a treatise on astronomy

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TH E

C A B I N E T C Y C L O P A E D I A .CONDUCTED BY THE

REV. DIONYSIUS LARDNER, LL.D. F.R.S. L. & E.M.R .LA. F.R.A .S. F.L .S. F.Z .S. Hon. F.C.P.S. &c. &c.

ASSISTED BYEMINENT LITERARY AND SCIENTIFIC MEN.

ASTRONOMY.BY

SIR JOHN F. W. HERSCHEL, KN r. GUELP.F.R.S.L. & E. M .R.I.A . F .R.A.S. F.G.S. M.C.U.P.S.

CORR ESPOND ENT OF TH E ROYAL ACADEMY OP SCIENCES OP PARIS, ANDOTHEK FOREIGN SCIENTIFIC INSTITUTIONS.

L O N D O N :P RI NT E D F O R

LONGMAN, REES, ORME, BROWN, GREEN, & LONGMAN,P AT E RNO ST E R- RO W ;

AND JOHN TAYLOR,U P P E R G O W E R S T R E E T .

1833.


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" ET QUONIAM EADEM NATURA CUPIDITATEM ING EN UIT HO 11I-NIBUS VERI INVENIENDI, QUOD FACILLIME APPARET, CUM VACUICURIS, ETIAM QUID IN CCELO FIA T, SC IRE AVEMUS : H IS IN ITIIS I N -BUCTI OMNIA VERA DILIGIMUS ; ID EST, FID EL IA, SIM PLICIA ,CONSTANTIA; TUM VANA, FALSA, FALL END IA OD IM U S."

CI CE RO , D E F I N . B O N . E T M A L . i i, 14 .AND FORASMUCH AS NATURE ITSELF HAS IMPLANTED IN MA N

A CRAVING AFTER THE DISCOVERY OF TRUT H, (WHIC H APPEA RSMOST CLEARLY FROM TH IS, THAT , WH EN U NOPPRESSED BY CA RES,WE DELIGHT TO KNOW EVEN WHAT IS GOING ON IN THE HEAVENS,)

LED BY THIS INSTINCT, WE LEA RN TO LOVE ALL TRUTH FORITS OWN SAKE ; THAT IS TO SAY, WHATEVER IS F AIT HFU L, SIMPLE,AND CONSISTENT; WHILE WE HOLD IN ABHORRENCE WHATEVERIS EMPTY, DECEPTIVE, OR UNTRUE.;


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TH E

CABINETOF

NATURAL PHILOSOPHY.CONDUCTED BY THE

REV. DIONYSIUS LARDNER, LL.D. F.R.S. L.&E.M .R.I.A. F.R.A.S. F.L.S. F.Z.S. Hon. F.C.P.S. &c.&c.AS S I S T E D B Y

EMINENT SCIENTIFIC MEN.

A S T R O N O M Y .BT

SIR JOHN F. W. HERSCHEL, KNT. GUELP.F.R.S.L.&E. M.R.LA. F.R.A.S. F.G.S. M.C.U.P.S.

CORRESPONDENT OF THE ROYAL ACADEMY OP SCIENCES OF PARIS, ANDOTHER FOREIGN SCIENTIFIC INSTITUTIONS.

L O N D O N :PRINTED FOR

LONGMAN, RE ES, ORME, BROW N, GREEN, & LONGM AN,PATERNOSTER-KOW J

AND JOHN TAYLOR,UPPER GOWER STREET;

1833.


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CONTENTS.INTRODUCTION P a g e l

CHAP. LGeneral NotionsForm and Magnitude of the Earth. Horizon and its

Dip. Th e Atmosphere. Refraction. Twilight. Appearances re-suiting from Diurnal Motion.Parallax. First Step towards formingan Idea of the Distance of the Stars. Definitions. - - 9CHAP. I I .

Of the Natu re of Astronomical Instrum ents and Observations in general. Of Sidereal and Solar T ime. Of the Measurement of Time. Clocks, Chronometers, the Transit Instrument. Of the Measurementof Angular Intervals. Application of th e Telescope to Instrum ents de-stined to that Purpose. Of the Mural Circle. Determination of Polavand Horizontal Points. The Level. Plumb Line.Artificial Horizon. Collimator.Of Compound Instruments with Co-ordinate Circles, theEquatorial. Altitude and Azimuth Instrument. Of the Sextant andReflecting Circle. Principle of Repetition. - - - 61

CHAP. I I I .OP GEOGRAPHY.

Of th e Figure of the Ear th Its exact Dimensions. Its Form that ofEqu ilibrium modified by Centrifugal Force. Variation of Gravity onits Surface. Statical and Dynam ical M easures of Gravity. The Pen-dulum. Gravity to a Spheroid. Other Effects of Earth's Rotation. Trade Winds. Determination of Geographical Positions. Of Lati-tudes. Of Long itudes Conduct of a Trigonometrical Survey. OfMaps. Projections of the Sphere. Measurement of Heights by theBarometer. - - - - - 107

CHAP. IV.O F URANO G RAP H Y.

Construc tion of Celestial Maps and Globes by Observations of RightAscension and Declination. Celestial Objects distinguished into Fixedand E rratic. Of the Constellations Na tural Regions in the Heavens. Th e Milky Way. Th e Zodiac. Of the Ecliptic.Celestial Lati-tudes and Longitudes. Precession of the Equinoxes. Nutation. Aberration. Uranographical Problem s. - - - 157


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VI CONTENTS.

C H A P . V .OF THE SUN'S MOTION.

Apparent Motion of the Sun not uniform. Its app arent D iam eter alsovariable. Variation of its Distance concluded. Its apparent Orbit anEllipse about the Focus. Law of the Angular Velocity. Equable D e-scription of Areas. Parallax of the Sun. Its Distance and Mag-nitude. Copernican Exp lanation of th e Sun's apparen t Motion. Parallelism of the Ea rth's Axis. The Seasons. Heat received fromthe Sun in different Pa rts of the Orbit. - - Pa ge 184CHAP. VI .

Of the Moon. Its Sidereal Period. Its apparent Diameter. Its Paral-lax, D istance, and real Diameter. First Approximation to its Orbit. An Ellipse about the Earth in the Focus. Its Excentricity and Inclina-tion. Motion of th e Nodes of its Orbit. Occu ltations. SolarEclipses. Phases of th e Moon. Its synodical Period. Lun ar Eclipses. Motion of the Apsides of its Orbit.Physical Constitution of theMoon. Its Mountains. Atmosphere. Rotation on Axis. Libra-tion. Appearance of the Ea rth from it. - - - 213

CHAP. VI I .Of Terrestrial Gravity. Of the Law of universal Gravitation. Paths ofProjectiles; apparent real.The Moon retained in her Orbit by Gra -vity. Its Law of Diminution. Laws of Elliptic Motion. Orbit ofthe Earth round the Sun in accordance with these Laws. Masses ofthe Earth and Sun compared. Density of the Sun. Force of Gravityat its Surface." Disturbing Effect of the Sun on the Moon's Motion. 232

CHAP . VI I I .OF THE SOLAR SYSTEM.

Apparent Motions of the Planets. Their Stations and Retrogradations. Th e Sun their natu ral Center of Motion. Inferior Planets. TheirPhase s, Periods, &c.Dimensions and Form of their Orbits. Transitsacross the Sun. Superior Planets, their Distances, Periods, &c. Kep-ler's Laws and th eir In terpretation. Elliptic Elements of a Planet'sOrbit. Its Heliocentric and Geocentric Place. Bode's Law of Pla-netary Distances. The four U ltra-Zodiacal Planets. Physical Pecu-liarities observable in each of the Pla nets . - . 243CHAP. IX.

OF THE SATELLITES.Of the Moon, as a Satellite of the Ea rth. General Proximity of Satellitesto their Prim aries, and consequent Subordination of the ir M otions. Masses of the Prim aries concluded from th e Periods of th eir Satellites.Maintenance of Kepler's Laws in th e secondary Systems. Of Ju pi-ter's Satellites. Their Eclipses, &c. Velocity of Light discovered bytheir Means. Satellites of Saturn Of Ura nus. - . 28g


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CONTENTS. VUCHAP. X.OF COMETS.

G r e a t N u m b e r of recorded Comets . T h e N u m b e r of u n reco rd ed pro-bab ly muc h g rea ter . Desc r ip t ion of a Comet. Comets wit hou t Tai ls . In c reas e and D e c a y of their Tai ls . Th eir Motions . Subject to theg en e ra l L aws of Plan e t a ry M o t io n . E lem en t s of the i r Orb i t s. Pe r i -o d i c R e t u r n of cer ta in Comets . Hal ley ' s . Encke ' s . Bie la 's . Di-m en s io n s of Comets . Th ei r Res i s tance by the E th e r , g rad u a l Decay ,and possible Dispers ion in Space. . . . P a g e 300C H A P . XI .

OP PERTURBATIONS.Subject propounded. Superposition of small Motions. Problem of Three

Bodies. Estimation of disturbing Forces. Motion of Nodes. Changes of Inclination. Compensation operated in a whole Revolutionof the Node. Lagrange's Theorem of the Stability of the Inclinations. Change of the Obliquity of the Ecliptic. Precession of the Equi-noxes. Nutation. Theorem respecting forced Vibrations. Of theTides.Variation of Elements of the Planet's OrbitsPeriodic andSecular. Disturbing Forces considered as Tangential and RadiaL Effects of Tangential Force: 1st, in Circular Orbits; 2d, in Elliptic. Compensations effected. Case of near Commensurability of MeanMotions. The great Inequality of Jupiter and Saturn explained. Thelong Inequality of Venus and the Earth. Lunar Variation Effectof the Radial Force. Mean Effect of the Period and Dimensions of theDisturbed Orbit. Variable Part of its Effect. Lunar Evection. Secu-lar Acceleration of the Moon's Motion. Permanence of the Axes andPeriods. Theory of the secular Variations of the Excentricities andPerihelia. Motion of the Lunar Apsides Lagrange's Theorem ofthe Stability of the Excentricities Nutation of the Lunar Orbit. Perturbations of Jupiter's Satellites. . . . 312

CHAP. XII.OF SIDEREAL ASTRONOMY.

Of the Stars generally. Their Distribution into Classes according totheir apparent Magnitudes. Their apparent Distribution over theHeavens. Of the Milky Way. Annual Parallax Real Distances,probable Dimensions, and Nature of the Stars. Variable Stars. Tem-porary Stars. Of Double Stars. Their Revolution about each otherin elliptic Orbits. Extension of the Law of Gravity to such Systems. Of coloured Stars. Proper Motion of the Sun and Stars.SystematicAberration and Parallax. Of compound Sidereal Systems. Clustersof Stars. Of Nebula?. Nebulous Stars. Annular and PlanetaryNebulae. Zodiacal Light. - - - 372

CHAP. XIII.OF TBE CALENDAR. . . . 40$


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V I 1 1 C O N T E N T S .P a g eSynop t ic Ta b le o f th e E le me nts o f th e So lar Sys tem - . - 416

Synopt ic Tab le o f the E l em ent s o f th e Orb i t s o f the Sa te l l i t es , sofar as t h e y a re k n o w n . . . . . . . 417I . T h e M oon - - . . . . . . 417I I . Satel l i tes of Ju pi te r 417I I I . Satelli tes of Sa tu rn . . . . . 418I V . Sa te lli tes of U r a n u s . . . . 418

IN D EX - - - - - 419


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TREATISEON

ASTRONOMY.

I N T R O D U C T I O N .(1 .) I N entering upon any scientific purs uit, one of thestu de nt's first endeavours ought to be, to prepare hismind for the reception of truth, by dismissing, or atleast loosening his hold on, all such crude and hastilyadopted notions respecting the objects and relations heis about to examine as may tend to embarrass or mis-lead h i m ; and to strengthen himself, by something ofan effort and a resolve, for the unp rejudiced admissionof any conclusion which shall appear to be supported bycareful observation and logical argument, even should itprove of a nature adverse to notions he may have pre-viously formed for himself, or taken up, without exa-m ina tion, on the credit of others. Such an effort is, infact, a commencement of that intellectual disciplinewhich forms one of the most important ends of allscience. I t is the first movem ent of approach towardsthat state of mental purity which alone can fit us for afull and steady perception of m oral beau ty as well asphysical adaptation. It is the " euphrasy and rue"with which we must " purge our sight" before we canreceive and contemplate as they are the lineaments oftruth and nature.(2.) There is no science which, more than astronomy^stands in need of such a prepa ration, or draws more


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2 A TREAT ISE ON ASTRONOMY.largely on that intellectual liberality which is ready loadopt whatever is demonstrated, or concede whatever isrendered highly probable, however new and uncommonthe points of view may be in which objects the mostfamiliar may thereby become placed. Almost all itsconclusions stand in open and striking contradictionwith those of superficial and vulgar observation, andwith what appears to every one, until he has understoodand weighed the proofs to the contrary, the most po-sitive evidence of his senses. Thu s, the earth on whichhe stands, and which has served for ages as the un-shaken foundation of the firmest structures, either of artor nature, is divested by the astronomer of its attributeof fixity, and conceived by him as turning swiftly on itscentre, and at the same time moving onwards throughspace with great rapidity. The sun and the moon,which appear to untaught eyes round bodies of no veryconsiderable size, become enlarged in his imaginationinto vast globes, the one approaching in magnitude tothe earth itself, the other immensely surpassing it. Theplanets, which appear only as stars somewhat brighterthan the rest, are to him spacious, elaborate, and habit-able worlds; several of them vastly greater and farmore curiously furnished than the earth he inhabits, asthere are also others less so; and the stars themselves,properly so called, which to ordinary apprehension presentonly lucid sparks or brilliant atoms, are to him suns ofvarious and transcendent glory effulgent centres oflife and light to myriads of unseen worlds: so that when,after dilating his thoughts to comprehend the grandeurof those ideas his calculations have called up, and ex-hausting his imagination and the powers of his lan-guage to devise similes and metaphors iEustrative ofthe immensity of the scale on which his universe is con-structed, he shrinks back to his native sphe re; he findsit, in comparison, a mere poin t; so lost even in theminute system to which it belongs as to be invisibleand unsuspected from some of its principal and remotermembers.


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INTRODUCTION.

(3 .) The re is hardly any thing which sets in astronger light the inherent power of truth over the mindof man, when opposed hy no motives of interest or pas.sion, than the perfect readiness with which all these con-clusions are assented to as soon as their evidence is clearlyapprehended, and the tenacious hold they acquire overour belief wh en once admitted . In the conduct, ther e-fore of this volume, we shall take it for granted th atour reader is more desirous to learn the system w hichit is its object to teach as i t now stan ds, tha n to raiseor revive objections against i t ; and tha t, in short,he comes to the task with a willing m in d ; an assumptionwhich will not only save ourselves the trouble of piling a r-gument on argument to convince the sceptical, but willgreatly facilitate his actual progress, inasmuch as he willfind it at once easier and more satisfactory to pursue fromthe outset a straight and definite path, than to be'con-stantly stepping aside, involving himself in perplexitiesand circuits, wh ich, after all, can only term inate infinding himself compelled to adopt our road.(4.) The method, therefore, we propose to followis neither strictly the analytic nor the synthetic, butrather such a combination of both, with a leaning to thelatter, as may best suit with a didactic composition.Our object is net to convince or refute opponents, norto enq uire, un de r th e semblance of an assumed ign o-rance, for principles of which we are all the time in fullpossession but simply to teach what we know. T hemoderate limit of a single volume, and the necessity ofbe ing on every po int, w ithin that lim it, rath er diffuseand copious in explanation, as well as the eminentlymatured and ascertained character of the science itself,rend er this course both practicable and eligible. P ra c-ticable, because there is now no danger of any revolutionin astronomy, like those which are daily changing thefeatures of the less advanced sciences, superv ening, todestroy all our hypotheses, and throw our statementsinto confusion. Elig ible , because the space to be be -stowed, either in combating refuted systems, or in

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4 A TREA TISE ON ASTRONOMY.leading the reader forward by slow and measured stepsfrom the known to the unk now n, m ay be more ad van -tageously devoted to such exp lana tory illus tration s aswill impress on him a familiar and, as it were., a pra c -tical sense of the sequence of phenomena, and them anner in which they are produced. W e shall not,then, reject the analytic course where it leads moreeasily and directly to our objects, or in any way fetterourselves by a rigid adherence to m etho d. W ri ti n gonly to be understood, an d to com municate as m uc hinformation in as little space as possible, consistentlywith its distinct and effectual communication, we canafford to make no sacrifice to system, to form, or toaffectation.

(5 .) W e shall take for gran ted, from the outset,the Copernican system of the world; relying on theeasy, obvious, and na tu ra l exp lana tion it affords of allthe phenomena as they come to be described, to im-press the student with a sense of its truth, withouteither the formality of demonstration or the superfluoustedium of eulogy, calling to m ind tha t im po rta nt re -m ark of Bacon : " Theoriarum vires, arcta et quasise mutuo sustinente partium adaptatione, qua, quasi inorbem cohaerent, firmantur * ; " nor failing, how eve r, topoint out to the reader, as occasion offers, the contrastwhich its superior simplicity offers to the complicationof other hypotheses.(6.) The preliminary knowledge which it is desir-able that the student should possess, in order for themore advantageous perusal of the following pages, con-sists in the familiar practice of decimal and sexagesimalarithmetic; some moderate acquaintance with geometryand trigonometry, both plane and spherical; the ele-mentary principles of mechanics; and enough of opticsto understand the construction and use of the telescope,and some other of the simpler instru m ents . Fo r the

* The confirmation of theories relies on the compact adaptation of theirparts, by which, like those of an arch or dome, they mutually sustain eachother, and form a coherent whole.


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INTRODUCTION. 5acquisition of these we may refer him to those otherparts of this Cyclopaedia which profess to treat of theseveral subjects in ques tion. Of course, the more ofsuch knowledge he brings to the perusal, the easierwill be his progress, and the more complete the inform-ation gained; but we shall endeavour in every case, asfar as it can be done without a sacrifice of clearness, andof tha t useful brevity which consists in the absence ofprolixity and episode, to render what we have to say asindependent of other books as possible.

(7 .) After all, we m ust distinctly caution such ofour readers as may commence and terminate their astro-nomical studies with the present work (tho ugh of s uch,at least in the latter predicament,we trust the numberwill be few ), that its utmost pretension is to place themon the threshold of this particular wing of the temple ofScience, or rather on an eminence exterior to it, whencethey may obtain something like a general notion of itsstructure; or, at most, to give those who may wish toenter, a ground-plan of its accesses, and put them inpossession of the pass-word. Adm ission to its sanc-tua ry , and to the privileges and feelings of a vota ry,is only to be gained by one means, a sound andsufficient knowledge of mathem atics, the great instru-ment of all exact enquiry, without which no man canever make such advances in this or any other of thehigher departments of science, as can entitle him to forman independent opinion on any subject of discussionwithin their range. It is not without an effort thatthose who possess this knowledge can communicate onsuch subjects with those who do not, and adapt theirlanguage and their illustrations to the necessities of suchan intercourse. Propositions which to the one arealmost identica l, are theorems of import and difficultyto the other; nor is their evidence presented in thesame way to the m ind of each. I n teaching such pr o-positions, under such circumstances, the appeal has tobe made, not to the pure and abstract reason, but tothe sense of analogy, to practice and experience :

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0 A TREATISE ON ASTRONOMY.principles and modes of action have to be established,not by direct argument from acknowledged axioms, butby bringing forward and dwelling on simple and fami-liar instances in which the same principles and the sameor similar modes of action take place; thus erecting, asit were, in each particular case, a separate induction,and constructing at each step a little body of science tomeet its exigencies. The difference is that of pioneeringa road through an untraversed country and advancingat ease along a broad and beaten highw ay ; tha t isto say, if we are determined to make ourselves distinctlyunderstood, and will appeal to reason at all. As for themethod of assertion, or a direct demand on the faith ofthe student (though in some complex cases indispensable,where illustrative explanation would defeat its own endby becoming tedious and burdensome to both parties), itis one which we shall neither adopt ourselves nor wouldrecommend to others.

(8.) On the other hand, although it is something newto abandon the road of mathematical demonstration in thetreatment of subjects susceptible of it, and teach anyconsiderable branch of science entirely or chiefly by theway of illustration and familiar parallels, it is yet not im -possible that those who are already well acquainted withour subject, and whose knowledge has been acquired bythat confessedly higher and better practice which is in-compatible with the avowed objects of the present work,may yet find their account in its perusal,for this reason,that it is always of advantage to present any given bodyof knowledge to the mind in as great a variety of dif-ferent lights as possible. I t is a property of illustrationsof this kind to strike no two minds in the same man-ner, or with the same force ; because no two minds arestored with the same images, or have acquired theirnotions of them by similar habits. Accordingly, it mayvery well happen, that a proposition, even to one best ac -quainted with it, may be placed not merely in a new anduncommon, but in a more impressive and satisfactorylight by such a coursesome obscurity may be dissi-


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INTRODUCTION. 7pated, some inward misgiving cleared up, or even somelink supplied which m ay lead to the perception of connec-tions and deductions altogether unknow n before. A ndth e probability of this is increased when, as in th e presentinstance , the illustrations chosen have not been studiouslyselected from books, but are such as have presentedthemselves freely to the author's mind as being most inharm ony with his own vi ew s; by wh ich, of course, hem ean s to lay no claim to origina lity in all or any ofthem beyond what they may really possess.

(9 -) Besides, there are cases in the application ofmechanical principles with which the mathematical stu-dent is but too familiar, where, when the data are beforehim, and the numerical and geometrical relations of hisproblems all clear to his conception, when h is forces areestimated and his lines measured, nay, when even hehas followed up the application of his technical processes,and fairly arrived at his conclusion,there is still some-thing wanting in his mind not in the evidence, for hehas examined each link, and finds the chain completenot in the principle s, for those he well knows are toofirmly established to be shaken bu t precisely in themode of action. He has followed out a train of reason-ing by logical and technical rules, but the signs hehas employed are not pictures of nature, or have losttheir original meaning as such to his mind: he hasnot seen, as it were, the process of nature passing underhis eye in an instant of time, and presented as a wholeto his ima gination . A familiar parallel, or an illustra-tion draw n from some artificial of natu ral process, ofwhich he has that direct and individual impression whichgives it a rea lity and associates it w ith a nam e, will, inalmost every such case, supply in a moment this deficientfeature, will convert all his symbols into real pictures,and infuse an anim ated meaning into w hat was beforea lifeless succession of -words and signs. W e cannot,indeed, always promise ourselves to attain this degree ofvividness in our illustration s, nor are the po ints to beelucidated themselves always capable of being so parar

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8 A TRE AT ISE ON ASTRONOMY.phrased (if w e ma y use th e expression) by any singleinstance adducible in the ordinary course of experience ;but the object will at least be kept in view; and,, as weare very conscious of having, in making such attemptsgained for ourselves much clearer views of several of themore concealed effects of planetary perturbation thanwe had acquired by their mathem atical investigation indetail, we may reasonably hope that the endeavour willnot always be unattended with a similar success inothers.

(1 0 .) From wh at ha s been said, it will be evidentth at our aim is not to offer to the pu blic a technicaltreatise, in which the student of practical or theoreticalastronom y shall find consigned the min ute desc riptionof me thods of observation, or the formulae he re qu ire sprepared to his hand, or their demonstrations drawnout in detail. I n all these th e pre sen t work w ill befound me agre, and quite inadequate to his wa nts. I tsaim is entirely different; being to presen t in each case th emere ultimate rationale of facts, arguments, and pro-cesses ; and, in all cases of m ath em atic al application^avoiding whatever would tend to encumber its pageswith algebraic or geometrical symbols, to place underhis inspection th at central thre ad of comm on sense onwhich the pearls of analytical research are invariablyst ru n g ; bu t w hich , by the attention the latter claim forthemselves, is often concealed from the eye of the gazer,and not always disposed in the straightest and most con-venient form to follow by those wh o string the m . T h isis no fault of those who have conducted the enquiries towh ich we allude. T h e contention of m ind for w hichthey call is eno rm ous; and it m ay, perha ps, be owingto their experience of how little can be accomplished incarrying such processes on to their conclusion, by mereordinary clearness of head; and how necessary it oftenis to pay more attention to the purely mathematicalconditions wh ich ensure success, the hooks _an d-eye sof their equations and series, tha n to those w hich en -chain causes with their effects, and bo th w ith the hu m an


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C H A P . I. GEN ER A L N OTI ON S. 9reason, tha t we m ust attribute something of that in_distinctness of view which is often complained of as agrievance by the earnest student, and still m ore com-monly ascribed ironically to the native cloudiness of anatmosphere too sublime for vulgar comprehension. Wethink we shall render good service to both classes ofreaders, by dissipating, so far as our power lies, that acci-dental obscurity, and by showing ordinary untutoredcomprehension clearly w hat it can, and what it cannot,hope toattain.

CHAPTER I.GENERAL NOTIONS. FORM AND MAGNITUDE OF THE EA RT H.

HORIZON AND ITS DIP.' THE ATMO SPHERE. REFRACTION.TWILIGHT. APPEARA NCES RESULTING FROM DIURN AL M O-TION . PAR ALLAX. FIRST STEP TOWARDS FORMIN G AN IDEAOF THE DISTANCE OF THE STARS. DEFINITIONS.

(1 1 .) T H E magnitudes, distances, arrangement, andmotions of the great bodies which make up the visibleuniverse, their constitution and physical condition, sofar as they can be known to us , with their m utual in-fluences and actions on each other, so far as they can betraced by the effects produced, and established by legiti-mate reasoning, form the assemblage of objects to whichthe attention of the astronomer is directed. T he termastronomy* itself, which denotes the law or rule of theastra (by which the ancients understood not only thestars properly so called, but the sun, the moon, and allthe visible constituents of the heavens), sufficiently indi-cates this; and, although the term astrology, which de-notes the reason, theory, or interpretation of the stars f,has become degraded in its application, and confined to

* AO"7TJ, a star ; VO / M S , a law ; ornpt.


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1 0 A TREATISE ON ASTRONOMY. CHAP. I.superstitious and delusive attempts to divine future e'ventsby their dependence on pretended planetary influences,the same meaning originally attached itself to thatepithet.(12.) But, besides the stars and other celestial bo-dies, the earth itself, regarded as an individual body, isone principal object of the astronomer's consideration,and, indeed, the chief of all. I t derives its importance,in a practical as well as theoretical sense, not onlyfrom its proximity, and its relation to us as animatedbeings, who draw from it the supply of all our wants,but as the station from which we see all the rest, and asthe only one among them to which we can, in the firstinstance, refer for any determinate marks and measuresby which to recognize their changes of situation, or withwhich to compare their distances.(13.) To the reader who now for the first timetakes up a book on astronomy, it will no doubt seemstrange to class the earth with the heavenly bodies, andto assume any community of nature among things appa-rently so different. For what, in fact, can be more ap-parently different than the vast and seemingly immea-surable extent of the earth, and the stars, which appearbut as points, and seem to have no size at all ? Theearth is dark and opaque, while the celestial bodies arebrilliant. W e perceive in it no motion, while in themwe observe a continual change of place, as we view themat different hours of the day or night, or at differentseasons of the year. The ancients, accordingly, one ortwo of the more enlightened of them only ex'cepted, ad-mitted no such community of nature; and, by thusplacing the heavenly bodies and their movements with-out the pale of analogy and experience, effectually inter-cepted the progress of all reasoning from what passeshere below, to what is going on in the regions wherethey exist and move. Under such conventions, astronomy,as a science of cause and effect, could not exist, butmust be limited to a mere registry of appearances, un-connected with any attempt to account for them on rea-


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CHA P. I . GENERA L NOTIONS. 1 1sonable princ iples. T o get rid of this prejud ice, th er e-fore, is the first step tow ards acquiring a know ledge ofw hat is really the ca se ; and th e student has ma de hisfirst effort towards the acquisition of sound knowledge,when he has learnt to familiarize himself with the ideathat the earth, after all, may be nothing but a great star.How correct such an idea may be, and with what limit-ations and modifications it is to be admitted, we shall seepresently.

(1 4 .) I t is evident, tha t, to form any ju st notions ofth e arra nge m ent, in space, of a nu m ber of objects w hichwe cannot approach and exam ine, bu t of wh ich all th einform ation we can gain is by sitting still and w atch ingtheir evolutions, it must be very important for us toknow, in the first instance, whether what we call sittingstill is really such : w heth er the station from w hich weview the m , with ourselves, and all objects w hich i m -mediately surround us, be not itself in motion, unper-ceived by u s ; and if so, of w hat na ture th at mo tion isThe apparent places of a number of objects, and theirapp arent arrang em ent w ith respect to each othe r, will ofcourse be materially dependent on the situation of thespectator among t h e m ; and if this situation be liable tachange, unkn ow n to the spectator himself, an appearanceof change in the respective situations of the objects willarise, w ithou t the reality. If, the n, such be actually thecase, it will follow that all the movements we think weperceive among the stars will not be real movements, butthat some part, at least, of whatever changes of relativeplace we perceive among them must be merely apparent,th e results of th e sh ifting of o ur own point of view ;and that, if we would ever arrive at a knowledge of theirreal mo tions , it can only b e by first investigating ou rown , and m ak ing due allowance for its effects. T h u s ,the question whether the earth is in motion or at rest,and if in motion, what that motion is, is no idle enquiry,but one on which depends our only chance of arrivingat true conclusions respecting the constitution of theuniverse.


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1 2 A TREAT ISE ON ASTRONOMY. CH AP. I .(1 5 .) N or let it be thou ght strange tha t we shouldspeak of a m otion existing in the ea rth, unpe rceived by

its inha bitants : we m ust remem ber tha t it is of th eearth as a whole, w ith all that it holds w ithin its su b-stance, or sustains on its surface, that we are speaking;of a m otion comm on to the solid m ass b en eath , to th eocean wh ich flows aroun d it, the air th at rests upo n it ,and the clouds which float above it in the air. Such amotion, which should displace no terrestrial object fromits relative place am ong othe rs, interfere w ith nona tur al processes, and produce no sensations of shocksor je rk s, m igh t, it is very eviden t, subsist unde tectedby us . T he re is no peculiar sensation which adver-tises us that we are in motion. W e perceive jerks, orshocks, it is true, because these are sudden changesof motion, produced, as the laws of mechanics teachus, by sudden a nd powerful forces acting d ur in g sho rtti m e s ; and these forces, applied to our bodies, are w ha twe feel. When, for example, we are carried along ina carriage with the blinds down, or with our eyes closed(to keep us from seeing external objects), we perceive atremor arising from inequalities in the road, over whichthe carriage is successively lifted and let fall, b u t wehave no sense of progress. As the road is smoother, oursense of motion is diminished, though our rate of tra-velling is accelerated. Th ose wh o hav e travelled on thecelebrated railroad between Manchester and Liverpooltestify that but for the noise of the train, and the ra-pidity with which extern al objects seem to dart by the m ,the sensation is almost that of perfect rest.

(1 6 .) B ut it is on shipboard, wh ere a great systemis maintained in motion, and where we are surroundedwith a multitude of objects which participate with our-selves and each other in the common prog ress of th ewhole mass, that we feel most satisfactorily the identityof sensation between a state of motion and one of rest.In the cabin of a large and heavy vessel, going sm oothlybefore the wind in still wa ter, or draw n along a can al,not the smallest indication acqua ints us w ith the w ay it


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CHAP. I. APPARENT AND REAL MOTIONS. 13is m aking. W e read, sit , walk, and perform every cus-tom ary action as if we were on land. If we throw a ballinto the air, it falls back into our hand; or, if we drop it ,it ligh ts at our feet. Insec ts buzz around us as in thefree air ; and smoke ascends in the same manner as itwo uld do in an apa rtm ent on shore. If, indeed, we comeon deck, th e case is, in some respec ts, different; the air,not being carried along with us, drifts away smoke andother light bodiessuch as feathers abandoned to it app aren tly, in the op posite direction to tha t of the ship'sprogress ; but, in reality, they rem ain at rest^ and we leavethem b ehind in the air. Still, the illusion, so far as m as -sive objects and our own movements are concerned, re-mains complete; and w hen we look at the shore, we the nperceive the effect of our own motion transferred, in acon trary direction, to e xterna l objects external, that is,to the system of which we form a part.

" Provehimur portu, terraaque urbesque recedunt."(1 7- ) N ot only do external objects at rest appearin motion generally, with respect to ourselves when weare in motion among them, but they appear to move oneam ong the other they shift their relative apparentplaces. L et any one travelling rapidly along a hig hroad fix his eye steadily on any object, but at the sametime not entirely withdraw his attention from the general

landscap e, he will see, or thin k he sees, the wholelandscape thrown into rotation, and moving round thatobject as a ce n tr e ; all objects between it and himselfappearing to move backwards, or the contrary way to hisown m o tio n; and all beyond it , forwards, or in the di-rection in which he m ov es: bu t let him withdraw hiseye from th at object, and fix it on anoth er, a nearerone, for instan ce, im m ediately the appearance of ro -tation shifts also, and the apparent centre about whichthis illusive circulation is performed is transferredto the new object, w hich , for the m om ent, appears torest. T h is apparen t change of situation of objectsw ith respect to one ano ther, arising from a motion of


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1 4 A TRE ATISE ON ASTRONOMY. CH AP. I .the spectator, is called a parallactic m oti on ; and i t i s ,therefore, evident that, before we can ascertain whetherexternal objects are really in motion or not, or whattheir mo tions are, we mu st subdu ct, or allow for, anysuch parallactic motion which may exist .

(1 8 .) In order, however, to conceive the ear th asin motion, we must form to ourselves a conception of itsshape and size. N ow , an object cannot hav e shape andsize, unles s it is limited on all sides by some definiteoutline, so as to admit of1 our imagining it , at least, dis-connected from other bodies, an d ex isting insu lated inspace. T h e first ru de notion we form of the ea rth isthat of a flat surface, of indefinite extent in all directionsfrom the spot where we stand, above which are the airand sky ; below, to an indefinite pro fun dity, solid m at te r.T h is is a prejudice to be got rid of, like tha t of t he ea rth 'sim m ob ility ; but it is one m uch easier to rid ourselvesof, inasm uch as it originates only in our ow n m en talinactivity, in not questioning ourselves where we willplace a lim it to a thin g we have been accustom ed frominfancy to regard as immensely large; and does not, likethat, originate in the testimony of our senses undulyinterpreted . O n the contrary, the direct testimon y ofour senses lies the other way . W h en we see the sun setin the evening in the west, and rise again in th e east,as we cannot doubt that is the same sun we see after atem porary absence, we m us t do violence to all ou r n o -tions of solid matter, to suppose it to have made its waythrough the substance of the earth. I t m us t, therefo re,have gone under it , and that not by a mere subter-raneous channel; for if we notice the points where it setsand rises for many successive days, or for a whole year,we shall find them constantly shifting, round a verylarge extent of the horizon ; and, besides, th e m oon andstars also set and rise again in all points of the visiblehorizon. T h e conclusion is plain : the earth can not e x-tend indefinitely in depth downwards, nor indefinitely insurface la tera lly ; it m ust have not only bou nds in ahorizontal direction, but also an under side round which


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CHAP. I. GENERAL FORM OP THE E A R T H . 1 5the sun, moon, and stars can p a s s ; and that s ide must,at least, be so far like what we see, that it must have asky and sunshine, and a day when it is night to us, andvice versd ; where, in short,

" redit a nobis Aurora, diemque reducit.Nosque ubi primus equis oriens afflavit anhelis,Illic sera rubens accendit lumina Vesper." Georg.(19- ) As soon as we have familiarized ourselveswith the conception of an earth without foundations orf ixed supportsexist ing insulated in space from contactof every thing external, it becomes easy to imagine it inmotion or, rather, difficult to imagine it otherwise ;for, since there is nothin g to retain it in one place, shouldany causes of motion exist, or any forces act upon it, itmust obey their impulse. Let us next see what obviouscircumstances there are to help us to a knowledge of theshape of the earth.( 2 0 . ) Let us first examine what we can actuallysee of its shape. Now, it is not on land (unless, indeed,on uncommonly level and extensive plains)-that we cansee any th ing of the general figure of the ea r th ; thehills, trees, and other objects which roughen its surface,and break and elevate the line of the horizon, thoughobviously bea ring a most minute proportion to the wholeear th , are yet too considerable, with respect to ourselvesand to that small portion of it which we can see at asingle view, to allow of our forming any j udgmen t ofthe form of the wh ole, from th at of a par t so disfigured.But wi th the surface of the sea, or any vastly extendedlevel plain, the case is otherwise. If we sail out ofsight of land, whether we stand on the deck of the shipor climb the mast , we see the surface of the sea notlosing itself in distance and mist, but terminated by asharp, clear, well defined lin e, or offing as it is called,which runs all round us in a circle, having our sta-tion for its centre. T h a t this line is really a circle,we conclude, first, from the perfect apparent similarityof all its p a r t s ; and, secondly, from the fact of all itsparts appearing at the same distance from us, and


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1 6 A TREATISE ON ASTRONOMY. CHA P. I.that, evidently a moderate one;, and, thirdly, from this,that its apparent diameter, measured with an instrumentcalled the dip sector, is the same (except under somesingular atmospheric circumstances, which produce atemporary distortion of the outline), in whatever direc-tion the measure is taken, properties which belongonly to the circle among geometrical figures. If weascend a high eminence on a plain (for instance, one ofthe Egyptian pyramids), the same holds good.(21.) Masts of ships, however, and the edifices erect-ed by man, are trifling eminences compared to whatnature itself affords; iE tna, Teneriffe, Mowna Roa, areeminences from which no contemptible aliquot part ofthe whole earth's surface can be se en ; bu t from theseagainin those few and rare occasions when the trans-parency of the air will permit the real boundary of thehorizon, the true sea-line, to be seen the very sameappearances are witnessed, but with this remarkableaddition, viz. that the angular diameter of the visiblearea, as measured by the dip sector, is materially lessthan at a lower level; or, in other words, that the ap-parent size of the earth has sensibly diminished as wehave receded from its surface, while yet the absolutequantity of it seen at once has been increased.(2 2.) The same appearances are observed u ni-versally, in every part of the, earth 's surface visited byman. Now, the figure of a body which, however seen,appears always circular, can be no other than a sphereor globe.(2 3.) A diagram will elucidate this. Suppose theearth to be represented by the sphere L H N Q, whosecentre is C, and let A , G, M be stations at differentelevations above various points of its surface, representedby a, g, m respectively. From each of them (as fromM) let a line be drawn, as M N n , a tangent to the sur-face at N, then will this line represent the visual rayalong which the spectator at M will see the visiblehorizon; and as this tangent sweeps round M, andcomes successively into the positions MOo, M P p ,


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CHAP. I . GENERAL FORM OF THE EA RT H. 17M Q q, the point of contact N will mark out on the sur-face the circle N O P Q . T he area of this circle is the

portion of the earth's surface visible to a spectator at Mjand the angle N M Q included between the two extremevisual rays is the measure of its apparent angulardiam eter. Lea ving , at prese nt, out of consideration theeffect of refraction in the air below M , of wh ich morehereafter, and w hich always ten ds, in some degree, toincrease that angle, or render it more obtuse, this is theangle m easured by the dip sector. N ow , it is evident,1st, that as th e po int M is more elevated aboveTO, he pointimmediately below it on the sphere, the visible area,i.e. the spherical segment or slice N O P Q , increases;2dly, that the distance of the visible horizon* or bound-ary of our view from th e eye, viz. the line M N ,increase s; and, Sdly, tha t the angle N M Q becomes

i&i, to terminate.C


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1 8 A TREA TISE ON ASTRONOMY. CH AP. I .Jess obtuse, or, in other words, the apparent angulardiameter of the earth diminishes, being nowhere sogreat as 180 , or two righ t angles, but falling short ofit by some sensible quantity, and that more and morethe higher we ascend. The figure exhibits three statesor stages of elevation, with the horizon, &c. corre-sponding to each, a glance at which will explain ourm eanin g; or, limiting ourselves to the larger and moredistinct, M N O P Q , let the reader imagine B N M , M Qyto be the two legs of a ruler jointed at M, and kept ex-tended by the globe N m Q between them . I t is clear,that as the joint M is urged home towards the surface,the legs will open, and the ruler will become morenearly straight, but will not attain perfect straightness tillM is brought fairly up to contact with the surface at m,in which case its whole length will become a tangent tothe sphere at m, as is the line xy.

(24.) This explains what is meant by the dip ofthe horizon. M m, which is perpendicular to the ge-neral surface of the sphere at m, is also the directionin which a plumb-line* would hang; for it is an ob-served fact, that in all situations, in every part of theearth, the direction of a plumb-line is exactly perpen-dicular to the surface of still water; and, moreover, thatit is also exactly perpendicular to a line or surface trulyadjusted by a spirit-level.* Suppose, then, that at ourstation M we were to adjust a line (a wooden ruler forinstance) by a spirit-level, with perfect exactness; then,if we suppose the direction of this line indefinitely pro-longed both ways, as X M Y, the line so drawn will beat right angles to M m , and therefore parallel to xmy,the tangent to the sphere at m. A spectator placed atM will therefore see not only all the vault of the skyabove this line, as X Z Y , but also that portion or zone ofit which lies between X N and Y Q ; in other words, hissky will be more than a hemisphere by the zone Y Q X N .I t is the angular breadth of this redundant zone theangle Y M Q , "by which the visible horizon appeai-s de-

* See this instrument described in Chap. II,


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CHA P. I . EFFECT OF THE E A R T H ' S CURVATURE. 1 9pressed below the direction of a sp irit- lev el th at iscalled the dip of the horizon. It is a correction of con-stant use in nautical astronomy.(25.) From the foregoing explanations it appears,1st, That the general figure of the earth (so far as it canbe ga thered from this kind of observation) is th at of asph ere or globe. In th is we also includ e tha t of the sea,w hic h, w herever it exte nd s, covers and fills in those in -equalities and local irregula rities w hich ex ist on lan d,but which can of course only be regarded as triflingdeviations from the general o utline of the whole m ass,as we consider an orange not the less round for theroughnesses on its rind . 2dly, T h at the appearanceof a visible horizon, or sea offing, is a consequence ofthe curvature of the surface, and does not arise fromthe inability of the eye to follow objects to a greater dis-tance , or from atmosp heric indistinc tness. I t will beworth while to pursue the general notion thus acquiredinto some of its consequences, by which its consistencywith observations of a different kind, and on a largerscale, will be put to the test, and a clear conception beformed of the m ann er in wh ich the parts of the ear thare related to each other, and held together as a whole.

(26.) In the first place, then, every one who haspassed a little while at the sea side is aware that objectsm ay be seen perfectly w ell beyond the offing or visiblehor izonbut no t the whole of them . W e only seetheir up per pa rts. Th eir bases where they rest on, orrise o ut of the w ater, are hid from view by the sphericalsurface of th e sea, w hich protru des between them andourse lves. Supp ose a sh ip, for instan ce, to sail direc tlyaway from our station; at first, when the distance ofth e ship is sm all, a spectator, S, situated at some certainheight above the sea, sees the whole of the ship, evento the water line w here it rests on the sea, as at A . A sit recedes it diminishes, it is true, in apparent size, butstill the whole is seen down to the water line, till itreaches the visible horizon at B . B ut as soon as it ha spassed this distance, not only does the visible portion

o 2


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A TREATISE ON ASTRONOMY, CHAP. I.still continue to diminish in apparent size, but the hullbegins to disappear bod ily, as if sun k below th e surface.

When it has reached a certain distance, as at C, its hullhas entirely vanished, but the masts and sails remain,pres entin g th e appea rance c. B u t if, in t hi s state ofthings, the spectator quickly ascends to a higher station,T, whose visible horizon is at D, the hull comes again ins ig h t; and when he descends again he loses it . T heship still receding, the lower sails seem to sink below thew ater, as at d, and at length the whole disap pea rs:while yet the distinctness with which the last portion ofthe sail d is seen is such as to satisfy us that were itnot for the interposed segment of the sea, A B C D E , thedistance T E is no t so great as to hav e pre ve nte d anequally perfect view of the whole.(27 -) In this m ann er, therefore, if w e could mea-sure the heights and exact distance of two stationsw hich could barely be discerned from each otherover the edge of the ho rizo n, we could ascertainthe actual size of the earth itself; and, in fact, were itno t for the effect of refraction , by w hic h w e are enabledto see in some small degree round the interposed seg-m ent (as will be hereafter exp laine d), this would be atolerably good m ethod of ascertain ing it. Suppose Aand B to be two eminences, whose perpendicular heightsAffl an d B 6 (w hich , for sim plic ity, we will suppose to beexactly equ al) are kno w n, as well as their exact ho ri-zontal interval a D b, by m ea sur em en t; then i t is clearthat D, the visible horizon of both, will lie just half-way


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CH AP. I. SIZE OF THE EAR TH. 2 1between them, and if we suppose a D b to be the sphereof the earth, and C its c entre in the figure C D b B, we

know D b, the length of the arch of the circle betweenD and b, viz. half the measured interval, and b B, theexcess of its secant above its radius w h ic h is the heig htof B , data wh ich, by the solution of an easy geom etricalproblem, enable us to find the length of the radius D C.If, as is really the ca^e, we suppose both the he igh ts anddistance of the stations inconsiderable in comparisonwith the size of the earth, the solution alluded to is con-tained in the following proposition : The earth's diameter bears the same proportion to thedistance of the visible horizon from the eye as that dis-tance does to the height o f the eye above the sea level.When the stations are unequal in height the problemis a little more complicated.(2 8 .) A ltho ug h, as we hav e observed, the effect ofrefraction preve nts th is from being an exact m ethod ofascertaining the dimensions of the earth, yet it will suf-fice to afford such an app roxim ation to it as shall be ofuse in the present stage of the reader's knowledge, andhelp him to ma ny ju s t conceptions, on which accountwe shall exemplify its application in nu m bers . N ow , itappears by observation, th at two poin ts, each ten feetabove the surface, cease to be visible from each oth erover still water, and in average atmospheric circum-stances, at a distance of about 8 miles. B ut 10 feet isthe 5 2 8 th p art of a m ile, so tha t half their distance, or4 m iles, is to the heig ht of each as 4 x 528 or 21 12 : 1 ,and therefore in th e same proportion to 4 miles is the

c 3


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22 A TREATISE ON ASTRONOMY. CHAP. I.

length of the earth's diameter. It must, therefore^ beequal to 4 x 2 1 1 2 = 8448, or, in round numbers, about8000 miles, which is not very far from the truth.(29.) Such is the first rough result of an attemptto ascertain the earth's magnitude; and it will not beamiss if we take advantage of it to compare it with ob-jects we have been accustomed to consider as of vastsize, so as to interpose a few steps between it and ourordinary ideas of dimension. We have before likenedthe inequalities on the earth 's surface, arising from moun-tains, valleys, buildings, &c. to the roughnesses on the rindof an orange, compared with its general mass. Th e com-parison is quite free from exaggeration. The highestmountain known does not exceed five miles in perpen-dicular elevation: this is only one 1600th part of theearth's diameter; consequently, on a globe of sixteeninches in diameter, such a mountain would be repre-sented by a protuberance of no more than one hundredthpart of an inch, which is about the thickness of ordi-nary drawing-paper. Now as there is no entire con-tinent, or even any very extensive tract of land, known,whose general elevation above the sea is any thing likehalf this quantity, it follows, that if we would constructa correct model of our earth, with its seas, continents,and mountains, on a globe sixteen inches in diameter,the whole of the land, with the exception of a few pro-minent points and ridges, m ust be comprised on it withinthe thickness of thin writing-paper; and the highesthills, would be represented by the smallest visible grainsof sand.(30.) The deepest mine existing does not penetratehalf a mile below the surface: a scratch, or pin-hole,duly representing it, on the surface of such a globe asour model, would be imperceptible w ithout a magnifier.

(31.) The greatest depth of sea, probably, doesnot much exceed the greatest elevation of the con-tinents ; and would, of course, be represented by an ex-cavation, in about the same proportion, into the substanceof the globe: so that the ocean comes to be conceived


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CHAP. I . VISIBLE PORTION OF THE SURFACE. 23as a m ere film of liqu id, such as, on our m odel, wouldbe left by a brus h dipped in colour and draw n over thosepa rts intende d to represen t the se a: only, in so conceiv-ing it , we must bear in mind that the resemblance ex-tend s no farther tha n to proportion in point of qu an tity.T h e mechanical laws which would regulate the dis tri-bution and movements of such a film, and its adhesionto the surface, are altogether different from those whichgovern the phenomena of the sea.

(3 2 .) Las tly, the greatest extent of the earth's su r-face wh ich has ever been seen at once by m an , w asthat exposed to the view of M M . Biot and G ay -L us -sac, in their celebrated aeronautic expedition to theenormous height of 25,000 feet, or rather less thanfive miles. T o estimate the prop ortion of the arearisible from this elevation to the whole earth's surface,we must have recourse to the geometry of the sphere,which informs us that the convex surface of a sphericalsegment is to the whole surface of the sphere to whichit belongs as the versed sine, or thickness of the segment,is to the diameter of the sp he re ; and further, tha t thisthickness, in the case we are considering, is almost ex-actly equal to the perpendicular elevation of the point ofsight above the surface. T h e prop ortion, therefore, ofthe visible are a, in th is case, to the whole earth 's surface,is tha t of five miles to 8 0 0 0 , or 1 to 16 00 . T h e portionvisible from iEtna, the Peak of Teneriffe, or MownaRoa, is about one 4000th.

(3 3 .) W h e n w e ascend to any very considerableelevation above the surface of the earth, either in a bal-loon, or on m oun tains, we are m ade aw are, by m anyuneasy sensa tions, of an insufficient supp ly of air. T h ebarom eter, an instrum ent w hich informs us of the weightof air incumbent on a given horizontal surface, confirmsthis impression, and affords a direct measure of the rateof dim inution of the q uan tity of air which a given spaceinclud es as we recede from the surface. Fr om its i n -dications we learn, that when we have ascended to thehe igh t of 1 00 0 feet, we have left below us about one

c 4


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24 A TREATISE ON ASTRONOMY. CHAP. I.thirtieth of the whole mass of the a tmosphe re : tha t at10,600 feet of perpendicular elevation (which is ratherless than that of the summit of J E t n a * ) we have as-cended through about one t h i r d ; and at 18,000 feet(which is nearly that of Co topaxi) thro ug h one half thematerial, or, at least, the ponderable, body of air i ncum-bent on the earth 's surface. Fro m the progression ofthese numbers, as well as, a priori, from the nature ofth e air itself, which is compressible, i. e. capable of beingcondensed, or crowded into a smaller space in proportionto the incumbent pressure, it is easy to see that, althoughby rising still higher we should continually get abovemore and more of the air, and so relieve ourselves moreand more from the pressure with which it weighs uponus, yet the amount of this additional relief, or the pon-derable quantity of air surmounted, w ould be by no meansin proportion to the additional height ascended, but in aconstantly decreasing ratio. An easy calculation, how-ever, founded on our. experimental knowledge of the pro-perties of air, and the mechanical laws which regulateits dilatation and compression, is sufficient to show that ,a t an altitude above the surface of the earth not ex-ceeding the hundredth par t of its diameter, the tenui ty ,or rarefaction, of the air mus t be so excessive, thatnot only animal life could not subsist, or combustionbe maintained in it, but that the most delicate meanswe possess of ascertaining the existence of any air at allwould fail to afford the slightest perceptible indicationsof its presence.

(34.) Laying out of consideration, therefore, atpresent, all nice questions as to the probable existenceof a definite limit to the atmosphere, beyond whichthere is, absolutely and rigorously speaking, no air, it isclear, that, for all practical purposes, we may speak ofthose regions which are more distant above the earth 'ssurface than the hundred th par t of its diameter as voidof air, and of course of clouds (which are noth ing but

* The height of .Etna above the Mediterranean (as it results from abarometrical measurement of my own, made in July,1824. under very favour-able circumstances) is 10,(>72 English feet. Author.


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CHAP. I. OF THE ATMOSPHERE. 25

visible vapours, diffused and floating in the air, sustainedby it, and rendering it turbid as mud does water). Itseems probable, from many indications, that the greatestheight at which visible clouds ever exist does not exceedten mi l e s ; at which height the density of the air is aboutan eighth part of what it is at the level of the sea.

( 3 5 . ) We are thus led to regard the atmosphere ofair, with the clouds it supports , as constituting a coatingof equable or nearly equable thickness, enveloping ourglobe on all sides; or rather as an aerial ocean, of whichthe surface of the sea and land constitutes the bed, andwhose inferior portions or strata, within a few miles ofthe earth, contain by far the greater part of the wholemass, the density diminishing with extreme rapidity aswe recede upwards, till , within a very moderate distance(such as would be represented by the sixth of an inchon the model we have before spoken of, and which isnot more in proportion to the globe on which it rests,than the downy skin of a peach in comparison with thefruit within it), all sensible trace of the existence of airdisappears.

(36.) Arguments, however, are not wanting to renderi t, if not absolutely certain, at least in the highestdegree probable, that the surface of the aerial, like thatof the aqueous ocean, has a real and definite limit, asabove hinted at ; beyond which there is positively noair, and above which a fresh quantity of air, could it beadded from without, or carried aloft from below, insteadof dilating itself indefinitely upwards, would, after acertain very enormous but still finite enlargement ofvolume, sink and merge, as water poured into the sea,and distribute itself among the mass beneath. W iththe truth of this conclusion, however, astronomy hasl i t t le concern; all the effects of the atmosphere in mo-difying astronomical phenomena being the same, whe-ther it be supposed of definite extent or not.

(37.) Moreover, whichever idea we adopt, it is equallycertain that, within those limits in which it possessesany appreciable density, its constitution is the same over


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26 A TREATISE ON ASTRONOMY. CHAP. I .all points of the earth's surface; that is to say, onth e great scale, and leaving out of consideration tem po raryand local causes of derangement, such as winds, andgreat fluctuations, of the nature of waves, which prevailin i t to an immense ex te nt : in other w ords, tha t th e lawof diminution of the air 's density as we recede upwardsfrom the level of the sea is the same in every column intowhich we may conceive it divided, or from whatever pointof the surface we m ay set out. I t m ay therefore beconsidered as consisting of successively superposed strataor layers, each of the form of a spherical shell, concen-tric w ith th e gen eral surface of th e sea an d lan d, andeach of which is rarer, or specifically lighter, than thatimmediately beneath i t ; and denser, or specificallyheavier, than tha t imm ediately above it . T h is kind ofdistribu tion of its pond erable mass is necessitated bythe laws of the equilibrium of fluids, whose resultsbarometric observations demonstrate to be in perfectaccordance with experience.It must be observed, however, that with this dis-tribution of its strata the inequalities of mountainsand valleys hav e no concern : thes e exercise no m oreinfluence in modifying their general spherical figurethan the inequalities at the bottom of the sea interferewith the general sphericity of its surface.(3 8 .) I t is the power wh ich air possesses, in commonwith all transparent media, of refracting the rays of light,or bend ing the m out of the ir stra igh t cou rse, w hic h ren


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CH A P. I . REFRACTION .of the ea rth 's surface KAk; and let LI, Mm , Nn,represen t th e successive stra ta o r laye rs, of decreasingdensity, into which we may conceive the atmosphereto be divided, and whic h are spherical surfaces concentricw ith K /e, the earth's surface. L et S represent a star, orother heavenly body, beyond the utmost limit of the atm o-sphe re ; then , if the air were aw ay, the spectator w ouldsee it in th e direction of the straigh t line A S . B u t, inreality, wh en the ray. of light SA reaches the atmosphere,suppose at d, it will, by the laws of optics, begin to benddownwards, and take a m ore inclined direction, as d c.This bending will at first be imperceptible, owing to the

extrem e tenuity of the upperm ost st ra ta ; but as itadvances downwards, the strata continually increasingin density, it will continually undergo greater and greaterrefraction in the same direction ; and thu s, instead ofpursuing the straight line S dA,it will describe a curveS d c b a, continually more and more concave down-wards, and will reach the earth, not at A, but at acertain point a, nearer to S. This ray, consequently,w ill not reach th e spectator's eye. T h e ray by whichhe will see the star is, therefore, no t S dA, but anotherray which, had there been no atmosphere would have


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2 8 A TREATISE ON ASTRONOMY. CHA P. I.struck the earth at K, a point behind the spectator ;but which, being bent by the a ir in to the curve S D C B A ,actually strikes on A . N ow , it is a law of o ptics,that an object is seen in the direction which the visualray has at the instant of arriving at the eye, withoutrega rd to wh at may have been otherw ise its coursebetween the object and th e eye. H en ce the star S willbe seen, not in the direction A S, b ut in th at of A s,a tangent to the curve S D C B A , at A . B ut because thecurve described by the refracted ray is concave down-wards, the tangent As will lie above A S, the unrefractedray: consequently the object S will appear more elevatedabove the horizon A H , when seen throu gh the refractingatmosp here, than it would appear were there no such atm o-sph ere. Since, how ever, the disposition of the strata isthe same in all directions around A, the visual ray willnot be made to deviate laterally, bu t will rem ain con-stantly in the same vertical plane, S A C ' , passing throu ghthe eye, the object, and the earth's centre.(40.) The effect of the air's refraction, then, is toraise all the heavenly bodies higher above the horizon inappearance th an they are in reality. A ny such body,situated actually in the true horizon, will appear aboveit, or will have some certain apparent altitude (as it iscalled ). N ay , even some of those actually below thehorizon, and which would therefore be invisible but forthe effect of refraction, are, by that effect, raised aboveit and brought into sight. T h u s, the sun, wh en situatedat P below th e true ho rizon , A H , of the sp ectator, becomesvisible to him, as if it stood at p, by the refracted rayP q r t A, to which A p is a tangent.(4 1. ) T he exact estimation of the am ount of atmo -spheric refraction, or the strict determination of the angleS A*, by which a celestial object at any assigned altitude,H A S , is raised in appearance above its true place, is, u n -fortunate ly, a very difficult subject of ph ys ica l enq uir y,and one on w hich geometers (from wh om alone we canlook for any information on the subject) are not yet en-tirely agreed. T h e difficulty arises from th is, th at t he


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CHA P. I . REFRAC TION. 2Qdensity of any stratum of air (on which its refractingpower depends) is affected not merely by the superin-cumbent pressure, but also by its temperature or degreeof he at. NoWj although we know that as we recede fromthe earth's surface the temperature of the air is constantlydiminishing, yet the law, or amount of this diminution atdifferent h eig ht s, is not yet fully ascertained. M oreover,th e refrac ting pow er of air is perceptib ly affected by itsmoisture j and this , too, is not th e same in every pa rt of anaerial column; neither are we acquainted with the lawsof its distribu tion. T h e consequence of our ignorance onthese p oints is to introdu ce a corresponding degree of u n -certainty into the determination of the amount of refrac-tion, which affects, to a certain appreciable extent, ourknowledge of several of the most important data ofastronomy. T h e unce rtainty thus induced is, however,confined w ithin such very narrow lim its as to be nocause of embarrassment, except in the most delicate en-qu iries, and to call for no further allusion in a treatiselike the present.

(42.) A " Ta ble of R ef ra cti on s/' as it is called, ora statement of the amount of apparent displacementarising from this cause, at all altitudes, or in every situ-ation of a heavenly bod y, from the ho rizon to the zenith *,or po int of the sky vertically above the spectator, and , un derall the circumstances in which astronomical observationsare usually performed which may influence the result, isone of the most important and indispensable of all astro-nomical tables, since it is only by the use of such a tablewe are enabled to ge t rid of an illusion which m us totherwise perve rt all our notions respecting the celestialm otions. Such have been, accordingly, constructed w ithgrea t care, and are to be found in every collection ofastronomical tables.f O ur design, in the present trea -tise, will not adm it of the introduction of ta bl es ; andwe must, therefore, content ourselves here, and in si-

From an Arabic word of this signification.f Vide " Requisite Tables to be used with the Nautical Alm anac." Seealso N autical Almanac for 1833, Dr. Pearson's Astronomical Tables, andMr. Baily's Astronomical Tables and Formulae.


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30 A TBEATISE ON ASTRONOMY. CHAP. I .

milar cases, with referring the reader to works espe-cially destined to furnish these useful aids to calculation.I t is, however, desirable that he should bear in mind thefollowing general notions of its amount , and law ofvariation.( 4 3 . ) 1st. In the zenith there is no refract ion; a ce-lestial object, situated vertically over head, is seen in itstrue direction, as if there were no atmosphere.2dly. In descending from the zenith to the horizon,the refraction continually increases; objects near thehorizon appearing mo re elevated by it above their truedirections than those at a high alt i tude.3dly. The rate of its increase is nearly in proportionto the tangent of the apparent angular distance of theobject from the zenith. But this rule, which is not farfrom the t ru th , at moderate zenith distances, ceases togive correct results in the vicinity of the horizon, wherethe law becomes much m ore complicated in its expression.

4thly . The average amo unt of refraction, for an objecthalf-way between the zenith and horizon, or at an ap-parent altitude of 45, is about 1' (more exact ly 57") , aquantity hardly sensible to the naked eye; but at thevisible horizon it amounts to no less a quanti ty than S3',which is rather more than the greatest apparent diameterof either the sun or the moon. Hence it follows, thatwhen we see the lower edge of the sun or moon jus t ap.parently resting on the horizon, its who le disk is in realitybelow it, and would be entirely out of sight and con-cealed by the convexity of the earth but for the bendinground it, which the rays of l ight have undergone in theirpassage through the air, as alluded to in art. 40.(44 . ) It follows from this, that one obvious effectof refraction m ust be to shorten the duration of night anddarkness, by actually prolonging the stay of the sun,andmoon above the horizon. But even after they are set,the influence of the atmosphere still continues to sendus a portion of their l ight ; not, indeed, by direct trans-mission, but by reflection upon the vapours, and minutesolid particles, which float in it, and, perhaps, also on


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CHA P. I. TWILIGHT. 3 1the actual material atoms of the air itself. To understandhow this takes place, we mu st recollect, tha t it is n otonly by the direct light of a luminous object that wesee, but that whatever portion of its light which wouldnot otherwise reach our eyes is intercepted in its course,and thro w n back, or laterally, upon u s, becomes to us am ean s of illum inatio n. Such reflective obstacles alwaysexist floating in the air: T h e whole course of a su n-beam penetrating through the chink of a window-shutterinto a dark room is visible as a bright line in the a i r ;and even if it be stifled, or let out through an oppositecrevice, the light scattered through the apartment, fromthis source is sufficient to prevent entire darkness in theroom . T h e lum inous lines occasionally seen in the air,in a sky full of partially broken clouds, wh ich the vulgarterm " the sun drawing water," are similarly caused.They are sunbeams, through apertures in clouds, par-tially intercepted and reflected on the dust and vapoursof the air below. T h u s it is with those solar rays whic h,after the sun is itself concealed by the convexity of theearth, continue to traverse the higher regions of the at-,mosphere above our heads, and pass through and out ofit, w ithou t directly striking on the earth at all. Someportion of them is intercepted and reflected by the float-ing particles above mentioned, and thrown back, or la-terally, so as to reach us, and afford us that secondaryillum ination , wh ich is twiligh t. T h e course of such rayswill be immediately understood from the annexed figure,in wh ich A B C D is the earth ; A a point on its sur-face, where the sun S is in the act of setting; its last lowerray S A M ju st g razing the surface at A, while its supe-rior rays S N , S O , traverse the atmosphere above Awithout striking the earth, leaving it finally at the pointsP,Q^El, after being more or less bent in passing throughit, the lower most, the higher less, and that which, likeS R O , merely grazes the exterior lim it of the atmos phere,not at all. L et us consider several points, A , B , C, D , eachmore remote than the last from A, and each more deeplyinvolved in the earth's shadow, which occupies the whole


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32 A T K E AT I S E O N AS T RO NO M Y. C H A P . I.space from A beneath the line A M . N ow , A ju st receivesthe sun's last direct ray, and, besides, is illuminated by

th e whole reflective atmo sphere P Q R T . I t thereforereceives tw ilight from the whole sky . T h e po int B , towhich the sun has set, receives no direct solar light, norany, direct or reflected, from all that part of its visibleatmosphere which is below A P M ; bu t from the lenti-cular portion P R * , which is traversed by the sun 's rays,and w hich lies above the visible horiz on B R of B , itreceives a twilight, which is strongest at R, the pointimm ediately below w hich the sun is , and fades awaygradually towards P , as the lum inous par t of the atmo -sphere thin s off. A t C , only the last or thin ne st portion ,P Q 2 of the lenticular segment, thus illuminated, liesabove th e horizon, C Q , of tha t pl ac e: he re, then , thetwilight is feeble, and confined to a small space in andnear the horizon, which the sun has qu itted, w hile at Dthe twilight has ceased altogether.(45.) When the sun is above the horizon, it i l lu-minates the atmosphere and clouds, and these again dis-perse and scatter a portion of its light in all directions, soas to send some of its ray s to every ex posed p oin t, fromevery point of the sky. T h e generally diffused ligh t, the re-fore, which we enjoy in the day time , is a phenom enon


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CHAP. I . DAYLIGHT, TERRE STRIAL REFRACTION. 3 3originating in the very same causes as the twilight.W e re i t no t for th e reflective and scattering power ofthe atmosphere, no objects would be visible to us outof direct sunshine; every shadow of a passing cloudwo uld be pitchy darkness ; the stars would be visibleall da y, and every apartm ent, into wh ich the sun hadnot direct admission, would be involved in nocturnalobsc urity. T hi s scattering action of the atmosph ere onthe solar light, it should be observed, is greatly increasedby th e irregu larity of tem peratu re caused by the samelum inary in its different pa rts, which , du ring the da y-time, throw s it into a constant state of und ulation, an d,by thus bringing together masses of air of very unequaltemperatures, produces partial reflections and refractionsat their common boundaries, by which much light istur ne d aside from the direct course, and diverted to thepurposes of general illumination.

(4 6 .) Fro m th e explanation we have given, in arts. 3$.and 40., of the nature of atmospheric refraction, and themo de in wh ich i t is produced in the progress of a ray of lightthrough successive strata, or layers, of the atmosphere, itwill be evident, th at w henever a ray passes obliquely froma higher level to a lower one, or vice versa, its course isnot rectilinear, bu t concave do w nw ar ds ; and of courseany object seen by means of such a ray, must appeardeviated from its true place, whether that object be,like the celestial bodies, entirely beyond the atmosphere,or, like the summits of mountains, seen from the plains,or oth er te rre strial s tations, at different levels, seen fromeach o ther , im m ersed in it. Eve ry difference of level,accompanied, as it must be, with a difference of den-sity in th e aerial strata, mu st also have , correspondingto it, a certain am ount of refr ac tion ; less, indeed, thanwhat would be produced by the whole atmosphere, butstill often of very appreciable, an d even considerable,am ou nt. T h is refraction between terrestrial stations istermed terrestrial refraction, to distinguish it from thattotal effect which is only produced on celestial objects, or

D


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Si< A TR EA TISE ON ASTRONOMY. CH AP. I .such as are beyond the atmosphere, and which is calledcelestial or astronomical refraction.(4 7 .) A no ther effect of refraction is to dis tort thevisible forms and proportions of objects seen near thehorizon. T h e sun , for instanc e, w hich , at a consider-able altitude, always appears rou nd , assumes, as it ap -proaches the horizon, a flattened or oval outline; itshorizontal diameter being visibly greater than that in avertical direction. W h en very near the horizon , this flat-tening is evidently more considerable on the lower sidethan on the upper ; so that the apparent form is neithercircular nor elliptic, bu t a species of o val, w hich de-viates m ore from a circle below th an above. T h is sin-gular effect, which any one may notice in a fine sunset,arises from th e rap id rate at w hich th e refraction in-creases in approach ing the horizo n. W e re every visiblepoint in the sun's circumference equally raised by re -fraction, it would still appear circular, tho ug h displaced:but the lower portions being more raised than the upper,the vertical diameter is thereby shortened, while the twoextremities of its horizontal diameter are equally raised,and in parallel directions, so that its apparent length re-ma ins the same. T h e dilated size (gen erally) of thesun or moon, when seen near the horizon, beyond whatthey appear to have when high up in the sky, has no-th in g to do w ith refraction. I t is an illusion of thejudgment, arising from the terrestrial objects interposed,or placed in close comparison w ith th em . In thatsituation we view and judge of them as we do of ter-restrial ob jects in detail, and w ith an acquired habitof atten tion to pa rts . Aloft we have no associations toguide us, and their insulation in the expanse of sky leadsus rather to undervalue than to overrate their apparentm agnitud es. Actual m easurem ent w ith a prop er instru-ment corrects our error, without, however, dispelling ourillusion. B y this we learn, tha t th e sun , wh en ju st oilthe horizon, subtends at our eyes almost exactly thesame, and the moon a materially less angle, than when


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CHAP. I. OF THE SPHERE OP THE HEAVENS. 35seen at a great altitude in the sky, owing to the effect ofwhat is called parallax, to be explained presently.

(48.) After what has been said of the small ex-te nt of t he atm osph ere in comparison of the mass ofth e ea rth , we shall have little h esitation in a dm ittingthose luminaries which people and adorn the sky, andwhich, while they obviously form no part of the earth,an d receive no suppo rt from it, are yet not borne alongat random like clouds upon the air, nor drifted by thew ind s, to be externa l to our atmo sphere. As such wehav e considered them w hile speaking of their refractions a s existing in the imm ensity of space beyond, andsituated, perhaps, for any thing we can perceive to thecontrary, at enormous distances from us and from eachother.

(4 9 .) Could a spectator exist unsustained by theearth, or any solid support, he would see around him atone view the whole contents of spacethe visible con-stituents of the universe: and, in the absence of anymeans of judging of their distances from him, wouldrefer them, in the directions in which they were seenfrom his station, to the concave surface of an imaginarysphere, having his eye for a centre, and its surface atsome vast indeterminate distance. Perh aps he m ightju dg e those w hich appear to him large and b right, to benearer to him than the smaller and less brilliant; but,independent of other means of judging, he would haveno warrant for this opinion, any more than for the ideathat all were equidistant from him, and really arranged onsuch a spherical surface. Ne vertheless, there would be noimpropriety in his referring their places, geometricallyspeaking, to those points of such a purely imaginarysphere, which their respective visual rays intersect;and there w ould be mu ch advantage in so doing , asby that means their appearance and relative situationcould be accurately measured, recorded, and mappeddow n. T h e objects in a landscape are at every varietyof distance from the eye, yet we lay them all down in apictu re on one plane> and at one distan ce, in their actua l

D 2


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36 A TREATISE ON ASTRONOMY. CHAP. I.apparent proportions, and the likeness is not taxed withincorrectness, though a man in the foreground shouldbe represented larger than a mounta in in the distance.So it is to a spectator of the heavenly bodies pictured,projected, or mapped down on tha t imaginary sphere wecall the sky or heaven. T h u s , we may easily conceivetha t the moon, which appears to us as large as the sun,though less bright , may owe that apparent equality toits greater proximity, and may be real ly much less ;while both the moon and sun may only appear largerand brighter than the stars, on account of the remotenessof the latter.( 5 0 . ) A spectator on the earth's surface is pre-vented, by the great mass on which he stands, fromseeing into all that port ion of space which is belowh i m , or to see which he must look in any degree down-wards. It is t rue that , if his place of observation beat a great elevation, the dip of the horizon will bringwithin the scope of vision a little more than a hemi-sphere, and refraction, wherever he may be situated,will enable him to look, as it were, a little round thecorne r ; but the zone thus added to his visual rangecan hardly ever, unless in very extraordinary circum-stances *, exceed a couple of degrees in breadth , and isalways ill seen on account of the vapours near thehorizon. Unless, the n, by a change of his geographicalsituation, he should shift his horizon (which is alwaysa plane touching the spherical convexity of the earth athis s ta t ion) ; or unless, by some movements proper tothe heavenly bodies, they should of themselves comeabove his horizon ; or, lastly, unless, by some rotationof the earth itself on its centre, the point of its surface

* Such as the following, for instance:The late Mr. Sadler, the celebratedaeronaut, ascended in a balloon from Dublin at about 2 o'clock in theafternoon, and was wafted across the channel. About sunset he ap-proached the English coast, when the balloon descended near the surfaceof the sea. By this time the sun was set, and the shades of eveningbegan to close in. He threw out nearly all his ballast, and suddenlysprung upwards to a great height, and by so doing witnessed the wholephenomenon of a western sunrise. He subsequently descended in Wales,and witnessed a second sunset on the same evening. I have this anecdotefrom Dr. Lardner, who was present at his ascent, and read his own accountof the voyage.Author.


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CHAP. I . CHANGE OF LOCAL SITUATION. 37which he occupies should be carried round, and pre-sented towa rds a different region of sp ac e; he wouldnev er ob tain a sight of alm ost one half the objectsex tern al to our atm osph ere. B ut if any of these casesbe supposed, m ore, or all, m ay come into view accordingto the circumstances.

(51.) A traveller, for example, shifting his lo-cality on our globe, will obtain a view of celestial ob-jec ts invisible from his original station, in a way whichm ay be not inaptly illustrated by comparing him to aperson standing in a park close to a large tree. T h emassive obstacle presented by its trunk cuts off his viewof all those parts of the landscape which it occupies asan object; but by walking round it a complete succes-sive view of the whole pan oram a m ay be obtained. J u s tin the same wa y, if we set off from any statio n, asLondon, and travel southwards, we shall not fail tonotice that many celestial objects which are never seenfrom London come successively into view, as if risingup above the horizon, nig ht after ni gh t, from the so uth,although it is in reality our horizon, which, travellingwith us southwards round the sphere, sinks in succes-sion bene ath the m . T h e novelty and splendour of fresh

**

* *

*

constellations thus gradually brought into view in theclear calm nig hts of tropical c limates, in long voyages toD 3


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3 g A TREATISE ON ASTRONOMY. CHAP. I .the south, is dwelt upon by all wh o hav e enjoyed thisspectacle, and never fails to im pres s itself on the recol-lection among the most delightful and interesting of theassociations connected w ith exten sive trav el. A glanceat the accompanying figure, exhibiting three successivestations of a traveller, A, B, C, with the horizon cor-responding to e ach, w ill place th is process in clearerevidence than any description.(5 2. ) A g ai n : suppos

a treatise on astronomy

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