally, on the protuberant
matter about the equator, and of course the incli-
nation of the axis of the Earth to the centre of
the Sun must be altered; and the effects of this
variation being the same on both sides of the e-
quator, it occasions the extremities of the axis to
form an ellipse. The nutation of the Earth's axis.
has been computed by Astronomers for every time
of the year, by comparing the attractions of the Sun
and Moon together, and is set down in the Ephe-
meris; at least, the different angles formed between
the equator and ecliptic is noted for different times
of the year, which depends on this circumstance,
united with the precession of the equinoxes.
When we reflect on the variety of circumstances
which must be allowed for, by all Astronomers,
in their observations of the phenomena of the
heavenly bodies, we are astonished at the success
and patience with which they prosecute their re-
searches. They must certainly be endowed with
a most extraordinary spirit of investigation, and
firmness of intellect, to surmount all obstacles,
without regard to the length of time passed in
these amazing exertions of body and mind. Those
men deserve our admiration,
Whose curious thoughts with active freedom soar,
And trace the wonders of creating pow'r.
Mrs. E. CARTER.
I
LECTURE IX.
267
I will now proceed to explain the phenomena
this machine is constructed for exhibiting, both by
it and by diagrams.
The Earth's motion on its axis, as I have before
observed, is always equal, and is performed in 23
hours, 56 minutes, 4 seconds, and therefore the
sidereal days are always precisely of the same
length; that is, any star perceived on our meridi-
an, at 12 o'clock one night, will appear in the
same situation at 56 minutes 4 seconds past 11
the next night, by a well-regulated clock. But,
as the Earth has a progressive motion also, by
which it advances alınost a degree eastward in its
orbit, in the time it turns once on its axis, the Sun
does not perform his apparent revolution, or his re-
appearance on our meridian is not effected, in ex-
actly the time a given star performs its apparent
revolution in.
The solar days are not all equal among them-
selves, on account of the obliquity of the equator
to the ecliptic, which causes the Sun to be some-
times longer than in others in the time of two of
its conjunctions with a particular meridian; there-
fore the solar days are sometimes more and some-
times less than 24 hours, never being exactly that
length but on four days in the whole year, as at all
other times the central solar ray is inclined to the
equatorial motion; but on those four days it is pa-
rallel with it, and therefore the Sun will transit
the meridian exactly in the 24 hours,
The
268
LECTURES ON ASTRONOMY.
The Earth turns 366 times on its axis, whilst
the Sun performs 365 of his apparent revolutions,
or the Earth the 365 parts of its orbit; because,
as the Earth advances almost a degree, or the
365th part of its orbit, eastward, whilst it turns
once on its axis, it requires as much more than
one turn on its axis to complete the natural or so-
lar day as it has advanced in its orbit in that time;
therefore we have one more sidereal than solar
day in the year; consequently the sidereal days,
or the times that our Earth revolves on its axis,
in performing its annual revolution, are 366 in the
year.
The inequality of the solar days amongst
themselves is occasioned by the obliquity of the
orbit of our Earth to the plane of the equator,
which occasions the Earth's motion in it (and on
which they depend) to be sometimes swifter and
sometimes slower than the mean rate of 24
hours.
The Ephemeris contains tables of the equation
of time, which is the difference between mean
time, or that shewn by a well-regulated clock and
solar time, for all other times except the four days
already mentioned.
The reason of the motion of the Earth on its
axis bringing the same degree of the equator to
our meridian at the same time, each evening, is
because the equator is perpendicular to the axis of
its motion; whereas the ecliptic, or Sun's appa-
rent path, being inclined to that motion, the equal
motion of the Earth on its axis, which brings e-
qual
LECTURE IX.
269
qual portions of the equator to the meridian in
equal times, must bring unequal portions of the
ecliptic, and the difference is in proportion to the
obliquity of the ecliptic to the equator.
The popular mode of illustrating this position is
by placing patches, at equal distances from each
other, on the equator and ecliptic of a globe, be-
ginning both from the first point of Aries, and con-
tinuing them through one half of both those circles,
and at the same distances throughout. Then sup-
posing two Suns to be starting together from Aries,
one in the ecliptic, and the other in the equator;
on turning the globe, all the patches from Aries to
Cancer, on the ecliptic, will arrive at the meri-
dian before those on the equator; which shews
that the Sun, during that time, is before the clock.
When Cancer is at the meridian, the patches on
the equator and ecliptic answer to each other, and
arrive at the meridian at the same instant; there-
fore the Sun and clock will be together on that
day.
From Cancer to Libra the patches on the eclip-
tic will arrive later at the meridian than their cor-
responding ones on the equator; which shews,
that, whilst the Sun is in the intervening signs be-
tween Libra and Cancer, he will appear on our
meridian later each day than 12 o'clock. This
shews one difference of the solar days amongst
themselves, or the equation of time. By taking
off the patches and fixing the index to any hour,
and only observing it at the different periods and
stations,
270
LECTURES ON ASTRONOMY.
stations, you will see the variation between solar
and sidereal time; by remarking any point of the
equator at the meridian, and the degree of the
ecliptic at it, at the same time, and turning the
globe round, until those two points again arrive at
the meridian, you will perceive that they return to
the same situation exactly in 24 hours. But, as
the Earth advances almost a degree easterly in its
orbit in that time, the place of the Sun must be
transferred one degree east of the Earth's place
on the equator; and, when that degree of the
ecliptic comes to the meridian, you will perceive
that the Sun's place has taken four minutes more
in arriving at the meridian than the Earth's place.
This illustrates the difference between solar and
sidereal time, although this globe always brings
the same degree of the equator to the meridian in
24 hours instead of only 23 hours 56 minutes ;
therefore all that must be observed as accurate, in
this problem, is the difference of time, not the ab-
solute length of time, in which the Earth revolves
on its axis.
When the Sun is at the first of Aries, the first
of Cancer, the first of Libra, and the first of Ca-
pricorn, being parallel with the Earth's equable
motion, the same degrees of the ecliptic and
equator will be on the meridian at the same.
time.
I have taken the liberty of altering the illustra-
tion of these problems a little from the original,
and also of introducing some auxiliary circumstan-
ces,
LECTURE IX.
271
ces, for the purpose of rendering it more perspicu-
ous.
When the Earth is advancing towards the Sun,
its motion is accelerated; but, when it is receding
from that luminary, its motion is retarded. The
circumstances of the accelerated and retarded mo-
tion of the Earth happen alternately. In one
half of its orbit it is the former, and in the other
half the latter; therefore the solar and cqual days
do not agree exactly in the time of the day, ex-
cept on four days of the year; that is, when the
Earth is in those two points of its orbit at which it
is at its greatest and least distance from the Sun,
the first denominated apogee or aphelion, and
the latter the perigee or perihelion, and when in
the two medium points between these two. The
difference between solar and mean or equal time
depends on the unequal motion of the Earth in
its orbit, compared with the equable motion of
the Earth on its axis, whereby they do not perfect-
ly agree together in the time of the day but four
times in the year, namely, on the 14th of April,
the 15th of June, the 31st of August, and the
21st of December; and the inequality of the solar
days amongst themselves depends on the different
obliquity of the plane of the Earth's orbit to the
ecliptic in different parts of it, whereby it is not
in the same plane, or without some obliquity, ex-
cept four days in the year, on which four days the
Sun and the same degree of the equator transit the
meridian at the same instant. These four days do
not
272
LECTURES ON ASTRONOMY.
not happen always at the same times, on account
of the intercalary day introduced every fourth
year; but the real times of their being at these
four points of the ecliptic, each year, are shewn
by the Ephemeris.
The tellurium pleasingly and conveniently exhi-
bits the difference between solar and sidereal time.
I will fix the Earth on the first degree of Capri-
corn, being that point of the ecliptic opposite to
the Sun's place, for (we will suppose) the 21st of
June, fixing the time of his being in apogee or
aphelion, or at his greatest distance from the
Earth, to be on that day in working this problem,
although it does not always happen on the same
day of the year, for reasons previously given. This
situation of the Earth and the Sun answers in this
case to the longest day in northern latitudes, and
I fix on the 21st of June, as its deviation from it
is very trifling. I will now rectify the globe by
means of the arm K L, fig. 2, placing the northern
polar circle entirely on the illuminated side of the
terminator, and I will turn the handle of the machine
till the index under the globe points to 12 o'clock of
sidereal time; I then place the index on the sun-
dial to 12 o'clock of solar time. As I turn the Earth
on in its orbit easterly, you will perceive for a few
days the dials will nearly correspond in time, on
account of the little difference of their respective
motions; although the index which shews sidereal
or rather mean time will point to 12 each day, a
little before the solar one. This difference of mo-
tion
LECTURE IX.
273
tion will be continually increasing, so that when
the Earth has performed half its annual revolu-
tion, and the Sun appears at Capricorn, the side-
real dial will have gained 12 hours on the solar
one. This situation of the Earth represents its
perihelion, or nearest distance from the Sun, as
represented at B, fig. 1, plate 9; which is also
the time of the shortest day in northern lati-
tudes.
Whilst the Sun is completing the other half
of his apparent annual revolution, from Capricorn
to Cancer, the sidereal dial will continue to gain
upon the solar one; so that, when the Sun is ar-
rived at Cancer, the sidereal index will have ad-
vanced through the whole 24 hours, gaining a
whole day in the entire revolution of the Earth in
its orbit.
The situation of the Sun when at Cancer is that
of his greatest distance from the Earth, or aphe-
lion, as represented at A, fig. 1, plate 9. This is
the time of the longest day in northern lati-
tudes.
I hope I have explained this in a rational way,
so as to make these circumstances better under-
stood than they generally are. One thing remains
to be observed of the effects of this instrument, as
it exactly corresponds with the actual cause of the
difference in solar and equal time, which is, that
the reason of the dial's shewing the two times is
because the sidereal advances along with the Earth
in its orbit, at the same time that it corresponds
T
with
274
LECTURES ON ASTRONOMY.
with its diurnal motion: the Earth's axis being
made to alter its inclination to the central solar
ray, as it actually does in the heavens, (although
the Earth nearly preserves its parallelism, in regard
to the plane of its orbit, which is always about
66½ degrees,) its inclination to the central solar ray
is variable; and it is this which causes the Sun to
appear to move north and south on our meridian,
which the central solar ray of this instrument
shews; and, of course, when he is at the highest
point on it, he must remain the longest time with
us, by reason of the great angle he makes with
the horizon; and, when at the lowest point on it,
he must remain the shortest time above the hori-
zon; and, at all the intermediate degrees, interme-
diate lengths of time.
On this instrument, the teeth in which the wheel
works, which gives the Earth its progressive mo-
tion, are disposed in the manner, and according to
the number of degrees, into which all circles are
divided, namely 360; therefore the Earth and dial
advance nearly a degree of that circle in each re-
volution of the Earth on its axis; so that, at the
end of its annual revolution, it has turned 366
times on its axis in performing it, thus according
with sidereal time. But our year is not reckoned
according to either of those times, but according
to what is called tropical, being computed by the
period which elapses between the Sun being on
the solstitial point of Capricorn one year, which is
in
LECTURE IX.
275
in December, and his return to it the next, which
is found to be performed in 365 days, 5 hours, 48
minutes, and 54 seconds. This is called the civil
year, and is that observed by all nations. But this
civil is sometimes called a common year, and
year
sometimes a leap-year.
In a common civil year, the odd hours and mi-
nutes are left out of the account, and it consists of
365 days, containing only seven months of 31
days, four of 30 days, and one of 28 days. But
then, to make up for the odd hours and minutes
omitted in the common years, every fourth year is
made to contain 366 days, which brings the time
nearly to answer to the course of the Sun. Its de-
viation from that I have informed you of before,
and also how it is allowed for.
Having explained the causes of the difference of
sidereal and solar time, and illustrated them by this
instrument, I will now exhibit the causes of the
vicissitude of the seasons, as also the different
lengths of the days and nights throughout the
year.
The Earth is now again on the first degree of
Capricorn, and the annual index pointing to the
first degree of Cancer, which is the situation of
the Earth for the longest day in northern latitudes;
the whole of the northern polar circle being on the
illuminated side of the terminator.
London being the capital city of England, I will
make the meridian of that place to correspond
T 2
with
276
LECTURES ON ASTRONOMY.
with the central solar ray, placing the brass semi-
circle over it; and then the first degree of longi-
tude on the brass circle must be supposed to be at
the meridian of London, the celestial and terres-
trial longitude not agreeing; for, London is re-
moved many degrees from the first degree of ce-
lestial longitude, which is always at the intersec-
tion of the equator and ecliptic.
The meridian of London being thus placed op-
posite the central solar ray, and the solar index
pointing to 12 o'clock, denoting the time of the
Sun being on the meridian when he is in the first
degree of Cancer, we shall perceive, by observing
the time on the sun-dial of the spot which repre-
sents London on this globe, transiting the termi-
nator, the time of sun-setting at London, on that
day in which he is in the first degree of Cancer.
Then, noting the time of London being on the
dark side of the terminator, we shall know the
length of the night; and, on noticing the time
of its appearing on the light side of the termina-
tor, we shall perceive the time of sun-rising; and,
lastly, comparing our last observation with the
time London again arrives on the dark side of the
terminator, we shall know the length of the day at
that period. At the latitude of London, and all
places on that parallel, this will be the longest day
in the year and the shortest night. In like man-
ner the length of the days and nights at any place
on our globe may be known by observing its lati-
tude, which this moveable brass meridian will
shew,
LECTURE IX.
277
shew, by reference to the parallels of latitude, and
meridians or longitude; for, by fixing this globe
for any one place, and for any one time in the
year, we may know the situation and circumstan-
ces of all other places, without farther trouble of
rectifying the globe.
In pursuing our present investigation, we will
fix upon London to make particular observation
of the length of day and night, and of the sea-
sons. When the instrument is adjusted to the si-
tuation of London for the 21st of June, the Sun's
place appearing in Cancer, all the parallels to the
equator on this globe will be cut by the terminator
into two unequal parts, excepting those contained
within the northern and southern polar circles.
When the Sun is in the first degree of Cancer, the
whole of the northern polar region is on the illu-
minated side of the terminator, and therefore we
know that the inhabitants of that region must at
that time, when the Sun is in the first degree
of Cancer, have perpetual day, never losing sight
of the Sun; whereas those of the southern polar
region must have perpetual night. But you will
observe, as the Earth performs its annual revolu-
tion, these regions have, in some parts of them,
variety in the length of their respective days and
nights, and that it is only at the extremity of the
poles that they have a continuance of such days
and nights as I have been describing; also that at
the northern pole they will have six months day,
whilst the Sun is passing from Aries to Libra, and
T 3
at
278
LECTURES ON ASTRONOMY.
at the southern pole six months night; but that, as
the Sun passes from Libra to Aries, these circum-
stances will be reversed to each.
The Sun, when in the beginning of Cancer, is
perpendicular to the tropic of Cancer, and there-
fore in the zenith of all the inhabitants of that pa-
rallel; of course his rays must fall perpendicularly
and abundantly on them.
If the axis of the Earth were not inclined to the
plane of its orbit, we should not have the pleasing
and useful vicissitude of seasons that is now af-
forded us.
All the planets of our system, of the diurnal
motion of which we are assured, have their axes
inclined to the plane of their orbits; but that of
Jupiter being very little, his days and nights must
be nearly equal all the year through; therefore he
cannot experience much variety of seasons. As
the Earth advances in its orbit, by preserving its
parallelism, the inclination of its axis, and the si-
tuation of places on it, in respect to the Sun, are
continually changing, as you will perceive whilst I
am turning the globe on in the ecliptic of this in-
strument; for, as it advances easterly from Capri-
corn to Aries, the northern polar circle will recede
farther and farther from the Sun, getting more and
more on the dark side of the terminator; so that
when the annual index points to the first of Libra,
which is the time of the autumnal equinox, the
terminator will divide the northern polar circles
into two equal parts, and also all the parallels to
the
LECTURE IX.
279
the equator; consequently the days and nights must
be equal to each other all over the globe. In this
situation of the globe, you will perceive that the
Sun acts equally on every part of the protuberant
matter about the equator, and therefore that the
axis can suffer no nutation. The Sun is now
perpendicular to all the inhabitants of the equa-
tor.
On turning the Earth on in its orbit to Cancer,
the days are found to be perpetually decreasing to
the inhabitants of London, and to all the inhabi-
tants of northern latitudes. When the Earth ar-
rives at Cancer, and the annual index points to the
first of Capricorn, the day will be the shortest at
London of the whole year, and of course the night
the longest. The length of both will be shewn by
the sun-dial; also the whole of the northern polar
circle will now be on the dark side of the termina-
tor, and the whole of the southern on the illumina-
ted side of it. The central solar ray, when the
Sun is in the first of Capricorn, points to the tropic
of Capricorn, and the days at London are then
shorter than the nights.
By turning the Earth on till the Sun is in Aries,
we again see how all the parallels to the equator
are equally divided by the terminator, this being
the time of the vernal equinox; so that the days
and nights are again equal to each other all over
the globe, and the Sun rises and sets at six o'clock
at every place on it. From this time, till the Sun
is again in Cancer, the days at London will be
T 4
continually
280
LECTURES ON ASTRONOMY.
continually increasing. Thus you have had
a full view of all the phenomena of our Earth,
dependant on the inclination of its axis. For the
information of those who may not have the oppor-
tunity of exemplifying these circumstances, by this
or similar instruments, I will endeavour to explain
the vicissitude of the seasons by a diagram.
Let plate 12 represent the situation of the Earth
and the Sun, at the four quarters of the year.
In this figure, S is the Sun, A the situation of the
Earth in respect to the Sun in June; in which si-
tuation of it, the Sun's place is transferred to Can-
cer, and the whole of the northern polar circle of
our Earth is turned towards the Sun, and therefore
those regions must enjoy perpetual day. We also
observe, that the central solar ray (which is repre-
sented by the broad line EF) points exactly to the
tropic of Cancer; and, therefore, that the inha-
bitants of that tropic receive the direct influence of
the Sun's rays at this time. The line which di-
vides the dark from the enlightened part of the
globe now cuts all the parallels to the equator,
excepting the polar circles, into two unequal parts,
and therefore the days and nights are unequal to
each other, in all those parts not included within
the polar circles.
When the Earth has arrived at C, that part of
its orbit in which it is at Aries, and the Sun is in
Libra, the time of the autumnal equinox, the e-
quator and the parallels to it being cut into two
equal parts by the terminating line, the days and
nights

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North
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CAPRICORN
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June
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September
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PACIFIC
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SOUTH
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March
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OF
LECTURE IX.
281
nights are of an equal length all over the globe.
In this situation of our Earth, the central solar ray
points directly to the equator, and is therefore
perpendicular to the inhabitants of that lati-
tude.
As the Earth moves on in its orbit, the northern
polar circle will continually be receding more and
more from the Sun; and, when the Earth has arri-
ved at D, or at Cancer, and the Sun appears in
Capricorn, the northern polar circle will be wholly
on the dark side of the Earth, and the southern
polar circle on the enlightened side. The circum-
stances of those regions will be exactly the same,
whilst the Earth is going from hence to Capricorn,
as was observed of the northern polar regions,
whilst the Earth was passing from Capricorn to
Cancer; and those of all the places in southern la-
titudes will, in the mean time, be the same with
those which were observed of all the places in
northern latitudes, in the foregoing half of the
Earth's revolution; which circumstances it is un-
necessary to repeat, as the application to them has
been fully made in the illustration of this subject,
by means of the tellurium.
The next object which offers itself to our consi-
deration is the Moon, which accompanies the
Earth in its annual revolution; of which I shall
first treat in the theory, and afterwards explain
all her phenomena by the lunarium, fig. 2, plate
11.
According
282
LECTURES ON ASTRONOMY.
According to Sir Isaac Newton, this constant
companion of the Earth is not of so dense a nature
as the Earth is, her proportion of density to it
being only as five to nine; and her mass as one to
twenty-six. Her apparent diameter at her mean
distance from the Earth is 32′ 12″.
The Moon's axis is inclined to the plane of her
orbit in about 6 degrees, and is variable, like that
of the Earth, to the plane of the ecliptic, and is
effected by the same means. The plane of the
Moon's orbit is also inclined to the ecliptic; the
quantity of the angle between them is also varia-
ble, on account of a trifling nutation of the axis
of the Moon; but, at a mean rate, this angle is
about 5°.
The physical cause of the motion of the Moon,
round the Earth and the Sun, you are already ac-
quainted with; but her varieties remain to be
treated of. These also depend on the universal ef-
fects of gravity and attraction; for, although some
of them are peculiar to the Moon, and other se-
condary planets, yet they are all the result of the
same laws.
You must be sensible, that, if the Sun acted in
the same degree on the Earth and Moon, and at
all times uniformly so, their motions would be re-
gularly performed round the centre of gravity be-
tween them, as it could not alter their respective
individual action on each other; but, the contrary
of this supposition being the fact, and the Sun
being nearest to one when farthest from the other,
one
LECTURE IX.
283
one must be more affected by the Sun's attraction
when the other is less so; therefore their action
upon each other, at different times, must by this
means be variable; and it has been found exces-
sively difficult to allow for these varieties, because
the Sun's attraction does not act upon them in
lines parallel to each, but in such as form an angle
between them, therefore the different degree of
obliquity, with which it acts on each, must cause
great difficulty in calculating the different aspects,
&c. of the Moon, and render this physical calcu-
lation a more arduous task than any other annually
entered into by mathematicians. The great New-
ton, it is true, has furnished the materials for ma-
thematicians to work with; yet it must require
great skill and mental labour to complete this fa-
bric of sublime calculation, so as to afford a true
register of those facts it is to represent to the
mind.
The figure of the Moon's orbit is nearly that of
an ellipse; but, owing to the varieties in her affec-
tions, and their inequalities amongst themselves,
not regularly so.
The only equable motion of the Moon is that
with which she revolves on her axis, her revolu-
tion on which is performed exactly in a synodical
month, or 29 days and a half. This is discover-
able by the spots on her disk, which prove that
she always presents nearly the same face to us at
the same times, though subjected to a little varia-
tion in this respect, both in regard to her cquato-
rial
284
LECTURES ON ASTRONOMY,
rial and meridional parts, by which we sometimes
see more of one side of her globe easterly, or wes-
terly, and sometimes of her polar regions. These
are called her librations. The former of these
appearances is occasioned by the Moon's motion
on her axis being equal, and that in her orbit un-
equal; by reason of which, according to the dif-
ference of her situation in her orbit at the time of
a particular phase, sometimes more of one side of
her is seen, and sometimes more of her other side.
The latter appearance proceeds from the change
of place of the nodes, or different inclination of
her axis to the Earth at one time than another, in
the same time of her period, by which we some-
times see more of the polar region, and the parts
nearer to the other, at the time of a particular
phase. We see both the poles during the revolu-
tion of the Moon round the Earth, by reason of
the axis of the Moon preserving its parallelism in
the whole of its revolution, the same as we have
observed of the Earth on the tellurium, by which
sometimes one pole of the Moon, and sometimes
the other, will be turned towards the Earth.
The path of the Moon being inclined to the e-
cliptic, the two points, from which straight lines
would be parallel to the central solar ray, are call-
ed the Moon's nodes, which are, of course, in
two opposite points of her orbit. That, from
which the Moon ascends northerly from the eclip-
tic, is called her ascending node; and that, by
which it descends southerly from the ecliptic, is
called
LECTURE IX.
285
called her descending node. The line from one
node to the other is called the line of the nodes;
the situation of which, in regard to the ecliptic, is
variable, and its motion contrary to the order of
the signs, being performed in a westerly direc-
tion.
The line of the nodes is only imaginary, being
nominated to express that part of the orbit of the
Moon which would, if produced, be parallel to
the central solar ray.
On account of the irregularities in the affections
of the Sun and Earth upon the Moon, this plane,
or line of the nodes, will be affected something in
the same way that the line of the nodes, or inter-
sections of the ecliptic and equator of our Earth
are, by reason of the Sun's superior power of at-
traction on the Moon in those two points of its or-
bit, arising from their being in a direct line with
him.
This effect producing an acceleration of the
Moon to that parallel situation, and by degrees
bringing the line of the nodes quite round in a
contrary direction, which is proved by the change
of situation to which the Moon's nodes are known
to be subject, and which causes them to be conti-
nually changing their places in the ecliptic, in a
contrary direction to their progressive motion, and
to bring them round to the same point in the eclip-
tic from which this motion is first observed, in
about 19 years.
The
286
LECTURES ON ASTRONOMY.
The inclination of the plane of the Moon's orbit
to the ecliptic is variable, and is affected in the
same way as the nutation of the Earth's axis is ;
for, the Sun acts on the poles of the Moon's axis
also. When it is in that part of its orbit nearest
to the Sun, the Sun must attract the Moon in a
greater degree than when it is most remote from
it; and, if it happens to be inclined to the Sun, it
will be drawn down from its natural declination by
the power of the Sun; but, when the line of the
nodes is in conjunction with the Sun, the inclina-
tion of the axis of the Moon cannot be affected by
it, because the axis is then perpendicular to the
Sun's power. Fig. 1, plate 13, is a map of the
Moon, which I have taken the liberty of copying
from Dr. Hutton, as it is particularly illustrative,
exhibiting all the remarkable spots, such as the
cavities and highly-illuminated parts of that orb,
as seen through a telescope; which appearances
are supposed to arise from the high lands and val-
leys, &c. on her surface. I have also subjoined
the names given to those appearances by the disco-
verers of them, which are those of remarkable as-
tronomers and philosophers, or of countries, islands,
or seas.
In fig. 1, plate 13, the Moon is represented at
her mean libration; the figures are for references
to the names, and that spot marked with an aste-
risk is supposed to be one of the volcanoes disco-
vered by Dr. Herschel.
Do

Plate XIIL
East
Fig. 1.
South
38
37
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Fig. 3.
North
Fig. 2.
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B
West
TConder sculpt
LECTURE IX.
287
Do not imagine that the ideas formed of moun-
tains and valleys in the Moon are mere conjecture,
unsupported by such evidences as are deducible
from all the phenomena of inaccessible objects, be-
cause I assure you they have all the visible charac-
teristics that can be expected of objects so remote,
as I will explain to you, and which your know-
ledge of the effects of light and shade will render
intelligible.
In all situations of the Moon, the elevated parts
cast a triangular shadow from the side in oppo-
sition to the Sun; also the cavities are always
dark on the side next the Sun, and illuminated on
the opposite side, exactly in the manner as we ob-
serve of light and shade on opake bodies, and
those which are hollow, when made to cast sha-
dow and appear light by any partial illumination.
These appearances are found likewise to increase
and diminish, according to what is perceived of
any globular body turning on its axis.
In regard to volcanoes in the Moon, although it
is very possible there may be such eruptions, yet
the observations which are intended to authenti-
cate this idea are not so satisfactory, I should sup-
pose, as those who have advanced them could
wish; because the theory is by no means sanc-
tioned by those undeniable demonstrations dedu-
cible from the other phenomena of the Moon; nor
will it ever be possible, in my opinion, that they
should.
Various
288
LECTURES ON ASTRONOMY.
Various are the opinions respecting those cir-
cumstances of the Moon, that are for and against
its having an atmosphere. If I may venture to
give mine on a subject so ably defended on both
sides, I should maintain that it has; as I think the
arguments on that side of the question are better
supported than on the contrary side; for, as Sir
Isaac Newton has proved that the atmosphere of
the Moon, if it has one, cannot be, by one-third,
so dense as ours; the density of the Moon being
but one-third that of the Earth, and therefore the
atmosphere on its surface weighing only one-third,
its compression must be in proportion to that with
which it is attracted by the Moon; and so its ef-
fects cannot be more evident to us than they are
perceived to be.
The Moon, in circulating round the Earth, ac-
cording to her situation in respect to that and to the
Sun, presents more or less of her illuminated face
to us; but, at one part of her orbit, it is wholly
turned from us.
From the different phases she exhibits to us, we
also know that her form is globular, although,
from the laws of centrifugal and centripetal for-
ces, we know that it cannot be perfectly spheri-
cal.
When the Moon is in opposition to the Sun, or
in the opposite sign to him, she turns the whole of
her illuminated side towards the Earth, and is seen
by us on our meridian at midnight. She is then
said to be full, appearing as represented at A,
fig.
LECTURE IX.
289
fig. 2, plate 13, in the ecliptic circle EFGH, to
which the place of the Moon is transferred by a
spectator on the Earth; because it moves nearly
in that apparent path. S is the Sun in his proper
situation, in respect to the Earth, at the time of
full Moon; and ABCD the Moon in four diffe-
rent and opposite points of her orbit.
As the Earth at T moves easterly in her orbit,
the Moon changes her figure as viewed from the
Earth, the western part of her illuminated surface
declining from the Earth, in her departing from
her opposition to the Sun; and, when she is in
quadrature with the Sun, or only as at B, three
signs from the place of the Sun, as viewed from
the Earth, she appears like a crescent, on our me-
ridian, at six o'clock in the morning. From this
place, as she advances easterly towards her con-
junction with the Sun, she diminishes in appear-
ance to us, because more and more of her enlight-
ened face is turned from us, by her now getting
between the Sun and us; and, when in conjunction
with him, as at C, the whole of her illuminated face
is turned from us, she being in a direct line between
the Earth and the Sun. This obscuration continues
about four days, when she again begins to shew a
part of her illuminated surface; and we see her
on an evening, soon after sun-set, in the shape of
a fine crescent. When she is in conjunction with
the Sun, we say it is New Moon. From her con-
junction at C, as she is advancing towards her
quadrature at D, she is continually increasing in
U
her
290
LECTURES ON ASTRONOMY.
her apparent size; and, when she is arrived at D,
we again see her on our meridian at six o'clock in
the morning, and exactly half full, or bisected.
From the time of this quadrature, till she again ar-
rives at her place of opposition to the Sun, or at
full, as at A, she is continually increasing in size,
till Full Moon again at T.
These changes she goes through in the course
of 29 days, 12 hours, and 44 minutes, which
time is called her lunar synodical month, in con-
tradistinction to her periodical lunar month, - the
former being the time of all her changes of ap-
pearance as referred to the Earth, and the latter
(which is performed in 27 days 7 hours) being the
time of her performing her revolution round the
Earth. The period of her being in conjunction
with the Sun, as at C, and her return to it again,
is also called a lunation.
The places of the Moon, when she is at new
and full, or in conjunction and opposition, are
called the syzygies. From either of the syzygies
to the quadrature, the gravity of the Moon to-
wards the Earth is continually increasing; and, the
attraction of the Sun also acting contrary to her
progressive motion, these two forces counteract
each other in a degree, by which the motion of
the Moon in her orbit is continually retarded; but,
from the quadratures to the syzygies, the Sun and
Earth conspiring in their effects, the motion in her
orbit is perpetually accelerated.
These
LECTURE IX.
291
These varieties of the affections to which the
Moon is subject occasion her orbit to deviate
something from the form of a regular ellipse, al-
though it is rather oval. - The Moon's diameter is
to that of the Earth as 20 to 73, being computed
at 2180 miles. Hence the surface of the Moon is
to that of the Earth as 1 to 13; so that the Earth
must reflect 13 times as much light upon the Moon
as the Moon does upon the Earth.
The Moon cannot have any great variety of sea-
sons, as her axis is almost perpendicular to the
plane of her orbit.
The sloping ring, Q D, of the instrument, fig.
3, plate 10, is to represent the plane of the Moon's
orbit, which should be inclined at a mean rate in
an angle of 5° 18′ to the ecliptic plate of the or-
rery, as shewn by the plane of the nodes & 8,
which is distinguished by a brass wire fixed from
A to B. In this instrument, the line of the nodes
has the motion I have previously mentioned, con-
trary to the order of the signs, as may be seen by
comparing its situation at different times, in re-
spect to the signs and degrees described on the
plate under it, which represents the ecliptic.
These also shew that the Moon cannot be exactly
in the plane of the ecliptic, except when she is in
her nodes; as, in all other parts of her orbit, she
goes either north or south of that part, which de-
viation from it is called her latitude, and does not
exceed about 5° 18′ on each side of the plane of
the ecliptic, or central solar ray, as mentioned a-
U 2
bove,
292
LECTURES ON ASTRONOMY.
bove, which are called her highest and lowest
situations in her orbit, and which are seen on this
ring, these degrees and minutes being engraved
on it.
That part of the plate RS, under the Earth
and Moon, which has the names of the signs
engraved on it, is moveable in a socket; so that,
in working problems by this machine, those signs
may be made to correspond with the large ecliptic
of the orrery; thus, Whatever sign the Sun
should appear in from our Earth on the large
plate, that sign of the small plate should be placed
next the Sun; because, both the Sun and Moon
are transferred to that circle in the heavens. On
the outside of the signs, on the small ecliptic
circle of the lunarium, are engraved the days of
the Moon's synodical and also her periodical month;
by comparing which with the signs and degrees
on the small ecliptic plate, (those two circles mo-
ving independently of each other,) the difference
between the periodical lunar month and the syno-
dical lunar month is clearly seen, as well as the
cause of that difference. The ellipse X is to
shew the Moon's elliptical orbit, on which are
marked apogee and perigee, to denote the Moon's
greatest and least distance from the Earth.
I shall explain the difference between the perio-
dical and synodical month, first by a diagram,
and afterwards by this instrument.
The difference between them depends on the
progressive motion of the Earth, together with
that
LECTURE IX.
293
that of the Moon, round the Sun, compared with
their motion round the centre of gravity between
themselves. The centre of gravity between them
is exhibited by the pin at Q, being as much
nearer to the Earth as the Earth is larger than the
Moon. If these two bodies had not a progressive
motion round the Sun, the synodical and periodical
months would be of the same length.
Let ABCD, fig. 3, plate 13, represent the
great ecliptic, to which the place of the Sun is
transferred, and 1234 the small ecliptic, to which
the place of the Moon is transferred, and TO
the Earth in its orbit. First, suppose the Earth
to be in her orbit at T, and the place of the Moon
to be at 1, in the line T 1 A; then, as the Earth
and Moon are performing their periodical monthly
revolution round the centre of gravity between
them, which is performed in twenty-seven days
and a half, they will also advance in their an-
nual revolutions round the Sun; and, therefore,
when they have performed their periodical months,
they will have advanced a whole sign in the ecliptic,
to O. But the Moon will not again appear in con-
junction with the Sun, or in a right line with the
Earth and Sun, until she has described the arc
EF, which is wanted to complete her synodical
month, or time of being in the same sign with the
Sun in respect to the Earth, the difference be-
tween that and her periodical month being the
quantity of that arc. I shall now illustrate this
by the lunarium.
U 3
I
294
LECTURES ON ASTRONOMY.
I will place the Moon in conjunction with the
Sun, as in the diagram, and fix the ecliptic plate
under the Earth and Moon, by the large one,
so that the place of the Sun and Moon, as sup-
posed to be seen from the Earth, may be in the
same sign and egree of the ecliptic, letting the
days of the month under the Earth and Moon
correspond with those set down in an Epheme-
ris, or as exhibited by the large plate of the
orrery.
On turning this instrument, you will perceive
that the Moon moves in an orbit inclined to the
ecliptic, and that it turns once round upon its
axis whilst it is performing its synodical month,
and that it will return to the same point of the
small ecliptic, or perform its periodical month in
twenty-seven days and a half; but will not again
appear in conjunction with the Sun in less than
twenty-nine days and a half, as may be seen by
the days of the month under the Earth and Moon.
The annual index will point out the cause of this,
which is, the Earth and Moon having advanced
nearly a whole sign in their annual orbit round
the Sun in that time. The Moon's motion round
the Earth is from west to east, and the apparent
annual motion of the Sun is also from west to
east, being both in the same direction, but with
different velocities, the Earth getting the start
of the Moon, in respect to her situation with
the Sun, which requires her to travel two days
longer
LECTURE IX.
295
longer in order to overtake, or again be in con-
junction with, the Sun and Earth.
This instrument shews the difference of the face
of the Moon, exhibited at different times, for the
same phase, on account of the revolution of the
nodes, but not that difference occasioned by the
obliquity of its axis, as it is always perpendicular
to the plane of its orbit, on this instrument, con-
trary to fact. The different phases of the Moon
are also pleasingly illustrated by the lunarium;
and the places of the nodes exactly correspond
with those perceived throughout any space of
time, if once made to answer to their proper
stations and times; as also the Moon's age and
phases for any length of time, by one adjustment,
to those which take place at any given period.
Having examined into some of the phenomena
of the Moon, I shall postpone what remains to be
observed of it till my next Lecture, and conclude
this by referring to the foregoing part of it, in
which we treated of the variety of the seasons.
Every reflecting mind that minutely examines into
the causes of the vicissitude of the seasons will
not stop there, but will proceed to examine into
the benefits arising from them, and the inferences
deducible from those benefits. For, being sensible
that the whole course of nature is intended to
convey instruction to rational beings, it next com-
pares, then judges, and finally is amply repaid
by the consolations deducible from the minutest
circumstance in nature.
U 4
Thus,
296
LECTURES ON ASTRONOMY.
we
Thus, perceiving the Sun to be the chief natural
agent employed in regulating the seasons,
next discover that his power is circumscribed by
such laws as render his agency most efficacious
to us; and, although acting as an agent, yet that
he is subject to a controlling infallible power; from
which observations we are led to judge of the
benevolence and impartiality of all the dispensa-
tions of the Deity; deducible from the above,
and from observing that He bestows on each
portion of his creation an equal portion of his
blessing.
Independant of the constitutional advantages
afforded animal and vegetable nature by the vi-
cissitude of seasons, we may rejoice in them on
account of the vigour of our mental enjoyments;
which are thus insured and continued to us. If
we had perpetual sunshine, it would cease to
afford us the delight we now experience in its
return to us, after a temporary absence of its en-
livening influence.
With what charms is the vegetable creation
decked in spring, which delight us as much by
their renovation as their real beauties! Succeeding
the total deprivation of such grateful objects, they
communicate a pleasing sympathetic renovation
in all sensible minds, exhilarating the spirits, thus
animated by their gay and lively influence. What
is there in art or invention that compensates for
the charms of nature? Those native beauties,
ever new and varying, always serve to delight the
eye,
LECTURE IX.
297
eye, improve the fancy, and cheer the heart.—
Happy is it for those who have so improved a
taste for rational studies, so to fill their time at the
period of temporary decay and deprivation of ob-
jects so charming, as to escape from the vain de-
lusions that destroy the health and enervate the
minds of thousands, by which they are prevented
from relishing the benefits and sweets of returning
spring. Whereas, those, who have cultivated their
minds, and stored them with useful knowledge,
will, at the return of each vernal period, ever
taste new delights; and, when autumn deprives
them of the charms of nature, they will enjoy
them in prospect; and, by considering them ra-
tionally, look forward to their return with pleasing
satisfaction.
Who can behold the renewal of all nature in
spring without inferring their own resurrection,
of which it is so striking an emblem? For, as
the tree sheds its leaf in autumn, so shall our
mortal part die away; and, as that renews its
foliage in spring, so shall we flourish again. Thus
we perceive it to be with all the vegetable world,
and also with many insects. One instance this
moment presents itself, which I think a striking
figure of our present degenerated, and also of
our future exalted, state, although evinced in the
humble caterpillar.
This insect changes its natural state of existence
in a manner analogous to our translation from this
life to a better; for, after being to all appearance
dead,
298
LECTURES ON ASTRONOMY.
dead, it rises again in a new and beautiful form.
In the winter of its age, foresceing, we may sup-
pose,
its approaching change, it begins to prepare
its tomb, and works unremittingly till it is shut
out from all visible means of subsistence: in this
state it continues a certain time, and then rises
again from its temporary obscurity to a life of joy ;
in which new and beautiful form it wings its way
with exalted renovation, soaring above those
things, which, in its former degraded state, ap-
peared its proper sphere of action, relishing only
the most refined pleasures.
How emblematical is this of our existence!
We now find pleasure in the gratification of those
senses our bodies are endowed with, which here-
after we shall lose, with them, all relish for. Like
this insect, we must pass our allotted time in our
present state, then be entombed, and to all ap-
pearance dead; yet shall that Power, which
supports the chrysalis in its state of apparent ina-
nity, sustain our spiritual part; - and, finally, at
the time decreed by divine command, we shall
rise again to a most pure, a most ennobled, state,
in which our present body shall not appear; but
we shall be so clothed as to fit us for the par-
ticipation of those enjoyments, which the refined
nature of our situation shall require. Therefore,
the decay of our mortal part, instead of being a
subject for regret, if we improve our mental en-
joyments in proportion, conveys the greatest con-
solation to a reflecting mind, by the assurance it
gives
LECTURE IX.
299
gives us of a better state than this; first, by the
necessity of a new form for the enjoyments it
promises; and, secondly, by a consciousness of
having a mind capable of such participations.
And the inference we may justly and finally make,
upon the consolation this change of form brings
with it, is, that, were we to rise from the grave
incumbered with our bodily infirmities, we should
be unfit for a purer state or more exalted gratifi-
cations.
to
Such are the consoling testimonies perpetually
arising in the contemplative mind; that investi-
gates nature for the most useful purposes,
strengthen the judgement, fortify the mind, refine
and exalt the ideas, rectify, expand, and ennoble,
the heart.
Thou, Pow'r Supreme, by whose command I live,
The grateful tribute of my praise receive.
To thy indulgence I my being owe,
And all those joys which from that being flow;
Thy skill my elemental clay refin'd,
The vagrant particles in order join'd;
With perfect symmetry compos'd the whole,
And stamp'd thy sacred image on my soul:
A soul susceptible of endless joy,
Whose frame nor force nor time can e'er destroy ;
Which shall survive when nature claims my breath,
And bid defiance to the darts of death;
To realms of bliss with active freedom soar,
And live when earth and skies shall be no more.
Author of life! in vain my tongue essays,
For this immortal gift, to speak thy praise!
How
300
LECTURES ON ASTRONOMY.
How shall my heart its grateful sense reveal,
When all the energies of words must fail?
O may its influence in my life appear,
And ev'ry action prove my thanks sincere !
Mrs. E. CARTER.
END OF THE NINTH LECTURE.
[ 301 ]
LECTURE X.
OF THE LAWS OF SHADOW.
OF ECLIPSES.
THE PHENOMENA OF THE TIDES CONSI-
DERED; AND HOW PRODUCED.
DING ADDRESS TO MY PUPILS.
CONCLU-
Was ev'ry fault'ring tongue of man,
ALMIGHTY FATHER! silent in thy praise,
Thy works themselves would raise a genʼral voice;
E'en in the depth of solitary woods,
By human foot untrod, proclaim thy pow'r,
And to the choir celestial Thee resound,
Th'eternal Cause, Support, and End of All!
THOMSON.
PREVIOUS to my acquainting you with the
phenomena of eclipses, it will be necessary to
say something of the laws of shadow.
Every illuminated object must cast a shadow
in a direction parallel to the rays of light by which
it is illuminated. The more intense the light, the
stronger will the shadow appear, because the con-
trast is the greater; not that the shadow is of itself
darker, for, all perfectly opake bodies will cause
the same degree of shade.
If the luminous body and the body illumined
are of the same size, and parallel to each other,
the shadow cast by the latter will be exactly of
the
302
LECTURES ON ASTRONOMY.
the same dimensions with the former. But, when
these two bodies are unequal to each other, and
the luminous body, for instance, is larger than
the opake one, then the shadow always becomes
less and less as it recedes from the body; and,
when the opake body is larger than the luminous
one, the shadow increases the farther it goes from
the body; the rays diverging or spreading conti-
nually in the latter case, but converging or ap-
proaching continually in the former.
That faint shade, which is seen between the
dark shadow, cast by an object, and the light,
when the luminous body is larger than the opake
one, is called a penumbra. It arises from the
larger and luminous body sending some of its rays.
into those parts, in which its direct influence can-
not dart, on account of the interposed body.
The penumbra will be darker or lighter gradually,
from the extremity of the diameter towards the
dark shadow subtended by the opake body; so
that the outer part will be lightest, because it will
receive more of the Sun's rays than that part which
is nearly behind the opake one; and, as the sha-
dow of the opake body becomes gradually less and
less, the penumbra grows gradually broader and
broader. These positions you may understand by
looking at fig. 1, plate 14, in which S is intended
to represent the Sun, and T the Earth. You per-
ceive that the latter is much less than the former.
Suppose the dark shadow of the Earth, received
on a plane at that distance, as at M, it would be
diminished


Plate XIV.
M2
M.Bryan delin
Fig. 1.
F
Fig. 2.
E
F
E
Fig. 3
H
D
7
CO
F
B
Fig. 4.
E
M
H
B
D
B
T.Conder sculp
OF
707
LECTURE X.
303
diminished in its apparent size to the diameter
AB; but, as some of the rays from the Sun must
enter between the lines ET and EF, they will
cause the shadow to be fainter in those parts.
The word eclipse is adopted to express these
deprivations of light, and is derived from a Greek
word which signifies a fainting or dying away,
and is therefore very properly expressive of what
happens to the Moon by the intervention of the
Earth between it and the Sun; although not e-
qually so when used to signify the circumstance
of the intervention of the Moon between us and
the Sun. For, in the former case, the Moon is
absolutely deprived of the Sun's light; but, in the
latter, the Sun loses nothing of his wonted splen-
dor. Yet, as the same term is always used to
express both circumstances, we must conform to
the popular mode.
When the Moon passes through the shadow
of the Earth, being deprived of the Sun's light,
she becomes invisible to us, or rather in such parts
of her only as pass through the Earth's shadow;
as, on account of the obliquity of the Moon's
orbit to the orbit of the Earth, she is not totally
eclipsed; that is, her whole diameter does not
pass through the shadow of the Earth, excepting
when these obscurations happen at the time of
the Moon being in or near the line of the nodes.
When the Moon is exactly in the line of the
nodes, she is said to be centrally and totally e-
clipsed,
304
LECTURES ON ASTRONOMY.
clipsed, because her centre passes exactly through
the axis of the Earth's shadow. When the Moon
is within 12 degrees of the line of the nodes, at
the time of her being full, she will be partially
eclipsed; but, when she is more than 12 degrees
from it, at the time of full Moon, she will pass
clear of the Earth's shadow. Thus you perceive
the reason why the Moon is not eclipsed every
time of her being at full; and that this is occasioned
by the plane of the Moon's orbit being inclined to
that of the Earth; whereas, if these two orbits
were in the same plane, the whole of the Moon's
diameter would pass through the shadow of the
Earth every time she was in opposition to the Sun,
and she would be totally eclipsed at every full
'Moon; by which, the great advantages, procured
by her superior illumination at those periods,
would be lost to us.
If the Earth and Sun were both of a size,
the shadow cast by the Earth would continue
the same size with itself to any distance; and,
therefore, the remotest planets of the system would
be involved in obscurity as well as the Moon;
which not happening to the superior planets,
Mars, Jupiter, Saturn, or the Georgium Sidus,
we are certain that the Sun and Earth are not
of the same size: also, that the Earth must be
less than the Sun; otherwise, its shadow, by
continually extending itself, would, as in the for-
mer case, reach the orbit of the most distant
planet in the system. Thus, we are certain, by
these
LECTURE X.
305
these as well as every other possible deduction,
that the Sun is larger than the Earth.
The Earth being less than the Sun, and of a
spherical form, the shadow it casts must be a
cone, terminating in a point at a certain distance
from it, and falling upon that point directly oppo-
site to the Sun's place in the ecliptic.
A lunar eclipse, which is the one I have been
particularly describing, is in the same degree to
all the inhabitants of the Earth; only observed
at different hours, at different places, according to
the longitude or meridian of each place. The
shadow appears fainter on those parts of the
Moon by which she makes her ingress and re-
gress; because the shadow cast by the atmosphere
of the Earth is fainter than that cast by the Earth
itself, as H I, fig. 1, plate 14.
A total and central eclipse of the Moon is re-
presented in fig. 1, plate 14; the Sun, Earth, and
Moon, being all in a direct line, as the Moon
is at the time of the nodes.
Solar eclipses, as they are called, can never
happen but when the Moon is in or near the line
of her nodes at the time of new Moon, or of
her being in the same sign with the Sun. These
eclipses, like those of the Moon, are either total
or partial, and are occasioned by the shadow of
the Moon cast upon the Earth.
The Moon being less than the Sun, subtends
a conical shadow; and, as she is less than the
Earth, only a small part of it can be involved in
X
her
306
LECTURES ON ASTRONOMY.
her shadow; so that, eclipses of the Sun, whether
partial or total, are not at all parts at the same
time, but to a small portion of the Earth only,
and which is supposed to be no more than 180
miles broad at the greatest, or a total, eclipse of
the Sun.
When the Moon is more than 17 degrees from
her nodes, at the time of new Moon, she hides
only a very small portion of the Sun; but, the
nearer she is to them, the greater will be his ob-
scuration; and, when in the nodes, the Sun will
be totally eclipsed. The beginning and end of an
eclipse of the Sun will happen at different times.
at different places; and the degrees of it will
appear differently to different parts of our globe.
To some it may appear partial, to others total, at
the same time. That part of the Earth which is
in a direct line with the Sun and Moon will have
a greater eclipse of the Sun than those parts which
are farthest from that central line between them.
In total eclipses of the Sun, the limb of the
Moon is surrounded by a pale circle of light,
which, on first entering on its passage over that
luminary, is perceived to have a vibration, as also
in its departing from it; a circumstance produced
to authenticate the idea of the Moon having an
atmosphere; which appears to me an indisputable
fact, although much has been advanced to con-
tradict that idea; such as its always appearing
of the same uniform brightness when our atmos-
phere is clear; whereas, if she have an atmosphere,
they
LECTURE X.
307
they suppose this would not be the case; which
conclusion proceeds, I imagine, from not consi-
dering the extreme rarity of the Moon's atmos-
phere, which would not permit those evidences
of its existence required by them. Others main-
tain, that, as no seas nor lakes are in the Moon,
there can be no atmosphere, being no water to
be raised in vapour. Even supposing there is no
water on the surface of the Moon, as some have
inferred from the external appearance of that
body; yet, I should suppose that there may be
a subterraneous store for the
purposes of vegeta-
tion; and that from thence it might be raised by the
heat of the Sun, in the same manner as the sub-
terranean waters of our Earth.
Independant of my observation on it, others
have denied the positions from which the idea
of the Moon not having an atmosphere have been
deduced. They have asserted, that the Moon
does not appear always of the same brightness,
even when our atmosphere is clear; but that her
brilliancy is also affected by the different state of
her own atmosphere at different times. Lastly,
the Moon's atmosphere being so much less dense
than ours, it may not cause any sensible refraction
of a star, viewed through it from the Earth ;
which is another observation made by those who
will not allow the Moon to have an atmosphere.
On summing up the arguments for and against
these circumstances of the Moon, I think we
X 2
may
308
LECTURES ON ASTRONOMY.
may naturally conclude
that the Moon has an
atmosphere, and is not destitute of water.
Fig. 2, plate 14, represents the situation of the
Sun, Moon, and Earth, at the time of a total
and central eclipse of the Sun: S the Sun, M the
Moon, and T the Earth; also b b the penumbra,
and a a the dark shadow of the Moon. The
Moon's atmosphere is too rare to cast any shadow,
and therefore is not noticed in this diagram.
If the Moon's nodes had not that retrograde
motion which I have explained to you, they would
be in conjunction with the Sun every six months;
and, therefore, there would be a regular return
of the same eclipse in that time. But the eclipses
happen so much sooner each year than the pre-
ceding, as proves this motion of the nodes, and
the quantity of it; so that it is known that they
have a retrograde motion, and that the period
of their retrogression through all the signs of the
ecliptic is performed in about nineteen years.
Again; if in nineteen years there were exactly
a certain number of courses of the Moon, this
would be the period of their returning, according
to their aspects; so that we should have exactly
the same eclipses as had happened in the former
nineteen years.
But this is not the case, as the
Moon performs thirty courses and a quarter, whilst
the periodical retrogression of her nodes is com-
pleting. However, this difficulty has been sur-
mounted by remarking the time in which 223
courses of the Moon are performed; which is
found
LECTURE X.
309
found to be eighteen years, eleven days, seven hours,
and forty-three minutes; after which period, the
conjunction of the Sun with the same nodes occurs.
Thus a period is obtained, in which we know that
the same eclipses will happen again, although not
exactly at the same time.
The most common number of eclipses in the
year is, two of the Sun and two of the Moon; yet
in some years there are six, and in others only two,
on account of the disagreement between the periods
of the eclipses and those of time,
As the apparent diameters of the Sun and Moon
are nearly equal, the duration of a total eclipse of
the Sun never exceeds two minutes; but the same
eclipse of the Moon may continue above three
hours, because the shadow of the Earth, where the
Moon passes through it, is near three times as large
as the diameter of the Moon.
As eclipses happen always in those months in
which the Sun enters the signs where the Moon's
nodes are situated, and the nodes being directly op-
posite to each other, the time of eclipses will occur
at about six months distance from each other; so
that, if one happens in January, there will be ano-
ther in July following.
Tables are constructed for the purpose of calcu-
lating eclipses for any length of time, by allowing
the three minutes eleven seconds that the nodes
of the Moon revolve in a retrograde direction each
day; and as, in 18 years, 11 days, 7 hours, 43 mi-
nutes, the Earth and Moon advance each just as
X 3
far
310
LECTURES ON ASTRONOMY.
far beyond a complete revolution in the ecliptic as
the nodes want of completing their retrograde one,
they will meet at that time, and be in the same re-
spective situation to each other that they were in
18 years, 11 days, 7 hours, 43 minutes before.
Astronomy and Geography have both been much
benefited by the observation of eclipses. In the
former, they have authenticated the idea of the
comparative sizes of the Sun, Moon, and Earth,
and the period of the Moon's retrogression; and,
in the latter, the rotundity of the Earth, and the lon-
gitude of places on it, have been also ascertained
by them.
What I have advanced, respecting eclipses of the
Sun and Moon, may be very pleasingly exhibited
by the lunarium. On turning the Earth and Moon
on in the Earth's annual orbit, you will perceive
that the Moon and the Earth are not in a direct line
with the centre of the Sun, except at the time of
the Moon's nodes, and when in opposition and
conjunction; therefore, when the Moon is at new
or full, at the time of the nodes, there will be in the
former case an eclipse of the Sun, and in the latter
an eclipse of the Moon. The period of these eclip-
ses being known for any time, if we fix the line of
the nodes in their proper situation for either of them,
and turn the Earth and Moon on in the Earth's
annual orbit, we shall see when all the rest will
happen through any space of time. If we continue
our observations for the whole 18 years 11 days, we
shall perceive that there will be 223 courses of the
Moon
LECTURE X.
311
Moon in that time; at the expiration of which
period, the Sun and Moon will be in conjunction, at
the same node and in the same sign they were in 18
years 11 days before; and shall also be able to
ascertain every eclipse of the Sun and Moon which
may occur in the intermediate time.
I shall now dismiss this subject, having, I think,
explained it very fully; and shall proceed to con-
sider those affections of the Sun and Moon,
which cause the flux and reflux of the waters of the
ocean.
The rising of the tides is occasioned, in one re-
spect, by the same principle as causes the Earth to
be an oblate spheroid, but not in all: the concurring
circumstances are these ;-the velocity of their ex-
ternal parts being increased by the extension of those
parts and their being acted upon by two forces.
But to be more particular. The surface of the
Earth being more than half covered with water,
and a fluid being more easily drawn from its situa-
tion, by any power, than a solid,—the fluid parts of
the Earth must be more affected by the attraction
of the Sun and Moon, than the solid parts of it.
This causes the tides in our seas; and it is also well
known that they are principally produced by the at-
traction of the Moon, as they are found to corres-
pond with her periods, and to be in proportion to
them.
The Sun's power in raising the tides must be but
small in comparison to that of the Moon, on account
X 4
of
312
LECTURES ON ASTRONOMY.
of his great distance from the Earth. In fact, it
may rather be considered as counteracting the ef-
fects of the Moon, in certain circumstances of it,
than as occasioning any sensible flux or reflux.
Kepler was the first who produced a rational
theory of the tides, and Newton has confirmed it on
the known principles of gravity or attraction.
The sea is observed to ebb and flow alternately
twice in twenty-four hours forty-eight minutes;
rising continually for about six hours, and falling in
the same space of time.
The time of high water at any place is about
forty-eight minutes later every day; because the
Moon is twenty-four hours forty-eight minutes from
being on and returning to the meridian of a place in
one day, which is called a lunar day. The sea flows,
or it is high water, always at the time of the Moon
being nearly on the meridian of any place, or in the
point of the ecliptic opposite the meridian, below
the horizon. The sea ebbs, or it is low water,
whenever the Moon passes nearly the horizon of any
place, either in rising or setting to it.
The waters of any place are raised the highest
when the Moon is on the meridian of a place, and
when she is on the opposite meridian; the cause of
which you will perfectly understand when I treat of
the physical causes of the tides..
The Sun always raises the waters a little when
he is on our meridian, and when at the opposite one;
but his tides are not distinguished from the others,
because they are made evident only by diminishing
them;
LECTURE X.
313
them; when acting in opposition to the Moon's
attraction, they produce what are called neap-tides;
and, when in conjunction with it, spring or high
tides so that at the time of new and full Moon
we have high tides; and, at the quarters, low
tides.
The attraction of the Moon must, as well as
that of the Sun, affect the equatorial parts of the
Earth more than those which are nearer to the
poles, both on account of its less obliquity to the
equator than to the poles, and also on account
of the increase of matter about the equator.
The degrees of the comparative effects of the
Sun and Moon on the tides are not the same every
day, according to the periods of the Moon, or
the relative situations of the Sun and Moon to
cach other; because the lunar and natural days
do not correspond in time, the lunar being about
twenty-four hours forty-eight minutes, and the
natural or solar day about twenty-four hours.
The tides are equal to each other at cach re-
turning situation of the Moon in respect to the
Earth and Sun: therefore, when the Moon is in
conjunction with the Sun, we have the highest
tides of all; when she is in opposition to him,
nearly as high as when in conjunction; but, when
in quadrature with him, we have the lowest tides
of all, because they act cross-ways on the Earth.
When the Sun and Moon are in the syzygies, or
in opposition and conjunction, at the time of the
equinoxes, we have the highest tides of all, because
then
314
LECTURES ON ASTRONOMY.
then the Sun is in the plane of the equator, and
the Moon the same, or very nearly so. But, as
the Earth is nearer to the Sun in winter than in
summer, these tides happen rather before the ver-
nal equinox and after the autumnal. The degree
of these tides is variable, as they depend on the
situation of the Moon's nodes at those times, and
the time of its being new or full Moon.
The mean comparative forces of the Sun and
Moon attracting the waters are supposed to be
as 1 to 4; therefore, the total effect of the
Moon's attraction must be in proportion to the
difference. The action of the Sun has been sup-
posed sufficient of itself to raise the waters of
our seas about two feet, whence that of the Moon
may, at a mean rate, raise them nine feet; that
is, at a medium. From this we infer, that at
spring-tides the water will be raised eleven feet
by the Sun and Moon acting conjointly; and, at
neap-tides, or when they are acting cross-ways to
each other, seven feet; allowing for what is
added to the individual power of the Moon in
one case, and what is subtracted from it in the
other, by the action of the Sun.
Let the line
I shall now apply these observations, and il-
lustrate them by diagrams. In fig. 3, plate 14,
let M represent the Moon in her orbit 00;
ABCD the Earth in its orbit E F.
from D to M be considered as that of their at-
traction, by which they are made to revolve
round the centre of gravity at H; and let this
centre
LECTURE X.
315
centre of gravity be supposed 40 times nearer to
the Earth than to the Moon, as it is in fact, on
account of the Earth containing 40 times as much
matter as the Moon.
Every body, moving round a centre, endeavours
to fly off from that centre by its centrifugal force;
and, as that part which is farthest from that centre
moves faster than that which is nearest to it, this
causes that part of the Earth which is opposite
to the Moon to exert a greater force from its
centre than that which is nearest to the centre
of gravity, or facing that and the Moon; and,
of course, causes the tides on that part to rise by
the centrifugal force, and those facing the Moon
by the Moon's attraction or centripetal force.
Without allowing for the centrifugal force, we
could not account for the tide rising on opposite
meridians at the same time; for, the power of
the Sun, even when on the opposite meridian
to the Moon, would of itself not occasion any
considerable degree of tide; but these two forces,
having been allowed, account for the water being
raised on both sides of the Earth at the same
time, as at C and D.
As the nearer any part of the Earth is to the
attracting power, the more it must be affected by
it we readily conceive, that the part of the Earth
at D must be more affected by the Moon's attrac-
tion than the parts CAB, or the centre of the
Earth T, and will of course cause it to approach the
Moon in the manner and in the proportion as from
4 to 6.
By
316
LECTURES ON ASTRONOMY.
By whatever means, and in whatever degree,
the waters of the sea are raised in one part, they
must be proportionably depressed in another; so
that when the Moon raises the waters at 4 and 6,
and the centrifugal force at 3 and 5, they must be
reduced at 7 and 8.
The waters at 3 and 5, and 4 and 6, are raised
to the same height, because action and re-action
are equal, in proportion to the quantities of matter;
and therefore the centrifugal force on one side of
the Earth (occasioned by its moving round the
centre of gravity between itself and the Moon) oc-
casions the waters on the Earth, opposite to the
Moon, to be raised in the same degree as the
Moon's attraction causes them to be raised on the
other side. For, as these two forces balance each
other, the fluid parts of the Earth must be equally
affected on both sides of it. You know, that if it
were not for this centrifugal force, the Moon
would fall into the Earth by the superior attraction
of the latter, as I have before observed of the pla-
nets and the Sun, it being the same in all of them.
The centrifugal and centripetal forces counteract-
ing each other, all bodies revolving round a centre
will keep at a proper distance from each other,
preserving an equilibrium; by which means such
effects as would be destructive to harmony and
earthly existence are prevented. -Thus, we find
all things regulated by weight and measure!
The effects of the centripetal and centrifugal
forces on the seas of our globe may be familiarly
illustrated
LECTURE X.
317
illustrated by any flexible body suspended from a
cord, and whirled round by the hand. The hand,
or the centripetal force, being considered the
same as the Moon's attraction, and the force the
body exerts from the centre, or its centrifugal
force, will cause the body to swell out in two
opposite parts; the one next the hand, and the
other opposite to it. These effects exactly corres-
pond with those produced by the Moon's attrac-
tion, and the centrifugal force, on the waters of
the Earth. You will also observe that the flexible
body, in proportion as it extends itself in those
two directions, will become depressed on the two
other sides of it, the same as the waters are on
the parts of the Earth 7 and 8.
What are called neap-tides (which are those in
which the water is not raised quite so high as in
the illustration I have given you of high and low
tides) are occasioned by the Sun and Moon acting
cross-ways to each other; as thus: Suppose
ABCD, fig. 4, plate 14, to be the Earth, and T
its centre; from which you perceive four lines are
drawn, one to the Moon at E, another to the
Moon at F, and through the latter to the Sun at
S; a third to D, and another to B.
When the Moon is at the quadrature, or 90 de-
grees from the Sun's place in the ecliptic, as at E
and B, her attraction on the waters at A and B.
will not be sufficient to raise them so high as when
she is at F; because, when the Sun and Moon
both attract in the same direction, as at F, they
will
318
LECTURES ON ASTRONOMY.
will raise the water higher than when they act
cross-ways to each other, as they do when the
Moon is at E and the Sun at S. Therefore the
latter is called neap or low tide; for, although
the waters will be raised in those parts and at
those situations of the bodies, yet at a mean rate
they will not be so high by one-fourth. But,
when the Sun and Moon act conjointly on the
waters, as at C, F, S, then the waters will be
raised one-fourth more than a mean or common
tide; and these are called spring-tides, the de-
pression in one case, and the elevation in the o-
ther, being in proportion to the effects of the two
bodies, acting in opposite directions on the Earth.
And, as the effects of the tide are on the part of
the Earth at C, such will they be on the opposite
part D, for the reasons before given.
When the Moon is at G and K, or 45° from
the Sun's place in the ecliptic, being at the mean
distance between the place of the highest and
lowest tide, the tides are at a mean rate.
The height of the tide, at all times, must be
regulated by the circumstances of the place; as
also the time of its being at its height: because,
for example, if the inlet is narrow, it will rise
higher and quicker than when it is broader, from
the opposition of the shores to the waters, which
is the reason that they rise but little in the open
ocean.
The highest tide does not happen when the
Moon is exactly on the meridian of a place on the
Earth,
LECTURE X.
319
Earth, or on the opposite meridian to it, but some
time afterwards; because any fluid, receiving a cer-
tain impulse, will continue its motion, in the direc-
tion of its impulse, after the power has ceased. Thus
the Moon's attraction, causing the waters to rise
to a certain height, will, on account of the motion
communicated, cause it to rise higher; so that its
tides are higher than accounted for by attraction
only, and are at the highest, about three hours af-
ter the Moon is on the meridian, or opposite me-
ridian, of any place;
any place; for, although the impulse
has ceased, yet the effects of it are continued.
The air, or atmosphere of the Earth, being
lighter than water, must be affected by the Moon's
attraction, and in a greater degree than the waters
are. The effect of the Moon's attraction on our
atmosphere is one cause of the high winds about
the time of the equinoxes; but the change of its
temperature is the principal cause.
As all that relates to the different temperature of
our atmosphere seems connected with the theory
of the Earth, I will endeavour to explain the na-
ture of its agitation at different times, and in dif-
ferent parts of it."
*
You are already acquainted with the expansion
of air by heat, and the contraction by cold, to
which it is subject; also with the effects produced
* I shall not go into a physical consideration of the air, being
foreign to my present purpose, and as I have already delivered two
lectures wholly on that subject for the information of my pu-
pils.
on
320
LECTURES ON ASTRONOMY.
on the animal constitution, by the changes in its
temperature and weight; I shall, therefore, pro-
ceed to inform you, how these effects are pro-
duced.
When the air, in one region of the atmosphere,
is, by the attraction of the Moon, or any other
cause, dilated, it must, by that expansion, force
itself into another, which, if it happens to be less
rare, will occasion a wind or agitation. But the
principal cause of the cxtension of the air is heat;
so that when the Sun, or rather the reflection
from the Earth, has heated the air to a certain de-
gree, it becomes lighter or more rare in those
parts than in the adjacent, which causes the cold-
er or denser air to rush into it, in order to restore
the equilibrium of weight and pressure.
The
rushing of the colder air into the rarer causes that
agitation we call wind; and, when the states of
the different regions of air are in a great degree
unequal to each other, and proceed from different
quarters of it, on account of the heterogeneous
particles with which they are loaded, on rushing
into contact with each other, they cause tempests
and hurricanes.
But these apparent discords of nature produce
the most harmonious and beneficial effects, purify-
ing the air from all noxious vapours, dispersing
the contaminated particles, and thereby preventing
an accumulation unfavourable to animal exist-
ence and thus an influx of fresh air is poured
into all regions, so as to produce an equilibrium,
and
LECTURE X.
321
and to sustain a healthful temperature in all;-by
moderating the heat of the parts and regions most
dilated by the Sun, as the southern, with an influx
of air from those which are colder, and meliorating
those of the colder or northern regions by the
warm air of the southern. The former of these
effects is most sensibly felt by the inhabitants of
the tropics, on whom the Sun's beams fall with ac-
cumulated ardour, which cause the air in those
parts to be much heated during his influence.
Yet these effects being less sensible on the sur-
face of the waters of the ocean, by which the
tropics are surrounded, on account of their absorb-
ing a great quantity of the Sun's rays, when the
Sun sinks below the horizon of those islands, the
air regains its equilibrium: the cooler air of the
ocean, rushing into the heated air, refreshes and
purifies it by its coolness and wholesome nitrous
impregnation.
Within the torrid zone, an easterly wind blows
the whole year, the constancy of which is very
useful to navigators; for which reason it is called
the trade-wind. The cause of this wind has been dif-
ferently defined; but the most rational mode of ac-
counting for its uniforın action is the following:
the regions between the tropics being more heated,
on account of their less obliquity to the Sun, and
receiving more of his rays than any
any other part of
our globe, and the atmosphere in those parts ha-
ving acquired an extension by the heat;
on the
Sun's departure from any spot, the colder air will
Y
rush
322
LECTURES ON ASTRONOMY.
rush in, as it were, to restore the equilibrium.
This may occasion the constancy of the wind in
question. Its direction may be accounted for thus:
the diurnal motion of the Earth being from west
to east, the apparent motion of the Sun is in a con-
trary direction, and thus the Sun passes it, as it
were, westerly. That part of the atmosphere.
which is at any time subjected to his influence
being most heated on his retreating westerly from
that part, the colder air rushing in behind, as I
before observed, will cause a constant succession
of wind from the east in those parts.
The cold air west of the Sun's place cannot rush.
into the heated air, on account of his approach to
it; yet that from the north and south may; and
therefore which ever side of the equator the Sun
is on, the cross wind from that quarter, combining
with the easterly, causes it to be north-east or
south-east; but the power of each is in proportion
to their direction or current. When the Sun is on
the south side of the equator, the wind blows
south-east; when on the northern, it blows north-
east.
The trade-winds are not regular, excepting in
the open ocean; for, near islands, the heat re-
flected from their surfaces, in some degree, coun-
teracts the natural cause of the trade-winds.
When this is the case, navigators call these effects
land-winds. They blow from shore in the day,
but to shore at night; for which we can rea-
dily
LECTURE Xx.
323
dily account, on the principles previously explain-
ed. And here ends our present scrutiny.
Oh, that I had eloquence divine, that I might
express the aggregated force of the power, wis-
dom, benevolence, and every other attribute of
the Deity, with which they strike my imagination!
But, alas! that is impossible. Let us, then, as
Thomson elegantly and comprehensively expresses,
-"muse his praise."
CONCLUSION,
WITH what pleasure, my dear young friends,
have I conducted you through the variegated field
of nature! and I hope with advantage, by planting
the infant shoots of that harmonious uniformity,
benevolence, and order, you therein observed;
and that you will cultivate the impressions you
have received, so as to bring forth the fruits of
those virtues, which, let your situation in this sub-
lunary state be what it may, even ever so obscure,
will, like the Sun's beams on the humble convol-
vulus, render you conspicuous by the sweet robes
of grace and harmony with which they will adorn
you; or, should your rank be exalted in society,
by your communicable goodness, you will shine
with intrinsic lustre, not with the false colouring
which flattery gives to wealth; for, the effects of
Y 2
your
324
LECTURES ON ASTRONOMY.
your virtues shall proclaim your title to praise and
honour. Thus, in all situations, you will find
virtue to be your best friend, the most likely to
make you happy in yourselves, and loved and re-
spected by the world.
If the instruction I have been so happy in deli-
vering to you has this effect on your minds, I shall
be amply repaid for all my labour, (if I may use
that term to express an occupation in which I de-
light, and in which I glory,) in having excited
your attention to those subjects, which will furnish
you with arguments to confute the unbelieving,
-consolation to soften your sorrows, elevation
of ideas to heighten your joys, and with such
a disposition of mind as will secure your happi-
ness both here and hereafter.
END OF THE TENTH AND LAST LECTURE.
Plate XV.
וא
·F
M
Fig. 1.
Fig. 3.
Fig. 5.
N
K
Ꮐ
Tangents
Chords
For Fig. 8. See over leaf.
Bryan delint
E
D
B
G
F
Fig. 2.
Fig. 4.
Fig. 6.
Hypothenuse
C
Perpendicular
B
Base
Fig. 9.
Fig. 7
F
{
C
B
E
TConder sculp!
[ 325 ]
ELEMENTS
OF
TRIGONOMETRY.
TRIGONOMETRY is that part of mathematics
which is used in estimating the sides, and ascer-
taing the quantity, of the angles in any triangle;
a branch of knowledge absolutely necessary to
Astronomers, in order to their finding the real
sizes and distances of the heavenly bodies, viz.
by comparing the angles they subtend with the
semi-diameter of our Earth or its orbit.
Every triangle has six parts, namely, three sides
and three angles, as fig. 1, plate 15, represents.
AB, AC, CB, are the three sides, and A, B, C,
the three angles.
The angles are always measured by the arc of a
circle described on the angular point. Thus, if I
want to know the quantity of the angle B, fig. 1,
plate 15, I place one point of my compasses at
Y 3
the
326
ELEMENTS OF TRIGONOMETRY.
the angular point B, and describe the arc of a cir-
cle between the two legs A B, BC; and whatever
number of degrecs of a circle is contained under
it, is the quantity of the angle; as in this figure
45° being the half of a quarter of the circle
DEFG, the angle is said to contain 45°. Every
circle being divided into 360 degrees, the number
of degrees contained between two radii of a circle
must be the quantity of the angle. If the number
of degrees between the two legs be 90, the angle
is called a right angle, and the legs are perpendi-
cular to each other, as fig. 2. If the arch of the
circle contained between the two legs be less than
90 degrees, it is called an acute angle, as fig. 3.
If the arch of the circle be more than 90 de-
grees, as fig. 4, the angle is called obtuse.
An obtuse angle may contain any number of
degrees between 90 and 180 degrees, or within a
semi-circle; but, at 180 degrees, the lines beco-
ming straight in the same direction with each o-
ther, as at A B, the angle vanishes.
What an acute angle wants of 90° is called its
complement; as in fig. 3, the angle being 22°,
the complement is 674°.
What an obtuse angle wants of 180° is called
the supplement of that angle to a semi-circle.
The three angles of any plane triangle, added
together, make 180 degrees, as shewn by fig. 5,
plate 15. This is the case, let the angles be
drawn in any possible proportions. Hence, if
one angle be right, the other two must be acute.
By
ELEMENTS OF TRIGONOMETRY.
327
By this rule, if two angles of any triangle be
known, the third is easily found, being only the
quantity of the semi-circle, or the number of de-
grees wanted to make the three angles contain
half a circle, or 180°.
A triangle, which has one right angle, is called
a right-angled triangle, as fig. 6; in which B is
the right angle, and A,. C, the acute angles. In
right-angled triangles, the longest leg is called the
hypothenuse, as AC; the leg on which it rests,
the base, as A B; and the other leg, the perpen-
dicular, as C B.
When neither of the angles is a right one, the
figure is called an oblique angled triangle, as
fig. 5.
If the angles of one triangle be equal to the an-
gles of another triangle, although the sides are of
different sizes, the sides of the former will then
be proportioned to the sides of the latter.
All triangles have their greatest sides opposite to
their greatest angles; and, if all the angles of a
triangle are equal, the sides will also be equal to
each other.
If
any three of the six parts of a triangle be gi-
ven, (excepting the three angles,) all the rest
may be known from them.
Any angle, notwithstanding the length of the
lines which contain it, will be an equal portion of
a circle; as the arc EF, which contains an e-
qual number of degrees with the arc IK in
fig. 5.
Y 4
The
328
ELEMENTS OF TRIGONOMETRY.
The place where the lines mect which form the
angle is always considered as the centre of a cir-
cle; and, when letters of reference are described
on an angle, the middle of the three letters should
be placed on the angular point.
The diameter of a circle, or sphere, is a line
passing through its centre, and meeting its cir-
cumference at two opposite points, as at G, N,
fig. 7.
Half the diameter of a sphere, or circle, is call-
ed its radius, or semi-diameter, as G H.
The chord of an arc of a circle, or sphere, is a
line drawn from the end of one radius to another,
as IN; and, whatever number of degrees the arc
contains, the chord subtends the same num-
ber.
The sine, or right sine, is a line drawn from the
extremity of an arch perpendicular to the radius
drawn from the other extremity, as OP.
A tangent touches a circle only at one point,
which may be any where on the surface of it, as
GQ.
By the lines drawn from the centre of the circle
to the tangent, or line of tangents, you perceive
that no angle can be formed with it at 90 degrees,
because it is parallel with the radius or semi-dia-
meter of the figure: therefore, if a heavenly body
is at so great a distance from the Earth, that it will
not form an angle with the semi-diameter of it, or of
its orbit, it will be impossible to ascertain its size,
or its distance from it, unless there is an interme-
diate
ELEMENTS OF TRIGONOMETRY.
329
diate object near enough to it to form one. Where-
as, when we can form an angle with it, or by the
aid of an intermediate object, by making observa-
tion of it at two different stations on the Earth,
(within the semi-diameter of the Earth or its orbit,)
we can discover by trigonometry its real size and
distance, allowing for the visual diminution of ob-
jects at certain distances, parallax, and refrac-
tion.
Although a quadrant does not give a real mea-
sure of the size and the distance of the heavenly
bodies, yet, by ascertaining their comparative si-
zes and distances, mathematicians are able, by
making the proper computations necessary to the
laws just mentioned, to estimate their real si-
zes.
Parallax is the difference of the place of a
heavenly body as taken from the surface of the
Earth, and supposed to be taken from its centre.
Refraction making a heavenly body appear higher
than its true place, and parallax making it appear
lower, (as I have explained to you in my Lectures,)
these two effects are in general not much different
from each other, and therefore little allowance
need to be made for them, unless in cases of great
nicety.
The angle made by a quadrant or a semi-circle
with the centre of a planet, by observation at two
different places on the Earth, or of two different
parts of its annual orbit, is used to ascertain the
distance of the heavenly body from the Earth; as,
by
330
ELEMENTS OF TRIGONOMETRY.
by knowing what portion of the diameter or se-
mi-diameter of the Earth or its orbit is contained
between the two places of observation, we can
estimate the other parts by that quantity; for, by
that rule in trigonometry, which shews us, when
two angles and one side of a triangle are known,
what the other angle and the other two sides
must be, we can know the distance of a heavenly
body from the Earth. And when all the angles
and sides are found, such as is the proportion of
those angles and sides to the one side, such will
be the actual quantity in comparison of the com-
puted, by means of the known, quantity in the
distances between the two places of observation,
which forms the base of the triangle.
The sizes of the planets are known by an angle
formed by their diameter compared with their
known distances.
The fixed stars, as I have before observed, have
no sensible parallax, and therefore their sizes and
distances are not known. This has been settled
by observations taken of them at two opposite
places of the Earth's orbit, when no sensible dif-
ference has been perceived; the index on the plate
of the quadrant always pointing to the same de-
gree at every place, and the plumb-line always in-
tersecting the same degree on the plane of the
quadrant at each, when the sights have been di-
rected towards a fixed star.
The forming of angles, to determine the size
and distance of a heavenly body, is performed ex-
actly
ELEMENTS OF TRIGONOMETRY.
331
actly as we do the size and distance of inacces-
sible objects on the Earth; but the former is in-
volved in some computations unnecessary to the
latter, namely, parallax and refraction. Fortu-
nately, however, for those who are not fond of
calculation, or are incapable of entering into the
depth of mathematics, those circumstances have
been settled on just principles, so that we need
not enter into such abstruse studies, but may find
ample gratification in the application of the know-
ledge we have obtained, by applying the quadrant
to ascertain their observations. Yet, as even this
application may not in all respects be convenient
to many, so far as relates to the apparent sizes
and distances of the heavenly bodies, on account
of the journeys they must take for such purposes,
those, who wish for a local use only of the qua-
drant, may find sufficient amusement in observing
the height of the heavenly bodies above the hori-
zon, their situation in respect to the constellations,
their latitude and longitude, and their distances in
diameters from the Earth, which the quadrant will
furnish them with the means of, aided by trigono-
metry; also the sizes and distances of objects on
the Earth, accessible and inaccessible. As to the
rest, with reference to the Ephemeris, they may
satisfy themselves by the information it contains.
A telescope being a necessary instrument for
the observation of the phases of the planets, and
their peculiar characteristical appearances, I re-
commend, to all those who wish for that amuse-
ment,
332
ELEMENTS OF TRIGONOMETRY.
ment, to purchase the sort represented fig. 8, plate
15, which is a reflecting telescope, it being, I
think, for the common purposes of celestial ob-
servation, the best of any within my knowledge.
I have one by me, made by W. and J. Jones,
Holborn, which I much prefer to a 21-feet achro-
matic refractor, that I formerly had. Being fur-
nished with an equatorial, or semi-circle, it an-
swers particularly well for ascertaining the dis-
tances of bodies from each other; as those who
can travel may, by the use of it, ascertain the dis-
tances of any of the planets from the Sun or from
each other by their own observation of them; and
those who do not wish to extend their speculations.
to those things, which have been so clearly set-
tled as to need no farther illustration, may amuse
themselves by applying this instrument to terres-
trial purposes, such as ascertaining the sizes of and
distances between objects on the Earth, either
accessible or inaccessible. For common celestial
purposes this instrument is particularly well adap-
ted, having a motion regulated to the equatorial
or horizontal motion of the Earth; also a vertical
motion, which is nicely adjusted to shew the angle
of the equator and the ecliptic. When the instru-
ment is fixed for any particular angle of those two
circles, it will preserve its parallelism through the
whole of them, describing exactly the equatorial
motion.
A B, fig. 8, plate 15, is a brass tube two feet in
length, containing the great speculum at the end,
A:

JONES, London
C
D
E
F
G
B
Fig. 8
Plate XVI.
Tonder selp
ELEMENTS OF TRIGONOMETRY.
333
A; and the small one near the end, B. The ver-
tical motion is produced by the semi-circular arch
C, and the pinion at D. The horizontal motion
is produced by the two arms EE, and the endless
screw at F. G represents a mahogany cylindrical
block, cut at half the angle of the equator 19°
14', with the horizon of a place situate in latitude
52°. When one half this cylinder is turned half
round, the block will give the whole circle of the
equator.
The telescope, block, and stand, being placed
nearly in the meridian, as may be done by the
compass below, allowing for the variation of it,
the apparent motions of the heavenly bodies will
be followed with less trouble than with a common
stand; for, there will be no occasion to alter the
vertical directions of the instrument in order to
keep them in the field of the telescope, or by
turning it either to the right or left, the equatorial
motion exactly following that apparent motion in
the heavens. Whereas, when using a telescope
mounted in the common manner, we have both the
vertical and horizontal positions of the instrument
to rectify, on account of the apparent motions just
mentioned.
TRIGONO-
[334]
TRIGONOMETRICAL PROBLEMS.
ALL sides or lines are estimated by a scale of
equal parts; as, inches, feet, yards, miles, &c.;
therefore, in all problems in trigonometry, we first
make a scale of equal parts by which to estimate
their length or quantity, allowing each of those
parts to be equal to any quantity we please, ac-
cording to the height or distance of the object we
wish to make those observations of. If it is near
or low, by feet or yards; if high or distant, by
miles. When we want only to know the height
of an object on the Earth, or its distance from it,
a quadrant is perfectly adapted to the observation;
but, if we want to ascertain the distance between
two objects that are remote from our place of
observation, an equatorial will answer our purpose
best.
Although I have fully explained the quadrant
in my Lectures, yet it may not be unnecessary to
recall attention to some circumstances of its ad-
justment, as probably, in applying the instrument
to the purposes it is designed to answer, these
might be neglected.
Previous to taking an observation of the height
of a heavenly body above the horizon, and its si-
tuation in respect to the points of the compass, —
render the plate of it parallel with the horizon, by
means
TRIGONOMETRICAL PROBLEMS.
335
means of the screws, as directed; and, also, make
the correspondent points of the compass to an-
swer to those in the heavens by means of a
small compass-box, allowing for the variation. In
observing the height of a heavenly body above the
horizon, direct the sights to the object, and notice
the degree cut by the plumb-line on the plane of
the quadrant; then will the number of degrees,
from the plumb-line to the end of the quadrant
farthest from your eye, be the same as the object is
above your horizon; and, as is the number of
degrees from the plumb-line on the plane of the
quadrant to the end next your eye, so is the dis-
tance of the object from your zenith-point. Also,
the degree on the plate of the quadrant, over
which your quadrant stands, shews the point of
the compass, or the meridian, on which the ob-
ject is.
Thus, by this instrument, at one place of ob-
servation and by one adjustment of it, the relative
height of any celestial object above the horizon of
the place, such as of the Moon, planets, and
stars, at night, and the Sun by day, may be
found; also their distance from the zenith-point,
and their situation in respect to the points of the
compass.
PROBLEM I.
I shall now endeavour to instruct you how to
obtain the height and distance of objects on the
Earth,
336
TRIGONOMETRICAL PROBLEMS.
Earth, by the use of the quadrant and the aid of
mathematics.*
First, draw a scale of equal parts, or choose one
ready-made; then adjust your quadrant, and di-
rect the sights to the top of the object, the height
of which you want to know. Observe the degree
of the quadrant cut by the plumb-line, which will
shew you how many degrees the top of the object
is from the plane of your observation. If the ob-
ject is accessible to you, measure its distance from
the place of the quadrant, and set down what num-
ber of feet or yards, &c. that distance contains.
Next, project a triangle, by drawing a straight line
horizontally for its base, or the distance of the bot-
tom of the object from your place of observation ;
and, from your scale of equal parts, take as many
for the length of this line for the base of your tri-
angle as there are feet or yards in the distance
measured.
Suppose the distance of your place of observa-
tion to the foot of the object be 50 yards, and you
find by the quadrant that the top of the object is
30 degrees elevated above that plane ; -- you
take
from your scale 50 of the equal parts, which you
* In explaining the problems, which concern altitudes and dis-
tances of objects on the Earth, I shall only refer to the quadrant,
being of more common use, as they may be performed by it, al-
though the semi-circle belonging to the telescope will answer the
purpose as well. When we wish to ascertain the distances of two
objects from each other, we must use the equatorial, and there-
fore I shall refer to it.
apply
Plate XVII.
D
C
B
E. Fig. 2.
Fig. 1.
300
Fig. 3.
M.Bryan delin.©
100
90
62°
285
D7643
30
F
Ꮐ
50
29
B
C
Fig. 4.
B
D
B
Fig. 5.
265
208
b
A
С
150
d
go
150
130
B
OyT.
D
T.Conder sculpt
TRIGONOMETRICAL PROBLEMS.
337
·
apply upon the line for the length of the base of
the triangle, as A B in fig. 1, plate 16; then draw
an indefinite line, BC, perpendicular to the far-
ther extremity of it. Lastly, by means of a pro-
tractor laid along the line AB, its centre at A,
mark off 30° through that point, drawing the line
AC, cutting the perpendicular line in C, which
will be the top of the object: then, by taking the
length of the line BC between the compasses, and
applying it to your scale of equal parts, it will be
found to measure 30 yards nearly, which is there-
fore the height of the object required.
PROBLEM II.
Suppose you wish to know the height of an ob-
ject which is below the level of your place of ob-
servation, as represented fig. 2, plate 16. You
must first measure the height of the tower or hill
on which you stand, by observation of it, the same
as of the object in the foregoing Problem, or bare-
ly by letting down a line or cord, if it be a per-
pendicular tower, &c. Then go to the top of the
hill or tower, &c. and, adjusting your quadrant,
fix it so that you can just see the bottom of the
object, as at G, and observe the degree cut by
the plumb-line, which shews how many degrees it
is from the end of the quadrant next your eye; that
is, the depression of the object below the level of
your place of observation. Then direct the line of
Ꮓ
sight
338
TRIGONOMETRICAL PROBLEMS.
sight to the top of the object, as at F, and again
observe what depression it has from the level of
your observation by your quadrant, and the obser-
vation is completed. To construct this case, draw
CD equal to the given height of the tower or hill
from your scale of equal parts; also, draw the
base-line DG perpendicular to DC, and CE pa-
rallel to DG; then draw the two lines CG and
CF so as to form the given angles of depression;
lastly, at the point G raise the perpendicular GF,
which will be the height of the òbject FG, as re-
quired.
PROBLEM III.
To measure the height of an inaccessible object
on the Earth, you must measure a certain portion
of the ground, in a straight line, between that and
your place of observation, in order to observe it
from two stations; and, by comparing the obser-
vations with the known distance measured, you
will obtain both its real height and distance.
Suppose AB, fig. 3, plate 16, to be a castle at
a great distance from you, the bottom of which is
about level with your eye at C. After having
measured a certain space of ground in a line be-
tween it and you, take from your scale of equal
parts as many as will be equal to the number of
feet you have measured, and draw a line to re-
present that distance, containing the same num-
ber of parts of your scale. Suppose we say 100
feet
TRIGONOMETRICAL PROBLEMS.
339
feet for the distance measured, and that 100 parts
of your scale is equal to CD: having done so,
look through the sights of your quadrant at the
top of the object A B at A, and remark what de-
gree is cut by the plumb-line:
suppose 29°;
then remove to D, and make the same observa-
tion :
suppose 52°; then, from the angular
point C, draw a semi-circle, and form an angle
with your base-line, from C to A, of 29°, and
from D to A 52°; and, where those two lines.
meet at A, let fall a perpendicular on the end of
your base-line from A to B. Then, on measuring
the number of parts of your scale between D and
B, you will find it contain 764, which, added to
your measured distance of 100 feet, makes the
distance of the object from your place of observa-
tion 176 feet, and its height will be found to be
972 feet.
The figure shews, also, that, the farther the ob-
ject is from us, the smaller is the angle under
which it is viewed.
PROBLEM IV.
To measure only the distance of an inaccessible
object, on land or at sea, you may proceed diffe-
rently from the last Problem, pursuing a more
simple method.
Fix on any two spots on the right and left of
the object, as at A and B of the object C, fig. 4,
Z 2
plate
340
TRIGONOMETRICAL PROBLEMS.
plate 16, and fix a mark at each station: then
measure the distance between the two places, and
take as many parts of your scale as will answer
for the number of yards, or other settled equal
quantities, that are contained in such distance, and
draw a line to represent that distance: then go to
one of the stations, as A, and, fixing your qua-
drant, look through the sight to the post at the
other station, and observe the degree at which
the index points on the plate of the quadrant, and
set it down; then turn the quadrant round till you
see the object C at the station A, observing the
degree to which the index points on the plate;
and set down the angle it makes with your eye at
A, which is the number of degrees between the
two set down; then, from the extremity of your
line at A, draw a line, forming an angle of that
number of degrees with your base-line. Then
proceed to your other station, as at B, and look
through the sights of your quadrant at the other
post at A, and observe the degree at which the
index points set it down as before, and turn the
quadrant till you see the object at C, observing
the difference between the degrees at which the
index points in the two directions, and draw a
line through that degree of it: then, where these
two lines intersect each other, will be the place of
the object at C. Lastly, draw a straight perpen-
dicular line, CD, from the place of the object at
C to the base-line; and, whatever quantity of
your scale that line contains, such will be the
mean
TRIGONOMETRICAL PROBLEMS.
341
mean distance of the object from your place of
observation, which, as well as the two distances.
AC, BC, may be measured by your scale of
equal parts.
PROBLEM V.
Although it is necessary, for those who want to
calculate the diameters and distances of the hea-
venly bodies, to remove to places of different lon-
gitude or latitude, yet, those having been settled
for us, we may, by the use of the quadrant, find
the distance of any heavenly body from us at any
time, by the number of its own semi-diameters,
and multiplying them by the known number of
miles they contain, as thus: if, for instance,
we wish to know how many of his diameters the
Sun is distant from us at any time, with a qua-
drant graduated into degrees and minutes, we take
the altitude of the upper and lower limb of the Sun
in degrees and minutes from one station; then, sub-
tracting the one from the other, we see the diffe-
rence, which shews the whole diameter of the Sun,
which, in this Problem, we will suppose to be
32′. Then, by drawing a horizontal line, and,
on the extremity of it, describing a quadrant, and
drawing two lines for the two angles the Sun
makes with our place of observation, we shall
find the figure as represented in fig. 9, plate 15,
where CE denotes the diameter of the Sun, and
AC or AB his distance from the Earth. These
Z 3
two
342
TRIGONOMETRICAL PROBLEMS.
two being measured by your scale of equal parts,
and the one number divided by the other, it shews
how often the Sun's diameter is contained in his
distance. Or otherwise, without construction, by
calculation only, thus:- by proportion as 32 mi-
nutes is to 90 degrees, or 5,400 minutes, so is
CE, which suppose to be 1, to the arch of the
quadrant DF, which thence comes out 169 near-
ly. Then, because the quadrant of a circle is in
proportion to its radius, as 11 is to 7, it will be as
11 is to 7, so is 169 (equal to DF) to AB, which
comes out 108 nearly; shewing that the distance
in this case is about 108 times his diameter.
Having found the distance of any heavenly body
in its own diameters from us, its distance in miles
is found by multiplying by the known number of
miles in its diameter. The Sun is supposed to be
800,000 miles in diameter, the Moon 2,175, Mer-
cury 2,460, Venus 7,906, Mars 4,444, Jupiter
81,155, and Saturn 67,870.
In winter, the Sun is about 108 or 110 of his
diameters from the Earth; but, in summer, the
angle is less, and he must therefore be farther
from it.
PROBLEM VI.
To find the distance of two inaccessible objects
from each other on the Earth, and from two dif
ferent stations, instead of a quadrant, a semi-cir-
cle is used, which is divided into 180 degrees,
with
TRIGONOMETRICAL PROBLEMS.
343
with a moveable index and sights, as in a qua-
drant, and which is added to the telescope, fig. 8,
plate 15, the tube of the telescope answering in
the most perfect manner for the line of sight.
Having measured the space of ground between
two places, to the right and left of the two objects,
as at A, B, fig. 5, plate 16, from a scale of equal
parts, lay down a line containing the number of
parts equal to the number of yards in the ground
measured, which let us suppose to be 150 yards.
Placing the semi-circle on a stand, and looking
from each station to the post at the other station,
and the two objects, mark the degrees at which
the index points in both situations of the line of
sight, and the objects at C and D. As, suppose
at the station A, the sight, pointing to the object
D, cuts off 39°, and that to the object C 108°;
also, at the station B, the sight directed to the ob-
ject C cuts off 43°, and to the object D 108°.
Then, to construct this, having made the line
AB equal to 150 parts for the distance between
the two places by the scale of equal parts, with
the protractor laid at A and B, mark off those de-
grees; and, through these marks, draw the lines
AC, AD, BC, BD. The intersections of these
lines will be the places of the two objects C, D.
Then draw a line from one to the other, as from
C to D. Lastly, on applying the compasses to all
the lines, and then to the scale of equal parts, we
find the distance of the two objects CD from each
other to be 265 yards, from A to C 202, from A
Z 4
to
344
TRIGONOMETRICAL PROBLEMS.
to D 268, from B to C 285, and from B to D
180.
I think I have introduced sufficient of the prin-
ciples of Trigonometry for familiar purposes, and
therefore I shall not extend my observations be-
yond these limits, by attempting to launch into
the mazy labyrinths of more intricate calculation,
spherical trigonometry, parallax, and refraction.
PROBLEMS
[345]
PROBLEMS
ON THE
CELESTIAL GLOBE.
THE GENERAL PRINCIPLES. OF A CELESTIAL
GLOBE EXPLAINED.
I SHALL subjoin such problems as are calculated
to apply the observations made by Astronomers, of
the different circumstances and aspects of the
heavenly bodies, for different periods, by reference
to the Ephemeris.
As the globes which are used to convey an idea
of celestial phenomena are differently constructed
or mounted, although I have given a description of
one in my Lectures, yet I think it necessary to in-
form you of the general principles of a celestial
globe, in which they all agree.
The celestial globe represents all the fixed stars
of the ethereal regions perceived by us. These
have, we know, been divided into classes, and
grouped
346
CELESTIAL PROBLEMS.
grouped into clusters or constellations, and are
distinguished by characters, according to both.
There are two circles which intersect each other
on this globe; one is called the ecliptic, represent-
ing the Sun's apparent path in the heavens; and
the other the equator, or the circle of our Earth,
exactly in the midst between the two poles, and
which, in using the celestial globe, is transferred
in idea to the heavens. The former is distinguished
by eight circles drawn parallel to it on each side,
including the 12 signs of the zodiac, divided into
30° each, composing together a complete circle of
360°. The latter, when transferred in idea to the
heavens, is called the equatorial, because it only
appears to divide the sphere of the heavens into
two equal parts, by being equally distant from both
extremities of its apparent diurnal motion; or, also,
the equinoctial, because when the Sun is in it, the
nights (and days) are equal every where. Parallel
to the equatorial, and at 23 degrees from it, on
each side, a circle is drawn, which touches the
ecliptic in two points, one on the north and the
other on the south side of the equatorial; these
circles are called the tropics, or solstices. Through
the two points where the tropics touch the ecliptic,
a great circle of the sphere passes perpendicularly,
called the solstitial colure. Where the ecliptic and
equatorial intersect each other, another great circle,
in like manner, passes, called the equinoctial colure.
The polar circles are those drawn at 23 degrees
from each pole.
The
CELESTIAL PROBLEMS.
347
The horizon of the celestial globe is considered
as the plane of our situation on the Earth, which is
transferred in idea to the centre of this globe, be-
cause the surface of it represents that great sphere
of the heavens which appears to surround the
Earth; and for which latter reason, when we wish
to represent the apparent annual and diurnal motion
of the heavens, or the Sun or planets, we must turn
this globe from east to west, although the real
annual motion of the planets is performed in a con-
trary direction, from west to east.
On the plane of the horizon of this globe (which
always represents the visible horizon of any place
on the Earth, when the latitude of the place is
brought to touch the edge of it) are delineated the
figures and signs of the zodiac; the degrees of
which correspond to the days of the months, as also
the months to the signs which the Sun is known to
be in at each period. The principal and collateral
points of the compass are also described on it. The
brass circle which crosses the globe, north and
south, is called the general meridian, because it
serves to represent that circle which passes over
every place on the Earth, when the latitude of any
place on it is brought to the edge of the horizon.
A dial is always a necessary appendage to a globe;
its application will be understood in the Pro-
blems.
The latitude of the stars is counted on those cir-
cles of this globe drawn perpendicularly to the eclip-
tic, and which intersect each other at the poles of
the
348
CELESTIAL PROBLEMS.
the ecliptic.
Their longitude is reckoned on the
ecliptic, and the lines drawn parallel to it. But
the latitude of the planets is counted on that part
of those lines only, which is included within the
eight parallels drawn on each side of the ecliptic,
because they never depart beyond those limits,
north or south of it; and their longitude is counted
on the ecliptic, and the eight parallels on each side
of it. The longitude of the heavenly bodies is
reckoned from the first degree of the sign Aries;
and their latitude from the ecliptic-circle, towards
the poles of the ecliptic. This globe should be
furnished with a quadrant of altitude, to shew the
height of a celestial body above our horizon at any
time.
These general principles being applicable to all
descriptions of celestial globes, however mounted,
will render the manner of working problems on
them perfectly intelligible.
Previous to making observation, by means of a
celestial globe, of the time when any celestial
phenomenon is to take place, it is necessary to
know the latitude of your place of observation;
which, if unknown to you, as at sea, or you have
not a terrestrial globe at hand, you may discover it
by the aid of the stars.
PROBLEM
CELESTIAL PROBLEMS.
349
PROBLEM I.
To find the latitude of a place by the observation of
two stars.
Find the Sun's place in the ecliptic for the time,
either by the horizon of the globe, or else more
accurately by an Ephemeris. Bring the Sun's place
on the globe to the meridian of it, which will be
the situation of the Sun for 12 o'clock at noon on
that day. At night, when the stars are visible, let
the Sun's place at noon be at the meridian, and fix
the index of your globe to 12 o'clock, that being
the Sun's place for 12 o'clock on that day. Then
turn the globe on, from east to west, till the index
points to the time of your making the observation,
and fix your globe there. Then observe two stars,
one of which should be exactly on your meridian at
the time, and the other, either at the east or west
points of your horizon, as viewed in the heavens,
which may be known by a compass. Bring the
star you have actually seen on your meridian to the
brass meridian of your globe; then, observing care-
fully not to let your globe move east or west, move
it, together with the brass meridian, either north
or south, till the star you observed at either the
east or west point of your horizon comes to that
place of the horizon of your globe; and whatever
elevation the pole has, when the two stars have the
same
350
CELESTIAL PROBLEMS.
same situation in respect to your meridian and
horizon on the globe, as in the heavens, such
will be the latitude of the place of observation.
the height of the pole above the horizon, at any
place, always being equal to the latitude of it.*
;
If a globe is not furnished with a compass, which
is a necessary appendage, a box-compass must be
used, and the globe always fixed by it, allowing for
the variation, and according to the longitude of the
place; which being always expressed in the Ephe-
meris what it is at a certain degree of terrestrial
longitude, that is at Greenwich, its variation at
places of different longitude may be known pretty
nearly.
*The longitude of places on the Earth occasions the Sun to be
sooner or later upon our meridian at one place than another; so
that, in fixing a celestial globe to work problems by it, we only
refer to the Sun's place for 12 o'clock at noon, and we know the
appearance of all the celestial phenomena will accord with the ob-
servations taken by Astronomers, if we fix the meridian of the
globe to the latitude of the place of observation; as then, notwith-
standing the change of longitude, which causes the difference of
time, the latitude being known, allows for it; or the clocks at
each place being regulated by the Sun being on the meridian of
each, the phenomena will correspond with the time set down in.
the Ephemeris, if the latitude is brought to the horizon, the globe
then representing the visible horizon of that place; and therefore
the phenomena of the heavens will appear as set down in the
Ephemeris, according to the clocks at that place, although not at
the same actual time as at Greenwich, it being the same hour of
the day at each place; therefore we need not regard the longitude.
of places on the Earth, if we have a clock or watch regulated by
the Sun at the place of observation, in order to know when to look
for it.
PROBLEM
CELESTIAL PROBLEMS.
351
PROBLEM II.
To know what stars will be above our horizon for a
particular evening after sun-set.
We rectify the globe to the latitude of the place
of observation, and bring the Sun's place for 12
o'clock at noon, for the given day, to the brass
meridian, and fix the index to 12 o'clock; we then
look in the Ephemeris for the time twilight ends.
Then, turning the globe westerly, agreeably to the
apparent motion of the stars, we observe when the
index points to the given hour; and, leaving it in
that situation, perceive all the stars visible at that
time, as they correspond with those which are
above the horizon of the globe. Again, looking
for the beginning of twilight in the morning, and
turning the globe till the index points to the hour
twilight begins, we see all the stars which will be
above our horizon during the whole of that night,
and the length of time they will remain above it.
PROBLEM III.
To know what evening a particular star will be on
our meridian.
We must bring that star to the meridian, and
fix the index to 12 o'clock. Then turn the globe
half
352
CELESTIAL PROBLEMS
half round till the index again points to 12 o'clock,
and, observing what sign of the ecliptic is then at
the meridian, look on the horizon of the globe for
its correspondent day, which will be the Sun's
place, and the day that the given star will be on
our meridian at 12 o'clock at night.
PROBLEM IV.
To find the Sun's declination, which is its distance
north or south of the equator.
Rectify the globe for the Sun's place, i. e. bring
that degree and sign of the ecliptic the Sun is in
for any day to the meridian. The degree of the
brass meridian, which stands over it, is his declina-
tion for that day.*
PROBLEM V.
To find the right ascension of the Sun, or a star.
When the Sun's place is at the meridian, we
observe the degree of the equator which is under
* The globe I have is. furnished with a semi-circle of declina-
tion, which is very useful, as, by a sliding piece of brass on it, I
can fix it to any particular spot, and see the different declination
of the Sun for any hour of the day, or observe the progress of a
planet more conveniently,
the
CELESTIAL PROBLEMS.
353
meridian at the same time, as that will be the
right ascension of the Sun for that day on which
the Sun is in that place of the ecliptic. Then, for
the observation of the right ascension of a star, we
bring the star to the meridian, and the degree of
the equator lying over it is its right ascension.*
PROBLEM VI.
To find the longitude and latitude of a star or planet
by the celestial globe.
Screw the quadrant of altitude to the brass meri-
dian, and bring it over that pole of the ecliptic
which lies on the same side of the ecliptic-circle
on the globe with the star: then the degree of the
ecliptic-circle, over which the quadrant lies, is the
longitude; and the number of degrees, from that
spot to the star, its latitude; being its distance from
the ecliptic-circle.
* The right ascension and declination of the Sun and planets
change every day, but those of the stars are always the same.
A a
PROBLEM
354
CELESTIAL PROBLEMS
PROBLEM VII.
To find the time of the Sun's rising and setting;
also his amplitude, or distance from the east or
west cardinal points of the horizon, at those times;
and the length of the day and night at any given
place and time.
Elevate the pole to the latitude of the place;
bring the Sun's place for that day to the brass meri-
dian, and fix the index at 12 o'clock. Turning the
globe till the Sun's place in the ecliptic touches
the western edge of the horizon, observe the hour
on the globe to which the index points; that will
be the time of sun-setting at that latitude: and the
number of degrees, between the west point of the
horizon and the point of it where the Sun is, will
be its amplitude. Then, turning the globe till the
Sun's place transits the horizon on the eastern edge
of it, and observing the time by the dial, that is
the time of his rising; and, by the distance of the
Sun's place from the east point of the horizon, we
know its amplitude at rising. Lastly, by doubling
the time of his setting, we find the length of the
day; and, by doubling the time of his rising, the
length of the night.
PROBLEM
CELESTIAL PROBLEMS.
355
PROBLEM VIII.
To find the beginning and end of twilight.
Rectify the globe to the latitude and Sun's place;
and, if the globe has a circle fixed below the horizon
of it, as the one represented in the plate has, then
only observe how long the place of the Sun is in
passing from that to the upper side of the horizon,
for the duration of the morning twilight; and the
length of time it is in passing through the same
space in setting, for the length of the evening
twilight. But, if the globe is not furnished with
this wire, then fix the quadrant of altitude to the
brass meridian at the zenith-point, and, bringing it
down to the horizon, observe when the Sun's place
cuts it at 18° below the horizon; this will be the
beginning of twilight in the morning; and, by
turning the quadrant to the other side of the meri-
dian, you will also perceive the time of twilight
ending in the evening.
PROBLEM IX.
To find the oblique ascension and descension of any
star, as seen from a particular place.
Elevate the globe to the latitude of the place,
and bring the star to the eastern edge of the
horizon;
A a 2
356
CELESTIAL PROBLEMS.
horizon; then the degree of the equatorial, cut by
it, shews the star's oblique ascension or obliquity
to the ecliptic. Again, turn the star to the western
edge of the horizon, and the oblique descension
will be found by the degree of the equator cut
by the horizon.*
PROBLEM X.
To find the rising and setting of any star, also its
continuance above and below our horizon, and the
time of its southing or culminating.
Rectify the globe; bring the Sun's place to the
brass meridian, fixing the index to 12 o'clock ;
then, turning the globe till the given star is at the
eastern edge of the meridian, the index will shew
the time of its rising; when at the meridian, it will
shew the time of its southing, or passing the
meridian; and, when it is at the western edge of
the horizon, the time of its setting; and, finally,
the time of its being above or below our horizon
is found by doubling the times of its rising and set-
ting, as mentioned in a former Problem for the
Sun.
* The Sun and planets oblique ascension and descension alter
each day, to the same latitude; but the oblique ascension and
descension of the fixed stars do not alter.
PROBLEM
#
CELESTIAL PROBLEMS.
357
PROBLEM XI.
To find the altitude and azimuth of the Sun, or of a
star or planet, for a given hour.
Rectify the globe for the latitude and the Sun's
place; screw the quadrant of altitude to the meri-
dian of the globe at the zenith-point, and fix the
index to 12 o'clock; then turn the globe as usual,
westerly, till the index points to the hour fixed
upon; and, laying the edge of the quadrant over
the Sun, star, or planet, the degree against it will
shew its altitude above the horizon for that time;
and the end of the quadrant at the horizon, the azi-
muth of the star, or its bearing, or the direction in
which it lies in respect to the north and south
points of the compass at rising and setting.
vertical circle passing through the east and west
points of the compass is called the prime vertical
or azimuth.*
The
*The azimuth of the Sun, or of a star or planet, means its
distance from the north and south points of the horizon, at rising
and setting.
A a 3
PROBLEM
358
CELESTIAL PROBLEMS.
PROBLEM XII.
To discover all the stars that are either rising or
setting, or on your meridian, at a particular
hour.
Having rectified the globe for the latitude and
Sun's place, as usual, and fixed the index to the
given hour; all the stars under the brass meridian
are upon the meridian in the heavens, those on
the castern edge of the horizon are rising, and
those on the western side of it are setting.
PROBLEM XIII.
To find the place of a planet on the globe, in order
to transfer your observation of it to the heavens.
Find its longitude and latitude, in the Ephemeris,
for the given day; which is always set down for
the noon of that day in the Ephemeris. Or else
its declination and right ascension. Mark that
place with a pencil; or, if you have a semi-circle
of declination, place the sliding piece of brass on
it, over the place of the planet on the globe: then,
looking for the group of stars in the heavens it
appears in, you will readily find it there. If you
find by your Ephemeris that more than one planet
will
CELESTIAL PROBLEMS.
359
will be above your horizon, and fit for observation
on any evening, put patches on the different places,
in like manner; and, by directing a pointed stick
from the spots on the globe to the heavens, it will
point to each of them; observing previously to fix
your globe, by the compass, to your meridian and
latitude.
PROBLEM XIV.
To find the time of the rising and setting of any of
the planets, also the time of their being on the
meridian, and their bearings in respect to the
points of the compass, at rising and setting, for
any evening; having previously found their places
in the Ephemeris, and that they will be proper for
observation on that evening.
Rectify the globe for the meridian by the com-
pass, the Sun's place, and the latitude of the place
of observation, and fix the index to 12 o'clock.
Then turn the globe westerly, and observe, by the
index, the time when each black patch appears
above the horizon on the eastern side, as that will
shew its hour of rising, and its amplitude or
distance from the east point of the horizon: turning
them on, you will see the time of their southing,
or being on your meridian, also of their setting, and
the western amplitude.
A a 4
PROBLEM
360
CELESTIAL PROBLEMS.
PROBLEM XV.
To find the length of the day and night at any place
between the equator and polar circles.
Rectify the globe to the latitude and Sun's place,
and fix the index at 12 o'clock. When the Sun's
place transits the horizon on the western side of
the meridian, that will be the time of sun-setting;
when it rises above the horizon, on the eastern
side, that will be his time of rising; and, by sub-
tracting the length of the night from 24, you will
find the length of the day. If the place is in north
latitude, you elevate the north pole above the ho-
rizon; if in south latitude, the south pole is raised
and the north pole depressed.
PROBLEM XVI.
To find the length of the longest and shortest day at
any place north of the equator, the latitude of
which does not exceed 66 degrees, being the dis-
tance between the equator and polar circles: be-
yond the latter, it would be tedious to extend our
observations.
For the longest day, rectify the globe for the
latitude of the place, also for the Sun's place when
in the tropic of Cancer, (which is the longest day
at
CELESTIAL PROBLEMS.
361
at all places north of the equator,) and bring it
to the brass meridian; then fix the index to 12
o'clock, which is the noon of that day. On turn-
ing the globe back towards the eastern side of the
horizon, and observing the time that the Sun's
place touches it, you will perceive the time of
sun-rising for that day, at that latitude; then,
turning the globe naturally, or westerly, till the
Sun's place touches the western edge of the hori-
zon, the time of sun-setting for that day will be
seen, and, consequently, the length of the day
at that place.
PROBLEM XVII.
To find the length of the longest day at any place
in southern latitudes, within 66 degrees of the
equator; also the shortest day in the same, and
also in northern latitudes.
Elevate the south pole above the horizon to the
given latitude, and bring the Sun's place, when at
the solstitial point, or in the tropic of Capricorn,
to the brass meridian, and work the Problem as
the last. For the shortest days in northern lati-
tudes, the Sun's place, when in the tropic of Ca-
pricorn, is brought to the meridian, and the north
pole elevated. For the shortest day in southern
latitudes, the Sun's place, in the tropic of Cancer,
is brought to the meridian; and the south pole
elevated
362
CELESTIAL PROBLEMS.
elevated above the horizon, and the Problem is
performed as for the longest days.
PROBLEM XVIII.
To find when a star rises or sets cosmically.
Rectify the globe for the latitude of the place;
observe what point of the ecliptic is at the eastern
side of the horizon with that star; then look on
the horizon of the globe to see what day the Sun
is on that sign, which will be that in which the
star will rise with the Sun, or cosmically. Then
bring the same star to the western edge of the ho-
rizon, and observe what point of the ecliptic is
at the horizon at the same time with it, which
will shew the day that star sets with the Sun, or
cosmically.
The same observations may be made of the pla-
nets, by finding their places in an Ephemeris.
PROBLEM XIX.
To find when a star or planet rises at sun-setting,
or achronically; also, when it sets achronically,
or at sun-rising.
Rectify the globe to the latitude of the place;
bring the star to the eastern edge of the horizon,
and
CELESTIAL PROBLEMS.
363
and observe what point of the ecliptic is at the
same time at the western edge of the horizon. -
The latter being the place of sun-setting, by look-
ing at the month and day on which the Sun is in
that sign and degree, the day on which that star
rises achronically will be found. If the star is
brought to the western edge of the horizon, and
the point of the ecliptic, which is at the same time
at the eastern edge of it, is observed, and its cor-
respondent day, that on which that star sets achro-
nically will be found.
PROBLEM XX.
To find the Sun's meridian-altitude for any day.
Rectify the globe for the latitude and Sun's
place; and, when the Sun's place is at the meri-
dian, the degrees between that point and the
horizon, counted on the brass meridian, will be
its altitude for that day.
The only Problem remaining to be explained to
you (being, with those I have already acquainted
you, all that are most worthy your attention) is
that of the Harvest-Moon.
PROBLEM
364
CELESTIAL PROBLEMS.
PROBLEM XXI.
Of the phenomenon of the Harvest-Moon.
At the time of the autumnal equinox, when the
Moon is at or near the full, she rises for several
nights together nearly at the same time, which
circumstance being particularly useful to farmers,
by affording them a longer continuance of light
for gathering in their harvest with more security,
it has been called the Harvest-Moon.
We have every reason to suppose that this, like
all other of the dispensations of Providence, was
intended for our benefit; particularly so, as we
know this circumstance does not occur in those
situations where it would be unnecessary; and,
the more rationally this phenomenon is considered,
the more will the justice of the idea of its being a
kind of provision of Providence appear. For, is
it not reasonable to suppose, that the Power, who
makes the Earth team with plenty for the support
of his creatures, does also take care to prevent
such benefit from being lost or defeated, which
might be the case, in this uncertain climate, if
the produce of the fields were left too long upon
the ground?
The Moon can be full but twice a year in
or near the line of her nodes, or where she makes
the least angles with the Earth's orbit, which are,
when
CELESTIAL PROBLEMS.
365
when her orbit intersects the equator, and the Sun
is also in the equator, and opposite to the Moon.
The points of the ecliptic, at which the Moon's
orbit intersects it, are called the Moon's nodes:
they are variable.* The full Moon always hap-
pens when the Moon is in the opposite sign to
the Sun.
Rectify the globe for the latitude of some place
in northern latitude; suppose to those on the same
parallel with London, or 514 degrees; then bring
the Sun's place for the autumnal equinox, which
is the first degree of the sign Libra, to the brass
meridian, and fix the index at 12 o'clock. Sup-
posing the Sun to be in the first degree of Libra,
the Moon must, at the same time, be at full, and
in the first degree of Aries, and both the Sun and
Moon in the equator. On turning the globe
westerly, till the Sun's place touches the horizon
on the western edge, you will see the time of sun-
setting for that day; and, on looking at the eastern
edge of the horizon, you will perceive the Moon
rising at the same time that the Sun sets. By
placing patches on the globe, agreeably to the
popular mode of illustrating this phenomenon, at
* This is also a wise ordination of Providence; as, were the
line of the nodes fixed to those two points of the ecliptic where
it intersects the equator, we should have a total eclipse of the
Moon at each autumnal equinox; or, were they fixed to any points
of the ecliptic, we should, twice a year, be deprived of some part
of the Moon's illumination, which would be inconvenient, but at
no time so much as at the time of the autumnal equinox.
every
366
CELESTIAL PROBLEMS.
every 13° of the ecliptic from Aries, to be more
accurate in working this Problem, look for the place
of the Moon's nodes, and place the patches accord-
ing to the inclination she has at that time to the
ecliptic, by placing two pins on the place of her
nodes, and carrying a string round the globe in
their direction; when, by placing the patches in the
same at 13° from each other, you will see the time
very accurately of the Moon rising; and for six
days you will find there will not be more than
about an hour's difference between the time of
the Sun setting and the Moon rising. This you will
be able to ascertain, by allowing only one degree
of the Sun's apparent motion in the ecliptic, east-
erly, whilst you allow 13° of the Moon's apparent
motion in the ecliptic, in the same direction, in
24 hours, as that will be agreeably to the true
relative proportions of the ecliptic, passed over by
the Earth and the Moon in that time. Then, by
turning the globe on for six days, till the patch at
each degree on the ecliptic for the Sun's place comes
to the western edge of the horizon, and the patch at
each degree of the Moon's apparent motion appears
at the eastern edge of the horizon, being the time
of the Sun setting and the Moon rising; by refer-
ence to the index, the difference of each, for each
time, will be seen; and, if the twilight is allowed
for, you will perceive that there will be continual
illumination for six days and nights, at the time of
the autumnal equinox, in that latitude.
As
CELESTIAL PROBLEMS.
367
As the latitudes increase, the difference between
the time of the Sun setting and the Moon rising
will be less; but, as they decrease, the difference
will be greater; as may be seen, by fixing the
globe for different latitudes. And, as all the times
must differ according to the place of the Moon's
nodes, the nearer those are to the equinoctial
point, the less will be the difference of time, and
the greater will be the advantage by the continu-
ance of the phenomena; but, in respect to the latter,
not so near as to cause an eclipse of the Moon.
The places of the Moon's nodes change every
month.
I have an opportunity, by the use of the orrery,
to amuse my pupils with many pleasing and clear
problems of the aspects of the heavenly bodies, and
all the phenomena of the heaven and Earth, with
the principles of which we are acquainted; but to
introduce them all in this work, would be of no
utility to those who have not a similar apparatus ;
and, to those who have, the elucidation of those
circumstances may be inferred from what I have
explained in my Lectures, of the planetarium,
lunarium, and tellurium, which compose this
orrery.
AN
[369]
AN
EXPLANATION
OF THE
TABLE S
CONTAINED IN
WHITE's EPHEMERIS;
Also of the Terms used to express the Circumstances, of which
it is meant to give previous Information.
AN Ephemeris is a daily register of all the mo-
tions of the heavenly bodies, and their places, as-
pects, &c. which have been anticipated by Ma-
thematicians and Astronomers.*
B b
It
* There is a very comprehensive Ephemeris and Nautical Al-
manac, printed for the Board of Longitude, under the immediate
inspection of that very learned Astronomer and Mathematician,
the Rev. Dr. Nevil Maskelyne, his Majesty's Astronomer Royal,
which I recommend to all scientific navigators: but, as it includes
matter foreign to my plan, such as nautical calculations, 1 purpose
giving a general idea of White's Ephemeris only, which contains
all that is necessary to astronomical observations. The distin-
guishing honour the Astronomer Royal has been pleased to confer
on
370
KEY TO THE EPHEMERIS.
It exhibits the places of the planets, both as
seen from the Sun and from the Earth; the former
are called the heliocentric, and the latter the geo-
centric places of the planets.
All the calculations noted in the Ephemeris
have been made according to apparent time, or
12 o'clock at noon, when the Sun is on the meri-
dian, and to correspond to the meridian at Green-
wich.
Apparent time differing from equal time, as I
have explained in my Lectures; the former being
that at which the Sun transits the meridian each
day at noon of the civil, or, as it is called, the na-
tural, day, which is not always in the same inter-
vals of time; and the latter depending on the e-
quable motion of the Earth's rotation, which is
called sidereal time. To allow for the difference
of those times, we are obliged to use an equation
of time; and, in the right-hand column of every
left-hand page of the Monthly Calendar in the
Ephemeris, the equation is seen for every day in
the year; that is, how much the clock is before
or after the Sun. We must add or subtract the
on my publication, by allowing it his respectable sanction, will
ever live in my memory, and must be considered a convincing
proof of the superiority and liberality of his mind, which could
prompt him to encourage the faint beamy lustre of this reflected
light, when likely to serve the purpose of more general informa-
tion, notwithstanding the great and intrinsic illumination of his
own understanding; knowing, that, like the Moon, it might be
of use where the sun-beams of his intelligence had not entered.
difference,
KEY TO THE EPHEMERIS.
371
difference, in order to find out mean time by
which to regulate our clocks. Every phenome-
non being calculated according to solar or ap-
parent time in the Ephemeris, it is unnecessary
to equate the time for the observation of them; —
all we have to do, in order to know the true time
of their appearing, and being in such situations in
respect to the Earth, the Sun, and each other, is
to rectify for the latitude and meridian of our
place. As they are all estimated for the latitude
and meridian of Greenwich, which is reckoned at
51 degrees north latitude, and the first meridian
of the heavens, which is at the first degree of
Aries, and, whatever is the difference of longitude,
such will be the difference of time in which the
phenomena will appear to an observer at a diffe-
rent longitude, allowing four minutes for every
degree of longitude, because that is the difference
of the Sun's time in transiting between two me-
ridians of places, which differ one degree in those
longitudes, but which need not be allowed for if
we have a clock properly regulated by the Sun,
&c. as it is the apparent motion only which is
considered in the Ephemeris or in using a celestial
globe, and therefore the longitude of places, in
that case, is not reckoned agreeably to the ter-
restrial longitude, but only according to the meri-
dian or Sun's longitude for the time.
In the table at the bottom of each left-hand
page of the Monthly Calendar, the heliocentric
places of the planets for every sixth day are shewn,
which
Bb 2
372
KEY TO THE EPHEMERIS.
which are their true places: Saturn's time of ri-
sing and setting is also set down under the table
of equation in these pages. In the table at the
bottom of each right-hand page of the Monthly
Calendar is the geocentric rising and setting of all
the planets; A means afternoon, and M morning;
also, N north and S south declination, which are
only their apparent places and declination.
The noon of the civil day is called the first hour
of the astronomical day, Astronomers beginning to
count their day from the time of the Sun being on
the meridian, and counting up to his again being
in that situation. The upper part of the right-
hand pages shews the lengths of the days and
nights for every sixth day; also the place of
the Moon's node, and the latitude of the planets.
The middle part of those pages shews the Sun's
longitude or place in the ecliptic, also the Moon's
longitude and latitude, together with the longi-
tude of all the planets. D means when their mo-
tions are direct, or according to the order of the
signs, and R when they appear retrograde. Every
thing in the right-hand monthly pages accords with
the appearances only of those bodies as viewed
from the Earth, that is, their geocentric pheno-
mena. The upper part of the left-hand pages of
the Calendar contains the Moon's age, the time of
Sun rising and setting, its declination north or
south of the equator, also the same of the Moon,
and the equation of time. M D, in these tables,
means mid-day, or noon.
Spec.
KEY TO THE EPHEMERIS.
373
Spec. Phænomenorum, p. 38 and 39 Ephemeris,
is intended to acquaint us with events and appear-
ances, that we may look out for them at the proper
times and in the proper places: such as the con-
junctions, oppositions, and quadratures of the Sun
and Moon with the planets; the Sun's entrance
into each of the 12 signs of the zodiac; the time of
the planets appearing stationary; the Moon's times
of
apogee and perigee; the planets aphelion, peri-
helion, and greatest elongations. The days of the
month are in the left-hand column; and on the
right side of the characters are the hours, which
are counted from 12 o'clock at noon of the civil
day up to 24.
Pages 36 and 37 contain the times of the emer-
sions and immersions of Jupiter's satellites; and are
useful in determining the longitude of places, or
their distance from the longitude of Greenwich;
which application of these observations to that
purpose is fully explained in the Ephemeris; as
are also every other circumstance in it, excepting
those I have explained, and those which are not
necessary to us, being expressive of circumstances
not within my plan of instruction: yet the terms
belonging to the latter should, I think, be under-
stood by all who use an Ephemeris ; therefore I
will subjoin an explanation of their intended appli-
cation in the Ephemeris.
Page 2, Chronological notes.
Golden Number is used to express any year
within the Lunar Cycle, which is 19 years.
Bb 3
The
Lunar
374
KEY TO THE EPHEMERIS.
Lunar Cycle* is that period in which the new and
full Moon return in the same order, on the same.
sign and day, as they did 19 years before; the
cause of which is explained in my tenth Lecture.
The Golden Number is put in the Ephemeris,
that we may know the distance of the Moon in
years from the last Cycle. To find the Golden
Number for any year, we first add 1 to the year:
suppose we say for the year 1797, add 1 to it, and
that will be 1798; divide that by 19, and the
remainder will be 12 for the Golden Number.
Cycle of the Sun, page 2, means a period of 28
years, which when elapsed, all the Sunday-letters,
and others, which are used to express the feasts,
return to their former place and order; the days of
the month to the same days of the week; the Sun's
place in the ecliptic to the same signs and degrees,
on the same months and days, so as not to differ
one degree. This has nothing to do with the
course of the Sun, but only with the Sundays,
from which it is called Cycle of the Sun, or
Sunday. To find the Cycle of the Sun for any year,
as for 1797, add 9 to it, and divide by 28, and
the remainder will be 14, which was the period of
the Cycle for that year.
Epact, in page 2, means that settled by the
Gregorian account, or Calendar, of 11 days, which
means the excess of the solar year, in regard to its
Cycle is a certain period or series, passing from first to last,
and then returning in the same order.
number
KEY TO THE EPHEMERIS.
375
number of months, or the odd days there are differ-
ence between 12 solar and 12 lunar months that
happen every year.
Roman Indiction, a manner of counting time.
among the Romans: it contains a Cycle of 15
years. At the time of the reformation of the
Calendar, in the year 1582, was counted the 10th
year of the Indiction. The Indiction is found by
adding 3 to the year, as 1797, which makes it
1800, and dividing it by 15, when there being no
remainder, the Indiction is set down in the Ephe-
meris 15.
Number of Direction is between 35, being the
limits between the earliest and latest day on which
Easter can fall, which is always between March 22
and April 25. It is called the Number of Di-
rection, because it directs when the first day of
Easter happens, and how many days after the 21st
of March.
The equation of the equinoctial points, set down
in p. 7 Ephemeris, is the result of a very nice
calculation of the precession of the equinoxes and
nutation of the Earth's axis. All these calculations
are very unnecessary for us to go into, and there-
fore I have only attempted to explain the nature
of them.
Bb 4
CHA-
[376
]
CHARACTERS OF BODIES BELONGING ΤΟ THE SOLAR SYSTEM,
AND OF THE
IMAGINARY CONSTELLATIONS of the ZODIAC.
Planets'
Cha-
racters.
Twelve Signs of the Zodiac.
Names of the
Planets.
The Letters of the Greek Alphabet,
Charac-
and their Names.
Names.
ters.
୫
O ADD+0+ Tot AS IT ∞∞
Sun.
ာ
Aries, the Ram.
A a
Alpha I
N
Moon.
Earth.
8
Taurus, the Bull.
B B C
Beta
2
II
Gemini, the Twins.
Γ γ Γ
Gamma 3
= w 0
Nu
13
Xi
14
3 +
Omicron 15
Mercury.
6
Cancer, the Crab.
A 8
Delta
4
Ππο Pi
16
Venus.
Mars.
Я
Leo, the Lion.
Εε
Epsilon
Ppę
Rho
17
me
Virgo, the Virgin,
Z
Zeta
6
ZoCs Sigma
18
67∞
Jupiter.
Libra, the Balance.
Saturn.
m
Scorpio, the Scorpion.
H n
90
Eta
Herschel, or
Sagittary, the Archer.
I
Theta
Iota
7∞
Ττ1
Tau
19
8 Yv
Upsilon 20
H
Georgium Sidus.
W
Capricorn, the Goat.
K x
Kappa
Ascending Node.
MN
Aquarius, the Water-Bearer.
Αλ
8
Descending Node.
*
Pisces, the Fishes.
M μ
Mu
9
ΙΟ
Lambda 11
12
Φ
Phi
21
X + C
Chi
22
не
Ωω
ते 3
Psi
23
Omega 24
[377]
CHARACTERS OF THE AFFECTIONS OF THE PLANETS AND
Characters.
SIGNIFICATIONS:
Also other Characters explained that are used in the Ephemeris.
Signification.
THEIR
8
•
Names.
Conjunction
Opposition
Sextile
Quartile
Trine
When two planets are in the same sign of the ecliptic.
When two planets are in opposite signs of the ecliptic.
When two planets are 60 degrees from each other.
When two planets are 90 degrees from each other.
When two planets are 120 degrees from each other.
Mark.
A degree.
A minute of a degree.
A second of a degree.
A third of a degree.
Signification.
There are 60 minutes in a degree, and 60 seconds in a minute.
A. M. or m.
P. M. or a.
h. m. s.
Ante-Meridian, or Morning.
Post-Meridian, or Afternoon.
Hours. Minutes. Seconds.
]
378 ]
A VIEW OF THE
SOLAR SYSTEM.
[See Plate 6.]
Mercury.
Venus.
Earth.
Mars.
Jupiter.
Saturn.
Herschel, or
Georgium
Sidus.
Greatest elongation of inferior, and
parallax of superior, planets
28° 20
47° 48′
**
47° 24'
11° 51′
6° 29′
3° 44
Periodical Revolutions
D. H. M. D. H. M.
87 23 15224 16 49
D.
365
H. M. D. H. M. D. H. M. D.
6 9686 23 304332 8 5110761 14 364
H. M.
D. H.
30445 18
H. M.
Diurnal Rotations
***
23 22
H. M. S.
23 56
4
H. M. S.
24 39 22
H. M.
9 56
**
**
Inclinations of their orbits to the
ecliptic
7° 1
3° 23/31/2
1° 51′
1° 19
2° 30
480
sent
Place of the ascending node at pre- 15° 46′ of 14° 44′ of
Place of aphelion, or point farthest
from the Sun
***
Taurus.
Gemini.
17° 59' of
Taurus.
8° 50′ of
Cancer.
21° 48 of
Cancer.
13° 1' of
Cancer.
14° 13 of 9° 38′ of
Sagittarius. Aquarius. Capricorn.
9° 15 of
2° 61 of
Virgo.
10° 57% of
Libra.
45% of
Capricorn.
23° 23' of
Pisces.
[ 379
}
Greatest apparent diameters as
seen from the Earth
II"
58″
*
25"
46″
20"
4
Diameters in English miles, that of I
the Sun being 883,217
Miles.
Miles.
Miles.
Miles.
Miles.
Miles.
Miles.
S
3,222
7,687
7,964
4,189
89,170
79,042
35,109
Mean distance from the Sun in se-
mi-diameters of the Earth
Semi-dia.
Semi-dia.
Semi-dia.
Semi-dia.
Semi-dia.
Semi-dia.
Semi-dia.
9,210
17,210
23,799
36,262
123,778
227,028
453,000
Mean distance from the Sun in
English miles
Millions.
Millions.
Millions.
Millions.
Millions.
Millions.
Millions.
37
68
95
144
490
900
1,800
Eccentricities, or distance of the
focus from the centre
•
S
7,950,000
510,000
1,680,000 14,218,000 25,277,000 53,163,000
4,759,000
Proportion of heat and light, that
of the Earth being reckoned at
100 degrees
Proportion of bulk, that of the
668
191
100
43
370
ITO
276
TOUO
Sun being 1,380,000
8
S
13
す
​012
I
ว่า
1,424
1,000
90
[ 380 ]
CATALOGUE OF THE CONSTELLATIONS
IN THE
NORTHERN HEMISPHERE.
[See Plate 4.]
THE Ancients distinguished only 12 Constella-
tions, which occupy that part of the celestial con-
cave through which the Sun appears to pass in his
apparent revolution. These are called:
Aries, or the Ram, which consists of . .
46 stars.
Taurus, the Bull
109 stars.
Gemini, the Twins
94 stars.
Cancer, the Crab
75 stars.
Leo, the Lion
91 stars.
Virgo, the Virgin
93 stars.
•
•
Libra, the Balance
Scorpio, the Scorpion
Sagittarius, the Archer
Capricornus, the Goat.
Aquarius, the Water-Bearer
Pisces, the Fishes.
9 stars.
44 stars.
48 stars.
58 stars.
•
93 stars.
110 stars.
The


Equator
Pisces
Sticus
THE NORTHERN CELESTIAL HEMISPHERE.
Antinous
Aquila
Equuleus Delphings
Albayr
Sagi
Anser
Via Lactea
Cerberus
Hercules
Plate IV.
Pegasus
Tropicus,
Andromeda
000
Pisces
Aries
Cetus
ancki
Frigomus
Major
Trigon Caput
Minor ledu
Musca
ade
phe
Pacido
Draco
"N the
Serpe
Bootes
Te
Cassiopea
Camelopardalns
Ursa Minor
Aliath
Ursa Majoret
Asterion
Cor
Caroli
Chara
Auriga
go
Gemini
Lynx
Hyages
Orion
Lactea
00
T. Conder Sculp
a
Mons Menelaus
Arcturus
ma
Berenice
Caula
Lemis
Leo Minor
хориото
opicus
Leo
chpie
profecuis
Virgo)
Canicula
Procyon
Hydra
Equator
UNI
OF
M
CATALOGUE OF THE CONSTELLATIONS. 381
The 21 Constellations, mentioned by Ptolemy,
on the north side of the ecliptic, are:
The Great Bear, which consists of . . . 105 stars.
The Little Bear
12 stars.
The North-Pole Star, as it is called, is in
the Tail of the Little Bear.
49 stars.
40 stars.
53 stars.
11 stars.
The Dragon
•
Cepheus, a King of Ethiopia
Boötes, the Keeper of the Bear
The Northern Crown .
Hercules, with his Club, watching the
Dragon
Lyra, the Harp
.
Cygnus, the Swan
Cassiopeia
Perseus.
Auriga, the Waggoner
Ophiuchus, or Serpentarius
92 stars.
24 stars.
73 stars.
52 stars.
67 stars.
46 stars.
67 stars.
50 stars.
13 stars.
The Dolphin.
18 stars.
Equus Minor, the Colt
12 stars.
Pegasus.
67 stars.
Andromeda
66 stars.
And the Great Triangle .
4 stars.
The Serpent.
Sagitta, the Arrow
•
But
382 CATALOGUE OF THE CONSTELLATIONS.
But several other Constellations have been added
by succeeding Astronomers, of which, in the
Northern Hemisphere, are:
Anser, the Goose, which consists of . .
Aquila, the Eagle
Argo, the Ship
Berenice's Hair.
Cameleopardalis
Cerberus
•
•
Cor Caroli, Charles's Heart, is an extra
Star between Berenice and Ursa Major.
Greyhounds
Leo Minor, the Little Lion
Lynx
Lizard
•
Mens Menelaus
Musca, the Fly
Serpentarius
Sobieski's Shield
10 stars.
12 stars.
48 stars.
24 stars.
23 stars.
9 stars.
24 stars.
20 stars.
55 stars.
12 stars.
11 stars.
6 stars.
67 stars.
8 stars.
Trigonus Major, the Great Triangle
Trigonus Minor, the Little Triangle
10 stars.
5 stars.
Stars of the first Magnitude, or Class, in the
Constellations, are as follow:
Achernar, which is in the Constellation Eridanus.
Aldebaran, in the Head of Taurus, and which is
called the Bull's Eye.
Antares, in Scorpio.
Arcturus, in the Skirts of Boötes.
Basilicus,
CATALOGUE OF THE CONSTELLATIONS. 383
Basilicus, or Cor Leonis, in Leo.
Capella, in the Left Shoulder of Auriga.
Canopus, in Argo.
Lucida Lyra, in Lyra.
Regulus, in the Heart of Leo.
Rigal, in the Left Foot of Orion.
Spica Virginis, in Virgo.
Sirius, in Canis Major.
Seven Stars in the Great Bear, and 7 ditto in the
Little Bear.
The Polar Star is in the Tail of the Little Bear.
Other remarkable Stars are the 7 in Taurus, called
the Pleiades.
CATA-
[ 384 ]
CATALOGUE OF THE CONSTELLATIONS
NOTICED BY THE
ANCIENTS,
IN THE
SOUTHERN HEMISPHERE.
[See Plate 5.]
CETUS, the Whale
Lepus, the Hare
Orion . .
Eridanus, the River
.
8 stars.
25 stars.
93 stars.
72 stars.
Canis Major, the Great Dog
29 stars.
Canis Minor, the Little Dog
14 stars.
Argo, the Ship
The Hydra.
Crater, the Cup
Corvus, the Crow
The Centaur
•
Lupus, the Wolf
Ara, the Altar .
48 stars.
·
53 stars.
11 stars.
8 stars.
36 stars.
36 stars.
•
9 stars.
The Southern Crown
The Southern Fish .
12 stars.
15 stars.
To

Liluray
Spica
THE SOUTHERN CELESTIAL HEMISPHERE.
Serpentarius
75
Serpens
coypic
Ecliptis
Sagittarius
Lupus
Ara
Corona
Australis
Indus
CO
cus Capricorni
Corvus
Virgo
Chamelon
Crater
me
Equator
Hydra
entaurus
picus/Capricorni
osiers
0
Trianguli
Australe
Pavo
Apus
Antinous
Toucan
Plate V.
Equator
Capricornus
Aquarius
Piscis
Australis
Caronum
Achema
Piscis
Phoenix
Volans Feliptic Xiphias
Argo
Via Lactea
Major
Sirius
Columba
Noachi
Monoceros
00
T. Conder Sculp
O
Eridanus
Acpis
ropicus/Capricorn
Pisces
Eclipticus
00
Cetus
CATALOGUE OF THE CONSTELLATIONS. 385
To which have been added:
Anser Americanus, or Toucan, the Ame-
rican Goose
Apis, the Bee.
Xiphias, the Sword-Fish .
Charles's Oak .
Chameleon.
Corona Meridionalis, the Southern
Crown
Crossiers, four stars in the form of a
cross, near the Southern Pole.
9 stars.
4 stars.
7 stars.
13 stars.
10 stars.
12 stars.
Cyrus, the Crane
Hirundo, the Swallow
14 stars.
11 stars.
Indus, the Indian
12 stars.
Monoceros, the Unicorn
32 stars.
Noah's Dove.
10 stars.
Pavo, the Peacock
14 stars.
Phoenix.
13 stars.
Piscis Volans, the Flying-Fish
7 stars.
•
The Southern Triangle.
5 stars.
Cc
NAMES
[386]
NAMES OF THE SPOTS IN THE MOON.
[See Fig. 1, Plate 13.]
* Herschel's Volcano.
1 Grimaldi.
2 Gallileo.
3 Aristarchus.
4 Kepler.
5 Gassendi.
6 Schikard.
7 Harpalus.
8 Heraclides.
9 Lansberg.
10 Reinhold.
11 Copernicus.
12 Helicon.
13 Capannus.
14 Bulliald.
15 Eratosthenes.
16 Timocharis.
17 Plato.
19 Insula Sinus Medii.
18 Archimedes.
20 Pitatus.
21 Tycho.
22 Eudoxus.
23 Aristotle.
24 Manilius.
25 Menelaus.
26 Hermes.
27 Possidonius.
28 Dionysius.
29 Pliny.
30 Catharina Cyrillus
Theophilus.
31 Fracastor.
32 Promontorium Acu-
tum Censorinus.
33 Messala.
34 Promontorium Som-
nii.
35 Proclus.
36 Cleomedes.
37 Snell and Furner.
38 Petavius.
39 Longrenus.
40 Taruntius.
A Mare Humorum.
B Mare Nubium.
C Mare Imbrium.
D Mare Nectaris.
E Mare Tranquillitatis.
F Mare Serenitatis.
G Mare Fœcunditatis.
H Mare Crisium.
A
[387]
A
VOCABULARY
OF
B&G b
TERM S.
1
ABERRATION. An apparent change of place
in the fixed stars, occasioned by the progres-
sive motion of light, compounded with the an-
nual motion of the Earth in her orbit.
ACHRONICAL is used to express the rising of a
star or planet at sun-set, or of its setting at
sun-rise.
ALTITUDE. The height of the Sun, Moon, or
stars, above the horizon of any place, reckoned
on a verticle circle from the horizon to the
zenith.
AMPLITUDE is reckoned east and west, and is
the distance of the Sun or a star from the east
point of the horizon at rising, and from the
west point at setting.
Cc 2
ANDRO-
388
VOCABULARY OF TERMS.
ANDROMEDA.
A constellation of the northern
hemisphere, representing a woman chained.
According to the fable in mythology, it is sup-
posed to be formed in memory of the daugh-
ter of Cepheus and Cassiopeia, and wife of
Perseus; who, being chained to a rock to be
devoured by a sea-monster, was, at the insti-
gation of Juno, rescued by Perscus, whom she
afterwards married.
ANGLE. That portion of a circle contained
between lines, which have the same ra-
dius and touch each other in one point.
A RIGHT ANGLE is formed by two straight
lines, one drawn perpendicular to the
other.
OPPOSITE VERTICLE ANGLES are made
Ъ
L
C
by two right lines which cross each o- b
ther, and touch in the angular point
only.
A SPHERICAL ANGLE is an angle made.
by the meeting of two great circles,
which intersect or mutually cut each
other on the surface of a sphere, as the figure
A BC, or that made by the ecliptic and e-
quator.
AN ANGLE AT THE CENTRE OF A CIR-
CLE is formed by two radii of the cir-
cle, as a c b.
A MIXED ANGLE is formed by a right
line and a curved one.
Y
A
VOCABULARY OF TERMS.
389
A CURVILINEAR ANGLE is made by the
intersection of two curved lines.
لا
ANOMALY is the angular distance of a planet
from the aphelion.
ANOMALY, MEAN, is when the planet is at its
mean distance from the Sun.
ANTECEDENTIA.
An apparent motion of the
heavenly bodies, which is contrary to the or-
der of the signs, or from east to west.
APHELION. That place of a planet's orbit which
is farthest from the Sun, called by some of the
ancient Astronomers the apogee, because they
supposed the Earth to be in the centre of the
system. In referring the planets to the Sun,
we call it aphelion, using apogee only to ex-
press the greatest distance of the Moon from
the Earth; but, in reference to the Sun, we
use the term aphelion, which is expressive of
the same circumstance. Thus, also, perihe-
lion means the same as perigee; only the for-
mer is used to express the least distance of a
planet from the Sun, and the latter the nearest
approach of the Moon to the Earth.
APOGEE. The greatest distance of a planet from
the Earth.
APEX. The upper point.
APSES, or APSIDES, are the two points in the
orbits of the planets, in which they are at their
greatest and least distance from the Sun; and
of the Moon's orbit, in which it is at its greatest
and least distance from our Earth. The point
Cc 3
at
30
390
VOCABULARY OF TERMS.
at the greatest distance is called the higher
apsis; and that at the nearest distance, the
lower apsis. The higher apsis is also called
aphelion, in reference to that place of the
planets in respect to the Sun; and apogee in
respect to the place of the Moon in regard to
our Earth and the lower apsis is called the
perihelion, in reference to the Sun, and perigee
in reference to the Earth. The diameter of the
elliptical orbits, which unites the two apses, is
called the line of the apses, or of the apsides.
APPULSE. Near approach to any thing.
ASPECTS are the respective situations of the
Moon and planets with the Sun ; as, opposition,
trine, &c.
ARC OF A CIRCLE is any part of its a
circumference; as a b, or c d.
ARCH OF A CIRCLE. A part of a circle. The
same as ARC.
AREA. The surface contained within any boun-
dary.
ARGO. A constellation of the southern hemisphere,
in the form of a ship; which was placed there
by the Greeks, in order to celebrate the voyage
of the Argonauts, a body of fifty men, of whom
Jason was the chief, who went in search, as
was supposed by them, of the golden fleece.
The fable is thus related:-Phryxus and his
sister Helle, flying from the rage of their step-
mother Ino, went on board a ship, the ensign
of
VOCABULARY OF TERMS.
391
of which was a golden ram, and sailed in it to
Colchis, (now Mingrelia, and part of Georgia) :
that Helle was drowned in the sea, which they
named the Hellespont, but which is now called
the Dardanelles; and that the Argonauts went
in quest of this ship with the golden ram, which
they styled the golden fleece: that Jason, having
accomplished his design, consecrated the ship
to Neptune; or, according to others, to Mi-
nerva, and that it was translated into heaven.
Sir Isaac Newton is of opinion, that this was an
embassy sent by the Greeks during the intestine
divisions of Egypt, in the reign of Amenophis,
to persuade the nations on the coasts of the
Euxine and Mediterranean Seas, to take the
opportunity of shaking off the yoke of Egypt,
which had been laid upon them; and that
fetching the golden fleece was only a pretence
to cover their design.
ARMILLARY. Resembling a bracelet, (as the ar-
millary sphere,) being composed of circles only.
ATMOSPHERE. A collection of vapours surround-
ing the earth.
ATTRACTION.
The effect of an invisible natural
agent, which causes bodies to approach each
other.
AURORA. The morning twilight, or the light
occasioned by the refractive power of the atmo-
sphere, which causes the light of the Sun to be
seen, when that luminary is about 18 degrees
below our horizon.
Cc 4
AXIOM.
392
VOCABULARY OF TERMS.
AXIOM. A self-evident proposition.
AXIS OF A SPHERE AND OTHER SOLID. A straight
line passing through the centre of it to two
opposite points in the circumference. It is
that line round which any body will revolve,
being the line passing through its cen-
tre of gravity. When this line is not
spoken of in reference to motion, it is
called the diameter of a sphere, as a b;
and the centre of gravity of any other
solid body, as c d.
AZIMUTHS. Great circles, which are supposed
to pass through the zenith, and are perpendi-
cular to the horizon.
BAROMETER. An instrument constructed for
ascertaining the weight of the atmosphere, and
its variation, by the rising and falling of quick-
silver, or other fluid, in a tube. When the air
is heavy, as in clear weather, the quicksilver
rises in the tube, by the pressure of the air
on the quicksilver in the reservoir: when the
air is light, or foul, the quicksilver falls in the
tube, shewing the approach of foul weather.
CARDINAL POINTS. The east, west, north, and
south points of the compass. Of the ecliptic,
the first degrees of Aries, Cancer, Libra, and
Capricorn.
CAMELEOPARDALIS. A particular species of
animal peculiar to Africa. A new constellation
of the northern hemisphere.
CENTRI-
VOCABULARY OF TERMS.
393
CENTRIPETAL FORCE.
That by which a re-
volving body endeavours to approach the centre
of its orbit.
CENTRIFUGAL FORCE.
That by which a re-
volving body endeavours to fly off from the
centre of its orbit.
CENTAUR. A southern constellation. In fable,
Centaurs were supposed monsters, the upper
part human and the lower like a horse. They
always carried clubs, and were skilful in the
use of the bow. The fabulists tell us, that
Hercules vanquished these monsters.
CEPHEUS. A king of Æthiopia, father of Andro-
meda. According to the fable, he was taken
up into heaven along with his wife Cassiopeia
and his daughter, and placed near the Little
Bear.
CERBERUS. The name given by the ancients to
express a dog with three heads and three
mouths, which they supposed to be stationed
at the gate of the infernal regions; and that
when Hercules went down to bring Alcesta
back to her husband, from whom she had been
taken, he bound this dog with a chain, and
brought him into the upper regions. This
forms a small constellation of the northern
hemisphere.
CHORD. A chord is a right line which
extends between the two extremities of
the arc of a circle.
CHAOS. Confusion, irregular mixture.
о
CIRCLE.
394
VOCABULARY OF TERMS.
CIRCLE. A circle is a plane figure, included
within one line, called the circumference, which
is in every part of it equi-distant from the
centre.
CLOUD. A collection of vapours in the air.
COLLATERAL. The collateral points in cosmo-
graphy are the intermediate ones between the
cardinal.
COMA BERENICE.
A modern constellation of the
northern hemisphere, lying between the tail of
the Lion and Boötes. It is said to have been
formed by the Astronomer Conan, in order to
console the queen of Ptolemy Evergetes for the
loss of a lock of her hair, which had been
stolen from the temple of Venus, where she
had deposited it, having dedicated it to that
goddess on account of a victory obtained by her
husband.
B
CONE. A geometrical solid figure, consisting of
straight lines that arise from a circular base; and,
gradually declining from the surface
and circumference of the base, meet
in a point which is directly over the
centre of the base, like the figure A BC.
CONSEQUENTIA. A motion from west to east,
or according to the order of the signs.
CONTINENT.
A main land which is not inter-
rupted by seas; and so called, in contradistinc-
tion to island and peninsula.*
* An island is a tract of land surrounded by water; and a penin-
sula is a portion of land joining to a continent or main land by a
narrow neck, the rest being encompassed by water.
CON-
VOCABULARY OF TERMS.
395
CONVERGING. Tending to one point from different
places.
COSMICAL. A term used to express the rising
or setting of a planet or star with the Sun.
COSMOGRAPHY. The science of the general af-
fections or system of the world.
CUBE. A number in arithmetic arising from the
multiplication of a square number by its root.
As thus: suppose any number, as 2, be multi-
plied by itself, the product will be 4, which
makes the square. Then, if that square num-
ber be multiplied by its root 2, that will make
8 ; which latter is called the cube, or third
power of 2; and, with respect to the 8, the
number 2 is called the cube-root.
CUBE, in geometry. A regular body,
consisting of six square and equal
sides, and the angles, of course, all
equal and right.
CULMINATING. When the Sun or a star is passing
the meridian of any place.
CYCLOID. A certain curve formed by
the motion of a wheel. If a pendu-
lum be made to vibrate in this figure,
its oscillations will be all performed in equal
times.
CYLINDER. A round column which is neither
swelling nor diminishing.
DAY, NATURAL OR CIVIL. The time in which
the Earth completes its revolution on its axis.
DAY,
396
VOCABULARY OF TERMS.
DAY, ARTIFICIAL OR SOLAR. The time the
Sun is above the horizon of any place.
DAY, ASTRONOMICAL. That computation of
time which begins when the Sun transits the
meridian of any place, and ends at his return to
it again.
DECLINATION. The distance of a star from the
equator, north and south. The least declina-
tion of a star is its shortest distance from the
equator.
DEGREE. The 360th part of a circle. A degree
of the latitude of the Earth contains 69 English
miles, or 60 geographical or Italian miles.
The quantity of a degree of longitude differs at
every degree of latitude, from the equator to
the poles. At the equator, a degree of longitude
is supposed to contain 69 English miles; from
whence, the quantity of a degree of longitude
continually diminishes at every degree of lati-
tude, till it is nothing at the poles. In Dr.
Hutton's Dictionary, vol. i. p. 364, there are
tables for each degree of latitude.
DENSE. Close, approaching to solidity.
DIAGONAL. A right line which unites
two opposite angles, as a b in the
figure.
DIAMETER. The line which passes from one side
of a circumference, through the centre, to the
other side.
DIGIT. A measure by which the part of a lumi-
nary eclipsed is ascertained. The body eclipsed
being
VOCABULARY OF TERMS.
39**
being always supposed to be divided into 12
parts, called digits: as many of those parts as
are eclipsed, so many digits is the body said to
be eclipsed.
DIRECT, in optics, means the immediate effect or
direction of the primary rays; in contradistinc-
tion to those of reflected or refracted ones.
DISC. An apparently plane round surface.
DIVERGENCE. The spreading out of light as
it recedes from a centre.
DIURNAL. Relating to a day, or 24 hours.
DOMINICAL OR SUNDAY LETTER. One of the
first seven letters of the alphabet; the applica-
tion of which is fully explained in the Lectures.
ECLIPTIC-CIRCLE. The Sun's apparent path in
the heavens. It is called ecliptic, because
eclipses happen when the Moon is in this
circle.
EFFICIENT. Causing effects.
EFFLUVIA. Small particles flying off from bodies.
ELONGATION. The apparent distance of a planet
from the Sun, as seen from the Earth.
EMERGING. Rising from obscurity.
EMERSION. The re-appearance of a planet or the
Sun, after it has been eclipsed.
CD is
ELLIPSIS OR ELLIPSE. An oval figure formed
by cutting a cone obliquely to its axis.
a cone, and AB an ellipse cut obliquely
to the axis CD of the cone. The more a
obliquely the cone is cut to the axis, D
the longer the ellipse will be.
B
EPACT.
398
VOCABULARY OF TERMS.
EPACT. The Moon's age at the beginning of the
year, or the difference between the course of
the Moon and the Sun; as explained in the
Key to the Ephemeris.
EQUATOR. The circle which equates or divides
the globe of our Earth into two equal hemi-
spheres, being equally distant from the north
and south poles. When we speak of this circle,
in reference to the Sun or stars, we call it the
equinoctial.
EQUINOCTIAL POINTS OR EQUINOXES.
Those
two points of the globe where the ecliptic and
equatorial intersect each other.
EQUILIBRIUM. Equality of weight or power.
EQUI means equal, and is compounded with
other words, to denote equation, or equality.
ETHER. An element considered to be more sub-
tile than air or light, and an intermediate agent
which is supposed to fill the regions beyond the
atmosphere of the planets.
FLUX. Flowing in.
Focus. Where rays meet.
FOCII. The plural of focus.
GALAXY. The milky way; an innumerable quan-
tity of fixed stars.
GEOMETRY. The science of extension, quantity,
or magnitude.
GEOMETRICAL. Explained or described on the
principles of geometry.
GRADUATED. Marked with degrees.
GRAVITY.
VOCABULARY OF TERMS.
399
GRAVITY. Weight, attraction, tendency to a
centre.
GRAVITY, PARTICULAR, is that whereby bodies
descend towards the centre of the Earth.
GRAVITY, UNIVERSAL, is the existence of the
same principle in the heavenly regions.
HELIACAL. The heliacal rising of a star is its
transiting the horizon just before the Sun in
the morning. Heliacal setting of a star is
setting with the Sun, or when it is hid by the
Sun's beams on an evening, so as not to be seen
after that luminary has sunk below the horizon.
HELIOCENTRIC. The place of a planet, in which
it would appear from the centre of the Sun.
HEMISPHERE. The exact half of a sphere.
HORIZON. The line that terminates our view of
the heavens. The rational and the sensible
horizon are the same in relation to the fixed
stars, on account of their immense distance from
us: but, in regard to the planets, they are not
so; which produces what is called the horizon-
tal parallax of the Sun and planets, when we
are considering them.
HORIZONTAL LINE. That drawn parallel to the
horizon.
HORIZONTAL PARALLAX. The difference be-
tween the real place of a planet, or the Sun,
as viewed from the centre of our Earth; and its
apparent place, as viewed from its surface,
when the luminary is at the horizon. So that,
in regard to the true place of a planet, as
viewed
400
VOCABULARY OF TERMS.
viewed from the surface of the Earth, we allow
a parallax or this difference; and, when we
take the distance of the Sun, or a planet, from
it, this parallax shews that distance.
HYDRA. In mythology, a terrible monster which
was destroyed by Hercules. The poets and
painters describe it sometimes as a serpent with
many heads, and sometimes a human head with
serpents twined about it instead of hair. This
fable is supposed to have originated in a great
quantity of serpents which infested the marshes
of Lerna, near Mycene, which Hercules de-
stroyed by burning the reeds in which they
were ambushed. It is a southern constellation
which is intended to represent this imaginary
monster.
HYPOTHESIS. A supposition.
IMMERSION. The entrance of the Earth or Moon
into each other's shadow.
INCLINATION. The angle made by the orbit of
one planet with that of another.
INCIDENCE. The striking of one body on another.
The angle made by the direction of the moving
body with the other is called the angle of in-
cidence.
INCORPOREAL. Without body.
INERT. Motionless in itself.
INGRESS. The Sun's entrance into any sign or
degree of the ecliptic.
INTERCALLARY. Insertion of something super-
numerary, as the intercallary day in leap-year.
IN-
VOCABULARY OF TERMS.
401
INVERSELY. Contrary ways, or in a contrary
order.
LATENT. Secret, concealed.
LATITUDE, of places on the Earth, is counted
north and south from the equator. The latitude
of a star is its distance from the ecliptic, north
and south, towards the poles of the ecliptic.
The latitude of a planet is its distance from the
ecliptic, north and south, within certain boun-
daries.
LENS. A glass; plane, convex, or concave.
LIBRATION. Trepidation; a term used to ex-
press the irregular motion of the Moon's axis.
LONGITUDE of places on the Earth, in England,
is counted from the meridian of London or
Greenwich, east and west, upon the equator.
But longitude of the planets and stars is counted
on the ecliptic, east and west, from that inter-
section of the ecliptic and equator at Aries.
LUCID. Bright or glittering.
LUNAR ASPECTS are those of the Moon with the
Sun and planets; as, opposition, trine, quar-
tile, &c.
LIZARD. A creeping small animal; a celestial
constellation.
LYNX. A sharp-sighted spotted beast; a constel-
lation.
MATHEMATICS.
That science which contem-
plates whatever is capable of being numbered
or measured.
Dd
MATHE-
402
VOCABULARY OF TERMS.
MATHEMATICIAN.
matics.
One versed in the mathe-
MEAN DISTANCE. That between the greatest
and least distance of a planet from the Sun.
MEAN MOTION. That between the swiftest and
slowest motion of a heavenly body, and which
would take place if they moved in a perfect
circle.
MERIDIAN.
That great circle of the sphere
passing over any place, and through the north
and south poles of the world, being perpendi-
cular to the equator. This is the place of the
Sun at mid-day, or noon, at every place.
MERIDIAN, FIRST. The first meridian is arbi-
trary; most Astronomers fix it at the capital
city or place of observation to which they
belong.
MERIDIAN, MAGNETICAL. That to which the
poles of the magnet point.
METAPHOR. A figure of speech; a simile com-
prised in a word.
METAPHORICAL. Figurative; not real.
METAPHYSICIAN. One who considers the gene-
ral affections of incorporeal things.
METEORS. Appearances in the sky of a transitory
nature, such as clouds, thunder, &c.
MIRROR. Any thing which represents the images
of objects by reflection.
MODIFICATION. Change in the form, mixture,
&c. of any thing.
MOMENTUM.
VOCABULARY OF TERMS.
403
MOMENTUM.
The quantity of force or motion
in a moving body.
MINUTE. In time, the 60th part of an hour.
MINUTE. In motion, the 60th part of a de-
gree.
MONTH, LUNAR, is also called a periodical
month, being the time in which the Moon
revolves round the centre of gravity between
herself and the Earth. She performs this re-
volution in 27 days, 7 hours, and 43 minutes,
which is therefore the length of the lunar
month.
MONTH, SYNODICAL, is the period in which the
Sun, Moon, and Earth, are again in a direct
line with each other. It consists of 29 days
and a half, which is the period of each new
Moon.
MONTH, SOLAR AND CALENDAR. The time
of the Earth's moving through one sign, or
30 degrees, of the zodiac, which causes the
apparent motion of the Sun through that space,
and is performed in thirty days and a half, at a
mean computation.
NADIR. The point immediately under our feet,
opposite to the zenith.
NEBULA. A mist or fog, or cloud-like appea-
rance.
NEBULOUS STARS. Those perceived only by a
faint light, by which they are not distinctly
seen without the aid of glasses, such as the
milky way.
Dd?
Noc-
404
VOCABULARY OF TERMS.
NOCTURNAL. Nightly.
NODES. The two points of the ecliptic intersect-
ed by the orbit of a planet.
NUCLEUS. The central part of a comet.
OBLATE. Flatted at two opposite points of a
spheroid, called the poles.
OBLIQUE. Not directly, but slanting.
OCCULT. Hidden.
OCCULTATION.
Obscuration.
OCTANT. A term used for that situation or as-
pect of two planets when they are 45 degrees.
from each other.
OMNISCIENT. Infinitely wise, knowing all things.
OPAKE. Not transparent.
OPPOSITION. That situation of two heavenly
bodies in respect to each other when they are
180 degrees distant, or in opposite signs of
the ecliptic.
ORB. A circular figure.
ORBIT. The line described by the revolution of
a planet, or the curve in which it moves.
ORGANIZATION. Construction, in which the
parts are so disposed as to be subservient to
each other.
ORIENTAL. Eastern.
ORION. A Southern constellation consisting of
93 stars. In fable, a giant and famous hun-
ter, who, having told Diana that he could kill
more beasts than she could, she raised a scor-
pion which bit him, so that he died of the
wound. But Jupiter translated him into the
heavens,
VOCABULARY OF TERMS.
405
heavens, and made that constellation of him
which goes by his name.
OSCILLATION. Moving backwards and forwards
like a pendulum.
PARABOLA.
A curved figure arising
from the section of a cone when cut
by a plane parallel to one of its sides, B
as the section a de, parallel to the
side V B of the cone.
V
PARALLAX. The difference of place of a planet
as viewed from the centre of the Earth or Sun,
and as viewed from their surfaces.
PARALLEL LINES. Those which are
in the same plane, and which, if
ever so far extended, will never meet, being
every where at the same distance.
PARALLELOGRAM. A quadrangle,
the opposite sides of which are pa-
rallel.
PARALLELS, of latitude, are the lines drawn pa-
rallel to the equator of a terrestrial globe, and
supposed to be drawn parallel to the ecliptic
of a celestial sphere.
PENUMBRA. An imperfect shadow, or a partial
one, which is always perceived between the
perfect shadow and full light in an eclipse;
also between the perfect shadow and light of
any illuminated object which casts a shadow
behind it.
PERIGEON. That situation of a planet in its or-
bit nearest to the Earth.
Dd 3
PERI-
406
VOCABULARY OF TERMS.
PERIHELION. That point of a planet's orbit in
which it is at its least distance from the Sun.
PERIPHERY. The circumference of any regular
figure, as a circle.
PERSEUS. The son of Jupiter. He obtained the
helmet of Pluto, the buckler of Minerva, and
a faulchion of Mercury, with wings for his
feet. He rescued Andromeda from the mon-
ster which was sent abroad by Neptune, and
by whom she was to have been devoured.
She was chained to a rock by the command of
Cepheus, her father, for that purpose, in or-
der to stop the ravages this monster had com-
mitted; but, just as he was going to seize the
destined prey, Perseus, mounted on his horse
Pegasus, slew the monster and delivered the
lady.
PERIODIC. Happening at stated times.
PERPENDICULAR.
A line drawn in a
direction exactly transverse, or at c
B
A D
right angles, to another line, as A B, which
is perpendicular to CD.
PHASES. The different forms of the illuminated
part of a planet as seen from the Earth.
PHASIS. The appearance exhibited by any body
in its changes, as that of the Moon.
PHILOSOPHY. Knowledge natural and moral;
the course of the sciences.
PHLOGISTON. The inflammable part of a body.
PHOENIX. One of the constellations. A most
rare bird, and the only one of its species.
The
VOCABULARY OF TERMS.
407
The fable runs thus: That, after 1000 years,
a fire proceeds from its nest and consumes it;
but, from the ashes, an egg is generated, from
which the bird is again renewed.
Or thus:
- That, after 1000 years, it plucks off its
own feathers, and dies by mere decay of na-
ture; but that it first builds itself a funeral
pile of the branches of sweet-scented trees,
upon which it sits down and expires. That
from its ashes a worm proceeds, which changes
into a bird; and, according to Herodotus, it
takes up the remaining ashes of its parent, and
embalms them in a mass of myrrh. This bird
is described as very beautiful and rare, and
about the size of an eagle; the feathers of its
head and neck to be of a gold colour, and its
tail purple and carnation.
PHENOMENON (in the plural, Phenomena). Ex-
traordinary appearance in nature.
PHOSPHORUS. A chemical substance, which,
when exposed to the air, takes fire, or shines
in the dark.
PHYSICAL. Relating to matter or natural phi-
losophy; substance, in opposition to spirit.
t
PLANE. A flat superficies, neither convex nor
concave.
PLANETS. Those celestial bodies in our system
which have an evident motion peculiar to
themselves. They are supposed to be habita-
ble worlds, like our Earth, and to move round
the same Sun, their vivifying principle.
Dd 4
PLANO-
408
VOCABULARY OF TERMS.
PLANO-CONVEX, OR PLANO-CONCAVE.
Flat
on one side and a portion of a sphere on the
other.
POLAR. Lying near the poles.
POLARITY. Tendency to the poles.
POSTULATUM. Position assumed without proof.
PRIMARY. Original, first.
PRISM is a figure of any number of sides, and two
opposite equal bases or ends. That used for
optical purposes consists of only three sides.
It separates the rays of light, which come blen-
ded from the Sun, by the different degrees of
its refractive power, occasioned by its form,
by which a ray of light received on it passes.
more or less obliquely through it; and the
momentum of their individual motion, arising
from the different sizes of the particles, causes
some to be turned more aside than others, by
an interposed substance.
PROBLEM. A question proposed to be done.
PROJECTILE.
A body put in motion by one
force only, which always causes it to proceed
in a straight line.
PROMONTORY.
sea.
A high land jutting into the
QUADRANT. The fourth part of a circle. An
astronomical instrument.
QUADRANGLE, OR QUADRILATERAL.
Every
plane figure which is bounded by four right
lines is called quadrilateral, or a quadran-
gle.
1
QUA-
VOCABULARY OF TERMS.
409
QUADRATURE. The first or last quarter of the
Moon.
QUADRUPLE. Fourfold.
QUARTILE. When the planets are 90 degrees,
or a quarter of a circle, from each other.
QUIESCENCE. A state of rest.
RADIANT. Shining.
RADIATION. Emission of rays.
RADII. In the form of rays. The plural of ra-
dius.
RAREFACTION. Lightness, or thinness, procured
by the extension of a body, by which it is made
to occupy more room.
RATIO. Proportion.
RATIONALE. A solution, or account of the prin-
ciples of some opinions, action, hypothesis,
phenomenon, &c.
RAY OF LIGHT. The least particle of light that
can be separately impelled.
RAYS, CONVERGING. Those which tend to or
meet in a point. All convex lenses make the
rays converge, and concave ones make them
diverge.
REACTION. The resistance any body makes to
the force impressed on it. The action and re-
action of bodies upon each other are equal.
RECEIVER OF AN AIR-PUMP. A glass, under
which all the air contained in any thing may be
extracted by the operation of the pump.
RECTILINEAL. Right-lined.
REFLECTION. The act of throwing back.
REFLUX.
410
VOCABULARY OF TERMS.
REFLUX. Flowing out.
REFRACTION. The breaking or bending out of
the straight course in a moving body. The
variation of a ray of light from the straight line
which it would have passed on in, had not the
rays passed through a new medium.
REFRIGERATION. The property of cooling.
REGION. Place of any thing.
REGRESS. Passing backwards.
REGULATOR. That part of a machine which li-
mits or regulates its motion.
RESPIRATION. The act of breathing.
RETINA. The last or innermost coat of the eye,
being that on which the images of objects are
painted. The crystalline humour collects all
the rays from any luminous object, and throws
them on the retina, which is placed at its
focus.
RETROGRADE. Contrary to a direct motion.
RETROGRESSION. Moving backwards.
ROOT. A number multiplied by itself, the pro-
duct of which is called the square.
CUBE.
ROTARY. Whirling round.
See
REVERBERATION. The act of beating back.
REVOLUTION. The circular course of any thing
which returns to the point whence it began to
move.
SATELLITE. A small planet which revolves
round a larger.
SCIENCE. Knowledge founded on demonstration.
SECOND.
VOCABULARY OF TERMS.
411
SECOND. The 60th part of a minute in time, and
the same in motion.
SECTION. A cut or division which separates one
part from the rest.
SECTOR.
A mathematical instrument used for
laying down or measuring angles.
SEGMENT OF A CIRCLE. The part con-
tained under the arch, and a chord
of that arch; as a or b.
SEMI-CIRCLE. Half a circle, as A B.
SEMI-DIAMETER.
Half the diameter of
of a circle. It is sometimes called the
radius, or whole sine.
SENSATION. Perception by the senses.
A
a
C
B
e
SENSIBLE. Perceptible by one of the five sen-
ses.
SENSITIVE. Perception without reflection.
SENSORIUM. Seat of the senses, or where their
impressions are digested.
SEXTILE. The aspects of the planets when they
are 60 degrees from each other.
SIDEREAL. Something relating to the stars; as,
sidereal day, sidereal year, &c.
SOLAR. Belonging to the Sun.
SOLID. A solid has all the geometrical
dimensions; viz. length, breadth, and
thickness.
SOLSTITIAL POINTS. The Sun's most northern
and southern limits in the ecliptic.
SOURCE. Spring of action.
SPECIFIC
412
VOCABULARY OF TERMS.
SPECIFIC GRAVITY. Comparative weight; bulk
for bulk.
SPECIES. Sort.
SPHEROID. A body oblate or oblong, approach-
ing to the form of a sphere.
SPIRAL. Winding, curved.
SQUARE is a rectangle, having all its sides
equal, being composed of four right an-
gles and four equal sides.
SQUARE NUMBER. The product of a number
multiplied by itself; as 4 multiplied by itself,
or 4 times 4 are 16, which is the square of 4;
and 4 is the square-root of 16.
STRATA. Beds, layers.
STELLATED. In the form of stars.
SUBDIVIDED. A part divided into more parts.
SUBLUNARY. Beneath the Moon.
SUBTEND. To extend, under certain limitations.
SUBTERRANEOUS. Laying under the surface of
the Earth.
SUBTILE. Thin, fine, rare.
SUPERFICE. The surface of a solid. Lines are
1
the boundaries of a superfice. A point is the
extremity of a line. A plane is a level or flat
superfice.
SYMBOL. An emblem of some circumstance
which is expressed under a familiar sign or
figure.
SYNOD. A conjunction of the heavenly bodies.
SYNONYMOUS. The same thing expressed in dif-
ferent ways.
SYSTEM.
VOCABULARY OF TERMS.
413
SYSTEM. A scheme which unites many things
in order.
SYSTEMATIC. In a regular way.
SYZYGIES. The points of the Moon's orbit in
which she is at new and full.
TACITLY. Silently.
TANGENT OF A CIRCLE is a straight
line drawn without the circle perpen-
dicular to some radius, and it touches
the circle but in one point, as CD.
TANGIBLE.
TELESCOPE.
Perceptible by the touch.
An instrument furnished with len-
ses or mirrors, so placed as to bring the images
of distant objects near to the eye.
TEMPERATE. Moderate.
TEMPERATURE. Degree of heat.
TERRAQUEOUS. Composed of land and water.
THERMOMETER. An instrument which shews
the degree of heat or cold, by the expansion
or contraction of a certain quantity of quick-
silver.
THEORY. Not practice.
TORRID. Burning. The zone of the Earth be-
tween the tropics, where the rays of the Sun
fall most abundantly.
TRANSIT. The passage of a planet over the face
of the Sun or another planet, or some line of the
heavens.
TRANSVERSE.
In a cross direction.
TRIANGLE. A triangle has three sides and three
angles. For a full definition of a triangle, and
the
414
VOCABULARY OF TERMS.
the different sorts of them, see Elements of
Trigonometry.
TRIGONOMETRY. The art of measuring and es-
timating triangles.
TRINE. An aspect of the planets in which they
are 120 degrees, or the third of a circle, from
each other.
VACUUM. A space devoid of air or matter. It
is supposed there is no such thing in nature as
a perfect vacuum; that called so, and which
is procured by the air-pump, is only so in re-
spect to the atmosphere of the Earth, not to
the etherial fluid, which is supposed to per-
vade all things. Nor is it in this instance even
so in regard to the matter of light, as that
fluid must also exist under the receiver when
the air is exhausted.
VAPOUR. Any effluvia from terrestrial substances
that mingles with the air.
VIBRATE. To move to and fro, to tremble.
VERTICAL. Perpendicular to the horizon.
VESPER. The evening.
VITAL. Essential to life.
VOLCANO. A burning mountain.
UMBRA. A perfect shadow. Penumbra means
an imperfect one.
UNDULATION. A waving motion.
ZENITH. The point directly over our heads.
ZODIAC. A girdle which surrounds the apparent
sphere of the heavens, and extends 8 degrees
on
VOCABULARY OF TERMS.
415
on each side of the ecliptic, including the or-
bits of the planets.
ZONE. A girdle or belt.
THE END.
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