,illustration ,,path ,,of ,,biela',s ,,comet4 ,,letters ,,on ,,astronomy1 ,,in ,,which ,,the ,,elements ,,of ,,the ,,science ,,are ,,familiarly ,,explained ,,in ,,connection ,,with ,,biographical ,,sketches ,,of ,,the ,,most ,,eminent ,,astronomers4 ,,with ,,numerous ,,engravings4 ,,by ,,denison ,,olmsted1 ,,ll4,d41 ,,professor ,,of ,,natural ,,philosophy ,,and ,,astronomy ,,in ,,yale ,,college ,revised ,edition4 ,,including ,,the ,,latest ,,discoveries4 ,,new ,,york3 ,,harper ,,brothers1 ,,publishers1 #cbi #cca ,,pearl ,,street1 ,,franklin ,,square4 #ahee4 ,entered according to ,act of ,congress1 in the year #ahdj1 by ,,marsh1 ,,capen1 ,,lyon1 ,,and ,,webb1 in the ,clerk's ,office of the ,district ,court of ,massachusetts4 ,,advertisement ,,to ,,the ,,revised ,,edition4 ,,since the first publication of these ,letters1 in #ahdj1 the work has passed through numerous editions1 and received many tokens of public favor1 both as a class-book for schools and as a reading-book for the family circle4 ,the valuable discoveries made in the science within a few years have suggested an additional ,letter1 which is accordingly annexed to the series in the present revised form1 giving a brief but comprehensive notice of all the leading contributions with which ,astronomy has of late been enriched4 ,the form of ,letters was chosen on account of the greater freedom it admits1 both of matter and of style1 than a dress more purely scientific4 ,thus the technical portion of the work1 it was hoped1 might be relieved1 and the whole rendered attractive to the youthful reader of either sex by interspersing sketches of the master-builders who1 in successive ages1 have reared the great temple of ,astronomy1 composing1 as they do1 some of the most remarkable and interesting specimens of the human race4 ,the work was addressed to a female friend 7now no more71 who was a distinguished ornament of her sex1 and whose superior intellect and refined taste required that the work should be free from every thing superficial in matter or negligent in style2 and it was deemed by the writer no ordinary privilege that1 in the composition of the work1 an image at once so exalted and so pure was continually present to his mental vision4 ,,yale ,,college1 ,january1 #ahec4 ,,contents4 ,,preface1 #c ,,letter ,i4 ,introductory ,observations1 #i ,,letter ,,ii4 ,doctrine of the ,sphere1 #af ,,letter ,,iii4 ,astronomical ,instruments4--,telescope1 #bi ,,letter ,,iv4 ,telescope continued1 #cf ,,letter ,v4 ,observatories1 #db ,,letter ,,vi4 ,time and the ,calendar1 #ei ,,letter ,,vii4 ,figure of the ,earth1 #fi ,,letter ,,viii4 ,diurnal ,revolution1 #ha ,,letter ,,ix4 ,parallax and ,refraction1 #hi ,,letter ,x4 ,the ,sun1 #aja ,,letter ,,xi4 ,annual ,revolution4--,seasons1 #aaa ,,letter ,,xii4 ,laws of ,motion1 #abf ,,letter ,,xiii4 ,terrestrial ,gravity1 #acd ,,letter ,,xiv4 ,sir ,isaac ,newton4--,universal ,gravitation4--,figure of the ,earth's ,orbit4--,precession of the ,equinoxes1 #adc ,,letter ,,xv4 ,the ,moon1 #aeg ,,letter ,,xvi4 ,the ,moon4--,phases4--,harvest ,moon4--,librations1 #agb ,,letter ,,xvii4 ,moon's ,orbit4--,her ,irregularities1 #ahj ,,letter ,,xviii4 ,eclipses1 #aie ,,letter ,,xix4 ,longitude4--,tides1 #bjh ,,letter ,,xx4 ,planets4--,mercury and ,venus1 #bbe ,,letter ,,xxi4 ,superior ,planets3 ,mars1 ,jupiter1 ,saturn1 and ,uranus1 #bdc ,,letter ,,xxii4 ,copernicus4--,galileo1 #bed ,,letter ,,xxiii4 ,saturn4--,uranus4--,asteroids1 #bgd ,,letter ,,xxiv4 ,the ,planetary ,motions4--,kepler's ,laws4--,kepler1 #bia ,,letter ,,xxv4 ,comets1 #cab ,,letter ,,xxvi4 ,comets1 #ccd ,,letter ,,xxvii4 ,meteoric ,showers1 #cdf ,,letter ,,xxviii4 ,fixed ,stars1 #cfe ,,letter ,,xxix4 ,fixed ,stars1 #chc ,,letter ,,xxx4 ,system of the ,world1 #cib ,,letter ,,xxxi4 ,natural ,theology1 #djf ,,letter ,,xxxii4 ,recent ,discoveries1 #dad ,index1 #dbc ,,letters ,,on ,,astronomy4 ,,letter #a4 ,,introductory ,,observations4 ,ye sacred ,muses1 with whose beauty fired1 ,my soul is ravished1 and my brain inspired1 ,whose priest ,i am1 whose holy fillets wear2 ,would you your poet's first petition hear1 ,give me the ways of wandering stars to know1 ,the depths of heaven above1 and earth below2 ,teach me the various labors of the moon1 ,and whence proceed th' eclipses of the sun2 ,why flowing tides prevail upon the main1 ,and in what dark recess they shrink again2 ,what shakes the solid earth1 what cause delays ,the ,summer nights1 and shortens ,winter days4 ,dryden's ,virgil ,,to ,,mrs4 ,c---- ,m----4 ,,dear ,,madam1--,in the conversation we recently held on the study of ,astronomy1 you expressed a strong desire to become better acquainted with this noble science1 but said you had always been repelled by the air of severity which it exhibits1 arrayed as it is in so many technical terms1 and such abstruse mathematical processes3 or1 if you had taken up some smaller treatise1 with the hope of avoiding these perplexities1 you had always found it so meager and superficial1 as to afford you very little satisfaction4 ,you asked1 if a work might not be prepared1 which would convey to the general reader some clear and adequate knowledge of the great discoveries in astronomy1 and yet require for its perusal no greater preparation1 than may be presumed of every well-educated ,english scholar of either sex4 ,you were pleased to add the request1 that ,i would write such a work1--a work which should combine1 with a luminous exposition of the leading truths of the science1 some account of the interesting historical facts with which it is said the records of astronomical discovery abound4 ,having1 moreover1 heard much of the grand discoveries which1 within the last fifty years1 have been made among the fixed stars1 you expressed a strong desire to learn more respecting these sublime researches4 ,finally1 you desired to see the argument for the existence and natural attributes of the ,deity1 as furnished by astronomy1 more fully and clearly exhibited1 than is done in any work which you have hitherto perused4 ,in the preparation of the proposed treatise1 you urged me to supply1 either in the text or in notes1 every elementary principle which would be essential to a perfect understanding of the work2 for although1 while at school1 you had paid some attention to geometry and natural philosophy1 yet so much time had since elapsed1 that your memory required to be refreshed on the most simple principles of these elementary studies1 and you preferred that ,i should consider you as altogether unacquainted with them4 ,although1 to satisfy a mind1 so cultivated and inquisitive as yours1 may require a greater variety of powers and attainments than ,i possess1 yet1 as you were pleased to urge me to the trial1 ,i have resolved to make the attempt1 and will see how far ,i may be able to lead you into the interior of this beautiful temple1 without obliging you to force your way through the jargon of the schools4 ,astronomy1 however1 is a very difficult or a comparatively easy study1 according to the view we take of it4 ,the investigation of the great laws which govern the motions of the heavenly bodies has commanded the highest efforts of the human mind2 but profound truths1 which it required the mightiest efforts of the intellect to disclose1 are often1 when once discovered1 simple in their complexion1 and may be expressed in very simple terms4 ,thus1 the creation of that element1 on whose mysterious agency depend all the forms of beauty and loveliness1 is enunciated in these few monosyllables1 ,and ,god said1 let there be light1 and there was light2 and the doctrine of universal gravitation1 which is the key that unlocks the mysteries of the universe1 is simply this1--that every portion of matter in the universe tends towards every other4 ,the three great laws of motion1 also1 are1 when stated1 so plain1 that they seem hardly to assert any thing but what we knew before4 ,that all bodies1 if at rest1 will continue so1 as is declared by the first law of motion1 until some force moves them2 or1 if in motion1 will continue so1 until some force stops them1 appears so much a matter of course1 that we can at first hardly see any good reason why it should be dignified with the title of the first great law of motion2 and yet it contains a truth which it required profound sagacity to discover and expound4 ,it is1 therefore1 a pleasing consideration to those who have not either the leisure of the ability to follow the astronomer through the intricate and laborious processes1 which conducted him to his great discoveries1 that they may fully avail themselves of the results of this vast toil1 and easily understand truths which it required ages of the severest labor to unfold4 ,the descriptive parts of astronomy1 or what may be called the natural history of the heavens1 is still more easily understood than the laws of the celestial motions4 ,the revelations of the telescope1 and the wonders it has disclosed in the sun1 in the moon1 in the planets1 and especially in the fixed stars1 are facts not difficult to be understood1 although they may affect the mind with astonishment4 ,the great practical purpose of astronomy to the world is1 enabling us safely to navigate the ocean4 ,there are indeed many other benefits which it confers on man2 but this is the most important4 ,if1 however1 you ask1 what advantages the study of astronomy promises1 as a branch of education1 ,i answer1 that few subjects promise to the mind so much profit and entertainment4 ,it is agreed by writers on the human mind1 that the intellectual powers are enlarged and strengthened by the habitual contemplation of great objects1 while they are contracted and weakened by being constantly employed upon little or trifling subjects4 ,the former elevate1 the latter depress1 the mind1 to their own level4 ,now1 every thing in astronomy is great4 ,the magnitudes1 distances1 and motions1 of the heavenly bodies2 the amplitude of the firmament itself2 and the magnificence of the orbs with which it is lighted1 supply exhaustless materials for contemplation1 and stimulate the mind to its noblest efforts4 ,the emotion felt by the astronomer is not that sudden excitement or ecstasy1 which wears out life1 but it is a continued glow of exalted feeling1 which gives the sensation of breathing in a purer atmosphere than others enjoy4 ,we should at first imagine1 that a study which calls upon its votaries for the severest efforts of the human intellect1 which demands the undivided toil of years1 and which robs the night of its accustomed hours of repose1 would abridge the period of life2 but it is a singular fact1 that distinguished astronomers1 as a class1 have been remarkable for longevity4 ,i know not how to account for this fact1 unless we suppose that the study of astronomy itself has something inherent in it1 which sustains its votaries by a peculiar aliment4 ,it is the privilege of the student of this department of ,nature1 that his cabinet is already collected1 and is ever before him2 and he is exempted from the toil of collecting his materials of study and illustration1 by traversing land and sea1 or by penetrating into the depths of the earth4 ,nor are they in their nature frail and perishable4 ,no sooner is the veil of clouds removed1 that occasionally conceals the firmament by night1 than his specimens are displayed to view1 bright and changeless4 ,the renewed pleasure which he feels1 at every new survey of the constellations1 grows into an affection for objects which have so often ministered to his happiness4 ,his imagination aids him in giving them a personification1 like that which the ancients gave to the constellations2 7as is evident from the names which they have transmitted to us27 and he walks abroad1 beneath the evening canopy1 with the conscious satisfaction and delight of being in the presence of old friends4 ,this emotion becomes stronger when he wanders far from home4 ,other objects of his attachment desert him2 the face of society changes2 the earth presents new features2 but the same sun illumines the day1 the same moon adorns the night1 and the same bright stars still attend him4 ,when1 moreover1 the student of the heavens can command the aid of telescopes1 of higher and higher powers1 new acquaintances are made every evening4 ,the sight of each new member of the starry train1 that the telescope successively reveals to him1 inspires a peculiar emotion of pleasure2 and he at length finds himself1 whenever he sweeps his telescope over the firmament1 greeted by smiles1 unperceived and unknown to his fellow-mortals4 ,the same personification is given to these objects as to the constellations1 and he seems to himself1 at times1 when he has penetrated into the remotest depths of ether1 to enjoy the high prerogative of holding converse with the celestials4 ,it is no small encouragement1 to one who wishes to acquire a knowledge of the heavens1 that the subject is embarrassed with far less that is technical than most other branches of natural history4 ,having first learned a few definitions1 and the principal circles into which1 for convenience1 the sphere is divided1 and receiving the great laws of astronomy on the authority of the eminent persons who have investigated them1 you will find few hard terms1 or technical distinctions1 to repel or perplex you2 and you will1 ,i hope1 find that nothing but an intelligent mind and fixed attention are requisite for perusing the ,letters which ,i propose to address to you4 ,i shall indeed be greatly disappointed1 if the perusal does not inspire you with some portion of that pleasure1 which ,i have described as enjoyed by the astronomer himself4 ,the dignity of the study of the heavenly bodies1 and its suitableness to the most refined and cultivated mind1 has been recognised in all ages4 ,virgil celebrates it in the beautiful strains with which ,i have headed this ,letter1 and similar sentiments have ever been cherished by the greatest minds4 ,as1 in the course of these ,letters1 ,i propose to trace an outline of the history of astronomy1 from the earliest ages to the present time1 you may think this the most suitable place for introducing it2 but the successive discoveries in the science cannot be fully understood and appreciated1 until after an acquaintance has been formed with the science itself4 ,we must therefore reserve the details of this subject for a future opportunity2 but it may be stated1 here1 that astronomy was cultivated the earliest of all the sciences2 that great attention was paid to it by several very ancient nations1 as the ,egyptians and ,chaldeans1 and the people of ,india and ,china1 before it took its rise in ,greece4 ,more than six hundred years before the ,christian era1 however1 it began to be studied in this latter country4 ,thales and ,pythagoras were particularly distinguished for their devotion to this science2 and the celebrated school of ,alexandria1 in ,egypt1 which took its rise about three hundred years before the ,christian era1 and flourished for several hundred years1 numbered among its disciples a succession of eminent astronomers1 among whom were ,hipparchus1 ,eratosthenes1 and ,ptolemy4 ,the last of these composed a great work on astronomy1 called the ',almagest1' in which is transmitted to us an account of all that was known of the science by the ,alexandrian school4 ,the ',almagest' was the principal text-book in astronomy1 for many centuries afterwards1 and comparatively few improvements were made until the age of ,copernicus4 ,copernicus was born at ,thorn1 in ,prussia1 in #adgc4 ,previous to his time1 the doctrine was held1 that the earth is at rest in the centre of the universe1 and that the sun1 moon1 and stars1 revolve about it1 every day1 from east to west2 in short1 that the apparent motions of the heavenly bodies are the same with their real motions4 ,but ,copernicus expounded what is now known to be the true theory of the celestial motions1 in which the sun is placed in the centre of the solar system1 and the earth and all the planets are made to revolve around him1 from west to east1 while the apparent diurnal motion of the heavenly bodies1 from east to west1 is explained by the revolution of the earth on its axis1 in the same time1 from west to east2 a motion of which we are unconscious1 and which we erroneously ascribe to external objects1 as we imagine the shore is receding from us1 when we are unconscious of the motion of the ship that carries us from it4 ,although many of the appearances1 presented by the motions of the heavenly bodies1 may be explained on the former erroneous hypothesis1 yet1 like other hypotheses founded in error1 it was continually leading its votaries into difficulties1 and blinding their minds to the perception of truth4 ,they had advanced nearly as far as it was practicable to go in the wrong road2 and the great and sublime discoveries of modern times are owing1 in no small degree1 to the fact1 that1 since the days of ,copernicus1 astronomers have been pursuing the plain and simple path of truth1 instead of threading their way through the mazes of error4 ,near the close of the sixteenth century1 ,tycho ,brahe1 a native of ,sweden1 but a resident of ,denmark1 carried astronomical observations 7which constitute the basis of all that is valuable in astronomy7 to a far greater degree of perfection than had ever been done before4 ,kepler1 a native of ,germany1 one of the greatest geniuses the world has ever seen1 was contemporary with ,tycho ,brahe1 and was associated with him in a part of his labors4 ,galileo1 an ,italian astronomer of great eminence1 flourished only a little later than ,tycho ,brahe4 ,he invented the telescope1 and1 both by his discoveries and reasonings1 contributed greatly to establish the true system of the world4 ,soon after the commencement of the seventeenth century1 7#afbj17 ,lord ,bacon1 a celebrated ,english philosopher1 pointed out the true method of conducting all inquiries into the phenomena of ,nature1 and introduced the inductive method of philosophizing4 ,according to the inductive method1 we are to begin our inquiries into the causes of any events by first examining and classifying all the facts that relate to it1 and1 from the comparison of these1 to deduce our conclusions4 ,but the greatest single discovery1 that has ever been made in astronomy1 was the law of universal gravitation1 a discovery made by ,sir ,isaac ,newton1 in the latter part of the seventeenth century4 ,the discovery of this law made us acquainted with the hidden forces that move the great machinery of the universe4 ,it furnished the key which unlocks the inner temple of ,nature2 and from this time we may regard astronomy as fixed on a sure and immovable basis4 ,i shall hereafter endeavor to explain to you the leading principles of universal gravitation1 when we come to the proper place for inquiring into the causes of the celestial motions1 as exemplified in the motion of the earth around the sun4 ,,letter ,,ii4 ,,doctrine ,,of ,,the ,,sphere4 ,all are but parts of one stupendous whole1 ,whose body ,nature is1 and ,god the soul4--,pope4 ,,let us now consider what astronomy is1 and into what great divisions it is distributed2 and then we will take a cursory view of the doctrine of the sphere4 ,this subject will probably be less interesting to you than many that are to follow2 but still1 permit me to urge upon you the necessity of studying it with attention1 and reflecting upon each definition1 until you fully understand it2 for1 unless you fully and clearly comprehend the circles of the sphere1 and the use that is made of them in astronomy1 a mist will hang over every subsequent portion of the science4 ,i beg you1 therefore1 to pause upon every paragraph of this ,letter2 and if there is any point in the whole which you cannot clearly understand1 ,i would advise you to mark it1 and to recur to it repeatedly2 and1 if you finally cannot obtain a clear idea of it yourself1 ,i would recommend to you to apply for aid to some of your friends1 who may be able to assist you4 ,astronomy is that science which treats of the heavenly bodies4 ,more particularly1 its object is to teach what is known respecting the sun1 moon1 planets1 comets1 and fixed stars2 and also to explain the methods by which this knowledge is acquired4 ,astronomy is sometimes divided into descriptive1 physical1 and practical4 ,descriptive astronomy respects facts2 physical astronomy1 causes2 practical astronomy1 the means of investigating the facts1 whether by instruments or by calculation4 ,it is the province of descriptive astronomy to observe1 classify1 and record1 all the phenomena of the heavenly bodies1 whether pertaining to those bodies individually1 or resulting from their motions and mutual relations4 ,it is the part of physical astronomy to explain the causes of these phenomena1 by investigating the general laws on which they depend2 especially1 by tracing out all the consequences of the law of universal gravitation4 ,practical astronomy lends its aid to both the other departments4 ,the definitions of the different lines1 points1 and circles1 which are used in astronomy1 and the propositions founded upon them1 compose the doctrine of the sphere4 ,before these definitions are given1 ,i must recall to your recollection a few particulars respecting the method of measuring angles4 7,see ,fig4 #a1 page #ah47 ,a line drawn from the centre to the circumference of a circle is called a radius1 as ,c ,d1 ,c ,b1 or ,c ,k4 ,any part of the circumference of a circle is called an arc1 as ,a ,b1 or ,b ,d4 ,an angle is measured by an arc included between two radii4 ,thus1 in ,fig4 #a1 the angle contained between the two radii1 ,c ,a and ,c ,b1 that is1 the angle ,a ,c ,b1 is measured by the arc ,a ,b4 ,every circle1 it will be recollected1 is divided into three hundred and sixty equal parts1 called degrees2 and any arc1 as ,a ,b1 contains a certain number of degrees1 according to its length4 ,thus1 if the arc ,a ,b contains forty degrees1 then the opposite angle ,a ,c ,b is said to be an angle of forty degrees1 and to be measured by ,a ,b4 ,but this arc is the same part of the smaller circle that ,e ,f is of the greater4 ,the arc ,a ,b1 therefore1 contains the same number of degrees as the arc ,e ,f1 and either may be taken as the measure of the angle ,a ,c ,b4 ,as the whole circle contains three hundred and sixty degrees1 it is evident1 that the quarter of a circle1 or quadrant1 contains ninety degrees1 and that the semicircle ,a ,b ,d ,g contains one hundred and eighty degrees4 ,illustration ,fig4 #a4 ,the complement of an arc1 or angle1 is what it wants of ninety degrees4 ,thus1 since ,a ,d is an arc of ninety degrees1 ,b ,d is the complement of ,a ,b1 and ,a ,b is the complement of ,b ,d4 ,if ,a ,b denotes a certain number of degrees of latitude1 ,b ,d will be the complement of the latitude1 or the colatitude1 as it is commonly written4 ,the supplement of an arc1 or angle1 is what it wants of one hundred and eighty degrees4 ,thus1 ,b ,a is the supplement of ,g ,d ,b1 and ,g ,d ,b is the supplement of ,b ,a4 ,if ,b ,a were twenty degrees of longitude1 ,g ,d ,b1 its supplement1 would be one hundred and sixty degrees4 ,an angle is said to be subtended by the side which is opposite to it4 ,thus1 in the triangle ,a ,c ,k1 the angle at ,c is subtended by the side ,a ,k1 the angle at ,a by ,c ,k1 and the angle at ,k by ,c ,a4 ,in like manner1 a side is said to be subtended by an angle1 as ,a ,k by the angle at ,c4 ,let us now proceed with the doctrine of the sphere4 ,a section of a sphere1 by a plane cutting it in any manner1 is a circle4 ,great circles are those which pass through the centre of the sphere1 and divide it into two equal hemispheres4 ,small circles are such as do not pass through the centre1 but divide the sphere into two unequal parts4 ,the axis of a circle is a straight line passing through its centre at right angles to its plane4 ,the pole of a great circle is the point on the sphere where its axis cuts through the sphere4 ,every great circle has two poles1 each of which is every where ninety degrees from the great circle4 ,all great circles of the sphere cut each other in two points diametrically opposite1 and consequently their points of section are one hundred and eighty degrees apart4 ,a great circle1 which passes through the pole of another great circle1 cuts the latter at right angles4 ,the great circle which passes through the pole of another great circle1 and is at right angles to it1 is called a secondary to that circle4 ,the angle made by two great circles on the surface of the sphere is measured by an arc of another great circle1 of which the angular point is the pole1 being the arc of that great circle intercepted between those two circles4 ,in order to fix the position of any place1 either on the surface of the earth or in the heavens1 both the earth and the heavens are conceived to be divided into separate portions1 by circles1 which are imagined to cut through them1 in various ways4 ,the earth thus intersected is called the terrestrial1 and the heavens the celestial1 sphere4 ,we must bear in mind1 that these circles have no existence in ,nature1 but are mere landmarks1 artificially contrived for convenience of reference4 ,on account of the immense distances of the heavenly bodies1 they appear to us1 wherever we are placed1 to be fixed in the same concave surface1 or celestial vault4 ,the great circles of the globe1 extended every way to meet the concave sphere of the heavens1 become circles of the celestial sphere4 ,the horizon is the great circle which divides the earth into upper and lower hemispheres1 and separates the visible heavens from the invisible4 ,this is the rational horizon4 ,the sensible horizon is a circle touching the earth at the place of the spectator1 and is bounded by the line in which the earth and skies seem to meet4 ,the sensible horizon is parallel to the rational1 but is distant from it by the semidiameter of the earth1 or nearly four thousand miles4 ,still1 so vast is the distance of the starry sphere1 that both these planes appear to cut the sphere in the same line2 so that we see the same hemisphere of stars that we should see1 if the upper half of the earth were removed1 and we stood on the rational horizon4 ,the poles of the horizon are the zenith and nadir4 ,the zenith is the point directly over our heads2 and the nadir1 that directly under our feet4 ,the plumb-line 7such as is formed by suspending a bullet by a string7 is in the axis of the horizon1 and consequently directed towards its poles4 ,every place on the surface of the earth has its own horizon2 and the traveller has a new horizon at every step1 always extending ninety degrees from him1 in all directions4 ,vertical circles are those which pass through the poles of the horizon1 7the zenith and nadir17 perpendicular to it4 ,the meridian is that vertical circle which passes through the north and south points4 ,the prime vertical is that vertical circle which passes through the east and west points4 ,the altitude of a body is its elevation above the horizon1 measured on a vertical circle4 ,the azimuth of a body is its distance1 measured on the horizon1 from the meridian to a vertical circle passing through that body4 ,the amplitude of a body is its distance1 on the horizon1 from the prime vertical to a vertical circle passing through the body4 ,azimuth is reckoned ninety degrees from either the north or south point2 and amplitude ninety degrees from either the east or west point4 ,azimuth and amplitude are mutually complements of each other1 for one makes up what the other wants of ninety degrees4 ,when a point is on the horizon1 it is only necessary to count the number of degrees of the horizon between that point and the meridian1 in order to find its azimuth2 but if the point is above the horizon1 then its azimuth is estimated by passing a vertical circle through it1 and reckoning the azimuth from the point where this circle cuts the horizon4 ,the zenith distance of a body is measured on a vertical circle passing through that body4 ,it is the complement of the altitude4 ,the axis of the earth is the diameter on which the earth is conceived to turn in its diurnal revolution4 ,the same line1 continued until it meets the starry concave1 constitutes the axis of the celestial sphere4 ,the poles of the earth are the extremities of the earth's axis3 the poles of the heavens1 the extremities of the celestial axis4 ,the equator is a great circle cutting the axis of the earth at right angles4 ,hence1 the axis of the earth is the axis of the equator1 and its poles are the poles of the equator4 ,the intersection of the plane of the equator with the surface of the earth constitutes the terrestrial1 and its intersection with the concave sphere of the heavens1 the celestial1 equator4 ,the latter1 by way of distinction1 is sometimes denominated the equinoctial4 ,the secondaries to the equator1--that is1 the great circles passing through the poles of the equator1--are called meridians1 because that secondary which passes through the zenith of any place is the meridian of that place1 and is at right angles both to the equator and the horizon1 passing1 as it does1 through the poles of both4 ,these secondaries are also called hour circles because the arcs of the equator intercepted between them are used as measures of time4 ,the latitude of a place on the earth is its distance from the equator north or south4 ,the polar distance1 or angular distance from the nearest pole1 is the complement of the latitude4 ,the longitude of a place is its distance from some standard meridian1 either east or west1 measured on the equator4 ,the meridian1 usually taken as the standard1 is that of the ,observatory of ,greenwich1 in ,london4 ,if a place is directly on the equator1 we have only to inquire1 how many degrees of the equator there are between that place and the point where the meridian of ,greenwich cuts the equator4 ,if the place is north or south of the equator1 then its longitude is the arc of the equator intercepted between the meridian which passes through the place and the meridian of ,greenwich4 ,the ecliptic is a great circle1 in which the earth performs its annual revolutions around the sun4 ,it passes through the centre of the earth and the centre of the sun4 ,it is found1 by observation1 that the earth does not lie with its axis at right angles to the plane of the ecliptic1 so as to make the equator coincide with it1 but that it is turned about twenty-three and a half degrees out of a perpendicular direction1 making an angle with the plane itself of sixty-six and a half degrees4 ,the equator1 therefore1 must be turned the same distance out of a coincidence with the ecliptic1 the two circles making an angle with each other of twenty-three and a half degrees4 ,it is particularly important that we should form correct ideas of the ecliptic1 and of its relations to the equator1 since to these two circles a great number of astronomical measurements and phenomena are referred4 ,the equinoctial points1 or equinoxes1 are the intersections of the ecliptic and equator4 ,the time when the sun crosses the equator1 in going northward1 is called the vernal1 and in returning southward1 the autumnal1 equinox4 ,the vernal equinox occurs about the twenty-first of ,march1 and the autumnal1 about the twenty-second of ,september4 ,the solstitial points are the two points of the ecliptic most distant from the equator4 ,the times when the sun comes to them are called solstices4 ,the ,summer solstice occurs about the twenty-second of ,june1 and the ,winter solstice about the twenty-second of ,december4 ,the ecliptic is divided into twelve equal parts1 of thirty degrees each1 called signs1 which1 beginning at the vernal equinox1 succeed each other1 in the following order3 #a4 ,aries1 ,zodiac3 ,aries #b4 ,taurus1 ,zodiac3 ,taurus #c4 ,gemini1 ,zodiac3 ,gemini #d4 ,cancer1 ,zodiac3 ,cancer #e4 ,leo1 ,zodiac3 ,leo #f4 ,virgo1 ,zodiac3 ,virgo #g4 ,libra1 ,zodiac3 ,libra #h4 ,scorpio1 ,zodiac3 ,scorpio #i4 ,sagittarius1 ,zodiac3 ,sagittarius #aj4 ,capricornus1 ,zodiac3 ,capricornus #aa4 ,aquarius1 ,zodiac3 ,aquarius #ab4 ,pisces4 ,zodiac3 ,pisces ,the mode of reckoning on the ecliptic is by signs1 degrees1 minutes1 and seconds4 ,the sign is denoted either by its name or its number4 ,thus1 one hundred degrees may be expressed either as the tenth degree of ,cancer1 or as #cs #aj4 ,it will be found an advantage to repeat the signs in their proper order1 until they are well fixed in the memory1 and to be able to recognise each sign by its appropriate character4 ,of the various meridians1 two are distinguished by the name of colures4 ,the equinoctial colure is the meridian which passes through the equinoctial points4 ,from this meridian1 right ascension and celestial longitude are reckoned1 as longitude on the earth is reckoned from the meridian of ,greenwich4 ,the solstitial colure is the meridian which passes through the solstitial points4 ,the position of a celestial body is referred to the equator by its right ascension and declination4 ,right ascension is the angular distance from the vernal equinox measured on the equator4 ,if a star is situated on the equator1 then its right ascension is the number of degrees of the equator between the star and the vernal equinox4 ,but if the star is north or south of the equator1 then its right ascension is the number of degrees of the equator1 intercepted between the vernal equinox and that secondary to the equator which passes through the star4 ,declination is the distance of a body from the equator measured on a secondary to the latter4 ,therefore1 right ascension and declination correspond to terrestrial longitude and latitude1--right ascension being reckoned from the equinoctial colure1 in the same manner as longitude is reckoned from the meridian of ,greenwich4 ,on the other hand1 celestial longitude and latitude are referred1 not to the equator1 but to the ecliptic4 ,celestial longitude is the distance of a body from the vernal equinox measured on the ecliptic4 ,celestial latitude is the distance from the ecliptic measured on a secondary to the latter4 ,or1 more briefly1 longitude is distance on the ecliptic3 latitude1 distance from the ecliptic4 ,the north polar distance of a star is the complement of its declination4 ,parallels of latitude are small circles parallel to the equator4 ,they constantly diminish in size1 as we go from the equator to the pole4 ,the tropics are the parallels of latitude which pass through the solstices4 ,the northern tropic is called the tropic of ,cancer2 the southern1 the tropic of ,capricorn4 ,the polar circles are the parallels of latitude that pass through the poles of the ecliptic1 at the distance of twenty-three and a half degrees from the poles of the earth4 ,the elevation of the pole of the heavens above the horizon of any place is always equal to the latitude of the place4 ,thus1 in forty degrees of north latitude we see the north star forty degrees above the northern horizon2 whereas1 if we should travel southward1 its elevation would grow less and less1 until we reached the equator1 where it would appear in the horizon4 ,or1 if we should travel northwards1 the north star would rise continually higher and higher1 until1 if we could reach the pole of the earth1 that star would appear directly over head4 ,the elevation of the equator above the horizon of any place is equal to the complement of the latitude4 ,thus1 at the latitude of forty degrees north1 the equator is elevated fifty degrees above the southern horizon4 ,the earth is divided into five zones4 ,that portion of the earth which lies between the tropics is called the torrid zone2 that between the tropics and the polar circles1 the temperate zones2 and that between the polar circles and the poles1 the frigid zones4 ,the zodiac is the part of the celestial sphere which lies about eight degrees on each side of the ecliptic4 ,this portion of the heavens is thus marked off by itself1 because all the planets move within it4 ,after endeavoring to form1 from the definitions1 as clear an idea as we can of the various circles of the sphere1 we may next resort to an artificial globe1 and see how they are severally represented there4 ,i do not advise to begin learning the definitions from the globe2 the mind is more improved1 and a power of conceiving clearly how things are in ,nature is more effectually acquired1 by referring every thing1 at first1 to the grand sphere of ,nature itself1 and afterwards resorting to artificial representations to aid our conceptions4 ,we can get but a very imperfect idea of a man from a profile cut in paper1 unless we know the original4 ,if we are acquainted with the individual1 the profile will assist us to recall his appearance more distinctly than we can do without it4 ,in like manner1 orreries1 globes1 and other artificial aids1 will be found very useful1 in assisting us to form distinct conceptions of the relations existing between the different circles of the sphere1 and of the arrangements of the heavenly bodies2 but1 unless we have already acquired some correct ideas of these things1 by contemplating them as they are in ,nature1 artificial globes1 and especially orreries1 will be apt to mislead us4 ,i trust you will be able to obtain the use of a globe1#a to aid you in the study of the foregoing definitions1 or doctrine of the sphere2 but if not1 ,i would recommend the following easy device4 ,to represent the earth1 select a large apple1 7a melon1 when in season1 will be found still better47 ,the eye and the stem of the apple will indicate the position of the two poles of the earth4 ,applying the thumb and finger of the left hand to the poles1 and holding the apple so that the poles may be in a north and south line1 turn this globe from west to east1 and its motion will correspond to the diurnal movement of the earth4 ,pass a wire or a knitting needle through the poles1 and it will represent the axis of the sphere4 ,a circle cut around the apple1 half way between the poles1 will be the equator2 and several other circles cut between the equator and the poles1 parallel to the equator1 will represent parallels of latitude2 of which1 two1 drawn twenty-three and a half degrees from the equator1 will be the tropics1 and two others1 at the same distance from the poles1 will be the polar circles4 ,a great circle cut through the poles1 in a north and south direction1 will form the meridian1 and several other great circles drawn through the poles1 and of course perpendicularly to the equator1 will be secondaries to the equator1 constituting meridians1 or hour circles4 ,a great circle cut through the centre of the earth1 from one tropic to the other1 would represent the plane of the ecliptic2 and consequently a line cut round the apple where such a section meets the surface1 will be the terrestrial ecliptic4 ,the points where this circle meets the tropics indicate the position of the solstices2 and its intersection with the equator1 that of the equinoctial points4 ,the horizon is best represented by a circular piece of pasteboard1 cut so as to fit closely to the apple1 being movable upon it4 ,when this horizon is passed through the poles1 it becomes the horizon of the equator2 when it is so placed as to coincide with the earth's equator1 it becomes the horizon of the poles2 and in every other situation it represents the horizon of a place on the globe ninety degrees every way from it4 ,suppose we are in latitude forty degrees2 then let us place our movable paper parallel to our own horizon1 and elevate the pole forty degrees above it1 as near as we can judge by the eye4 ,if we cut a circle around the apple1 passing through its highest part1 and through the east and west points1 it will represent the prime vertical4 ,simple as the foregoing device is1 if you will take the trouble to construct one for yourself1 it will lead you to more correct views of the doctrine of the sphere1 than you would be apt to obtain from the most expensive artificial globes1 although there are many other useful purposes which such globes serve1 for which the apple would be inadequate4 ,when you have thus made a sphere for yourself1 or1 with an artificial globe before you1 if you have access to one1 proceed to point out on it the various arcs of azimuth and altitude1 right ascension and declination1 terrestrial and celestial latitude and longitude1--these last being referred to the equator on the earth1 and to the ecliptic in the heavens4 ,when the circles of the sphere are well learned1 we may advantageously employ projections of them in various illustrations4 ,by the projection of the sphere is meant a representation of all its parts on a plane4 ,the plane itself is called the plane of projection4 ,let us take any circular ring1 as a wire bent into a circle1 and hold it in different positions before the eye4 ,if we hold it parallel to the face1 with the whole breadth opposite to the eye1 we see it as an entire circle4 ,if we turn it a little sideways1 it appears oval1 or as an ellipse2 and1 as we continue to turn it more and more round1 the ellipse grows narrower and narrower1 until1 when the edge is presented to the eye1 we see nothing but a line4 ,now imagine the ring to be near a perpendicular wall1 and the eye to be removed at such a distance from it1 as not to distinguish any interval between the ring and the wall2 then the several figures under which the ring is seen will appear to be inscribed on the wall1 and we shall see the ring as a circle1 when perpendicular to a straight line joining the centre of the ring and the eye1 or as an ellipse1 when oblique to this line1 or as a straight line1 when its edge is towards us4 ,illustration3 ,fig4 #b4 ,it is in this manner that the circles of the sphere are projected1 as represented in the following diagram1 ,fig4 #b4 ,here1 various circles are represented as projected on the meridian1 which is supposed to be situated directly before the eye1 at some distance from it4 ,the horizon ,h ,o1 being perpendicular to the meridian1 is seen edgewise1 and consequently is projected into a straight line4 ,the same is the case with the prime vertical ,z ,n1 with the equator ,e ,q1 and the several small circles parallel to the equator1 which represent the two tropics and the two polar circles4 ,in fact1 all circles whatsoever1 which are perpendicular to the plane of projection1 will be represented by straight lines4 ,but every circle which is perpendicular to the horizon1 except the prime vertical1 being seen obliquely1 as ,z ,m ,n1 will be projected into an ellipse1 one half only of which is seen1--the other half being on the other side of the plane of projection4 ,in the same manner1 ,p ,r ,p1 an hour circle1 is represented by an ellipse on the plane of projection4 ,,footnote3 #a ,a small pair of globes1 that will answer every purpose required by the readers of these ,letters1 may be had of the publishers of this ,work1 at a price not exceeding ten dollars2 or half that sum for a celestial globe1 which will serve alone for studying astronomy4 ,,letter ,,iii4 ,,astronomical ,,instruments4----,,telescope4 ,here truths sublime1 and sacred science charm1 ,creative arts new faculties supply1 ,mechanic powers give more than giant's arm1 ,and piercing optics more than eagle's eye2 ,eyes that explore creation's wondrous laws1 ,and teach us to adore the great ,designing ,cause4--,beattie4 ,if1 as ,i trust1 you have gained a clear and familiar knowledge of the circles and divisions of the sphere1 and of the mode of estimating the position of a heavenly body by its azimuth and altitude1 or by its right ascension and declination1 or by its longitude and latitude1 you will now enter with advantage upon an account of those instruments1 by means of which our knowledge of astronomy has been greatly promoted and perfected4 ,the most ancient astronomers employed no instruments of observation1 but acquired their knowledge of the heavenly bodies by long-continued and most attentive inspection with the naked eye4 ,instruments for measuring angles were first used in the ,alexandrian school1 about three hundred years before the ,christian era4 ,wherever we are situated on the earth1 we appear to be in the centre of a vast sphere1 on the concave surface of which all celestial objects are inscribed4 ,if we take any two points on the surface of the sphere1 as two stars1 for example1 and imagine straight lines to be drawn to them from the eye1 the angle included between these lines will be measured by the arc of the sky contained between the two points4 ,thus1 if ,d ,b ,h1 ,fig4 #c1 page #cj1 represents the concave surface of the sphere1 ,a1 ,b1 two points on it1 as two stars1 and ,c ,a1 ,c ,b1 straight lines drawn from the spectator to those points1 then the angular distance between them is measured by the arc ,a ,b1 or the angle ,a ,c ,b4 ,but this angle may be measured on a much smaller circle1 having the same centre1 as ,g ,f ,k1 since the arc ,e ,f will have the same number of degrees as the arc ,a ,b4 ,the simplest mode of taking an angle between two stars is by means of an arm opening at a joint like the blade of a penknife1 the end of the arm moving like ,c ,e upon the graduated circle ,k ,f ,g4 ,in fact1 an instrument constructed on this principle1 resembling a carpenter's rule with a folding joint1 with a semicircle attached1 constituted the first rude apparatus for measuring the angular distance between two points on the celestial sphere4 ,thus the sun's elevation above the horizon might be ascertained1 by placing one arm of the rule on a level with the horizon1 and bringing the edge of the other into a line with the sun's centre4 ,illustration ,fig4 #c4 ,the common surveyor's compass affords a simple example of angular measurement4 ,here1 the needle lies in a north and south line1 while the circular rim of the compass1 when the instrument is level1 corresponds to the horizon4 ,hence the compass shows the azimuth of an object1 or how many degrees it lies east or west of the meridian4 ,it is obvious1 that the larger the graduated circle is1 the more minutely its limb may be divided4 ,if the circle is one foot in diameter1 each degree will occupy one tenth of an inch4 ,if the circle is twenty feet in diameter1 a degree will occupy the space of two inches1 and could be easily divided into minutes1 since each minute would cover a space one thirtieth of an inch4 ,refined astronomical circles are now divided with very great skill and accuracy1 the spaces between the divisions being1 when read off1 magnified by a microscope2 but in former times1 astronomers had no mode of measuring small angles but by employing very large circles4 ,but the telescope and microscope enable us at present to measure celestial arcs much more accurately than was done by the older astronomers4 ,in the best instruments1 the measurements extend to a single second of space1 or one thirty-six hundredth part of a degree1--a space1 on a circle twelve feet in diameter1 no greater than one fifty-seven hundredth part of an inch4 ,to divide1 or graduate1 astronomical instruments1 to such a degree of nicety1 requires the highest efforts of mechanical skill4 ,indeed1 the whole art of instrument-making is regarded as the most difficult and refined of all the mechanical arts2 and a few eminent artists1 who have produced instruments of peculiar power and accuracy1 take rank with astronomers of the highest celebrity4 ,i will endeavor to make you acquainted with several of the principal instruments employed in astronomical observations1 but especially with the telescope1 which is the most important and interesting of them all4 ,i think ,i shall consult your wishes1 as well as your improvement1 by giving you a clear insight into the principles of this prince of instruments1 and by reciting a few particulars1 at least1 respecting its invention and subsequent history4 ,the ,telescope1 as its name implies1 is an instrument employed for viewing distant objects4#b ,it aids the eye in two ways2 first1 by enlarging the visual angle under which objects are seen1 and1 secondly1 by collecting and conveying to the eye a much larger amount of the light that emanates from the object1 than would enter the naked pupil4 ,a complete knowledge of the telescope cannot be acquired1 without an acquaintance with the science of optics2 but one unacquainted with that science may obtain some idea of the leading principles of this noble instrument4 ,its main principle is as follows3 ,by means of the telescope1 we first form an image of a distant object1--as the moon1 for example1--and then magnify that image by a microscope4 ,illustration ,fig4 #d4 ,let us first see how the image is formed4 ,this may be done either by a convex lens1 or by a concave mirror4 ,a convex lens is a flat piece of glass1 having its two faces convex1 or spherical1 as is seen in a common sun-glass1 or a pair of spectacles4 ,every one who has seen a sun-glass1 knows1 that1 when held towards the sun1 it collects the solar rays into a small bright circle in the focus4 ,this is in fact a small image of the sun4 ,in the same manner1 the image of any distant object1 as a star1 may be formed1 as is represented in the following diagram4 ,let ,a ,b ,c ,d1 ,fig4 #d1 represent the tube of the telescope4 ,at the front end1 or at the end which is directed towards the object1 7which we will suppose to be the moon17 is inserted a convex lens1 ,l1 which receives the rays of light from the moon1 and collects them into the focus at a1 forming an image of the moon4 ,this image is viewed by a magnifier attached to the end ,b ,c4 ,the lens1 ,l1 is called the object-glass1 and the microscope in ,b ,c1 the eyeglass4 ,we apply a microscope to this image just as we would to any object2 and1 by greatly enlarging its dimensions1 we may render its various parts far more distinct than they would otherwise be2 while1 at the same time1 the lens collects and conveys to the eye a much greater quantity of light than would proceed directly from the body under examination4 ,a very few rays of light only1 from a distant object1 as a star1 can enter the eye directly2 but a lens one foot in diameter will collect a beam of light of the same dimensions1 and convey it to the eye4 ,by these means1 many obscure celestial objects become distinctly visible1 which would otherwise be either too minute1 or not sufficiently luminous1 to be seen by us4 ,but the image may also be formed by means of a concave mirror1 which1 as well as the concave lens1 has the property of collecting the rays of light which proceed from any luminous body1 and of forming an image of that body4 ,the image formed by a concave mirror is magnified by a microscope1 in the same manner as when formed by the concave lens4 ,when the lens is used to form an image1 the instrument is called a refracting telescope2 when a concave mirror is used1 it is called a reflecting telescope4 ,the office of the object-glass is simply to collect the light1 and to form an image of the object1 but not to magnify it3 the magnifying power is wholly in the eyeglass4 ,hence the principle of the telescope is as follows3 ,by means of the object-glass1 7in the refracting telescope17 or by the concave mirror1 7in the reflecting telescope17 we form an image of the object1 and magnify that image by a microscope4 ,the invention of this noble instrument is generally ascribed to the great philosopher of ,florence1 ,galileo4 ,he had heard that a spectacle maker of ,holland had accidentally hit upon a discovery1 by which distant objects might be brought apparently nearer2 and1 without further information1 he pursued the inquiry1 in order to ascertain what forms and combinations of glasses would produce such a result4 ,by a very philosophical process of reasoning1 he was led to the discovery of that peculiar form of the telescope which bears his name4 ,although the telescopes made by ,galileo were no larger than a common spyglass of the kind now used on board of ships1 yet1 as they gave new views of the heavenly bodies1 revealing the mountains and valleys of the moon1 the satellites of ,jupiter1 and multitudes of stars which are invisible to the naked eye1 it was regarded with infinite delight and astonishment4 ,reflecting telescopes were first constructed by ,sir ,isaac ,newton1 although the use of a concave reflector1 instead of an object-glass1 to form the image1 had been previously suggested by ,gregory1 an eminent ,scotch astronomer4 ,the first telescope made by ,newton was only six inches long4 ,its reflector1 too1 was only a little more than an inch4 ,notwithstanding its small dimensions1 it performed so well1 as to encourage further efforts2 and this illustrious philosopher afterwards constructed much larger instruments1 one of which1 made with his own hands1 was presented to the ,royal ,society of ,london1 and is now carefully preserved in their library4 ,newton was induced to undertake the construction of reflecting telescopes1 from the belief that refracting telescopes were necessarily limited to a very small size1 with only moderate illuminating powers1 whereas the dimensions and powers of the former admitted of being indefinitely increased4 ,considerable magnifying powers might1 indeed1 be obtained from refractors1 by making them very long2 but the brightness with which telescopic objects are seen1 depends greatly on the dimensions of the beam of light which is collected by the object-glass1 or by the mirror1 and conveyed to the eye2 and therefore1 small object-glasses cannot have a very high illuminating power4 ,now1 the experiments of ,newton on colors led him to believe1 that it would be impossible to employ large lenses in the construction of telescopes1 since such glasses would give to the images1 they formed1 the colors of the rainbow4 ,but later opticians have found means of correcting these imperfections1 so that we are now able to use object-glasses a foot or more in diameter1 which give very clear and bright images4 ,such instruments are called achromatic telescopes1--a name implying the absence of prismatic or rainbow colors in the image4 ,it is1 however1 far more difficult to construct large achromatic than large reflecting telescopes4 ,very large pieces of glass can seldom be found1 that are sufficiently pure for the purpose2 since every inequality in the glass1 such as waves1 tears1 threads1 and the like1 spoils it for optical purposes1 as it distorts the light1 and produces nothing but confused images4 ,the achromatic telescope 7that is1 the refracting telescope1 having such an object-glass as to give a colorless image7 was invented by ,dollond1 a distinguished ,english artist1 about the year #ageg4 ,he had in his possession a quantity of glass of a remarkably fine quality1 which enabled him to carry his invention at once to a high degree of perfection4 ,it has ever since been1 with the manufacturers of telescopes1 a matter of the greatest difficulty to find pieces of glass1 of a suitable quality for object-glasses1 more than two or three inches in diameter4 ,hence1 large achromatic telescopes are very expensive1 being valued in proportion to the cubes of their diameters2 that is1 if a telescope whose aperture 7as the breadth of the object-glass is technically called7 is two inches1 cost one hundred dollars1 one whose aperture is eight inches would cost six thousand four hundred dollars4 ,since it is so much easier to make large reflecting than large refracting telescopes1 you may ask1 why the latter are ever attempted1 and why reflectors are not exclusively employed8 ,i answer1 that the achromatic telescope1 when large and well constructed1 is a more perfect and more durable instrument than the reflecting telescope4 ,much more of the light that falls on the mirror is absorbed than is lost in passing through the object-glass of a refractor2 and hence the larger achromatic telescopes afford a stronger light than the reflecting1 unless the latter are made of an enormous and unwieldy size4 ,moreover1 the mirror is very liable to tarnish1 and will never retain its full lustre for many years together2 and it is no easy matter to restore the lustre1 when once impaired4 ,in my next ,letter1 ,i will give you an account of some of the most celebrated telescopes that have ever been constructed1 and point out the method of using this excellent instrument1 so as to obtain with it the finest views of the heavenly bodies4 ,,footnote3 #b ,from two ,greek words1 tle1 7tele17 far1 and schope1 7skopeo17 to see4 ,,letter ,,iv ,,telescope ,,continued4 ----the broad circumference ,hung on his shoulders like the moon1 whose orb ,through optic glass the ,tuscan artist views ,at evening1 from the top of ,fesol ,or in ,valdarno1 to descry new lands1 ,rivers or mountains1 in her spotted globe4--,milton4 ,the two most celebrated telescopes1 hitherto made1 are ,herschel's forty-feet reflector1 and the great ,dorpat refractor4 ,herschel was a ,hanoverian by birth1 but settled in ,england in the younger part of his life4 ,as early as #aggd1 he began to make telescopes for his own use2 and1 during his life1 he made more than four hundred1 of various sizes and powers4 ,under the patronage of ,george the ,third1 he completed1 in #aghi1 his great telescope1 having a tube of iron1 forty feet long1 and a speculum1 forty-nine and a half inches or more than four feet in diameter4 ,let us endeavor to form a just conception of this gigantic instrument1 which we can do only by dwelling on its dimensions1 and comparing them with those of other objects with which we are familiar1 as the length or height of a house1 and the breadth of a hogshead or cistern1 of known dimensions4 ,the reflector alone weighed nearly a ton4 ,so large and ponderous an instrument must require a vast deal of machinery to work it1 and to keep it steady2 and1 accordingly1 the framework surrounding it was formed of heavy timbers1 and resembled the frame of a large building4 ,when one of the largest of the fixed stars1 as ,sirius1 is entering the field of this telescope1 its approach is announced by a bright dawn1 like that which precedes the rising sun2 and when the star itself enters the field1 the light is insupportable to the naked eye4 ,the planets are expanded into brilliant luminaries1 like the moon2 and innumerable multitudes of stars are scattered like glittering dust over the celestial vault4 ,the great ,dorpat telescope is of more recent construction4 ,it was made by ,fraunhofer1 a ,german optician of the greatest eminence1 at ,munich1 in ,bavaria1 and takes its name from its being attached to the observatory at ,dorpat1 in ,russia4 ,it is of much smaller dimensions than the great telescope of ,herschel4 ,its object-glass is nine and a half inches in diameter1 and its length1 fourteen feet4 ,although the price of this instrument was nearly five thousand dollars1 yet it is said that this sum barely covered the actual expenses4 ,it weighs five thousand pounds1 and yet is turned with the finger4 ,in facility of management1 it has greatly the advantage of ,herschel's telescope4 ,moreover1 the sky of ,england is so much of the time unfavorable for astronomical observation1 that one hundred good hours 7or those in which the higher powers can be used7 are all that can be obtained in a whole year4 ,on this account1 and on account of the difficulty of shifting the position of the instrument1 ,herschel estimated that it would take about six hundred years to obtain with it even a momentary glimpse of every part of the heavens4 ,this remark shows that such great telescopes are unsuited to the common purposes of astronomical observation4 ,indeed1 most of ,herschel's discoveries were made with his small telescopes2 and although1 for certain rare purposes1 powers were applied which magnified seven thousand times1 yet1 in most of his observations1 powers magnifying only two or three hundred times were employed4 ,the highest power of the ,dorpat telescope is only seven hundred1 and yet the director of this instrument1 ,professor ,struve1 is of the opinion1 that it is nearly or quite equal in quality1 all things considered1 to ,herschel's forty-feet reflector4 ,it is not generally understood in what way greatness of size in a telescope increases its powers2 and it conveys but an imperfect idea of the excellence of a telescope1 to tell how much it magnifies4 ,in the same instrument1 an increase of magnifying power is always attended with a diminution of the light and of the field of view4 ,hence1 the lower powers generally afford the most agreeable views1 because they give the clearest light1 and take in the largest space4 ,the several circumstances which influence the qualities of a telescope are1 illuminating power1 distinctness1 field of view1 and magnifying power4 ,large mirrors and large object-glasses are superior to smaller ones1 because they collect a larger beam of light1 and transmit it to the eye4 ,stars which are invisible to the naked eye are rendered visible by the telescope1 because this instrument collects and conveys to the eye a large beam of the few rays which emanate from the stars2 whereas a beam of these rays of only the diameter of the pupil of the eye1 would afford too little light for distinct vision4 ,in this particular1 large telescopes have great advantages over small ones4 ,the great mirror of ,herschel's forty-feet reflector collects and conveys to the eye a beam more than four feet in diameter4 ,the ,dorpat telescope also transmits to the eye a beam nine and one half inches in diameter4 ,this seems small1 in comparison with the reflector2 but much less of the light is lost on passing through the glass than is absorbed by the mirror1 and the mirror is very liable to be clouded or tarnished2 so that there is not so great a difference in the two instruments1 in regard to illuminating power1 as might be supposed from the difference of size4 ,distinctness of view is all-important to the performance of an instrument4 ,the object may be sufficiently bright1 yet1 if the image is distorted1 or ill-defined1 the illumination is of little consequence4 ,this property depends mainly on the skill with which all the imperfections of figure and color in the glass or mirror are corrected1 and can exist in perfection only when the image is rendered completely achromatic1 and when all the rays that proceed from each point in the object are collected into corresponding points of the image1 unaccompanied by any other rays4 ,distinctness is very much affected by the steadiness of the instrument4 ,every one knows how indistinct a page becomes1 when a book is passed rapidly backwards and forwards before the eyes1 and how difficult it is to read in a carriage in rapid motion on a rough road4 ,field of view is another important consideration4 ,the finest instruments exhibit the moon1 for example1 not only bright and distinct1 in all its parts1 but they take in the whole disk at once2 whereas1 the inferior instruments1 when the higher powers1 especially1 are applied1 permit us to see only a small part of the moon at once4 ,i hope1 my friend1 that1 when you have perused these ,letters1 or rather1 while you are perusing them1 you will have frequent opportunities of looking through a good telescope4 ,i even anticipate that you will acquire such a taste for viewing the heavenly bodies with the aid of a good glass1 that you will deem a telescope a most suitable appendage to your library1 and as certainly not less an ornament to it than the more expensive statues with which some people of fortune adorn theirs4 ,i will therefore1 before concluding this letter1 offer you a few directions for using the telescope4 ,some states of weather1 even when the sky is clear1 are far more favorable for astronomical observation than others4 ,after sudden changes of temperature in the atmosphere1 the medium is usually very unsteady4 ,if the sun shines out warm after a cloudy season1 the ground first becomes heated1 and the air that is nearest to it is expanded1 and rises1 while the colder air descends1 and thus ascending and descending currents of air1 mingling together1 create a confused and wavy medium4 ,the same cause operates when a current of hot air rises from a chimney2 and hence the state of the atmosphere in cities and large towns is very unfavorable to the astronomer1 on this account1 as well as on account of the smoky condition in which it is usually found4 ,after a long season of dry weather1 also1 the air becomes smoky1 and unfit for observation4 ,indeed1 foggy1 misty1 or smoky1 air is so prevalent in some countries1 that only a very few times in the whole year can be found1 which are entirely suited to observation1 especially with the higher powers2 for we must recollect1 that these inequalities and imperfections are magnified by telescopes1 as well as the objects themselves4 ,thus1 as ,i have already mentioned1 not more than one hundred good hours in a year could be obtained for observation with ,herschel's great telescope4 ,by good hours1 ,herschel means that the sky must be very clear1 the moon absent1 no twilight1 no haziness1 no violent wind1 and no sudden change of temperature4 ,as a general fact1 the warmer climates enjoy a much finer sky for the astronomer than the colder1 having many more clear evenings1 a short twilight1 and less change of temperature4 ,the watery vapor of the atmosphere1 also1 is more perfectly dissolved in hot than in cold air1 and the more water air contains1 provided it is in a state of perfect solution1 the clearer it is4 ,a certain preparation of the observer himself is also requisite for the nicest observations with the telescope4 ,he must be free from all agitation1 and the eye must not recently have been exposed to a strong light1 which contracts the pupil of the eye4 ,indeed1 for delicate observations1 the observer should remain for some time beforehand in a dark room1 to let the pupil of the eye dilate4 ,by this means1 it will be enabled to admit a larger number of the rays of light4 ,in ascending the stairs of an observatory1 visitors frequently get out of breath1 and having perhaps recently emerged from a strongly-lighted apartment1 the eye is not in a favorable state for observation4 ,under these disadvantages1 they take a hasty look into the telescope1 and it is no wonder that disappointment usually follows4 ,want of steadiness is a great difficulty attending the use of the highest magnifiers2 for the motions of the instrument are magnified as well as the object4 ,hence1 in the structure of observatories1 the greatest pains is requisite1 to avoid all tremor1 and to give to the instruments all possible steadiness2 and the same care is to be exercised by observers4 ,in the more refined observations1 only one or two persons ought to be near the instrument4 ,in general1 low powers afford better views of the heavenly bodies than very high magnifiers4 ,it may be thought absurd1 to recommend the use of low powers1 in respect to large instruments especially1 since it is commonly supposed that the advantage of large instruments is1 that they will bear high magnifying powers4 ,but this is not their only1 nor even their principal1 advantage4 ,a good light and large field are qualities1 for most purposes1 more important than great magnifying power2 and it must be borne in mind1 that1 as we increase the magnifying power in a given instrument1 we diminish both the illumination and the field of view4 ,still1 different objects require different magnifying powers2 and a telescope is usually furnished with several varieties of powers1 one of which is best fitted for viewing the moon1 another for ,jupiter1 and a still higher power for ,saturn4 ,comets require only the lowest magnifiers2 for here1 our object is to command as much light1 and as large a field1 as possible1 while it avails little to increase the dimensions of the object4 ,on the other hand1 for certain double stars1 7stars which appear single to the naked eye1 but double to the telescope17 we require very high magnifiers1 in order to separate these minute objects so far from each other1 that the interval can be distinctly seen4 ,whenever we exhibit celestial objects to inexperienced observers1 it is useful to precede the view with good drawings of the objects1 accompanied by an explanation of what each appearance1 exhibited in the telescope1 indicates4 ,the novice is told1 that mountains and valleys can be seen in the moon by the aid of the telescope2 but1 on looking1 he sees a confused mass of light and shade1 and nothing which looks to him like either mountains or valleys4 ,had his attention been previously directed to a plain drawing of the moon1 and each particular appearance interpreted to him1 he would then have looked through the telescope with intelligence and satisfaction4 ,,letter ,v4 ,,observatories4 ,we1 though from heaven remote1 to heaven will move1 ,with strength of mind1 and tread the abyss above2 ,and penetrate1 with an interior light1 ,those upper depths which ,nature hid from sight4 ,pleased we will be1 to walk along the sphere ,of shining stars1 and travel with the year4--,ovid4 ,an observatory is a structure fitted up expressly for astronomical observations1 and furnished with suitable instruments for that purpose4 ,the two most celebrated observatories1 hitherto built1 are that of ,tycho ,brahe1 and that of ,greenwich1 near ,london4 ,the observatory of ,tycho ,brahe1 ,fig4 #e1 was constructed at the expense of the ,king of ,denmark1 in a style of royal magnificence1 and cost no less than two hundred thousand crowns4 ,it was situated on the island of ,huenna1 at the entrance of the ,baltic1 and was called ,uraniburg1 or the palace of the skies4 ,before ,i give you an account of ,tycho's observatory1 ,i will recite a few particulars respecting this great astronomer himself4 ,tycho ,brahe was of ,swedish descent1 and of noble family2 but having received his education at the ,university of ,copenhagen1 and spent a large part of his life in ,denmark1 he is usually considered as a ,dane1 and quoted as a ,danish astronomer4 ,he was born in the year #aedf4 ,when he was about fourteen years old1 there happened a great eclipse of the sun1 which awakened in him a high interest1 especially when he saw how ,illustration ,fig4 #e4 accurately all the circumstances of it answered to the prediction with which he had been before made acquainted4 ,he was immediately seized with an irresistible passion to acquire a knowledge of the science which could so successfully lift the veil of futurity4 ,his friends had destined him for the profession of law1 and1 from the superior talents of which he gave early promise1 and with the advantage of powerful family connexions1 they had marked out for him a distinguished career in public life4 ,they therefore endeavored to discourage him from pursuing a path which they deemed so much less glorious than that1 and vainly sought1 by various means1 to extinguish the zeal for astronomy which was kindled in his youthful bosom4 ,despising all the attractions of a court1 he contracted an alliance with a peasant girl1 and1 in the peaceful retirement of domestic life1 desired no happier lot than to peruse the grand volume which the nocturnal heavens displayed to his enthusiastic imagination4 ,he soon established his fame as one of the greatest astronomers of the age1 and monarchs did homage to his genius4 ,the ,king of ,denmark became his munificent patron1 and ,james the ,first1 ,king of ,england1 when he went to ,denmark to complete his marriage with a ,danish ,princess1 passed eight days with ,tycho in his observatory1 and1 at his departure1 addressed to the astronomer a ,latin ode1 accompanied with a magnificent present4 ,he gave him also his royal license to print his works in ,england1 and added to it the following complimentary letter3 ,nor am ,i acquainted with these things on the relation of others1 or from a mere perusal of your works1 but ,i have seen them with my own eyes1 and heard them with my own ears1 in your residence at ,uraniburg1 during the various learned and agreeable conversations which ,i there held with you1 which even now affect my mind to such a degree1 that it is difficult to decide1 whether ,i recollect them with greater pleasure or admiration4 ,admiring disciples also crowded to this sanctuary of the sciences1 to acquire a knowledge of the heavens4 ,the observatory consisted of a main building1 which was square1 each side being sixty feet1 and of large wings in the form of round towers4 ,the whole was executed in a style of great magnificence1 and ,tycho1 who was a nobleman by descent1 gratified his taste for splendor and ornament1 by giving to every part of the structure an air of the most finished elegance4 ,nor were the instruments with which it was furnished less magnificent than the buildings4 ,they were vastly larger than had before been employed in the survey of the heavens1 and many of them were adorned with costly ornaments4 ,the cut on page #df1 ,fig4 #f1 represents one of ,tycho's large and splendid instruments1 7an astronomical quadrant17 on one side of which was figured a representation of the astronomer and his assistants1 in the midst of their instruments1 and intently engaged in making and recording observations4 ,it conveys to us a striking idea of the magnificence of his arrangements1 and of the extent of his operations4 ,here ,tycho sat in state1 clad in the robes of nobility1 and supported throughout his establishment the etiquette due to his rank4 ,his observations were more numerous than all that had ever been made before1 and they were carried to a degree of accuracy that is astonishing1 when we consider that they were made without the use of the telescope1 which was not yet invented4 ,tycho carried on his observations at ,uraniburg for about twenty years1 during which time he accumulated an immense store of accurate and valuable facts1 which afforded the groundwork of the discovery of the great laws of the solar system established by ,kepler1 of whom ,i shall tell you more hereafter4 ,but the high marks of distinction which ,tycho enjoyed1 not only from his own ,sovereign1 but also from foreign potentates1 provoked the envy of the courtiers of his royal patron4 ,they did not indeed venture to make their attacks upon him while his generous patron was living2 but the ,king was no sooner dead1 and succeeded by a young monarch1 who did not feel the same ,illustration ,fig4 #f4 interest in protecting and encouraging this great ornament of the kingdom1 than his envious foes carried into execution their long-meditated plot for his ruin4 ,they represented to the young ,king1 that the treasury was exhausted1 and that it was necessary to retrench a number of pensions1 which had been granted for useless purposes1 and in particular that of ,tycho1 which1 they maintained1 ought to be conferred upon some person capable of rendering greater services to the state4 ,by these means1 they succeeded in depriving him of his support1 and he was compelled to retreat under the hospitable mansion of a friend in ,germany4 ,here he became known to the ,emperor1 who invited him to ,prague1 where1 with an ample stipend1 he resumed his labors4 ,but1 though surrounded with affectionate friends and admiring disciples1 he was still an exile in a foreign land4 ,although his country had been base in its ingratitude1 it was yet the land which he loved2 the scene of his earliest affection2 the theatre of his scientific glory4 ,these feelings continually preyed upon his mind1 and his unsettled spirit was ever hovering among his native mountains4 ,in this condition he was attacked by a disease of the most painful kind1 and1 though its agonizing paroxysms had lengthened intermissions1 yet he saw that death was approaching4 ,he implored his pupils to persevere in their scientific labors2 he conversed with ,kepler on some of the profoundest points of astronomy2 and with these secular occupations he mingled frequent acts of piety and devotion4 ,in this happy condition he expired1 without pain1 at the age of fifty-five4#c ,the observatory at ,greenwich was not built until a hundred years after that of ,tycho ,brahe1 namely1 in #afgf4 ,the great interests of the ,british nation1 which are involved in navigation1 constituted the ruling motive with the government to lend their aid in erecting and maintaining this observatory4 ,the site of the observatory at ,greenwich is on a commanding eminence facing the ,river ,thames1 five miles east of the central parts of ,london4 ,being part of a royal park1 the neighboring grounds are in no danger of being occupied by buildings1 so as to obstruct the view4 ,it is also in full view of the shipping on the ,thames2 and1 according to a standing regulation of the observatory1 at the instant of one o'clock1 every day1 a huge ball is dropped from over the house1 as a signal to the commanders of vessels for regulating their chronometers4 ,the buildings comprise a series of rooms1 of sufficient number and extent to accommodate the different instruments1 the inmates of the establishment1 and the library2 and on the top is a celebrated camera obscura1 exhibiting a most distinct and perfect picture of the grand and unrivalled scenery which this eminence commands4 ,this establishment1 by the accuracy and extent of its observations1 has contributed more than all other institutions to perfect the science of astronomy4 ,to preside over and direct this great institution1 a man of the highest eminence in the science is appointed by the government1 with the title of ,astronomer ,royal4 ,he is paid an ample salary1 with the understanding that he is to devote himself exclusively to the business of the observatory4 ,the astronomers royal of the ,greenwich observatory1 from the time of its first establishment1 in #afgf1 to the present time1 have constituted a series of the proudest names of which ,british science can boast4 ,a more detailed sketch of their interesting history will be given towards the close of these ,letters4 ,six assistants1 besides inferior laborers1 are constantly in attendance2 and the business of making and recording observations is conducted with the utmost system and order4 ,the great objects to be attained in the construction of an observatory are1 a commanding and unobstructed view of the heavens2 freedom from causes that affect the transparency and uniform state of the atmosphere1 such as fires1 smoke1 or marshy grounds2 mechanical facilities for the management of instruments1 and1 especially1 every precaution that is necessary to secure perfect steadiness4 ,this last consideration is one of the greatest importance1 particularly in the use of very large magnifiers2 for we must recollect1 that any motion in the instrument is magnified by the full power of the glass1 and gives a proportional unsteadiness to the object4 ,a situation is therefore selected as remote as possible from public roads1 7for even the passing of carriages would give a tremulous motion to the ground1 which would be sensible in large instruments17 and structures of solid masonry are commenced deep enough in the ground to be unaffected by frost1 and built up to the height required1 without any connexion with the other parts of the building4 ,many observatories are furnished with a movable dome for a roof1 capable of revolving on rollers1 so that instruments penetrating through the roof may be easily brought to bear upon any point at or near the zenith4 ,you will not perhaps desire me to go into a minute description of all the various instruments that are used in a well-constructed observatory4 ,nor is this necessary1 since a very large proportion of all astronomical observations are taken on the meridian1 by means of the transit instrument and clock4 ,when a body1 in its diurnal revolution1 comes to the meridian1 it is at its highest point above the horizon1 and is then least affected by refraction and parallax4 ,this1 then1 is the most favorable position for taking observations upon it4 ,moreover1 it is peculiarly easy to take observations on a body when in this situation4 ,hence the transit instrument and clock are the most important members of an astronomical observatory4 ,you will1 therefore1 expect me to give you some account of these instruments4 ,illustration ,fig4 #g4 ,the transit instrument is a telescope which is fixed permanently in the meridian1 and moves only in that plane4 ,the accompanying diagram1 ,fig4 #g1 represents a side view of a portable transit instrument1 exhibiting the telescope supported on a firm horizontal axis1 on which it turns in the plane of the meridian1 from the south point of the horizon through the zenith to the north point4 ,it can therefore be so directed as to observe the passage of a star across the meridian at any altitude4 ,the accompanying graduated circle enables the observer to set the instrument at any required altitude1 corresponding to the known altitude at which the body to be observed crosses the meridian4 ,or it may be used to measure the altitude of a body1 or its zenith distance1 at the time of its meridian passage4 ,near the circle may be seen a spirit-level1 which serves to show when the axis is exactly on a level with the horizon4 ,the framework is made of solid metal1 7usually brass17 every thing being arranged with reference to keeping the instrument perfectly steady4 ,it stands on screws1 which not only afford a steady support1 but are useful for adjusting the instrument to a perfect level4 ,the transit instrument is sometimes fixed immovably to a solid foundation1 as a pillar of stone1 which is built up from a depth in the ground below the reach of frost4 ,when enclosed in a building1 as in an observatory1 the stone pillar is carried up separate from the walls and floors of the building1 so as to be entirely free from the agitations to which they are liable4 ,the use of the transit instrument is to show the precise instant when a heavenly body is on the meridian1 or to measure the time it occupies in crossing the meridian4 ,the astronomical clock is the constant companion of the transit instrument4 ,this clock is so regulated as to keep exact pace with the stars1 and of course with the revolution of the earth on its axis2 that is1 it is regulated to sidereal time4 ,it measures the progress of a star1 indicating an hour for every fifteen degrees1 and twenty-four hours for the whole period of the revolution of the star4 ,sidereal time commences when the vernal equinox is on the meridian1 just as solar time commences when the sun is on the meridian4 ,hence the hour by the sidereal clock has no correspondence with the hour of the day1 but simply indicates how long it is since the equinoctial point crossed the meridian4 ,for example1 the clock of an observatory points to three hours and twenty minutes2 this may be in the morning1 at noon1 or any other time of the day1--for it merely shows that it is three hours and twenty minutes since the equinox was on the meridian4 ,hence1 when a star is on the meridian1 the clock itself shows its right ascension1 which you will recollect is the angular distance measured on the equinoctial1 from the point of intersection of the ecliptic and equinoctial1 called the vernal equinox1 reckoning fifteen degrees for every hour1 and a proportional number of degrees and minutes for a less period4 ,i have before remarked1 that a very large portion of all astronomical observations are taken when the bodies are on the meridian1 by means of the transit instrument and clock4 ,having now described these instruments1 ,i will next explain the manner of using them for different observations4 ,any thing becomes a measure of time1 which divides duration equally4 ,the equinoctial1 therefore1 is peculiarly adapted to this purpose1 since1 in the daily revolution of the heavens1 equal portions of the equinoctial pass under the meridian in equal times4 ,the only difficulty is1 to ascertain the amount of these portions for given intervals4 ,now1 the clock shows us exactly this amount2 for1 when regulated to sidereal time1 7as it easily may be17 the hour-hand keeps exact pace with the equator1 revolving once on the dial-plate of the clock while the equator turns once by the revolution of the earth4 ,the same is true1 also1 of all the small circles of diurnal revolution2 they all turn exactly at the same rate as the equinoctial1 and a star situated any where between the equator and the pole will move in its diurnal circle along with the clock1 in the same manner as though it were in the equinoctial4 ,hence1 if we note the interval of time between the passage of any two stars1 as shown by the clock1 we have a measure of the number of degrees by which they are distant from each other in right ascension4 ,hence we see how easy it is to take arcs of right ascension3 the transit instrument shows us when a body is on the meridian2 the clock indicates how long it is since the vernal equinox passed it1 which is the right ascension itself2 or it tells us the difference of right ascension between any two bodies1 simply by indicating the difference in time between their periods of passing the meridian4 ,again1 it is easy to take the declination of a body when on the meridian4 ,by declination1 you will recollect1 is meant the distance of a heavenly body from the equinoctial2 the same1 indeed1 as latitude on the earth4 ,when a star is passing the meridian1 if1 on the instant of crossing the meridian wire of the telescope1 we take its distance from the north pole1 7which may readily be done1 because the position of the pole is always known1 being equal to the latitude of the place17 and subtract this distance from ninety degrees1 the remainder will be the distance from the equator1 which is the declination4 ,you will ask1 why we take this indirect method of finding the declination8 ,why we do not rather take the distance of the star from the equinoctial1 at once8 ,i answer1 that it is easy to point an instrument to the north pole1 and to ascertain its exact position1 and of course to measure any distance from it on the meridian1 while1 as there is nothing to mark the exact situation of the equinoctial1 it is not so easy to take direct measurements from it4 ,when we have thus determined the situation of a heavenly body1 with respect to two great circles at right angles with each other1 as in the present case1 the distance of a body from the equator and from the equinoctial colure1 or that meridian which passes though the vernal equinox1 we know its relative position in the heavens2 and when we have thus determined the relative positions of all the stars1 we may lay them down on a map or a globe1 exactly as we do places on the earth1 by means of their latitude and longitude4 ,the foregoing is only a specimen of the various uses of the transit instrument1 in finding the relative places of the heavenly bodies4 ,another use of this excellent instrument is1 to regulate our clocks and watches4 ,by an observation with the transit instrument1 we find when the sun's centre is on the meridian4 ,this is the exact time of apparent noon4 ,but watches and clocks usually keep mean time1 and therefore1 in order to set our timepiece by the transit instrument1 we must apply to the apparent time of noon the equation of time1 as will be explained in my next ,letter4 ,a noon-mark may easily be made by the aid of the transit instrument4 ,a window sill is frequently selected as a suitable place for the mark1 advantage being taken of the shadow projected upon it by the perpendicular casing of the window4 ,let an assistant stand1 with a rule laid on the line of shadow1 and with a knife ready to make the mark1 the instant when the observer at the transit instrument announces that the centre of the sun is on the meridian4 ,by a concerted signal1 as the stroke of a bell1 the inhabitants of a town may all fix a noon-mark from the same observation4 ,if the signal be given on one of the days when apparent time and mean time become equal to each other1 as on the twenty-fourth of ,december1 no equation of time is required4 ,as a noon-mark is convenient for regulating timepieces1 ,i will point out a method of making one1 which may be practised without the aid of the telescope4 ,upon a smooth1 level plane1 freely exposed to the sun1 with a pair of compasses describe a circle4 ,in the centre1 where the leg of the compasses stood1 erect a perpendicular wire of such a length1 that the termination of its shadow shall fall upon the circumference of the circle at some hour before noon1 as about ten o'clock4 ,make a small dot at the point where the end of the shadow falls upon the circle1 and do the same where it falls upon it again in the afternoon4 ,take a point half-way between these two points1 and from it draw a line to the centre1 and it will be a true meridian line4 ,the direction of this line would be the same1 whether it were made in the ,summer or in the ,winter2 but it is expedient to draw it about the fifteenth of ,june1 for then the shadow alters its length most rapidly1 and the moment of its crossing the wire will be more definite1 than in the ,winter4 ,at this time of year1 also1 the sun and clock agree1 or are together1 as will be more fully explained in my next ,letter2 whereas1 at other times of the year1 the time of noon1 as indicated by a common clock1 would not agree with that indicated by the sun4 ,if the upper end of the wire is flattened1 and a small hole is made in it1 through which the sun may shine1 the instant when this bright spot falls upon the circle will be better defined than the termination of the shadow4 ,another important instrument of the observatory is the mural circle4 ,it is a graduated circle1 usually of very large size1 fixed permanently in the plane of the meridian1 and attached firmly to a perpendicular wall2 and on its centre is a telescope1 which revolves along with it1 and is easily brought to bear on any object in any point in the meridian4 ,it is made of large size1 sometimes twenty feet in diameter1 in order that very small angles may be measured on its limb2 for it is obvious that a small angle1 as one second1 will be a larger space on the limb of an instrument1 in proportion as the instrument itself is larger4 ,the vertical circle usually connected with the transit instrument1 as in ,fig4 #g1 may indeed be employed for the same purposes as the mural circle1 namely1 to measure arcs of the meridian1 as meridian altitudes1 zenith distances1 north polar distances1 and declinations2 but as that circle must necessarily be small1 and therefore incapable of measuring very minute angles1 the mural circle is particularly useful in measuring these important arcs4 ,it is very difficult to keep so large an instrument perfectly steady2 and therefore it is attached to a massive wall of solid masonry1 and is hence called a mural circle1 from a ,latin word1 7murus17 which signifies a wall4 ,the diagram1 ,fig4 #h1 page #ef1 represents a mural circle fixed to its wall1 and ready for observations4 ,it will be seen1 that every expedient is employed to give the instrument firmness of parts and steadiness of position4 ,the circle is of solid metal1 usually of brass1 and it is strengthened by numerous radii1 which keep it from warping or bending2 and these are made in the form of hollow cones1 because that is the figure which unites in the highest degree lightness and strength4 ,on the rim of the instrument1 at ,a1 you may observe a microscope4 ,this is attached to a micrometer1--a delicate piece of apparatus1 used for reading the minute subdivisions of angles2 for1 after dividing the limb of the instrument as minutely as possible1 it will then be necessary to magnify those divisions with the microscope1 and subdivide each of these parts with the micrometer4 ,thus1 if we have a mural circle twenty feet in diameter1 and of course nearly sixty-three feet in circumference1 since there are twenty-one thousand and six hundred minutes in the whole circle1 we shall find1 by calculation1 that one minute would occupy1 on the limb of such an instrument1 only about one thirtieth of an inch1 and a second1 only one eighteen hundredth of an inch4 ,we could not1 therefore1 hope to carry the actual divisions to a greater degree of minuteness than minutes2 but each of these spaces may again be subdivided into seconds by the micrometer4 ,illustration ,fig4 #h4 ,from these statements1 you will acquire some faint idea of the extreme difficulty of making perfect astronomical instruments1 especially where they are intended to measure such minute angles as one second4 ,indeed1 the art of constructing astronomical instruments is one which requires such refined mechanical genius1--so superior a mind to devise1 and so delicate a hand to execute1--that the most celebrated instrument-makers take rank with the most distinguished astronomers2 supplying1 as they do1 the means by which only the latter are enabled to make these great discoveries4 ,astronomers have sometimes made their own telescopes2 but they have seldom1 if ever1 possessed the refined manual skill which is requisite for graduating delicate instruments4 ,the sextant is also one of the most valuable instruments for taking celestial arcs1 or the distance between any two points on the celestial sphere1 being applicable to a much greater number of purposes than the instruments already described4 ,it is particularly valuable for measuring celestial arcs at sea1 because it is not1 like most astronomical instruments1 affected by the motion of the ship4 ,the principle of the sextant may be briefly described1 as follows3 it gives the angular distance between any two bodies on the celestial sphere1 by reflecting the image of one of the bodies so as to coincide with the other body1 as seen directly4 ,the arc through which the reflector is turned1 to bring the reflected body to coincide with the other body1 becomes a measure of the angular distance between them4 ,by keeping this principle in view1 you will be able to understand the use of the several parts of the instrument1 as they are exhibited in the diagram1 ,fig4 #i1 page #eh4 ,it is1 you observe1 of a triangular shape1 and it is made strong and firm by metallic cross-bars4 ,it has two reflectors1 ,i and ,h1 called1 respectively1 the index glass and the horizon glass1 both of which are firmly fixed perpendicular to the plane of the instrument4 ,the index glass is attached to the movable arm1 ,,id1 and turns as this is moved along the graduated limb1 ,,ef4 ,this arm also carries a vernier1 at ,d1 a contrivance which1 like the micrometer1 enables us to take off minute parts of the spaces into which the limb is divided4 ,the horizon glass1 ,h1 consists of two parts2 the upper part being transparent or open1 so that the eye1 looking through the telescope1 ,t1 can see through it a distant body1 as a star at ,s1 while the lower part is a reflector4 ,illustration ,fig4 #i4 ,suppose it were required to measure the angular distance between the moon and a certain star1--the moon being at ,m1 and the star at ,s4 ,the instrument is held firmly in the hand1 so that the eye1 looking through the telescope1 sees the star1 ,s1 through the transparent part of the horizon glass4 ,then the movable arm1 ,,id1 is moved from ,f towards ,e1 until the image of ,m is reflected down to ,s1 when the number of degrees and parts of a degree reckoned on the limb1 from ,f to the index at ,d1 will show the angular distance between the two bodies4 ,,footnote3 #c ,brewster's ,life of ,newton ,,letter ,,vi4 ,,time ,,and ,,the ,,calendar4 ,from old ,eternity's mysterious orb ,was ,time cut off1 and cast beneath the skies4--,young4 ,,having hitherto been conversant only with the many fine and sentimental things which the poets have sung respecting ,old ,time1 perhaps you will find some difficulty in bringing down your mind to the calmer consideration of what time really is1 and according to what different standards it is measured for different purposes4 ,you will not1 however1 ,i think1 find the subject even in our matter-of-fact and unpoetical way of treating it1 altogether uninteresting4 ,what1 then1 is time8 ,time is a measured portion of indefinite duration4 ,it consists of equal portions cut off from eternity1 as a line on the surface of the earth is separated from its contiguous portions that constitute a great circle of the sphere1 by applying to it a two-foot scale2 or as a few yards of cloth are measured off from a piece of unknown or indefinite extent4 ,any thing1 or any event which takes place at equal intervals1 may become a measure of time4 ,thus1 the pulsations of the wrist1 the flowing of a given quantity of sand from one vessel to another1 as in the hourglass1 the beating of a pendulum1 and the revolution of a star1 have been severally employed as measures of time4 ,but the great standard of time is the period of the revolution of the earth on its axis1 which1 by the most exact observations1 is found to be always the same4 ,i have anticipated a little of this subject1 in giving an account of the transit instrument and clock1 but ,i propose1 in this letter1 to enter into it more at large4 ,the time of the earth's revolution on its axis1 as already explained1 is called a sidereal day1 and is determined by the revolution of a star in the heavens4 ,this interval is divided into twenty-four sidereal hours4 ,observations taken on numerous stars1 in different ages of the world1 show that they all perform their diurnal revolution in the same time1 and that their motion1 during any part of the revolution1 is always uniform4 ,here1 then1 we have an exact measure of time1 probably more exact than any thing which can be devised by art4 ,solar time is reckoned by the apparent revolution of the sun from the meridian round to the meridian again4 ,were the sun stationary in the heavens1 like a fixed star1 the time of its apparent revolution would be equal to the revolution of the earth on its axis1 and the solar and the sidereal days would be equal4 ,but1 since the sun passes from west to east1 through three hundred and sixty degrees1 in three hundred and sixty-five and one fourth days1 it moves eastward nearly one degree a day4 ,while1 therefore1 the earth is turning round on its axis1 the sun is moving in the same direction1 so that1 when we have come round under the same celestial meridian from which we started1 we do not find the sun there1 but he has moved eastward nearly a degree1 and the earth must perform so much more than one complete revolution1 before we come under the sun again4 ,now1 since we move1 in the diurnal revolution1 fifteen degrees in sixty minutes1 we must pass over one degree in four minutes4 ,it takes1 therefore1 four minutes for us to catch up with the sun1 after we have made one complete revolution4 ,hence the solar day is about four minutes longer than the sidereal2 and if we were to reckon the sidereal day twenty-four hours1 we should reckon the solar day twenty-four hours four minutes4 ,to suit the purposes of society at large1 however1 it is found more convenient to reckon the solar days twenty-four hours1 and throw the fraction into the sidereal day4 ,then1 #bd;h4 #dm4 3 #bd;h4 33 #bd;h4 3 #bc;h4 #efm4 #ds4 ,that is1 when we reduce twenty-four hours and four minutes to twenty-four hours1 the same proportion will require that we reduce the sidereal day from twenty-four hours to twenty-three hours fifty-six minutes four seconds2 or1 in other words1 a sidereal day is such a part of a solar day4 ,the solar days1 however1 do not always differ from the sidereal by precisely the same fraction1 since they are not constantly of the same length4 ,time1 as measured by the sun1 is called apparent time1 and a clock so regulated as always to keep exactly with the sun1 is said to keep apparent time4 ,mean time is time reckoned by the average length of all the solar days throughout the year4 ,this is the period which constitutes the civil day of twenty-four hours1 beginning when the sun is on the lower meridian1 namely1 at twelve o'clock at night1 and counted by twelve hours from the lower to the upper meridian1 and from the upper to the lower4 ,the astronomical day is the apparent solar day counted through the whole twenty-four hours1 7instead of by periods of twelve hours each1 as in the civil day17 and begins at noon4 ,thus it is now the tenth of ,june1 at nine o'clock1 ,a4,m41 according to civil time2 but we have not yet reached the tenth of ,june by astronomical time1 nor shall we1 until noon to-day2 consequently1 it is now ,june ninth1 twenty-first hour of astronomical time4 ,astronomers1 since so many of their observations are taken on the meridian1 are always supposed to look towards the south4 ,geographers1 having formerly been conversant only with the northern hemisphere1 are always understood to be looking towards the north4 ,hence1 left and right1 when applied to the astronomer1 mean east and west1 respectively2 but to the geographer the right is east1 and the left1 west4 ,clocks are usually regulated so as to indicate mean solar time2 yet1 as this is an artificial period not marked off1 like the sidereal day1 by any natural event1 it is necessary to know how much is to be added to1 or subtracted from1 the apparent solar time1 in order to give the corresponding mean time4 ,the interval1 by which apparent time differs from mean time1 is called the equation of time4 ,if one clock is so constructed as to keep exactly with the sun1 going faster or slower1 according as the lengths of the solar days vary1 and another clock is regulated to mean time1 then the difference of the two clocks1 at any period1 would be the equation of time for that moment4 ,if the apparent clock were faster than the mean1 then the equation of time must be subtracted2 but if the apparent clock were slower than the mean1 then the equation of time must be added1 to give the mean time4 ,the two clocks would differ most about the third of ,november1 when the apparent time is sixteen and one fourth minutes greater than the mean4 ,but since apparent time is sometimes greater and sometimes less than mean time1 the two must obviously be sometimes equal to each other4 ,this is1 in fact1 the case four times a year1 namely1 ,april fifteenth1 ,june fifteenth1 ,september first1 and ,december twenty-fourth4 ,astronomical clocks are made of the best workmanship1 with every advantage that can promote their regularity4 ,although they are brought to an astonishing degree of accuracy1 yet they are not as regular in their movements as the stars are1 and their accuracy requires to be frequently tested4 ,the transit instrument itself1 when once accurately placed in the meridian1 affords the means of testing the correctness of the clock1 since one revolution of a star1 from the meridian to the meridian again1 ought to correspond exactly to twenty-four hours by the clock1 and to continue the same1 from day to day2 and the right ascensions of various stars1 as they cross the meridian1 ought to be such by the clock1 as they are given in the tables1 where they are stated according to the accurate determinations of astronomers4 ,or1 by taking the difference of any two stars1 on successive days1 it will be seen whether the going of the clock is uniform for that part of the day2 and by taking the right ascensions of different pairs of stars1 we may learn the rate of the clock at various parts of the day4 ,we thus learn1 not only whether the clock accurately measures the length of the sidereal day1 but also whether it goes uniformly from hour to hour4 ,although astronomical clocks have been brought to a great degree of perfection1 so as hardly to vary a second for many months1 yet none are absolutely perfect1 and most are so far from it1 as to require to be corrected by means of the transit instrument1 every few days4 ,indeed1 for the nicest observations1 it is usual not to attempt to bring the clock to a state of absolute correctness1 but1 after bringing it as near to such a state as can conveniently be done1 to ascertain how much it gains or loses in a day2 that is1 to ascertain the rate of its going1 and to make allowance accordingly4 ,having considered the manner in which the smaller divisions of time are measured1 let us now take a hasty glance at the larger periods which compose the calendar4 ,as a day is the period of the revolution of the earth on its axis1 so a year is the period of the revolution of the earth around the sun4 ,this time1 which constitutes the astronomical year1 has been ascertained with great exactness1 and found to be three hundred and sixty-five days five hours forty-eight minutes and fifty-one seconds4 ,the most ancient nations determined the number of days in the year by means of the stylus1 a perpendicular rod which casts its shadow on a smooth plane bearing a meridian line4 ,the time when the shadow was shortest1 would indicate the day of the ,summer solstice2 and the number of days which elapsed1 until the shadow returned to the same length again1 would show the number of days in the year4 ,this was found to be three hundred and sixty-five whole days1 and accordingly1 this period was adopted for the civil year4 ,such a difference1 however1 between the civil and astronomical years1 at length threw all dates into confusion4 ,for if1 at first1 the ,summer solstice happened on the twenty-first of ,june1 at the end of four years1 the sun would not have reached the solstice until the twenty-second of ,june2 that is1 it would have been behind its time4 ,at the end of the next four years1 the solstice would fall on the twenty-third2 and in process of time1 it would fall successively on every day of the year4 ,the same would be true of any other fixed date4 ,julius ,csar1 who was distinguished alike for the variety and extent of his knowledge1 and his skill in arms1 first attempted to make the calendar conform to the motions of the sun4 ,amidst the hurry of tumultuous war1 ,the stars1 the gods1 the heavens1 were still his care4 ,aided by ,sosigenes1 an ,egyptian astronomer1 he made the first correction of the calendar1 by introducing an additional day every fourth year1 making ,february to consist of twenty-nine instead of twenty-eight days1 and of course the whole year to consist of three hundred and sixty-six days4 ,this fourth year was denominated ,bissextile1 because the sixth day before the ,kalends of ,march was reckoned twice4 ,it is also called ,leap ,year4 ,the ,julian year was introduced into all the civilized nations that submitted to the ,roman power1 and continued in general use until the year #aehb4 ,but the true correction was not six hours1 but five hours forty-nine minutes2 hence the addition was too great by eleven minutes4 ,this small fraction would amount in one hundred years to three fourths of a day1 and in one thousand years to more than seven days4 ,from the year #cbe to the year #aehb1 it had1 in fact1 amounted to more than ten days2 for it was known that1 in #cbe1 the vernal equinox fell on the twenty-first of ,march1 whereas1 in #aehb1 it fell on the eleventh4 ,it was ordered by the ,council of ,nice1 a celebrated ecclesiastical council1 held in the year #cbe1 that ,easter should be celebrated upon the first ,sunday after the first full moon1 next following the vernal equinox2 and as certain other festivals of the ,romish ,church were appointed at particular seasons of the year1 confusion would result from such a want of constancy between any fixed date and a particular season of the year4 ,suppose1 for example1 a festival accompanied by numerous religious ceremonies1 was decreed by the ,church to be held at the time when the sun crossed the equator in the ,spring1 7an event hailed with great joy1 as the harbinger of the return of ,summer17 and that1 in the year #cbe1 ,march twenty-first was designated as the time for holding the festival1 since1 at that period1 it was on the twenty-first of ,march when the sun reached the equinox2 the next year1 the sun would reach the equinox a little sooner than the twenty-first of ,march1 only eleven minutes1 indeed1 but still amounting in twelve hundred years to ten days2 that is1 in #aehb1 the sun reached the equinox on the eleventh of ,march4 ,if1 therefore1 they should continue to observe the twenty-first as a religious festival in honor of this event1 they would commit the absurdity of celebrating it ten days after it had passed by4 ,pope ,gregory the ,thirteenth1 who was then at the head of the ,roman ,see1 was a man of science1 and undertook to reform the calendar1 so that fixed dates would always correspond to the same seasons of the year4 ,he first decreed1 that the year should be brought forward ten days1 by reckoning the fifth of ,october the fifteenth2 and1 in order to prevent the calendar from falling into confusion afterwards1 he prescribed the following rule3 ,every year whose number is not divisible by four1 without a remainder1 consists of three hundred and sixty-five days2 every year which is so divisible1 but is not divisible by one hundred1 of three hundred and sixty-six2 every year divisible by one hundred1 but not by four hundred1 again1 of three hundred and sixty-five2 and every year divisible by four hundred1 of three hundred and sixty-six4 ,thus the year #ahch1 not being divisible by four1 contains three hundred and sixty-five days1 while #ahcf and #ahdj are leap years4 ,yet1 to make every fourth year consist of three hundred and sixty-six days would increase it too much1 by about three fourths of a day in a century2 therefore every hundredth year has only three hundred and sixty-five days4 ,thus #ahjj1 although divisible by four1 was not a leap year1 but a common year4 ,but we have allowed a whole day in a hundred years1 whereas we ought to have allowed only three fourths of a day4 ,hence1 in four hundred years1 we should allow a day too much1 and therefore1 we let the four hundredth remain a leap year4 ,this rule involves an error of less than a day in four thousand two hundred and thirty-seven years4 ,the ,pope1 who1 you will recollect1 at that age assumed authority over all secular princes1 issued his decree to the reigning sovereigns of ,christendom1 commanding the observance of the calendar as reformed by him4 ,the decree met with great opposition among the ,protestant ,states1 as they recognised in it a new exercise of ecclesiastical tyranny2 and some of them1 when they received it1 made it expressly understood1 that their acquiescence should not be construed as a submission to the ,papal authority4 ,in #ageb1 the ,gregorian year1 or ,new ,style1 was established in ,great ,britain by act of ,parliament2 and the dates of all deeds1 and other legal papers1 were to be made according to it4 ,as above a century had then passed since the first introduction of the new style1 eleven days were suppressed1 the third of ,september being called the fourteenth4 ,by the same act1 the beginning of the year was changed from ,march twenty-fifth to ,january first4 ,a few persons born previously to #ageb have come down to our day1 and we frequently see inscriptions on tombstones of those whose time of birth is recorded in old style4 ,in order to make this correspond to our present mode of reckoning1 we must add eleven days to the date4 ,thus the same event would be ,june twelfth of old style1 or ,june twenty-third of new style2 and if an event occurred between ,january first and ,march twenty-fifth1 the date of the year would be advanced one1 since ,february #ast1 #agdj1 ,o4,s4 would be ,february #ast1 #agda1 ,n4,s4 ,thus1 ,general ,washington was born ,february #aath1 #agca1 ,o4,s41 or ,february #bb;d1 #agcb1 ,n4,s4 ,if we inquire how any present event may be made to correspond in date to the old style1 we must subtract twelve days1 and put the year back one1 if the event lies between ,january first and ,march twenty-fifth4 ,thus1 ,june tenth1 ,n4,s4 corresponds to ,may twenty-ninth1 ,o4,s42 and ,march #bjth1 #ahdj1 to ,march #hth1 #ahci4 ,france1 being a ,roman ,catholic country1 adopted the new style soon after it was decreed by the ,pope2 but ,protestant countries1 as we have seen1 were much slower in adopting it2 and ,russia1 and the ,greek ,church generally1 still adhere to the old style4 ,in order1 therefore1 to make the ,russian dates correspond to ours1 we must add to them twelve days4 ,it may seem to you very remarkable1 that so much pains should have been bestowed upon this subject2 but without a correct and uniform standard of time1 the dates of deeds1 commissions1 and all legal papers2 of fasts and festivals1 appointed by ecclesiastical authority2 the returns of seasons1 and the records of history1--must all fall into inextricable confusion4 ,to change the observance of certain religious feasts1 which have been long fixed to particular days1 is looked upon as an impious innovation2 and though the times of the events1 upon which these ceremonies depend1 are utterly unknown1 it is still insisted upon by certain classes in ,england1 that the ,glastenbury thorn blooms on ,christmas day4 ,although the ancient ,grecian calendar was extremely defective1 yet the common people were entirely averse to its reformation4 ,their superstitious adherence to these errors was satirized by ,aristophanes1 in his comedy of the ,clouds4 ,an actor1 who had just come from ,athens1 recounts that he met with ,diana1 or the moon1 and found her extremely incensed1 that they did not regulate her course better4 ,she complained1 that the order of ,nature was changed1 and every thing turned topsyturvy4 ,the gods no longer knew what belonged to them2 but1 after paying their visits on certain feast-days1 and expecting to meet with good cheer1 as usual1 they were under the disagreeable necessity of returning back to heaven without their suppers4 ,among the ,greeks1 and other ancient nations1 the length of the year was generally regulated by the course of the moon4 ,this planet1 on account of the different appearances which she exhibits at her full1 change1 and quarters1 was considered by them as best adapted of any of the celestial bodies for this purpose4 ,as one lunation1 or revolution of the moon around the earth1 was found to be completed in about twenty-nine and one half days1 and twelve of these periods being supposed equal to one revolution of the sun1 their months were made to consist of twenty-nine and thirty days alternately1 and their year of three hundred and fifty-four days4 ,but this disagreed with the annual revolution of the sun1 which must evidently govern the seasons of the year1 more than eleven days4 ,the irregularities1 which such a mode of reckoning would occasion1 must have been too obvious not to have been observed4 ,for1 supposing it to have been settled1 at any particular time1 that the beginning of the year should be in the ,spring2 in about sixteen years afterwards1 the beginning would have been in ,autumn2 and in thirty-three or thirty-four years1 it would have gone backwards through all the seasons1 to ,spring again4 ,this defect they attempted to rectify1 by introducing a number of days1 at certain times1 into the calendar1 as occasion required1 and putting the beginning of the year forwards1 in order to make it agree with the course of the sun4 ,but as these additions1 or intercalations1 as they were called1 were generally consigned to the care of the priests1 who1 from motives of interest or superstition1 frequently omitted them1 the year was made long or short at pleasure4 ,the week is another division of time1 of the highest antiquity1 which1 in almost all countries1 has been made to consist of seven days2 a period supposed by some to have been traditionally derived from the creation of the world2 while others imagine it to have been regulated by the phases of the moon4 ,the names1 ,saturday1 ,sunday1 and ,monday1 are obviously derived from ,saturn1 the ,sun1 and the ,moon2 while ,tuesday1 ,wednesday1 ,thursday1 and ,friday1 are the days of ,tuisco1 ,woden1 ,thor1 and ,friga1 which are ,saxon names for ,mars1 ,mercury1 ,jupiter1 and ,venus4#d ,the common year begins and ends on the same day of the week2 but leap year ends one day later than it began4 ,fifty-two weeks contain three hundred and sixty-four days2 if1 therefore1 the year begins on ,tuesday1 for example1 we should complete fifty-two weeks on ,monday1 leaving one day1 7,tuesday17 to complete the year1 and the following year would begin on ,wednesday4 ,hence1 any day of the month is one day later in the week1 than the corresponding day of the preceding year4 ,thus1 if the sixteenth of ,november1 #ahch1 falls on ,friday1 the sixteenth of ,november1 #ahcg1 fell on ,thursday1 and will fall1 in #ahci1 on ,saturday4 ,but if leap year begins on ,sunday1 it ends on ,monday1 and the following year begins on ,tuesday2 while any given day of the month is two days later in the week than the corresponding date of the preceding year4 ,,footnote3 #d ,bonnycastle's ,astronomy4 ,,letter ,,vii4 ,,figure ,,of ,,the ,,earth4 ,he took the golden compasses1 prepared ,in ,god's eternal store1 to circumscribe ,this universe1 and all created things2 ,one foot he centred1 and the other turned ,round through the vast profundity obscure1 ,and said1 ',thus far extend1 thus far thy bounds1 ,this be thy just circumference1 ,o ,world6'--,milton4 ,,in the earliest ages1 the earth was regarded as one continued plane2 but1 at a comparatively remote period1 as five hundred years before the ,christian era1 astronomers began to entertain the opinion that the earth is round4 ,we are able now to adduce various arguments which severally prove this truth4 ,first1 when a ship is coming in from sea1 we first observe only the very highest parts of the ship1 while the lower portions come successively into view4 ,were the earth a continued plane1 the lower parts of the ship would be visible as soon as the higher1 as is evident from ,fig4 #aj1 page #gj4 ,illustration ,fig4 #aj4 ,illustration ,fig4 #aa4 ,since light comes to the eye in straight lines1 by which objects become visible1 it is evident1 that no reason exists why the parts of the ship near the water should not be seen as soon as the upper parts4 ,but if the earth be a sphere1 then the line of sight would pass above the deck of the ship1 as is represented in ,fig4 #aa2 and as the ship drew nearer to land1 the lower parts would successively rise above this line and come into view exactly in the manner known to observation4 ,secondly1 in a lunar eclipse1 which is occasioned by the moon's passing through the earth's shadow1 the figure of the shadow is seen to be spherical1 which could not be the case unless the earth itself were round4 ,thirdly1 navigators1 by steering continually in one direction1 as east or west1 have in fact come round to the point from which they started1 and thus confirmed the fact of the earth's rotundity beyond all question4 ,one may also reach a given place on the earth1 by taking directly opposite courses4 ,thus1 he may reach ,canton in ,china1 by a westerly route around ,cape ,horn1 or by an easterly route around the ,cape of ,good ,hope4 ,all these arguments severally prove that the earth is round4 ,but ,i propose1 in this ,letter1 to give you some account of the unwearied labors which have been performed to ascertain the exact figure of the earth2 for although the earth is properly described in general language as round1 yet it is not an exact sphere4 ,were it so1 all its diameters would be equal2 but it is known that a diameter drawn through the equator exceeds one drawn from pole to pole1 giving to the earth the form of a spheroid1--a figure resembling an orange1 where the ends are flattened a little and the central parts are swelled out4 ,although it would be a matter of very rational curiosity1 to investigate the precise shape of the planet on which ,heaven has fixed our abode1 yet the immense pains which has been bestowed on this subject has not all arisen from mere curiosity4 ,no accurate measurements can be taken of the distances and magnitudes of the heavenly bodies1 nor any exact determinations made of their motions1 without a knowledge of the exact figure of the earth2 and hence is derived a powerful motive for ascertaining this element with all possible precision4 ,the first satisfactory evidence that was obtained of the exact figure of the earth was derived from reasoning on the effects of the earth's centrifugal force1 occasioned by its rapid revolution on its own axis4 ,when water is whirled in a pail1 we see it recede from the centre and accumulate upon the sides of the vessel2 and when a millstone is whirled rapidly1 since the portions of the stone furthest from the centre revolve much more rapidly than those near to it1 their greater tendency to recede sometimes makes them fly off with a violent explosion4 ,a case1 which comes still nearer to that of the earth1 is exhibited by a mass of clay revolving on a potter's wheel1 as seen in the process of making earthen vessels4 ,the mass swells out in the middle1 in consequence of the centrifugal force exerted upon it by a rapid motion4 ,now1 in the diurnal revolution1 the equatorial parts of the earth move at the rate of about one thousand miles per hour1 while the poles do not move at all2 and since1 as we take points at successive distances from the equator towards the pole1 the rate at which these points move grows constantly less and less2 and since1 in revolving bodies1 the centrifugal force is proportioned to the velocity1 consequently1 those parts which move with the greatest rapidity will be more affected by this force than those which move more slowly4 ,hence1 the equatorial regions must be higher from the centre than the polar regions2 for1 were not this the case1 the waters on the surface of the earth would be thrown towards the equator1 and be piled up there1 just as water is accumulated on the sides of a pail when made to revolve rapidly4 ,huyghens1 an eminent astronomer of ,holland1 who investigated the laws of centrifugal forces1 was the first to infer that such must be the actual shape of the earth2 but to ,sir ,isaac ,newton we owe the full developement of this doctrine4 ,by combining the reasoning derived from the known laws of the centrifugal force with arguments derived from the principles of universal gravitation1 he concluded that the distance through the earth1 in the direction of the equator1 is greater than that in the direction of the poles4 ,he estimated the difference to be about thirty-four miles4 ,but it was soon afterwards determined by the astronomers of ,france1 to ascertain the figure of the earth by actual measurements1 specially instituted for that purpose4 ,let us see how this could be effected4 ,if we set out at the equator and travel towards the pole1 it is easy to see when we have advanced one degree of latitude1 for this will be indicated by the rising of the north star1 which appears in the horizon when the spectator stands on the equator1 but rises in the same proportion as he recedes from the equator1 until1 on reaching the pole1 the north star would be seen directly over head4 ,now1 were the earth a perfect sphere1 the meridian of the earth would be a perfect circle1 and the distance between any two places1 differing one degree in latitude1 would be exactly equal to the distance between any other two places1 differing in latitude to the same amount4 ,but if the earth be a spheroid1 flattened at the poles1 then a line encompassing the earth from north to south1 constituting the terrestrial meridian1 would not be a perfect circle1 but an ellipse or oval1 having its longer diameter through the equator1 and its shorter through the poles4 ,the part of this curve included between two radii1 drawn from the centre of the earth to the celestial meridian1 at angles one degree asunder1 would be greater in the polar than in the equatorial region2 that is1 the degrees of the meridian would lengthen towards the poles4 ,the ,french astronomers1 therefore1 undertook to ascertain by actual measurements of arcs of the meridian1 in different latitudes1 whether the degrees of the meridian are of uniform length1 or1 if not1 in what manner they differ from each other4 ,after several indecisive measurements of an arc of the meridian in ,france1 it was determined to effect simultaneous measurements of arcs of the meridian near the equator1 and as near as possible to the north pole1 presuming that if degrees of the meridian1 in different latitudes1 are really of different lengths1 they will differ most in points most distant from each other4 ,accordingly1 in #agce1 the ,french ,academy1 aided by the government1 sent out two expeditions1 one to ,peru and the other to ,lapland4 ,three distinguished mathematicians1 ,bouguer1 ,la ,condamine1 and ,godin1 were despatched to the former place1 and four others1 ,maupertius1 ,camus1 ,clairault1 and ,lemonier1 were sent to the part of ,swedish ,lapland which lies at the head of the ,gulf of ,tornea1 the northern arm of the ,baltic4 ,this commission completed its operations several years sooner than the other1 which met with greater difficulties in the way of their enterprise4 ,still1 the northern detachment had great obstacles to contend with1 arising particularly from the extreme length and severity of their ,winters4 ,the measurements1 however1 were conducted with care and skill1 and the result1 when compared with that obtained for the length of a degree in ,france1 plainly indicated1 by its greater amount1 a compression of the earth towards the poles4 ,mean-while1 ,bouguer and his party were prosecuting a similar work in ,peru1 under extraordinary difficulties4 ,these were caused1 partly by the localities1 and partly by the ill-will and indolence of the inhabitants4 ,the place selected for their operations was in an elevated valley between two principal chains of the ,andes4 ,the lowest point of their arc was at an elevation of a mile and a half above the level of the sea2 and1 in some instances1 the heights of two neighboring signals differed more than a mile4 ,encamped upon lofty mountains1 they had to struggle against storms1 cold1 and privations of every description1 while the invincible indifference of the ,indians1 they were forced to employ1 was not to be shaken by the fear of punishment or the hope of reward4 ,yet1 by patience and ingenuity1 they overcame all obstacles1 and executed with great accuracy one of the most important operations1 of this nature1 ever undertaken4 ,to accomplish this1 however1 took them nine years2 of which1 three were occupied in determining the latitudes alone4#e ,i have recited the foregoing facts1 in order to give you some idea of the unwearied pains which astronomers have taken to ascertain the exact figure of the earth4 ,you will find1 indeed1 that all their labors are characterized by the same love of accuracy4 ,years of toilsome watchings1 and incredible labor of computation1 have been undergone1 for the sake of arriving only a few seconds nearer to the truth4 ,the length of a degree of the meridian1 as measured in ,peru1 was less than that before determined in ,france1 and of course less than that of ,lapland2 so that the spheroidal figure of the earth appeared now to be ascertained by actual measurement4 ,still1 these measures were too few in number1 and covered too small a portion of the whole quadrant from the equator to the pole1 to enable astronomers to ascertain the exact law of curvature of the meridian1 and therefore similar measurements have since been prosecuted with great zeal by different nations1 particularly by the ,french and ,english4 ,in #agfd1 two ,english mathematicians of great eminence1 ,mason and ,dixon1 undertook the measurement of an arc in ,pennsylvania1 extending more than one hundred miles4 ,illustration ,fig4 #ab4 ,illustration ,fig4 #ac4 ,these operations are carried on by what is called a system of triangulation4 ,without some knowledge of trigonometry1 you will not be able fully to understand this process2 but1 as it is in its nature somewhat curious1 and is applied to various other geographical measurements1 as well as to the determination of arcs of the meridian1 ,i am desirous that you should understand its general principles4 ,let us reflect1 then1 that it must be a matter of the greatest difficulty1 to execute with exactness the measurement of a line of any great length in one continued direction on the earth's surface4 ,even if we select a level and open country1 more or less inequalities of surface will occur2 rivers must be crossed1 morasses must be traversed1 thickets must be penetrated1 and innumerable other obstacles must be surmounted2 and finally1 every time we apply an artificial measure1 as a rod1 for example1 we obtain a result not absolutely perfect4 ,each error may indeed be very small1 but small errors1 often repeated1 may produce a formidable aggregate4 ,now1 one unacquainted with trigonometry can easily understand the fact1 that1 when we know certain parts of a triangle1 we can find the other parts by calculation2 as1 in the rule of three in arithmetic1 we can obtain the fourth term of a proportion1 from having the first three terms given4 ,thus1 in the triangle ,a ,b ,c1 ,fig4 #ab1 if we know the side ,a ,b1 and the angles at ,a and ,b1 we can find by computation1 the other sides1 ,a ,c and ,b ,c1 and the remaining angle at ,c4 ,suppose1 then1 that in measuring an arc of the meridian through any country1 the line were to pass directly through ,a ,b1 but the ground was so obstructed between ,a and ,b1 that we could not possibly carry our measurement through it4 ,we might then measure another line1 as ,a ,c1 which was accessible1 and with a compass take the bearing of ,b from the points ,a and ,c1 by which means we should learn the value of the angles at ,a and ,c4 ,from these data we might calculate1 by the rules of trigonometry1 the exact length of the line ,a ,b4 ,perhaps the ground might be so situated1 that we could not reach the point ,b1 by any route2 still1 if it could be seen from ,a and ,c1 it would be all we should want4 ,thus1 in conducting a trigonometrical survey of any country1 conspicuous signals are placed on elevated points1 and the bearings of these are taken from the extremities of a known line1 called the base1 and thus the relative situation of various places is accurately determined4 ,were we to undertake to run an exact north and south line through any country1 as ,new ,england1 we should select1 near one extremity1 a spot of ground favorable for actual measurement1 as a level1 unobstructed plain2 we should provide a measure whose length in feet and inches was determined with the greatest possible precision1 and should apply it with the utmost care4 ,we should thus obtain a base line4 ,from the extremities of this line1 we should take 7with some appropriate instrument7 the bearing of some signal at a greater or less distance1 and thus we should obtain one side and two angles of a triangle1 from which we could find1 by the rules of trigonometry1 either of the unknown sides4 ,taking this as a new base1 we might take the bearing of another signal1 still further on our way1 and thus proceed to run the required north and south line1 without actually measuring any thing more than the first1 or base line4 ,thus1 in ,fig4 #ac1 we wish to measure the distance between the two points ,a and ,o1 which are both on the same meridian1 as is known by their having the same longitude2 but1 on account of various obstacles1 it would be found very inconvenient to measure this line directly1 with a rod or chain1 and even if we could do it1 we could not by this method obtain nearly so accurate a result1 as we could by a series of triangles1 where1 after the base line was measured1 we should have nothing else to measure except angles1 which can be determined1 by observation1 to a greater degree of exactness1 than lines4 ,we therefore1 in the first place1 measure the base line1 ,a ,b1 with the utmost precision4 ,then1 taking the bearing of some signal at ,c from ,a and ,b1 we obtain the means of calculating the side ,b ,c1 as has been already explained4 ,taking ,b ,c as a new base1 we proceed1 in like manner1 to determine successively the sides ,c ,d1 ,d ,e1 and ,e ,f1 and also ,a ,c1 and ,c ,e4 ,although ,a ,c is not in the direction of the meridian1 but considerably to the east of it1 yet it is easy to find the corresponding distance on the meridian1 ,a ,m2 and in the same manner we can find the portions of the meridian ,m ,n and ,n ,o1 corresponding respectively to ,c ,e and ,e ,f4 ,adding these several parts of the meridian together1 we obtain the length of the arc from ,a to ,o1 in miles2 and by observations on the north star1 at each extremity of the arc1 namely1 at ,a and at ,o1 we could determine the difference of latitude between these two points4 ,suppose1 for example1 that the distance between ,a and ,o is exactly five degrees1 and that the length of the intervening line is three hundred and forty-seven miles2 then1 dividing the latter by the former number1 we find the length of a degree to be sixty-nine miles and four tenths4 ,to take1 however1 a few of the results actually obtained1 they are as follows3 ,places of observation4 ,latitude4 ,length of a deg4 in miles4 ,peru1 #jj #jj' #jj #fh4gcb ,pennsylvania1 #ci #ab #jj #fh4hif ,france1 #df #ab #jj #fi4jed ,england1 #ea #bi #ed-a_/b #fi4adf ,sweden1 #ff #bj #aj #fi4bib ,this comparison shows1 that the length of a degree gradually increases1 as we proceed from the equator towards the pole4 ,combining the results of various estimates1 the dimensions of the terrestrial spheroid are found to be as follows3 ,equatorial diameter1 #gibe4fdh miles4 ,polar diameter1 #ghii4agj ,average diameter1 #giab4dji ,the difference between the greatest and the least is about twenty-six and one half miles1 which is about one two hundred and ninety-ninth part of the greatest4 ,this fraction is denominated the ellipticity of the earth1--being the excess of the equatorial over the polar diameter4 ,the operations1 undertaken for the purpose of determining the figure of the earth1 have been conducted with the most refined exactness4 ,at any stage of the process1 the length of the last side1 as obtained by calculation1 may be actually measured in the same manner as the base from which the series of triangles commenced4 ,when thus measured1 it is called the base of verification4 ,in some surveys1 the base of verification1 when taken at a distance of four hundred miles from the starting point1 has not differed more than one foot from the same line1 as determined by calculation4 ,another method of arriving at the exact figure of the earth is1 by observations with the pendulum4 ,if a pendulum1 like that of a clock1 be suspended1 and the number of its vibrations per hour be counted1 they will be found to be different in different latitudes4 ,a pendulum that vibrates thirty-six hundred times per hour1 at the equator1 will vibrate thirty-six hundred and five and two thirds times1 at ,london1 and a still greater number of times nearer the north pole4 ,now1 the vibrations of the pendulum are produced by the force of gravity4 ,hence their comparative number at different places is a measure of the relative forces of gravity at those places4 ,but when we know the relative forces of gravity at different places1 we know their relative distances from the centre of the earth2 because the nearer a place is to the centre of the earth1 the greater is the force of gravity4 ,suppose1 for example1 we should count the number of vibrations of a pendulum at the equator1 and then carry it to the north pole1 and count the number of vibrations made there in the same time1--we should be able1 from these two observations1 to estimate the relative forces of gravity at these two points2 and1 having the relative forces of gravity1 we can thence deduce their relative distances from the centre of the earth1 and thus obtain the polar and equatorial diameters4 ,observations of this kind have been taken with the greatest accuracy1 in many places on the surface of the earth1 at various distances from each other1 and they lead to the same conclusions respecting the figure of the earth1 as those derived from measuring arcs of the meridian4 ,it is pleasing thus to see a great truth1 and one apparently beyond the pale of human investigation1 reached by two routes entirely independent of each other4 ,nor1 indeed1 are these the only proofs which have been discovered of the spheroidal figure of the earth4 ,in consequence of the accumulation of matter above the equatorial regions of the earth1 a body weighs less there than towards the poles1 being further removed from the centre of the earth4 ,the same accumulation of matter1 by the force of attraction which it exerts1 causes slight inequalities in the motions of the moon2 and since the amount of these becomes a measure of the force which produces them1 astronomers are able1 from these inequalities1 to calculate the exact quantity of the matter thus accumulated1 and hence to determine the figure of the earth4 ,the result is not essentially different from that obtained by the other methods4 ,finally1 the shape of the earth's shadow is altered1 by its spheroidal figure1--a circumstance which affects the time and duration of a lunar eclipse4 ,all these different and independent phenomena afford a pleasing example of the harmony of truth4 ,the known effects of the centrifugal force upon a body revolving on its axis1 like the earth1 lead us to infer that the earth is of a spheroidal figure2 but if this be the fact1 the pendulum ought to vibrate faster near the pole than at the equator1 because it would there be nearer the centre of the earth4 ,on trial1 such is found to be the case4 ,if1 again1 there be such an accumulation of matter about the equatorial regions1 its effects ought to be visible in the motions of the moon1 which it would influence by its gravity2 and there1 also1 its effects are traced4 ,at length1 we apply our measures to the surface of the earth itself1 and find the same fact1 which had thus been searched out among the hidden things of ,nature1 here palpably exhibited before our eyes4 ,finally1 on estimating from these different sources1 what the exact amount of the compression at the poles must be1 all bring out nearly one and the same result4 ,this truth1 so harmonious in itself1 takes along with it1 and establishes1 a thousand other truths on which it rests4 ,,footnote3 #e ,library of ,useful ,knowledge3 ,history of ,astronomy1 page #ie4 ,,letter ,,viii4 ,,diurnal ,,revolutions4 ,to some she taught the fabric of the sphere1 ,the changeful moon1 the circuit of the stars1 ,the golden zones of heaven4--,akenside4 ,,with the elementary knowledge already acquired1 you will now be able to enter with pleasure and profit on the various interesting phenomena dependent on the revolution of the earth on its axis and around the sun4 ,the apparent diurnal revolution of the heavenly bodies1 from east to west1 is owing to the actual revolution of the earth on its own axis1 from west to east4 ,if we conceive of a radius of the earth's equator extended until it meets the concave sphere of the heavens1 then1 as the earth revolves1 the extremity of this line would trace out a curve on the face of the sky2 namely1 the celestial equator4 ,in curves parallel to this1 called the circles of diurnal revolution1 the heavenly bodies actually appear to move1 every star having its own peculiar circle4 ,after you have first rendered familiar the real motion of the earth from west to east1 you may then1 without danger of misapprehension1 adopt the common language1 that all the heavenly bodies revolve around the earth once a day1 from east to west1 in circles parallel to the equator and to each other4 ,i must remind you1 that the time occupied by a star1 in passing from any point in the meridian until it comes round to the same point again1 is called a sidereal day1 and measures the period of the earth's revolution on its axis4 ,if we watch the returns of the same star from day to day1 we shall find the intervals exactly equal to each other2 that is1 the sidereal days are all equal4 ,whatever star we select for the observation1 the same result will be obtained4 ,the stars1 therefore1 always keep the same relative position1 and have a common movement round the earth1--a consequence that naturally flows from the hypothesis that their apparent motion is all produced by a single real motion2 namely1 that of the earth4 ,the sun1 moon1 and planets1 as well as the fixed stars1 revolve in like manner2 but their returns to the meridian are not1 like those of the fixed stars1 at exactly equal intervals4 ,the appearances of the diurnal motions of the heavenly bodies are different in different parts of the earth1--since every place has its own horizon1 and different horizons are variously inclined to each other4 ,nothing in astronomy is more apt to mislead us1 than the obstinate habit of considering the horizon as a fixed and immutable plane1 and of referring every thing to it4 ,we should contemplate the earth as a huge globe1 occupying a small portion of space1 and encircled on all sides1 at an immense distance1 by the starry sphere4 ,we should free our minds from their habitual proneness to consider one part of space as naturally up and another down1 and view ourselves as subject to a force 7gravity7 which binds us to the earth as truly as though we were fastened to it by some invisible cords or wires1 as the needle attaches itself to all sides of a spherical loadstone4 ,we should dwell on this point1 until it appears to us as truly up1 in the direction ,b ,b1 ,c ,c1 ,d ,d1 when one is at ,b1 ,c1 ,d1 respectively1 as in the direction ,a ,a1 when he is at ,a1 ,fig4 #ad4 ,let us now suppose the spectator viewing the diurnal revolutions from several different positions on the earth4 ,on the equator1 his horizon would pass through both poles2 for the horizon cuts the celestial vault at ninety degrees in every direction from the zenith of the spectator2 but the pole is likewise ninety degrees from his zenith1 when he stands on the equator2 and consequently1 the pole must be in the horizon4 ,here1 also1 the celestial equator would coincide with the prime vertical1 being a great circle passing through the east and west points4 ,since all the diurnal circles are parallel to the equator1 consequently1 they would all1 like the equator be perpendicular to the horizon4 ,such a view of the heavenly bodies is called a right sphere1 which may be thus defined3 a right sphere is one in which all the daily revolutions of the stars are in circles perpendicular to the horizon4 ,illustration ,fig4 #ad4 ,a right sphere is seen only at the equator4 ,any star situated in the celestial equator would appear to rise directly in the east1 at midnight to be in the zenith of the spectator1 and to set directly in the west4 ,in proportion as stars are at a greater distance from the equator towards the pole1 they describe smaller and smaller circles1 until1 near the pole1 their motion is hardly perceptible4 ,if the spectator advances one degree from the equator towards the north pole1 his horizon reaches one degree beyond the pole of the earth1 and cuts the starry sphere one degree below the pole of the heavens1 or below the north star1 if that be taken as the place of the pole4 ,as he moves onward towards the pole1 his horizon continually reaches further and further beyond it1 until1 when he comes to the pole of the earth1 and under the pole of the heavens1 his horizon reaches on all sides to the equator1 and coincides with it4 ,moreover1 since all the circles of daily motion are parallel to the equator1 they become1 to the spectator at the pole1 parallel to the horizon4 ,or1 a parallel sphere is that in which all the circles of daily motion are parallel to the horizon4 ,to render this view of the heavens familiar1 ,i would advise you to follow round in mind a number of separate stars1 in their diurnal revolution1 one near the horizon1 one a few degrees above it1 and a third near the zenith4 ,to one who stood upon the north pole1 the stars of the northern hemisphere would all be perpetually in view when not obscured by clouds1 or lost in the sun's light1 and none of those of the southern hemisphere would ever be seen4 ,the sun would be constantly above the horizon for six months in the year1 and the remaining six continually out of sight4 ,that is1 at the pole1 the days and nights are each six months long4 ,the appearances at the south pole are similar to those at the north4 ,a perfect parallel sphere can never be seen1 except at one of the poles1--a point which has never been actually reached by man2 yet the ,british discovery ships penetrated within a few degrees of the north pole1 and of course enjoyed the view of a sphere nearly parallel4 ,as the circles of daily motion are parallel to the horizon of the pole1 and perpendicular to that of the equator1 so at all places between the two1 the diurnal motions are oblique to the horizon4 ,this aspect of the heavens constitutes an oblique sphere1 which is thus defined3 an oblique sphere is that in which the circles of daily motion are oblique to the horizon4 ,suppose1 for example1 that the spectator is at the latitude of fifty degrees4 ,his horizon reaches fifty degrees beyond the pole of the earth1 and gives the same apparent elevation to the pole of the heavens4 ,it cuts the equator and all the circles of daily motion1 at an angle of forty degrees1--being always equal to what the altitude of the pole lacks of ninety degrees3 that is1 it is always equal to the co-altitude of the pole4 ,thus1 let ,h ,o1 ,fig4 #ae1 represent the horizon1 ,e ,q the equator1 and ,p ,p the axis of the earth4 ,also1 l l1 m m1 n n1 parallels of latitude4 ,then the horizon of a spectator at ,z1 in latitude fifty degrees1 reaches to fifty degrees beyond the pole2 and the angle ,e ,c ,h1 which the equator makes with the horizon1 is forty degrees1--the complement of the latitude4 ,as we advance still further north1 the elevation of the diurnal circle above the horizon grows less and less1 and consequently1 the motions of the heavenly bodies more and more oblique to the horizon1 until finally1 at the pole1 where the latitude is ninety degrees1 the angle of elevation of the equator vanishes1 and the horizon and the equator coincide with each other1 as before stated4 ,illustration ,fig4 #ae4 ,the circle of perpetual apparition is the boundary of that space around the elevated pole1 where the stars never set4 ,its distance from the pole is equal to the latitude of the place4 ,for1 since the altitude of the pole is equal to the latitude1 a star1 whose polar distance is just equal to the latitude1 will1 when at its lowest point1 only just reach the horizon2 and all the stars nearer the pole than this will evidently not descend so far as the horizon4 ,thus m m1 ,fig4 #ae1 is the circle of perpetual apparition1 between which and the north pole1 the stars never set1 and its distance from the pole1 ,o ,p1 is evidently equal to the elevation of the pole1 and of course to the latitude4 ,in the opposite hemisphere1 a similar part of the sphere adjacent to the depressed pole never rises4 ,hence1 the circle of perpetual occultation is the boundary of that space around the depressed pole1 within which the stars never rise4 ,thus m m1 ,fig4 #ae1 is the circle of perpetual occultation1 between which and the south pole1 the stars never rise4 ,in an oblique sphere1 the horizon cuts the circles of daily motion unequally4 ,towards the elevated pole1 more than half the circle is above the horizon1 and a greater and greater portion1 as the distance from the equator is increased1 until finally1 within the circle of perpetual apparition1 the whole circle is above the horizon4 ,just the opposite takes place in the hemisphere next the depressed pole4 ,accordingly1 when the sun is in the equator1 as the equator and horizon1 like all other great circles of the sphere1 bisect each other1 the days and nights are equal all over the globe4 ,but when the sun is north of the equator1 the days become longer than the nights1 but shorter1 when the sun is south of the equator4 ,moreover1 the higher the latitude1 the greater is the inequality in the lengths of the days and nights4 ,by examining ,fig4 #ae1 you will easily see how each of these cases must hold good4 ,most of the appearances of the diurnal revolution can be explained1 either on the supposition that the celestial sphere actually turns around the earth once in twenty-four hours1 or that this motion of the heavens is merely apparent1 arising from the revolution of the earth on its axis1 in the opposite direction1--a motion of which we are insensible1 as we sometimes lose the consciousness of our own motion in a ship or steam-boat1 and observe all external objects to be receding from us1 with a common motion4 ,proofs1 entirely conclusive and satisfactory1 establish the fact1 that it is the earth1 and not the celestial sphere1 that turns2 but these proofs are drawn from various sources1 and one is not prepared to appreciate their value1 or even to understand some of them1 until he has made considerable proficiency in the study of astronomy1 and become familiar with a great variety of astronomical phenomena4 ,to such a period we will therefore postpone the discussion of the earth's rotation on its axis4 ,while we retain the same place on the earth1 the diurnal revolution occasions no change in our horizon1 but our horizon goes round1 as well as ourselves4 ,let us first take our station on the equator1 at sunrise2 our horizon now passes through both the poles and through the sun1 which we are to conceive of as at a great distance from the earth1 and therefore as cut1 not by the terrestrial1 but by the celestial1 horizon4 ,as the earth turns1 the horizon dips more and more below the sun1 at the rate of fifteen degrees for every hour2 and1 as in the case of the polar star1 the sun appears to rise at the same rate4 ,in six hours1 therefore1 it is depressed ninety degrees below the sun1 bringing us directly under the sun1 which1 for our present purpose1 we may consider as having all the while maintained the same fixed position in space4 ,the earth continues to turn1 and in six hours more1 it completely reverses the position of our horizon1 so that the western part of the horizon1 which at sunrise was diametrically opposite to the sun1 now cuts the sun1 and soon afterwards it rises above the level of the sun1 and the sun sets4 ,during the next twelve hours1 the sun continues on the invisible side of the sphere1 until the horizon returns to the position from which it set out1 and a new day begins4 ,let us next contemplate the similar phenomena at the poles4 ,here the horizon1 coinciding1 as it does1 with the equator1 would cut the sun through its centre and the sun would appear to revolve along the surface of the sea1 one half above and the other half below the horizon4 ,this supposes the sun in its annual revolution to be at one of the equinoxes4 ,when the sun is north of the equator1 it revolves continually round in a circle1 which1 during a single revolution1 appears parallel to the equator1 and it is constantly day2 and when the sun is south of the equator1 it is1 for the same reason1 continual night4 ,when we have gained a clear idea of the appearances of the diurnal revolutions1 as exhibited to a spectator at the equator and at the pole1 that is1 in a right and in a parallel sphere1 there will be little difficulty in imagining how they must be in the intermediate latitudes1 which have an oblique sphere4 ,the appearances of the sun and stars1 presented to the inhabitants of different countries1 are such as correspond to the sphere in which they live4 ,thus1 in the fervid climates of ,india1 ,africa1 and ,south ,america1 the sun mounts up to the highest regions of the heavens1 and descends directly downwards1 suddenly plunging beneath the horizon4 ,his rays1 darting almost vertically upon the heads of the inhabitants1 strike with a force unknown to the people of the colder climates2 while in places remote from the equator1 as in the north of ,europe1 the sun1 in ,summer1 rises very far in the north1 takes a long circuit towards the south1 and sets as far northward in the west as the point where it rose on the other side of the meridian4 ,as we go still further north1 to the northern parts of ,norway and ,sweden1 for example1 to the confines of the frigid zone1 the ,summer's sun just grazes the northern horizon1 and at noon appears only twenty-three and one half degrees above the southern4 ,on the other hand1 in mid-winter1 in the north of ,europe1 as at ,st4 ,petersburgh1 the day dwindles almost to nothing1--lasting only while the sun describes a very short arc in the extreme south4 ,in some parts of ,siberia and ,iceland1 the only day consists of a little glimmering of the sun on the verge of the southern horizon1 at noon4 ,,letter ,,ix4 ,,parallax ,,and ,,refraction4 ,go1 wondrous creature6 mount where science guides1 ,go measure earth1 weigh air1 and state the tides2 ,instruct the planets in what orbs to run1 ,correct old ,time1 and regulate the sun4--,pope4 ,i ,,think you must have felt some astonishment1 that astronomers are able to calculate the exact distances and magnitudes of the sun1 moon1 and planets4 ,we should1 at the first thought1 imagine that such knowledge as this must be beyond the reach of the human faculties1 and we might be inclined to suspect that astronomers practise some deception in this matter1 for the purpose of exciting the admiration of the unlearned4 ,i will therefore1 in the present ,letter1 endeavor to give you some clear and correct views respecting the manner in which astronomers acquire this knowledge4 ,in our childhood1 we all probably adopt the notion that the sky is a real dome of definite surface1 in which the heavenly bodies are fixed4 ,when any objects are beyond a certain distance from the eye1 we lose all power of distinguishing1 by our sight alone1 between different distances1 and cannot tell whether a given object is one million or a thousand millions of miles off4 ,although the bodies seen in the sky are in fact at distances extremely various1--some1 as the clouds1 only a few miles off2 others1 as the moon1 but a few thousand miles2 and others1 as the fixed stars1 innumerable millions of miles from us1--yet1 as our eye cannot distinguish these different distances1 we acquire the habit of referring all objects beyond a moderate height to one and the same surface1 namely1 an imaginary spherical surface1 denominated the celestial vault4 ,thus1 the various objects represented in the diagram on next page1 though differing very much in shape and diameter1 would all be projected upon the sky alike1 and compose a part1 indeed1 of the imaginary vault itself4 ,the place which each object occupies is determined by lines drawn from the eye of the spectator through the extremities of the body1 to meet the imaginary concave sphere4 ,thus1 to a spectator at ,o1 ,fig #af1 the several lines ,a ,b1 ,c ,d1 and ,e ,f1 would all be projected into arches on the face of the sky1 and be seen as parts of the sky itself1 as represented by the lines ,a ,b1 ,c ,d1 and ,e ,f4 ,and were a body actually to move in the several directions indicated by these lines1 they would appear to the spectator to describe portions of the celestial vault4 ,thus1 even when moving through the crooked line1 from a to b1 a body would appear to be moving along the face of the sky1 and of course in a regular curve line1 from c to d4 ,illustration ,fig4 #af4 ,but1 although all objects1 beyond a certain moderate height1 are projected on the imaginary surface of the sky1 yet different spectators will project the same object on different parts of the sky4 ,thus1 a spectator at ,a1 ,fig4 #ag1 would see a body1 ,c1 at ,m1 while a spectator at ,b would see the same body at ,n4 ,this change of place in a body1 as seen from different points1 is called parallax1 which is thus defined3 parallax is the apparent change of place which bodies undergo by being viewed from different points4 ,illustration ,fig4 #ag4 ,the arc ,m ,n is called the parallactic arc1 and the angle ,a ,c ,b1 the parallactic angle4 ,it is plain1 from the figure1 that near objects are much more affected by parallax than distant ones4 ,thus1 the body ,c1 ,fig4 #ag1 makes a much greater parallax than the more distant body ,d1--the former being measured by the arc ,m ,n1 and the latter by the arc ,o ,p4 ,we may easily imagine bodies to be so distant1 that they would appear projected at very nearly the same point of the heavens1 when viewed from places very remote from each other4 ,indeed1 the fixed stars1 as we shall see more fully hereafter1 are so distant1 that spectators1 a hundred millions of miles apart1 see each star in one and the same place in the heavens4 ,it is by means of parallax1 that astronomers find the distances and magnitudes of the heavenly bodies4 ,in order fully to understand this subject1 one requires to know something of trigonometry1 which science enables us to find certain unknown parts of a triangle from certain other parts which are known4 ,although you may not be acquainted with the principles of trigonometry1 yet you will readily understand1 from your knowledge of arithmetic1 that from certain things given in a problem others may be found4 ,every triangle has of course three sides and three angles2 and1 if we know two of the angles and one of the sides1 we can find all the other parts1 namely1 the remaining angle and the two unknown sides4 ,thus1 in the triangle ,a ,b ,c1 ,fig4 #ah1 if we know the length of the side ,a ,b1 and how many degrees each of the angles ,a ,b ,c and ,b ,c ,a contains1 we can find the length of the side ,b ,c1 or of the side ,a ,c1 and the remaining angle at ,a4 ,now1 let us apply these principles to the measurements of some of the heavenly bodies4 ,illustration ,fig4 #ah4 ,illustration ,fig4 #ai4 ,in ,fig4 #ai1 let ,a represent the earth1 ,c ,h the horizon1 and ,h ,z a quadrant of a great circle of the heavens1 extending from the horizon to the zenith2 and let ,e1 ,f1 ,g1 ,o1 be successive positions of the moon1 at different elevations1 from the horizon to the meridian4 ,now1 a spectator on the surface of the earth1 at ,a1 would refer the moon1 when at ,e1 to h1 on the face of the sky1 whereas1 if seen from the centre of the earth1 it would appear at ,h4 ,so1 when the moon was at ,f1 a spectator at ,a would see it at p1 while1 if seen from the centre1 it would have appeared at ,p4 ,the parallactic arcs1 ,h h1 ,p p1 ,r r1 grow continually smaller and smaller1 as a body is situated higher above the horizon2 and when the body is in the zenith1 then the parallax vanishes altogether1 for at ,o the moon would be seen at ,z1 whether viewed from ,a or ,c4 ,since1 then1 a heavenly body is liable to be referred to different points on the celestial vault1 when seen from different parts of the earth1 and thus some confusion be occasioned in the determination of points on the celestial sphere1 astronomers have agreed to consider the true place of a celestial object to be that where it would appear1 if seen from the centre of the earth2 and the doctrine of parallax teaches how to reduce observations made at any place on the surface of the earth1 to such as they would be1 if made from the centre4 ,when the moon1 or any heavenly body1 is seen in the horizon1 as at ,e1 the change of place is called the horizontal parallax4 ,thus1 the angle ,a ,e ,c1 measures the horizontal parallax of the moon4 ,were a spectator to view the earth from the centre of the moon1 he would see the semidiameter of the earth under this same angle2 hence1 the horizontal parallax of any body is the angle subtended by the semidiameter of the earth1 as seen from the body4 ,please to remember this fact4 ,it is evident from the figure1 that the effect of parallax upon the place of a celestial body is to depress it4 ,thus1 in consequence of parallax1 ,e is depressed by the arc ,h h2 ,f1 by the arc ,p p2 ,g1 by the arc ,r r2 while ,o sustains no change4 ,hence1 in all calculations respecting the altitude of the sun1 moon1 or planets1 the amount of parallax is to be added3 the stars1 as we shall see hereafter1 have no sensible parallax4 ,it is now very easy to see how1 when the parallax of a body is known1 we may find its distance from the centre of the earth4 ,thus1 in the triangle ,a ,c ,e1 ,fig4 #ai1 the side ,a ,c is known1 being the semidiameter of the earth2 the angle ,c ,a ,e1 being a right angle1 is also known2 and the parallactic angle1 ,a ,e ,c1 is found from observation2 and it is a well-known principle of trigonometry1 that when we have any two angles of a triangle1 we may find the remaining angle by subtracting the sum of these two from one hundred and eighty degrees4 ,consequently1 in the triangle ,a ,e ,c1 we know all the angles and one side1 namely1 the side ,a ,c2 hence1 we have the means of finding the side ,c ,e1 which is the distance from the centre of the earth to the centre of the moon4 ,illustration ,fig4 #bj4 ,when the distance of a heavenly body is known1 and we can measure1 with instruments1 its angular breadth1 we can easily determine its magnitude4 ,thus1 if we have the distance of the moon1 ,e ,s1 ,fig4 #bj1 and half the breadth of its disk ,s ,c1 7which is measured by the angle ,s ,e ,c17 we can find the length of the line1 ,s ,c1 in miles4 ,twice this line is the diameter of the body2 and when we know the diameter of a sphere1 we can1 by well-known rules1 find the contents of the surface1 and its solidity4 ,you will perhaps be curious to know1 how the moon's horizontal parallax is found2 for it must have been previously ascertained1 before we could apply this method to finding the distance of the moon from the earth4 ,suppose that two astronomers take their stations on the same meridian1 but one south of the equator1 as at the ,cape of ,good ,hope1 and another north of the equator1 as at ,berlin1 in ,prussia1 which two places lie nearly on the same meridian4 ,the observers would severally refer the moon to different points on the face of the sky1--the southern observer carrying it further north1 and the northern observer further south1 than its true place1 as seen from the centre of the earth4 ,this will be plain from the diagram1 ,fig4 #ba4 ,if ,a and ,b represent the positions of the spectators1 ,m the moon1 and ,c ,d an arc of the sky1 then it is evident1 that ,c ,d would be the parallactic arc4 ,illustration ,fig4 #ba4 ,these observations furnish materials for calculating1 by the aid of trigonometry1 the moon's horizontal parallax1 and we have before seen how1 when we know the parallax of a heavenly body1 we can find both its distance from the earth and its magnitude4 ,beside the change of place which these heavenly bodies undergo1 in consequence of parallax1 there is another1 of an opposite kind1 arising from the effect of the atmosphere1 called refraction4 ,refraction elevates the apparent place of a body1 while parallax depresses it4 ,it affects alike the most distant as well as nearer bodies4 ,in order to understand the nature of refraction1 we must consider1 that an object always appears in the direction in which the last ray of light comes to the eye4 ,if the light which comes from a star were bent into fifty directions before it reached the eye1 the star would nevertheless appear in the line described by the ray nearest the eye4 ,the operation of this principle is seen when an oar1 or any stick1 is thrust into water4 ,as the rays of light by which the oar is seen have their direction changed as they pass out of water into air1 the apparent direction in which the body is seen is changed in the same degree1 giving it a bent appearance1--the part below the water having apparently a different direction from the part above4 ,thus1 in ,fig4 #bb1 page #if1 if ,s a x be the oar1 ,s a b will be the bent appearance1 as affected by refraction4 ,the transparent substance through which any ray of light passes is called a medium4 ,it is a general fact in optics1 that1 when light passes out of a rarer into a denser medium1 as out of air into water1 or out of space into air1 it is turned towards a perpendicular to the surface of the medium2 and when it passes out of a denser into a rarer medium1 as out of water into air1 it is turned from the perpendicular4 ,in the above case1 the light1 passing out of space into air1 is turned towards the radius of the earth1 this being perpendicular to the surface of the atmosphere2 and it is turned more and more towards that radius the nearer it approaches to the earth1 because the density of the air rapidly increases near the earth4 ,illustration ,fig4 #bb4 ,let us now conceive of the atmosphere as made up of a great number of parallel strata1 as ,a ,a1 ,b ,b1 ,c ,c1 and ,d ,d1 increasing rapidly in density 7as is known to be the fact7 in approaching near to the surface of the earth4 ,let ,s be a star1 from which a ray of light1 ,s a1 enters the atmosphere at a1 where1 being much turned towards the radius of the convex surface1 it would change its direction into the line a b1 and again into b c1 and c ,o1 reaching the eye at ,o4 ,now1 since an object always appears in the direction in which the light finally strikes the eye1 the star would be seen in the direction ,o c1 and1 consequently1 the star would apparently change its place1 by refraction1 from ,s to ,s1 being elevated out of its true position4 ,moreover1 since1 on account of the continual increase of density in descending through the atmosphere1 the light would be continually turned out of its course more and more1 it would therefore move1 not in the polygon represented in the figure1 but in a corresponding curve line1 whose curvature is rapidly increased near the surface of the earth4 ,when a body is in the zenith1 since a ray of light from it enters the atmosphere at right angles to the refracting medium1 it suffers no refraction4 ,consequently1 the position of the heavenly bodies1 when in the zenith1 is not changed by refraction1 while1 near the horizon1 where a ray of light strikes the medium very obliquely1 and traverses the atmosphere through its densest part1 the refraction is greatest4 ,the whole amount of refraction1 when a body is in the horizon1 is thirty-four minutes2 while1 at only an elevation of one degree1 the refraction is but twenty-four minutes2 and at forty-five degrees1 it is scarcely a single minute4 ,hence it is always important to make our observations on the heavenly bodies when they are at as great an elevation as possible above the horizon1 being then less affected by refraction than at lower altitudes4 ,since the whole amount of refraction near the horizon exceeds thirty-three minutes1 and the diameters of the sun and moon are severally less than this1 these luminaries are in view both before they have actually risen and after they have set4 ,the rapid increase of refraction near the horizon is strikingly evinced by the oval figure which the sun assumes when near the horizon1 and which is seen to the greatest advantage when light clouds enable us to view the solar disk4 ,were all parts of the sun equally raised by refraction1 there would be no change of figure2 but1 since the lower side is more refracted than the upper1 the effect is to shorten the vertical diameter1 and thus to give the disk an oval form4 ,this effect is particularly remarkable when the sun1 at his rising or setting1 is observed from the top of a mountain1 or at an elevation near the seashore2 for in such situations1 the rays of light make a greater angle than ordinary with a perpendicular to the refracting medium1 and the amount of refraction is proportionally greater4 ,in some cases of this kind1 the shortening of the vertical diameter of the sun has been observed to amount to six minutes1 or about one fifth of the whole4 ,the apparent enlargement of the sun and moon1 when near the horizon1 arises from an optical illusion4 ,these bodies1 in fact1 are not seen under so great an angle when in the horizon as when on the meridian1 for they are nearer to us in the latter case than in the former4 ,the distance of the sun1 indeed1 is so great1 that it makes very little difference in his apparent diameter whether he is viewed in the horizon or on the meridian2 but with the moon1 the case is otherwise2 its angular diameter1 when measured with instruments1 is perceptibly larger when at its culmination1 or highest elevation above the horizon4 ,why1 then1 do the sun and moon appear so much larger when near the horizon8 ,it is owing to a habit of the mind1 by which we judge of the magnitudes of distant objects1 not merely by the angle they subtend at the eye1 but also by our impressions respecting their distance1 allowing1 under a given angle1 a greater magnitude as we imagine the distance of a body to be greater4 ,now1 on account of the numerous objects usually in sight between us and the sun1 when he is near the horizon1 he appears much further removed from us than when on the meridian2 and we unconsciously assign to him a proportionally greater magnitude4 ,if we view the sun1 in the two positions1 through a smoked glass1 no such difference of size is observed2 for here no objects are seen but the sun himself4 ,twilight is another phenomenon depending on the agency of the earth's atmosphere4 ,it is that illumination of the sky which takes place just before sunrise and which continues after sunset4 ,it is owing partly to refraction1 and partly to reflection1 but mostly to the latter4 ,while the sun is within eighteen degrees of the horizon1 before it rises or after it sets1 some portion of its light is conveyed to us1 by means of numerous reflections from the atmosphere4 ,at the equator1 where the circles of daily motion are perpendicular to the horizon1 the sun descends through eighteen degrees in an hour and twelve minutes4 ,the light of day1 therefore1 declines rapidly1 and as rapidly advances after daybreak in the morning4 ,at the pole1 a constant twilight is enjoyed while the sun is within eighteen degrees of the horizon1 occupying nearly two thirds of the half year when the direct light of the sun is withdrawn1 so that the progress from continual day to constant night is exceedingly gradual4 ,to an inhabitant of an oblique sphere1 the twilight is longer in proportion as the place is nearer the elevated pole4 ,were it not for the power the atmosphere has of dispersing the solar light1 and scattering it in various directions1 no objects would be visible to us out of direct sunshine2 every shadow of a passing cloud would involve us in midnight darkness2 the stars would be visible all day2 and every apartment into which the sun had not direct admission would be involved in the obscurity of night4 ,this scattering action of the atmosphere on the solar light is greatly increased by the irregularity of temperature caused by the sun1 which throws the atmosphere into a constant state of undulation2 and by thus bringing together masses of air of different temperatures1 produces partial reflections and refractions at their common boundaries1 by which means much light is turned aside from a direct course1 and diverted to the purposes of general illumination4#f ,in the upper regions of the atmosphere1 as on the tops of very high mountains1 where the air is too much rarefied to reflect much light1 the sky assumes a black appearance1 and stars become visible in the day time4 ,although the atmosphere is usually so transparent1 that it is invisible to us1 yet we as truly move and live in a fluid as fishes that swim in the sea4 ,considered in comparison with the whole earth1 the atmosphere is to be regarded as a thin layer investing the surface1 like a film of water covering the surface of an orange4 ,its actual height1 however1 is over a hundred miles1 though we cannot assign its precise boundaries4 ,being perfectly elastic1 the lower portions1 bearing as they do1 the weight of all the mass above them1 are greatly compressed1 while the upper portions having little to oppose the natural tendency of air to expand1 diffuse themselves widely4 ,the consequence is1 that the atmosphere undergoes a rapid diminution of density1 as we ascend from the earth1 and soon becomes exceedingly rare4 ,at so moderate a height as seven miles1 it is four times rarer than at the surface1 and continues to grow rare in the same proportion1 namely1 being four times less for every seven miles of ascent4 ,it is only1 therefore1 within a few miles of the earth1 that the atmosphere is sufficiently dense to sustain clouds and vapors1 which seldom rise so high as eight miles1 and are usually much nearer to the earth than this4 ,so rare does the air become on the top of ,mount ,chimborazo1 in ,south ,america1 that it is incompetent to support most of the birds that fly near the level of the sea4 ,the condor1 a bird which has remarkably long wings1 and a light body1 is the only bird seen towering above this lofty summit4 ,the transparency of the atmosphere1--a quality so essential to fine views of the starry heavens1--is much increased by containing a large proportion of water1 provided it is perfectly dissolved1 or in a state of invisible vapor4 ,a country at once hot and humid1 like some portions of the torrid zone1 presents a much brighter and more beautiful view of the moon and stars1 than is seen in cold climates4 ,before a copious rain1 especially in hot weather1 when the atmosphere is unusually humid1 we sometimes observe the sky to be remarkably resplendent1 even in our own latitude4 ,accordingly1 this unusual clearness of the sky1 when the stars shine with unwonted brilliancy1 is regarded as a sign of approaching rain2 and when1 after the rain is apparently over1 the air is remarkably transparent1 and distant objects on the earth are seen with uncommon distinctness1 while the sky exhibits an unusually deep azure1 we may conclude that the serenity is only temporary1 and that the rain will probably soon return4 ,,footnote3 #f ,sir ,j4 ,herschel4 ,,letter ,x4 ,,the ,,sun4 ,great source of day6 best image here below ,of thy ,creator1 ever pouring wide1 ,from world to world1 the vital ocean round1 ,on ,nature write1 with every beam1 ,his praise4--,thomson4 ,,the subjects which have occupied the preceding ,letters are by no means the most interesting parts of our science4 ,they constitute1 indeed1 little more than an introduction to our main subject1 but comprise such matters as are very necessary to be clearly understood1 before one is prepared to enter with profit and delight upon the more sublime and interesting field which now opens before us4 ,we will begin our survey of the heavenly bodies with the ,,sun1 which first claims our homage1 as the natural monarch of the skies4 ,the moon will next occupy our attention2 then the other bodies which compose the solar system1 namely1 the planets and comets2 and1 finally1 we shall leave behind this little province in the great empire of ,nature1 and wing a bolder flight to the fixed stars4 ,the distance of the sun from the earth is about ninety-five millions of miles4 ,it may perhaps seem incredible to you1 that astronomers should be able to determine this fact with any degree of certainty4 ,some1 indeed1 not so well informed as yourself1 have looked upon the marvellous things that are told respecting the distances1 magnitudes1 and velocities1 of the heavenly bodies1 as attempts of astronomers to impose on the credulity of the world at large2 but the certainty and exactness with which the predictions of astronomers are fulfilled1 as an eclipse1 for example1 ought to inspire full confidence in their statements4 ,i can assure you1 my dear friend1 that the evidence on which these statements are founded is perfectly satisfactory to those whose attainments in the sciences qualify them to understand them2 and1 so far are astronomers from wishing to impose on the unlearned1 by announcing such wonderful discoveries as they have made among the heavenly bodies1 no class of men have ever shown a stricter regard and zeal than they for the exact truth1 wherever it is attainable4 ,ninety-five millions of miles is indeed a vast distance4 ,no human mind is adequate to comprehend it fully2 but the nearest approaches we can make towards it are gained by successive efforts of the mind to conceive of great distances1 beginning with such as are clearly within our grasp4 ,let us1 then1 first take so small a distance as that of the breadth of the ,atlantic ocean1 and follow1 in mind1 a ship1 as she leaves the port of ,new ,york1 and1 after twenty days' steady sail1 reaches ,liverpool4 ,having formed the best idea we are able of this distance1 we may then reflect1 that it would take a ship1 moving constantly at the rate of ten miles per hour1 more than a thousand years to reach the sun4 ,the diameter of the sun is towards a million of miles2 or1 more exactly1 it is eight hundred and eighty-five thousand miles4 ,one hundred and twelve bodies as large as the earth1 lying side by side1 would be required to reach across the solar disk2 and our ship1 sailing at the same rate as before1 would be ten years in passing over the same space4 ,immense as is the sun1 we can readily understand why it appears no larger than it does1 when we reflect1 that its distance is still more vast4 ,even large objects on the earth1 when seen on a distant eminence1 or over a wide expanse of water1 dwindle almost to a point4 ,could we approach nearer and nearer to the sun1 it would constantly expand its volume1 until finally it would fill the whole vault of heaven4 ,we could1 however1 approach but little nearer to the sun without being consumed by the intensity of his heat4 ,whenever we come nearer to any fire1 the heat rapidly increases1 being four times as great at half the distance1 and one hundred times as great at one tenth the distance4 ,this fact is expressed by saying1 that the heat increases as the square of the distance decreases4 ,our globe is situated at such a distance from the sun1 as exactly suits the animal and vegetable kingdoms4 ,were it either much nearer or much more remote1 they could not exist1 constituted as they are4 ,the intensity of the solar light also follows the same law4 ,consequently1 were we nearer to the sun than we are1 its blaze would be insufferable2 or1 were we much further off1 the light would be too dim to serve all the purposes of vision4 ,the sun is one million four hundred thousand times as large as the earth2 but its matter is not more than about one fourth as dense as that of the earth1 being only a little heavier than water1 while the average density of the earth is more than five times that of water4 ,still1 on account of the immense magnitude of the sun1 its entire quantity of matter is three hundred and fifty thousand times as great as that of the earth4 ,now1 the force of gravity in a body is greater1 in proportion as its quantity of matter is greater4 ,consequently1 we might suppose1 that the weight of a body 7weight being nothing else than the measure of the force of gravity7 would be increased in the same proportion2 or1 that a body1 which weighs only one pound at the surface of the earth1 would weigh three hundred and fifty thousand pounds at the sun4 ,but we must consider1 that the attraction exerted by any body is the same as though all the matter were concentrated in the centre4 ,thus1 the attraction exerted by the earth and by the sun is the same as though the entire matter of each body were in its centre4 ,hence1 on account of the vast dimensions of the sun1 its surface is one hundred and twelve times further from its centre than the surface of the earth is from its centre2 and1 since the force of gravity diminishes as the square of the distance increases1 that of the sun1 exerted on bodies at its surface1 is 7so far as this cause operates7 the square of one hundred and twelve1 or twelve thousand five hundred and forty-four times less than that of the earth4 ,if1 therefore1 we increase the weight of a body three hundred and fifty-four thousand times1 in consequence of the greater amount of matter in the sun1 and diminish it twelve thousand five hundred and forty-four times1 in consequence of the force acting at a greater distance from the body1 we shall find that the body would weigh about twenty-eight times more on the sun than on the earth4 ,hence1 a man weighing three hundred pounds would1 if conveyed to the surface of the sun1 weigh eight thousand four hundred pounds1 or nearly three tons and three quarters4 ,a limb of our bodies1 weighing forty pounds1 would require to lift it a force of one thousand one hundred and twenty pounds1 which would be beyond the ordinary power of the muscles4 ,at the surface of the earth1 a body falls from rest by the force of gravity1 in one second1 sixteen and one twelfth feet2 but at the surface of the sun1 a body would1 in the same time1 fall through four hundred and forty-eight and seven tenths feet4 ,the sun turns on his own axis once in a little more than twenty-five days4 ,this fact is known by observing certain dark places seen by the telescope on the sun's disk1 called solar spots4 ,these are very variable in size and number4 ,sometimes1 the sun's disk1 when viewed with a telescope1 is quite free from spots1 while at other times we may see a dozen or more distinct clusters1 each containing a great number of spots1 some large and some very minute4 ,occasionally1 a single spot is so large as to be visible to the naked eye1 especially when the sun is near the horizon1 and the glare of his light is taken off4 ,one measured by ,dr4 ,herschel was no less than fifty thousand miles in diameter4 ,a solar spot usually consists of two parts1 the nucleus and the umbra4 ,the nucleus is black1 of a very irregular shape1 and is subject to great and sudden changes1 both in form and size4 ,spots have sometimes seemed to burst asunder1 and to project fragments in different directions4 ,the umbra is a wide margin1 of lighter shade1 and is often of greater extent than the nucleus4 ,the spots are usually confined to a zone extending across the central regions of the sun1 not exceeding sixty degrees in breadth4 ,fig4 #bc exhibits the appearance of the solar spots4 ,as these spots have all a common motion from day to day1 across the sun's disk2 as they go off at one limb1 and1 after a certain interval1 sometimes come on again on the opposite limb1 it is inferred that this apparent motion is imparted to them by an actual revolution of the sun on his own axis4 ,we know that the spots must be in contact1 or very nearly so1 at least1 with the body of the sun1 and cannot be bodies revolving around it1 which are projected on the solar disk when they are between us and the sun2 for1 in that case1 they would not be so long in view as out of view1 as will be evident from inspecting the following diagram4 ,let ,s1 ,fig4 #bd1 page #ajf1 represent the sun1 and b a body revolving round it in the orbit a b c2 and let ,e represent the earth1 where1 of course1 the spectator is situated4 ,the body would be seen projected on the sun only while passing from b to c1 while1 throughout the remainder of its orbit1 it would be out of view1 whereas no such inequality exists in respect to the two periods4 ,illustration ,fig4 #bc4 ,illustration ,fig4 #bd4 ,if you ask1 what is the cause of the solar spots1 ,i can only tell you what different astronomers have supposed respecting them4 ,they attracted the notice of ,galileo soon after the invention of the telescope1 and he formed an hypothesis respecting their nature4 ,supposing the sun to consist of a solid body embosomed in a sea of liquid fire1 he believed that the spots are composed of black cinders1 formed in the interior of the sun by volcanic action1 which rise and float on the surface of the fiery sea4 ,the chief objections to this hypothesis are1 first1 the vast extent of some of the spots1 covering1 as they do1 two thousand millions of square miles1 or more1--a space which it is incredible should be filled by lava in so short a time as that in which the spots are sometimes formed2 and1 secondly1 the sudden disappearance which the spots sometimes undergo1 a fact which can hardly be accounted for by supposing1 as ,galileo did1 that such a vast accumulation of matter all at once sunk beneath the fiery flood4 ,moreover1 we have many reasons for believing that the spots are depressions below the general surface4 ,la ,lande1 an eminent ,french astronomer of the last century1 held that the sun is a solid1 opaque body1 having its exterior diversified with high mountains and deep valleys1 and covered all over with a burning sea of liquid matter4 ,the spots he supposed to be produced by the flux and reflux of this fiery sea1 retreating occasionally from the mountains1 and exposing to view a portion of the dark body of the sun4 ,but it is inconsistent with the nature of fluids1 that a liquid1 like the sea supposed1 should depart so far from its equilibrium and remain so long fixed1 as to lay bare the immense spaces occupied by some of the solar spots4 ,dr4 ,herschel's views respecting the nature and constitution of the sun1 embracing an explanation of the solar spots1 have1 of late years1 been very generally received by the astronomical world4 ,this great astronomer1 after attentively viewing the surface of the sun1 for a long time1 with his large telescopes1 came to the following conclusions respecting the nature of this luminary4 ,he supposes the sun to be a planetary body like our earth1 diversified with mountains and valleys1 to which1 on account of the magnitude of the sun1 he assigns a prodigious extent1 some of the mountains being six hundred miles high1 and the valleys proportionally deep4 ,he employs in his explanation no volcanic fires1 but supposes two separate regions of dense clouds floating in the solar atmosphere1 at different distances from the sun4 ,the exterior stratum of clouds he considers as the depository of the sun's light and heat1 while the inferior stratum serves as an awning or screen to the body of the sun itself1 which thus becomes fitted to be the residence of animals4 ,the proofs offered in support of this hypothesis are chiefly the following3 first1 that the appearances1 as presented to the telescope1 are such as accord better with the idea that the fluctuations arise from the motions of clouds1 than that they are owing to the agitations of a liquid1 which could not depart far enough from its general level to enable us to see its waves at so great a distance1 where a line forty miles in length would subtend an angle at the eye of only the tenth part of a second2 secondly1 that1 since clouds are easily dispersed to any extent1 the great dimensions which the solar spots occasionally exhibit are more consistent with this than with any other hypothesis2 and1 finally1 that a lower stratum of clouds1 similar to those of our atmosphere1 was frequently seen by the ,doctor1 far below the luminous clouds which are the fountains of light and heat4 ,such are the views of one who had1 it must be acknowledged1 great powers of observation1 and means of observation in higher perfection than have ever been enjoyed by any other individual2 but1 with all deference to such authority1 ,i am compelled to think that the hypothesis is encumbered with very serious objections4 ,clouds analogous to those of our atmosphere 7and the ,doctor expressly asserts that his lower stratum of clouds are analogous to ours1 and reasons respecting the upper stratum according to the same analogy7 cannot exist in hot air2 they are tenants only of cold regions4 ,how can they be supposed to exist in the immediate vicinity of a fire so intense1 that they are even dissipated by it at the distance of ninety-five millions of miles8 ,much less can they be supposed to be the depositories of such devouring fire1 when any thing in the form of clouds1 floating in our atmosphere1 is at once scattered and dissolved by the accession of only a few degrees of heat4 ,nothing1 moreover1 can be imagined more unfavorable for radiating heat to such a distance1 than the light1 inconstant matter of which clouds are composed1 floating loosely in the solar atmosphere4 ,there is a logical difficulty in the case3 it is ascribing to things properties which they are not known to possess2 nay1 more1 which they are known not to possess4 ,from variations of light and shade in objects seen at moderate distances on the earth1 we are often deceived in regard to their appearances2 and we must distrust the power of an astronomer to decide upon the nature of matter seen at the distance of ninety-five millions of miles4 ,i think1 therefore1 we must confess our ignorance of the nature and constitution of the sun2 nor can we1 as astronomers1 obtain much more satisfactory knowledge respecting it than the common apprehension1 namely1 that it is an immense globe of fire4 ,we have not yet learned what causes are in operation to maintain its undecaying fires2 but our confidence in the ,divine wisdom and goodness leads us to believe1 that those causes are such as will preserve those fires from extinction1 and at a nearly uniform degree of intensity4 ,any material change in this respect would jeopardize the safety of the animal and vegetable kingdoms1 which could not exist without the enlivening influence of the solar heat1 nor1 indeed1 were that heat any more or less intense than it is at present4 ,if we inquire whether the surface of the sun is in a state of actual combustion1 like burning fuel1 or merely in a state of intense ignition1 like a stone heated to redness in a furnace1 we shall find it most reasonable to conclude that it is in a state of ignition4 ,if the body of the sun were composed of combustible matter and were actually on fire1 the material of the sun would be continually wasting away1 while the products of combustion would fill all the vast surrounding regions1 and obscure the solar light4 ,but solid bodies may attain a very intense state of ignition1 and glow with the most fervent heat1 while none of their material is consumed1 and no clouds or fumes rise to obscure their brightness1 or to impede their further emission of heat4 ,an ignited surface1 moreover1 is far better adapted than flame to the radiation of heat4 ,flame1 when made to act in contact with the surfaces of solid bodies1 heats them rapidly and powerfully2 but it sends forth1 or radiates1 very little heat1 compared with solid matter in a high state of ignition4 ,these various considerations render it highly probable to my mind1 that the body of the sun is not in a state of actual combustion1 but merely in a state of high ignition4 ,the solar beam consists of a mixture of several different sorts of rays4 ,first1 there are the calorific rays1 which afford heat1 and are entirely distinct from those which afford light1 and may be separated from them4 ,secondly1 there are the colorific rays1 which give light1 consisting of rays of seven distinct colors1 namely1 violet1 indigo1 blue1 green1 yellow1 orange1 red4 ,these1 when separated1 as they may be by a glass prism1 compose the prismatic spectrum4 ,they appear also in the rainbow4 ,when united again1 in due proportions1 they constitute white light1 as seen in the light of the sun4 ,thirdly1 there are found in the solar beam a class of rays which afford neither heat nor light1 but which produce chemical changes in certain bodies exposed to their influence1 and hence are called chemical rays4 ,fourthly1 there is still another class1 called magnetizing rays1 because they are capable of imparting magnetic properties to steel4 ,these different sorts of rays are sent forth from the sun1 to the remotest regions of the planetary worlds1 invigorating all things by their life-giving influence1 and dispelling the darkness that naturally fills all space4 ,but it was not alone to give heat and light1 that the sun was placed in the firmament4 ,by his power of attraction1 also1 he serves as the great regulator of the planetary motions1 bending them continually from the straight line in which they tend to move1 and compelling them to circulate around him1 each at nearly a uniform distance1 and all in perfect harmony4 ,i will hereafter explain to you the manner in which the gravity of the sun thus acts1 to control the planetary motions4 ,for the present1 let us content ourselves with reflecting upon the wonderful force which the sun must put forth1 in order to bend out of their courses1 into circular orbits1 such a number of planets1 some of which are more than a thousand times as large as the earth4 ,were a ship of war under full sail1 and it should be required to turn her aside from her course by a rope attached to her bow1 we can easily imagine that it would take a great force to do it1 especially were it required that the force should remain stationary and the ship be so constantly diverted from her course1 as to be made to go round the force as round a centre4 ,somewhat similar to this is the action which the sun exerts on each of the planets by some invisible influence1 called gravitation4 ,the bodies which he thus turns out of their course1 and bends into a circular orbit around himself1 are1 however1 many millions of times as ponderous as the ship1 and are moving many thousand times as swiftly4 ,,letter ,,xi4 ,,annual ,,revolution4--,,seasons ,these1 as they change1 ,almighty ,father1 these ,are but the varied ,god4 ,the rolling year ,is full of ,thee4--,thomson4 ,,we have seen that the apparent revolution of the heavenly bodies1 from east to west1 every twenty-four hours1 is owing to a real revolution of the earth on its own axis1 in the opposite direction4 ,this motion is very easily understood1 resembling1 as it does1 the spinning of a top4 ,we must1 however1 conceive of the top as turning without any visible support1 and not as resting in the usual manner on a plane4 ,the annual motion of the earth around the sun1 which gives rise to an apparent motion of the sun around the earth once a year1 and occasions the change of seasons1 is somewhat more difficult to understand2 and it may cost you some reflection1 before you will settle all the points respecting the changes of the seasons clearly in your mind4 ,we sometimes see these two motions exemplified in a top4 ,when1 as the string is pulled1 the top is thrown forwards on the floor1 we may see it move forward 7sometimes in a circle7 at the same time that it spins on its axis4 ,let a candle be placed on a table1 to represent the sun1 and let these two motions be imagined to be given to a top around it1 and we shall have a case somewhat resembling the actual motions of the earth around the sun4 ,when bodies are at such a distance from each other as the earth and the sun1 a spectator on either would project the other body upon the concave sphere of the heavens1 always seeing it on the opposite side of a great circle one hundred and eighty degrees from himself4 ,recollect that the path in which the earth moves round the sun is called the ecliptic4 ,we are not to conceive of this1 or of any other celestial circle1 as having any real1 palpable existence1 any more than the path of a bird through the sky4 ,you will perhaps think it quite superfluous for me to remind you of this2 but1 from the habit of seeing the orbits of the heavenly bodies represented in diagrams and orreries1 by palpable lines and circles1 we are apt inadvertently to acquire the notion1 that the orbits of the planets1 and other representations of the artificial sphere1 have a real1 palpable existence in ,nature2 whereas1 they denote the places where mere geometrical or imaginary lines run4 ,you might have expected to see an orrery1 exhibiting a view of the sun and planets1 with their various motions1 particularly described in my ,letter on astronomical instruments and apparatus4 ,i must acknowledge1 that ,i entertain a very low opinion of the utility of even the best orreries1 and ,i cannot recommend them as auxiliaries in the study of astronomy4 ,the numerous appendages usually connected with them1 some to support them in a proper position1 and some to communicate to them the requisite motions1 enter into the ideas which the learner forms respecting the machinery of the heavens2 and it costs much labor afterwards to divest the mind of such erroneous impressions4 ,astronomy can be exhibited much more clearly and beautifully to the mental eye than to the visual organ4 ,it is much easier to conceive of the sun existing in boundless space1 and of the earth as moving around him at a great distance1 the mind having nothing in view but simply these two bodies1 than it is1 in an orrery1 to contemplate the motion of a ball representing the earth1 carried by a complicated apparatus of wheels around another ball1 supported by a cylinder or wire1 to represent the sun4 ,i would advise you1 whenever it is practicable1 to think how things are in ,nature1 rather than how they are represented by art4 ,the machinery of the heavens is much simpler than that of an orrery4 ,in endeavoring to obtain a clear idea of the revolution of the earth around the sun1 imagine to yourself a plane 7a geometrical plane1 having merely length and breadth1 but no thickness7 passing through the centres of the sun and the earth1 and extended far beyond the earth till it reaches the firmament of stars4 ,although1 indeed1 no such dome actually exists as that under which we figure to ourselves the vault of the sky1 yet1 as the fixed stars appear to be set in such a dome1 we may imagine that the circles of the sphere1 when indefinitely enlarged1 finally reach such an imaginary vault4 ,all that is essential is1 that we should imagine this to exist far beyond the bounds of the solar system1 the various bodies that compose the latter being situated close around the sun1 at the centre4 ,along the line where this great circle meets the starry vault1 are situated a series of constellations1--,aries1 ,taurus1 ,gemini1 c41--which occupy successively this portion of the heavens4 ,when bodies are at such a distance from each other as the sun and the earth1 ,i have said that a spectator on either would project the other body upon the concave sphere of the heavens1 always seeing it on the opposite side of a great circle one hundred and eighty degrees from himself4 ,the place of a body1 when viewed from any point1 is denoted by the position it occupies among the stars4 ,thus1 in the diagram1 ,fig4 #be1 page #aad1 when the earth arrives at ,e1 it is said to be in ,aries1 because1 if viewed from the sun1 it would be projected on that part of the heavens2 and1 for the same reason1 to a spectator at ,e1 the sun would be in ,libra4 ,when the earth shifts its position from ,aries to ,taurus1 as we are unconscious of our own motion1 the sun it is that appears to move from ,libra to ,scorpio1 in the opposite part of the heavens4 ,hence1 as we go forward1 in the order of the signs1 on one side of the ecliptic1 the sun seems to be moving forward at the same rate on the opposite side of the same great circle2 and therefore1 although we are unconscious of our own motion1 we can read it1 from day to day1 in the motions of the sun4 ,if we could see the stars at the same time with the sun1 we could actually observe1 from day to day1 the sun's progress through them1 as we observe the progress of the moon at night2 only the sun's rate of motion would be nearly fourteen times slower than that of the moon4 ,although we do not see the stars when the sun is present1 we can observe that it makes daily progress eastward1 as is apparent from the constellations of the zodiac occupying1 successively1 the western sky immediately after sunset1 proving that either all the stars have a common motion westward1 independent of their diurnal motion1 or that the sun has a motion past them from west to east4 ,we shall see1 hereafter1 abundant evidence to prove1 that this change in the relative position of the sun and stars1 is owing to a change in the apparent place of the sun1 and not to any change in the stars4 ,illustration ,fig4 #be4 ,to form a clear idea of the two motions of the earth1 imagine yourself standing on a circular platform which turns slowly round its centre4 ,while you are carried slowly round the entire of the circuit of the heavens1 along with the platform1 you may turn round upon your heel the same way three hundred and sixty-five times4 ,the former is analogous to our annual motion with the earth around the sun2 the latter1 to our diurnal revolution in common with the earth around its own axis4 ,although the apparent revolution of the sun is in a direction opposite to the real motion of the earth1 as regards absolute space1 yet both are nevertheless from west to east1 since these terms do not refer to any directions in absolute space1 but to the order in which certain constellations 7the constellations of the ,zodiac7 succeed one another4 ,the earth itself1 on opposite sides of its orbit1 does in fact move towards directly opposite points of space2 but it is all the while pursuing its course in the order of the signs4 ,in the same manner1 although the earth turns on its axis from west to east1 yet any place on the surface of the earth is moving in a direction in space exactly opposite to its direction twelve hours before4 ,if the sun left a visible trace on the face of the sky1 the ecliptic would of course be distinctly marked on the celestial sphere1 as it is on an artificial globe2 and were the equator delineated in a similar manner1 we should then see1 at a glance1 the relative position of these two circles1--the points where they intersect one another1 constituting the equinoxes2 the points where they are at the greatest distance asunder1 that is1 the solstices2 and various other particulars1 which1 for want of such visible traces1 we are now obliged to search for by indirect and circuitous methods4 ,it will aid you1 to have constantly before your mental vision an imaginary delineation of these two important circles on the face of the sky4 ,the equator makes an angle with the ecliptic of twenty-three degrees and twenty-eight minutes4 ,this is called the obliquity of the ecliptic4 ,as the sun and earth are both always in the ecliptic1 and as the motion of the earth in one part of it makes the sun appear to move in the opposite part1 at the same rate1 the sun apparently descends1 in ,winter1 twenty-three degrees and twenty-eight minutes to the south of the equator1 and ascends1 in ,summer1 the same number of degrees north of it4 ,we must keep in mind1 that the celestial equator and celestial ecliptic are here understood1 and we may imagine them to be two great circles delineated on the face of the sky4 ,on comparing observations made at different periods1 for more than two thousand years1 it is found1 that the obliquity of the ecliptic is not constant1 but that it undergoes a slight diminution1 from age to age1 amounting to fifty-two seconds in a century1 or about half a second annually4 ,we might apprehend that1 by successive approaches to each other1 the equator and ecliptic would finally coincide2 but astronomers have discovered1 by a most profound investigation1 based on the principles of universal gravitation1 that this irregularity is confined within certain narrow limits2 and that the obliquity1 after diminishing for some thousands of years1 will then increase for a similar period1 and will thus vibrate forever about a mean value4 ,as the earth traverses every part of her orbit in the course of a year1 she will be once at each solstice1 and once at each equinox4 ,the best way of obtaining a correct idea of her two motions is1 to conceive of her as standing still for a single day1 at some point in her orbit1 until she has turned once on her axis1 then moving about a degree1 and halting again1 until another diurnal revolution is completed4 ,let us suppose the earth at the ,autumnal equinox1 the sun1 of course1 being at the ,vernal equinox1--for we must always think of these two bodies as diametrically opposite to each other4 ,suppose the earth to stand still in its orbit for twenty-four hours4 ,the revolution of the earth on its axis1 from west to east1 will make the sun appear to describe a great circle of the heavens from east to west1 coinciding with the equator4 ,at the end of this period1 suppose the sun to move northward one degree1 and to remain there for twenty-four hours2 in which time1 the revolution of the earth1 will make the sun appear to describe another circle1 from east to west1 parallel to the equator1 but one degree north of it4 ,thus1 we may conceive of the sun as moving one degree north1 every day1 for about three months1 when it will reach the point of the ecliptic furthest from the equator1 which point is called the tropic1 from a ,greek word1 signifying to turn2 because1 after the sun has passed this point1 his motion in his orbit carries him continually towards the equator1 and therefore he seems to turn about4 ,the same point is also called the solstice1 from a ,latin word1 signifying to stand still2 since1 when the sun has reached its greatest northern or southern limit1 while its declination is at the point where it ceases to increase1 but begins to decrease1 there the sun seems for a short time stationary1 with regard to the equator1 appearing for several days to describe the same parallel of latitude4 ,when the sun is at the northern tropic1 which happens about the twenty-first of ,june1 his elevation above the southern horizon at noon is the greatest in the year2 and when he is at the southern tropic1 about the twenty-first of ,december1 his elevation at noon is the least in the year4 ,the difference between these two meridian altitudes will give the whole distance from one tropic to the other1 and consequently1 twice the distance from each tropic to the equator4 ,by this means1 we find how far the tropic is from the equator1 and that gives us the angle which the equator and ecliptic make with each other2 for the greatest distance between any two great circles on the sphere is always equal to the angle which they make with each other4 ,thus1 the ancient astronomers were able to determine the obliquity of the ecliptic with a great degree of accuracy4 ,it was easy to find the situation of the zenith1 because the direction of a plumb-line shows us where that is2 and it was easy to find the distances from the zenith where the sun was at the greatest and least distances2 respectively4 ,the difference of these two arcs is the angular distance from one tropic to the other2 and half this arc is the distance of either tropic from the equator1 and of course1 equal to the obliquity of the ecliptic4 ,all this will be very easily understood from the annexed diagram1 ,fig4 #bf4 ,let ,z be the zenith of a spectator situated at ,c2 ,z n the least1 and ,z s the greatest distance of the sun from the zenith4 ,from ,z s subtract ,z n1 and then s n1 the difference1 divided by two1 will give the obliquity of the ecliptic4 ,illustration ,fig4 #bf4 ,the motion of the earth in its orbit is nearly seventy times as great as its greatest motion around its axis4 ,in its revolution around the sun1 the earth moves no less than one million six hundred and forty thousand miles per day1 sixty-eight thousand miles per hour1 eleven hundred miles per minute1 and nearly nineteen miles every second2 a velocity nearly sixty times as great as the greatest velocity of a cannon ball4 ,places on the earth turn with very different degrees of velocity in different latitudes4 ,those near the equator are carried round on the circumference of a large circle2 those towards the poles1 on the circumference of a small circle2 while one standing on the pole itself would not turn at all4 ,those who live on the equator are carried about one thousand miles an hour4 ,in our latitude1 7forty-one degrees and eighteen minutes17 the diurnal velocity is about seven hundred and fifty miles per hour4 ,it would seem1 at first view1 quite incredible1 that we should be whirled round at so rapid a rate1 and yet be entirely insensible of any motion2 and much more1 that we could be going so swiftly through space1 in our circuit around the sun1 while all things1 when unaffected by local causes1 appear to be in such a state of quiescence4 ,yet we have the most unquestionable evidence of the fact2 nor is it difficult to account for it1 in consistency with the general state of repose among bodies on the earth1 when we reflect that their relative motions1 with respect to each other1 are not in the least disturbed by any motions which they may have in common4 ,when we are on board a steam-boat1 we move about in the same manner when the boat is in rapid motion1 as when it is lying still2 and such would be the case1 if it moved steadily a hundred times faster than it does4 ,were the earth1 however1 suddenly to stop its diurnal revolution1 all movable bodies on its surface would be thrown off in tangents to the surface with velocities proportional to that of their diurnal motion2 and were the earth suddenly to halt in its orbit1 we should be hurled forward into space with inconceivable rapidity4 ,i will next endeavor to explain to you the phenomena of the ,seasons4 ,these depend on two causes2 first1 the inclination of the earth's axis to the plane of its orbit2 and1 secondly1 to the circumstance1 that the axis always remains parallel to itself4 ,imagine to yourself a candle placed in the centre of a ring1 to represent the sun in the centre of the earth's orbit1 and an apple with a knittingneedle running through it in the direction of the stem4 ,run a knife around the central part of the apple1 to mark the situation of the equator4 ,the circumference of the ring represents the earth's orbit in the plane of the ecliptic4 ,place the apple so that the equator shall coincide with the wire2 then the axis will lie directly across the plane of the ecliptic2 that is1 at right angles to it4 ,let the apple be carried quite round the ring1 constantly preserving the axis parallel to itself1 and the equator all the while coinciding with the wire that represents the orbit4 ,now1 since the sun enlightens half the globe at once1 so the candle1 which here represents the sun1 will shine on the half of the apple that is turned towards it2 and the circle which divides the enlightened from the unenlightened side of the apple1 called the terminator1 will pass through both the poles4 ,if the apple be turned slowly round on its axis1 the terminator will successively pass over all places on the earth1 giving the appearance of sunrise to places at which it arrives1 and of sunset to places from which it departs4 ,if1 therefore1 the equator had coincided with the ecliptic1 as would have been the case1 had the earth's axis been perpendicular to the plane of its orbit1 the diurnal motion of the sun would always have been in the equator1 and the days and nights would have been equal all over the globe4 ,to the inhabitants of the equatorial parts of the earth1 the sun would always have appeared to move in the prime vertical1 rising directly in the east1 passing through the zenith at noon1 and setting in the west4 ,in the polar regions1 the sun would always have appeared to revolve in the horizon2 while1 at any place between the equator and the pole1 the course of the sun would have been oblique to the horizon1 but always oblique in the same degree4 ,there would have been nothing of those agreeable vicissitudes of the seasons which we now enjoy2 but some regions of the earth would have been crowned with perpetual spring1 others would have been scorched with the unremitting fervor of a vertical sun1 while extensive regions towards either pole would have been consigned to everlasting frost and sterility4 ,to understand1 then1 clearly1 the causes of the change of seasons1 use the same apparatus as before2 but1 instead of placing the axis of the earth at right angles to the plane of its orbit1 turn it out of a perpendicular position a little1 7twenty-three degrees and twenty-eight minutes17 then the equator will be turned just the same number of degrees out of a coincidence with the ecliptic4 ,let the apple be carried around the ring1 always holding the axis inclined at the same angle to the plane of the ring1 and always parallel to itself4 ,you will find that there will be two points in the circuit where the plane of the equator1 that you had marked around the centre of the apple1 will pass through the centre of the sun2 these will be the points where the celestial equator and the ecliptic cut one another1 or the equinoxes4 ,when the earth is at either of these points1 the sun shines on both poles alike2 and1 if we conceive of the earth1 while in this situation1 as turning once round on its axis1 the apparent diurnal motion of the sun will be the same as it would be1 were the earth's axis perpendicular to the plane of the equator4 ,for that day1 the sun would revolve in the equator1 and the days and nights would be equal all over the globe4 ,if the apple were carried round in the manner supposed1 then1 at the distance of ninety degrees from the equinoxes1 the same pole would be turned from the sun on one side1 just as much as it was turned towards him on the other4 ,in the former case1 the sun's light would fall short of the pole twenty-three and one half degrees1 and in the other case1 it would reach beyond it the same number of degrees4 ,i would recommend to you to obtain as clear an idea as you can of the cause of the change of seasons1 by thinking over the foregoing illustration4 ,you may then clear up any remaining difficulties1 by studying the diagram1 ,fig4 #bg1 on page #abb4 ,illustration ,fig4 #bg4 ,let ,a ,b ,c ,d represent the earth's place in different parts of its orbit1 having the sun in the centre4 ,let ,a1 ,c1 be the positions of the earth at the equinoxes1 and ,b1 ,d1 its positions at the tropics1--the axis n s being always parallel to itself4 ,it is difficult to represent things of this kind correctly1 all on the same plane2 but you will readily see1 that the figure of the earth1 here1 answers to the apple in the former illustration2 that the hemisphere towards n is above1 and that towards s is below1 the plane of the paper4 ,when the earth is at ,a and ,c1 the ,vernal and ,autumnal equinoxes1 the sun1 you will perceive1 shines on both the poles n and s2 and1 if you conceive of the globe1 while in this position1 as turned round on its axis1 as it is in the diurnal revolution1 you will readily understand1 that the sun would describe the celestial equator4 ,this may not at first appear so obvious1 by inspecting the figure2 but if you consider the point n as raised above the plane of the paper1 and the point s as depressed below it1 you will readily see how the plane of the equator would pass through the centre of the sun4 ,again1 at ,b1 when the earth is at the southern tropic1 the sun shines twenty-three and a half degrees beyond the north pole1 n1 and falls the same distance short of the south pole1 s4 ,the case is exactly reversed when the earth is at the northern tropic1 and the sun at the southern4 ,while the earth is at one of the tropics1 at ,b1 for example1 let us conceive of it as turning on its axis1 and we shall readily see1 that all that part of the earth which lies within the north polar circle will enjoy continual day1 while that within the south polar circle will have continual night2 and that all other places will have their days longer as they are nearer to the enlightened pole1 and shorter as they are nearer to the unenlightened pole4 ,this figure likewise shows the successive positions of the earth1 at different periods of the year1 with respect to the signs1 and what months correspond to particular signs4 ,thus1 the earth enters ,libra1 and the sun ,aries1 on the twenty-first of ,march1 and on the twenty-first of ,june1 the earth is just entering ,capricorn1 and the sun1 ,cancer4 ,you will call to mind what is meant by this phraseology1--that by saying the earth enters ,libra1 we mean that a spectator placed on the sun would see the earth in that part of the celestial ecliptic1 which is occupied by the sign ,libra2 and that a spectator on the earth sees the sun at the same time projected on the opposite part of the heavens1 occupied by the sign ,cancer4 ,had the axis of the earth been perpendicular to the plane of the ecliptic1 then the sun would always have appeared to move in the equator1 the days would every where have been equal to the nights1 and there could have been no change of seasons4 ,on the other hand1 had the inclination of the ecliptic to the equator been much greater than it is1 the vicissitudes of the seasons would have been proportionally greater1 than at present4 ,suppose1 for instance1 the equator had been at right angles to the ecliptic1 in which case1 the poles of the earth would have been situated in the ecliptic itself2 then1 in different parts of the earth1 the appearances would have been as follows3 ,to a spectator on the equator1 7where all the circles of diurnal revolution are perpendicular to the horizon17 the sun1 as he left the vernal equinox1 would every day perform his diurnal revolution in a smaller and smaller circle1 until he reached the north pole1 when he would halt for a moment1 and then wheel about and return to the equator1 in a reverse order4 ,the progress of the sun through the southern signs1 to the south pole1 would be similar to that already described4 ,such would be the appearances to an inhabitant of the equatorial regions4 ,to a spectator living in an oblique sphere1 in our own latitude1 for example1 the sun1 while north of the equator1 would advance continually northward1 making his diurnal circuit in parallels further and further distant from the equator1 until he reached the circle of perpetual apparition2 after which1 he would climb1 by a spiral course1 to the north star1 and then as rapidly return to the equator4 ,by a similar progress southward1 the sun would at length pass the circle of perpetual occultation1 and for some time 7which would be longer or shorter1 according to the latitude of the place of observation7 there would be continual night4 ,to a spectator on the pole of the earth and under the pole of the heaven1 during the long day of six months1 the sun would wind its way to a point directly over head1 pouring down upon the earth beneath not merely the heat of the torrid zone1 but the heat of a torrid noon1 accumulating without intermission4 ,the great vicissitudes of heat and cold1 which would attend these several movements of the sun1 would be wholly incompatible with the existence of either the animal or the vegetable kingdom1 and all terrestrial ,nature would be doomed to perpetual sterility and desolation4 ,the happy provision which the ,creator has made against such extreme vicissitudes1 by confining the changes of the seasons within such narrow bounds1 conspires with many other express arrangements in the economy of ,nature1 to secure the safety and comfort of the human race4 ,perhaps you have never reflected upon all the reasons1 why the several changes of position1 with respect to the horizon1 which the sun undergoes in the course of the year1 occasion such a difference in the amount of heat received from him4 ,two causes contribute to increase the heat of ,summer and the cold of ,winter4 ,the higher the sun ascends above the horizon1 the more directly his rays fall upon the earth2 and their heating power is rapidly augmented1 as they approach a perpendicular direction4 ,when the sun is nearly over head1 his rays strike us with far greater force than when they meet us obliquely2 and the earth absorbs a far greater number of those rays of heat which strike it perpendicularly1 than of those which meet it in a slanting direction4 ,when the sun is near the horizon1 his rays merely glance along the ground1 and many of them1 before they reach it1 are absorbed and dispersed in passing through the atmosphere4 ,those who have felt only the oblique solar rays1 as they fall upon objects in the high latitudes1 have a very inadequate idea of the power of a vertical1 noonday sun1 as felt in the region of the equator4 ,the increased length of the day in ,summer is another cause of the heat of this season of the year4 ,this cause more sensibly affects places far removed from the equator1 because at such places the days are longer and the nights shorter than in the torrid zone4 ,by the operation of this cause1 the solar heat accumulates there so much1 during the longest days of ,summer1 that the temperature rises to a higher degree than is often known in the torrid climates4 ,but the temperature of a place is influenced very much by several other causes1 as well as by the force and duration of the sun's heat4 ,first1 the elevation of a country above the level of the sea has a great influence upon its climate4 ,elevated districts of country1 even in the torrid zone1 often enjoy the most agreeable climate in the world4 ,the cold of the upper regions of the atmosphere modifies and tempers the solar heat1 so as to give a most delightful softness1 while the uniformity of temperature excludes those sudden and excessive changes which are often experienced in less favored climes4 ,in ascending certain high mountains situated within the torrid zone1 the traveller passes1 in a short time1 through every variety of climate1 from the most oppressive and sultry heat1 to the soft and balmy air of ,spring1 which again is succeeded by the cooler breezes of ,autumn1 and then by the severest frosts of ,winter4 ,a corresponding difference is seen in the products of the vegetable kingdom4 ,while ,winter reigns on the summit of the mountain1 its central regions may be encircled with the verdure of ,spring1 and its base with the flowers and fruits of ,summer4 ,secondly1 the proximity of the ocean also has a great effect to equalize the temperature of a place4 ,as the ocean changes its temperature during the year much less than the land1 it becomes a source of warmth to contiguous countries in ,winter1 and a fountain of cool breezes in ,summer4 ,thirdly1 the relative humidity or dryness of the atmosphere of a place is of great importance1 in regard to its effects on the animal system4 ,a dry air of ninety degrees is not so insupportable as a humid air of eighty degrees2 and it may be asserted as a general principle1 that a hot and humid atmosphere is unhealthy1 although a hot air1 when dry1 may be very salubrious4 ,in a warm atmosphere which is dry1 the evaporation of moisture from the surface of the body is rapid1 and its cooling influence affords a most striking relief to an intense heat without2 but when the surrounding atmosphere is already filled with moisture1 no such evaporation takes place from the surface of the skin1 and no such refreshing effects are experienced from this cause4 ,moisture collects on the skin2 a sultry1 oppressive sensation is felt2 and chills and fevers are usually in the train4 ,,letter ,,xii4 ,,laws ,,of ,,motion4 ,what though in solemn silence1 all ,move round this dark1 terrestrial ball6 ,in reason's ear they all rejoice1 ,and utter forth a glorious voice2 ,for ever singing1 as they shine1 ',the hand that made us is divine4'--,addison4 ,,however incredible it may seem1 no fact is more certain1 than that the earth is constantly on the wing1 flying around the sun with a velocity so prodigious1 that1 for every breath we draw1 we advance on our way forty or fifty miles4 ,if1 when passing across the waters in a steam-boat1 we can wake1 after a night's repose1 and find ourselves conducted on our voyage a hundred miles1 we exult in the triumphs of art1 which could have moved so ponderous a body as a steam-ship over such a space in so short a time1 and so quietly1 too1 as not to disturb our slumbers2 but1 with a motion vastly more quiet and uniform1 we have1 in the same interval1 been carried along with the earth in its orbit more than half a million of miles4 ,in the case of the steam-ship1 however perfect the machinery may be1 we still1 in our waking hours at least1 are made sensible of the action of the forces by which the motion is maintained1--as the roaring of the fire1 the beating of the piston1 and the dashing of the paddle-wheels2 but in the more perfect machinery which carries the earth forward on her grander voyage1 no sound is heard1 nor the least intimation afforded of the stupendous forces by which this motion is achieved4 ,to the pious observer of ,nature it might seem sufficient1 without any inquiry into second causes1 to ascribe the motions of the spheres to the direct agency of the ,supreme ,being4 ,if1 however1 we can succeed in finding the secret springs and cords1 by which the motions of the heavenly bodies are immediately produced and controlled1 it will detract nothing from our just admiration of the ,great ,first ,cause of all things4 ,we may therefore now enter upon the inquiry into the nature or laws of the forces by which the earth is made to revolve on her axis and in her orbit2 and having learned what it is1 that causes and maintains the motions of the earth1 you will then acquire1 at the same time1 a knowledge of all the celestial machinery4 ,the subject will involve an explanation of the laws of motion1 and of the principles of universal gravitation4 ,it was once supposed1 that we could never reason respecting the laws that govern the heavenly bodies from what we observe in bodies around us1 but that motion is one thing on the earth and quite another thing in the skies2 and hence1 that it is impossible for us1 by any inquiries into the laws of terrestrial ,nature1 to ascertain how things take place among the heavenly bodies4 ,galileo and ,newton1 however1 proceeded on the contrary supposition1 that ,nature is uniform in all her works2 that the same ,almighty arm rules over all2 and that ,he works by the same fixed laws through all parts of ,his boundless realm4 ,the certainty with which all the predictions of astronomers1 made on these suppositions1 are fulfilled1 attests the soundness of the hypothesis4 ,accordingly1 those laws1 which all experience1 endlessly multiplied and varied1 proves to be the laws of terrestrial motion1 are held to be the laws that govern also the motions of the most distant planets and stars1 and to prevail throughout the universe of matter4 ,let us1 then1 briefly review these great laws of motion1 which are three in number4 ,the ,,first ,,law is as follows3 every body perseveres in a state of rest1 or of uniform motion in a straight line1 unless compelled by some force to change its state4 ,by force is meant any thing which produces motion4 ,the foregoing law has been fully established by experiment1 and is conformable to all experience4 ,it embraces several particulars4 ,first1 a body1 when at rest1 remains so1 unless some force puts it in motion2 and hence it is inferred1 when a body is found in motion1 that some force must have been applied to it sufficient to have caused its motion4 ,thus1 the fact1 that the earth is in motion around the sun and around its own axis1 is to be accounted for by assigning to each of these motions a force adequate1 both in quantity and direction1 to produce these motions1 respectively4 ,secondly1 when a body is once in motion1 it will continue to move for ever1 unless something stops it4 ,when a ball is struck on the surface of the earth1 the friction of the earth and the resistance of the air soon stop its motion2 when struck on smooth ice1 it will go much further before it comes to a state of rest1 because the ice opposes much less resistance than the ground2 and1 were there no impediment to its motion1 it would1 when once set in motion1 continue to move without end4 ,the heavenly bodies are actually in this condition3 they continue to move1 not because any new forces are applied to them2 but1 having been once set in motion1 they continue in motion because there is nothing to stop them4 ,this property in bodies to persevere in the state they are actually in1--if at rest1 to remain at rest1 or1 if in motion1 to continue in motion1--is called inertia4 ,the inertia of a body 7which is measured by the force required to overcome it7 is proportioned to the quantity of matter it contains4 ,a steam-boat manifests its inertia1 on first starting it1 by the enormous expenditure of force required to bring it to a given rate of motion2 and it again manifests its inertia1 when in rapid motion1 by the great difficulty of stopping it4 ,the heavenly bodies1 having been once put in motion1 and meeting with nothing to stop them1 move on by their own inertia4 ,a top affords a beautiful illustration of inertia1 continuing1 as it does1 to spin after the moving force is withdrawn4 ,thirdly1 the motion to which a body naturally tends is uniform2 that is1 the body moves just as far the second minute as it did the first1 and as far the third as the second2 and passes over equal spaces in equal times4 ,i do not assert that the motion of all moving bodies is in fact uniform1 but that such is their tendency4 ,if it is otherwise than uniform1 there is some cause operating to disturb the uniformity to which it is naturally prone4 ,fourthly1 a body in motion will move in a straight line1 unless diverted out of that line by some external force2 and the body will resume its straight-forward motion1 whenever the force that turns it aside is withdrawn4 ,every body that is revolving in an orbit1 like the moon around the earth1 or the earth around the sun1 tends to move in a straight line which is a tangent#g to its orbit4 ,thus1 if ,a ,b ,c1 ,fig4 #bh1 represents the orbit of the moon around the earth1 were it not for the constant action of some force that draws her towards the earth1 she would move off in a straight line4 ,if the force that carries her towards the earth were suspended at ,a1 she would immediately desert the circular motion1 and proceed in the direction ,a ,d4 ,in the same manner1 a boy whirls a stone around his head in a sling1 and then letting go one of the strings1 and releasing the force that binds it to the circle1 it flies off in a straight line which is a tangent to that part of the circle where it was released4 ,this tendency which a body revolving in an orbit exhibits1 to recede from the centre and to fly off in a tangent1 is called the centrifugal force4 ,we see it manifested when a pail of water is whirled4 ,the water rises on the sides of the vessel1 leaving a hollow in the central parts4 ,we see an example of the effects of centrifugal action1 when a horse turns swiftly round a corner1 and the rider is thrown outwards2 also1 when a wheel passes rapidly through a small collection of water1 and portions of the water are thrown off from the top of the wheel in straight lines which are tangents to the wheel4 ,illustration ,fig4 #bh4 ,the centrifugal force is increased as the velocity is increased4 ,thus1 the parts of a millstone most remote from the centre sometimes acquire a centrifugal force so much greater than the central parts1 which move much slower1 that the stone is divided1 and the exterior portions are projected with great violence4 ,in like manner1 as the equatorial parts of the earth1 in the diurnal revolution1 revolve much faster than the parts towards the poles1 so the centrifugal force is felt most at the equator1 and becomes strikingly manifest by the diminished weight of bodies1 since it acts in opposition to the force of gravity4 ,although the foregoing law of motion1 when first presented to the mind1 appears to convey no new truth1 but only to enunciate in a formal manner what we knew before2 yet a just understanding of this law1 in all its bearings1 leads us to a clear comprehension of no small share of all the phenomena of motion4 ,the second and third laws may be explained in fewer terms4 ,the ,,second ,,law of motion is as follows3 motion is proportioned to the force impressed1 and in the direction of that force4 ,the meaning of this law is1 that every force that is applied to a body produces its full effect1 proportioned to its intensity1 either in causing or in preventing motion4 ,let there be ever so many blows applied at once to a ball1 each will produce its own effect in its own direction1 and the ball will move off1 not indeed in the zigzag1 complex lines corresponding to the directions of the several forces1 but in a single line expressing the united effect of all4 ,if you place a ball at the corner of a table1 and give it an impulse1 at the same instant1 with the thumb and finger of each hand1 one impelling it in the direction of one side of the table1 and the other in the direction of the other side1 the ball will move diagonally across the table4 ,if the blows be exactly proportioned each to the length of the side of the table on which it is directed1 the ball will run exactly from corner to corner1 and in the same time that it would have passed over each side by the blow given in the direction of that side4 ,this principle is expressed by saying1 that a body impelled by two forces1 acting respectively in the directions of the two sides of a parallelogram1 and proportioned in intensity to the lengths of the sides1 will describe the diagonal of the parallelogram in the same time in which it would have described the sides by the forces acting separately4 ,the converse of this proposition is also true1 namely1 that any single motion may be considered as the resultant of two others1--the motion itself being represented by the diagonal1 while the two components are represented by the sides1 of a parallelogram4 ,this reduction of a motion to the individual motions that produce it1 is called the resolution of motion1 or the resolution of forces4 ,nor can a given motion be resolved into two components1 merely4 ,these1 again1 may be resolved into others1 varying indefinitely1 in direction and intensity1 from all which the given motion may be considered as having resulted4 ,this composition and resolution of motion or forces is often of great use1 in inquiries into the motions of the heavenly bodies4 ,the composition often enables us to substitute a single force for a great number of others1 whose individual operations would be too complicated to be followed4 ,by this means1 the investigation is greatly simplified4 ,on the other hand1 it is frequently very convenient to resolve a given motion into two or more others1 some of which may be thrown out of the account1 as not influencing the particular point which we are inquiring about1 while others are far more easily understood and managed than the single force would have been4 ,it is characteristic of great minds1 to simplify these inquiries4 ,they gain an insight into complicated and difficult subjects1 not so much by any extraordinary faculty of seeing in the dark1 as by the power of removing from the object all incidental causes of obscurity1 until it shines in its own clear and simple light4 ,if every force1 when applied to a body1 produces its full and legitimate effect1 how many other forces soever may act upon it1 impelling it different ways1 then it must follow1 that the smallest force ought to move the largest body2 and such is in fact the case4 ,a snap of a finger upon a seventy-four under full sail1 if applied in the direction of its motion1 would actually increase its speed1 although the effect might be too small to be visible4 ,still it is something1 and may be truly expressed by a fraction4 ,thus1 suppose a globe1 weighing a million of pounds1 were suspended from the ceiling by a string1 and we should apply to it the snap of a finger1--it is granted that the motion would be quite insensible4 ,let us then divide the body into a million equal parts1 each weighing one pound2 then the same impulse1 applied to each one separately1 would produce a sensible effect1 moving it1 say one inch4 ,it will be found1 on trial1 that the same impulse given to a mass of two pounds will move it half an inch2 and hence it is inferred1 that1 if applied to a mass weighing a million of pounds1 it would move it the millionth part of an inch4 ,it is one of the curious results of the second law of motion1 that an unlimited number of motions may exist together in the same body4 ,thus1 at the same moment1 we may be walking around a post in the cabin of a steam-boat1 accompanying the boat in its passage around an island1 revolving with the earth on its axis1 flying through space in our annual circuit around the sun1 and possibly wheeling1 along with the sun and his whole retinue of planets1 around some centre in common with the starry worlds4 ,the ,,third ,,law of motion is this3 action and reaction are equal1 and in contrary directions4 ,whenever ,i give a blow1 the body struck exerts an equal force on the striking body4 ,if ,i strike the water with an oar1 the water communicates an equal impulse to the oar1 which1 being communicated to the boat1 drives it forward in the opposite direction4 ,if a magnet attracts a piece of iron1 the iron attracts the magnet just as much1 in the opposite direction2 and1 in short1 every portion of matter in the universe attracts and is attracted by every other1 equally1 in an opposite direction4 ,this brings us to the doctrine of universal gravitation1 which is the very key that unlocks all the secrets of the skies4 ,this will form the subject of my next ,letter4 ,,footnote3 #g ,a tangent is a straight line touching a circle1 as ,a ,d1 in ,fig4 #bh ,,letter ,,xiii4 ,,terrestrial ,,gravity4 ,to ,him no high1 no low1 no great1 no small1 ,he fills1 ,he bounds1 connects1 and equals all4--,pope4 ,,we discover in ,nature a tendency of every portion of matter towards every other4 ,this tendency is called gravitation4 ,in obedience to this power1 a stone falls to the ground1 and a planet revolves around the sun4 ,we may contemplate this subject as it relates either to phenomena that take place near the surface of the earth1 or in the celestial regions4 ,the former1 gravity1 is exemplified by falling bodies2 the latter1 universal gravitation1 by the motions of the heavenly bodies4 ,the laws of terrestrial gravity were first investigated by ,galileo2 those of universal gravitation1 by ,sir ,isaac ,newton4 ,terrestrial gravity is only an individual example of universal gravitation2 being the tendency of bodies towards the centre of the earth4 ,we are so much accustomed1 from our earliest years1 to see bodies fall to the earth1 that we imagine bodies must of necessity fall downwards2 but when we reflect that the earth is round1 and that bodies fall towards the centre on all sides of it1 and that of course bodies on opposite sides of the earth fall in precisely opposite directions1 and towards each other1 we perceive that there must be some force acting to produce this effect2 nor is it enough to say1 as the ancients did1 that bodies naturally fall to the earth4 ,every motion implies some force which produces it2 and the fact that bodies fall towards the earth1 on all sides of it1 leads us to infer that that force1 whatever it is1 resides in the earth itself4 ,we therefore call it attraction4 ,we do not1 however1 say what attraction is1 but what it does4 ,we must bear in mind1 also1 that1 according to the third law of motion1 this attraction is mutual2 that when a stone falls towards the earth1 it exerts the same force on the earth that the earth exerts on the stone2 but the motion of the earth towards the stone is as much less than that of the stone towards the earth1 as its quantity of matter is greater2 and therefore its motion is quite insensible4 ,but although we are compelled to acknowledge the existence of such a force as gravity1 causing a tendency in all bodies towards each other1 yet we know nothing of its nature1 nor can we conceive by what medium bodies at such a distance as the moon and the earth exercise this influence on each other4 ,still1 we may trace the modes in which this force acts2 that is1 its laws2 for the laws of ,nature are nothing else than the modes in which the powers of ,nature act4 ,we owe chiefly to the great ,galileo the first investigation of the laws of terrestrial gravity1 as exemplified in falling bodies2 and ,i will avail myself of this opportunity to make you better acquainted with one of the most interesting of men and greatest of philosophers4 ,galileo was born at ,pisa1 in ,italy1 in the year #aefd4 ,he was the son of a ,florentine nobleman1 and was destined by his father for the medical profession1 and to this his earlier studies were devoted4 ,but a fondness and a genius for mechanical inventions had developed itself1 at a very early age1 in the construction of his toys1 and a love of drawing2 and as he grew older1 a passion for mathematics1 and for experimental research1 predominated over his zeal for the study of medicine1 and he fortunately abandoned that for the more congenial pursuits of natural philosophy and astronomy4 ,in the twenty-fifth year of his age1 he was appointed1 by the ,grand ,duke of ,tuscany1 professor of mathematics in the ,university of ,pisa4 ,at that period1 there prevailed in all the schools a most extraordinary reverence for the writings of ,aristotle1 the preceptor of ,alexander the ,great1--a philosopher who flourished in ,greece1 about three hundred years before the ,christian era4 ,aristotle1 by his great genius and learning1 gained a wonderful ascendency over the minds of men1 and became the oracle of the whole reading world for twenty centuries4 ,it was held1 on the one hand1 that all truths worth knowing were contained in the writings of ,aristotle2 and1 on the other1 that an assertion which contradicted any thing in ,aristotle could not be true4 ,but ,galileo had a greatness of mind which soared above the prejudices of the age in which he lived1 and dared to interrogate ,nature by the two great and only successful methods of discovering her secrets1--experiment and observation4 ,galileo was indeed the first philosopher that ever fully employed experiments as the means of learning the laws of ,nature1 by imitating on a small what she performs on a great scale1 and thus detecting her modes of operation4 ,archimedes1 the great ,sicilian philosopher1 had in ancient times introduced mathematical or geometrical reasoning into natural philosophy2 but it was reserved for ,galileo to unite the advantages of both mathematical and experimental reasonings in the study of ,nature1--both sure and the only sure guides to truth1 in this department of knowledge1 at least4 ,experiment and observation furnish materials upon which geometry builds her reasonings1 and from which she derives many truths that either lie for ever hidden from the eye of observation1 or which it would require ages to unfold4 ,this method1 of interrogating ,nature by experiment and observation1 was matured into a system by ,lord ,bacon1 a celebrated ,english philosopher1 early in the seventeenth century1--indeed1 during the life of ,galileo4 ,previous to that time1 the inquirers into ,nature did not open their eyes to see how the facts really are2 but1 by metaphysical processes1 in imitation of ,aristotle1 determined how they ought to be1 and hastily concluded that they were so4 ,thus1 they did not study into the laws of motion1 by observing how motion actually takes place1 under various circumstances1 but first1 in their closets1 constructed a definition of motion1 and thence inferred all its properties4 ,the system of reasoning respecting the phenomena of ,nature1 introduced by ,lord ,bacon1 was this3 in the first place1 to examine all the facts of the case1 and then from these to determine the laws of ,nature4 ,to derive general conclusions from the comparison of a great number of individual instances constitutes the peculiarity of the ,baconian philosophy4 ,it is called the inductive system1 because its conclusions were built on the induction1 or comparison1 of a great many single facts4 ,previous to the time of ,lord ,bacon1 hardly any insight had been gained into the causes of natural phenomena1 and hardly one of the laws of ,nature had been clearly established1 because all the inquirers into ,nature were upon a wrong road1 groping their way through the labyrinth of error4 ,bacon pointed out to them the true path1 and held before them the torch-light of experiment and observation1 under whose guidance all successful students of ,nature have since walked1 and by whose illumination they have gained so wonderful an insight into the mysteries of the natural world4 ,it is a remarkable fact1 that two such characters as ,bacon and ,galileo should appear on the stage at the same time1 who1 without any communication with each other1 or perhaps without any personal knowledge of each other's existence1 should have each developed the true method of investigating the laws of ,nature4 ,galileo practised what ,bacon only taught2 and some1 therefore1 with much reason1 consider ,galileo as a greater philosopher than ,bacon4 ,bacon1 says ,hume1 pointed out1 at a great distance1 the road to philosophy2 ,galileo both pointed it out to others1 and made1 himself1 considerable advances in it4 ,the ,englishman was ignorant of geometry2 the ,florentine revived that science1 excelled in it1 and was the first who applied it1 together with experiment1 to natural philosophy4 ,the former rejected1 with the most positive disdain1 the system of ,copernicus2 the latter fortified it with new proofs1 derived both from reason and the senses4 ,when we reflect that geometry is a science built upon self-evident truths1 and that all its conclusions are the result of pure demonstration1 and can admit of no controversy2 when we further reflect1 that experimental evidence rests on the testimony of the senses1 and we infer a thing to be true because we actually see it to be so2 it shows us the extreme bigotry1 the darkness visible1 that beclouded the human intellect1 when it not only refused to admit conclusions first established by pure geometrical reasoning1 and afterwards confirmed by experiments exhibited in the light of day1 but instituted the most cruel persecutions against the great philosopher who first proclaimed these truths4 ,galileo was hated and persecuted by two distinct bodies of men1 both possessing great influence in their respective spheres1--the one consisting of the learned doctors of philosophy1 who did nothing more1 from age to age1 than reiterate the doctrines of ,aristotle1 and were consequently alarmed at the promulgation of principles subversive of those doctrines2 the other consisting of the ,romish priesthood1 comprising the terrible ,inquisition1 who denounced the truths taught by ,galileo1 as inconsistent with certain declarations of the ,holy ,scriptures4 ,we shall see1 as we advance1 what a fearful warfare he had to wage against these combined powers of darkness4 ,aristotle had asserted1 that1 if two different weights of the same material were let fall from the same height1 the heavier one would reach the ground sooner than the other1 in proportion as it was more weighty4 ,for example3 if a ten-pound leaden weight and a one-pound were let fall from a given height at the same instant1 the former would reach the ground ten times as soon as the latter4 ,no one thought of making the trial1 but it was deemed sufficient that ,aristotle had said so2 and accordingly this assertion had long been received as an axiom in the science of motion4 ,galileo ventured to appeal from the authority of ,aristotle to that of his own senses1 and maintained1 that both weights would fall in the same time4 ,the learned doctors ridiculed the idea4 ,galileo tried the experiment in their presence1 by letting fall1 at the same instant1 large and small weights from the top of the celebrated leaning tower of ,pisa4 ,yet1 with the sound of the two weights clicking upon the pavement at the same moment1 they still maintained that the ten-pound weight would reach the ground in one tenth part of the time of the other1 because they could quote the chapter and verse of ,aristotle where the fact was asserted4 ,wearied and disgusted with the malice and folly of these ,aristotelian philosophers1 ,galileo1 at the age of twenty-eight1 resigned his situation in the university of ,pisa1 and removed to ,padua1 in the university of which place he was elected professor of mathematics4 ,up to this period1 ,galileo had devoted himself chiefly to the studies of the laws of motion1 and the other branches of mechanical philosophy4 ,soon afterwards1 he began to publish his writings1 in rapid succession1 and became at once among the most conspicuous of his age1--a rank which he afterwards well sustained and greatly exalted1 by the invention of the telescope1 and by his numerous astronomical discoveries4 ,i will reserve an account of these great achievements until we come to that part of astronomy to which they were more immediately related1 and proceed1 now1 to explain to you the leading principles of terrestrial gravity1 as exemplified in falling bodies4 ,first1 all bodies near the earth's surface fall in straight lines towards the centre of the earth4 ,we are not to infer from this fact1 that there resides at the centre any peculiar force1 as a great loadstone1 for example1 which attracts bodies towards itself2 but bodies fall towards the centre of the sphere1 because the combined attractions of all the particles of matter in the earth1 each exerting its proper force upon the body1 would carry it towards the centre4 ,this may be easily illustrated by a diagram4 ,let ,b1 ,fig4 #bi1 page #adj1 be the centre of the earth1 and ,a a body without it4 ,every portion of matter in the earth exerts some force on ,a1 to draw it down to the earth4 ,but since there is just as much matter on one side of the line ,a ,b1 as on the other side1 each half exerts an equal force to draw the body towards itself2 therefore it falls in the direction of the diagonal between the two forces4 ,thus1 if we compare the effects of any two particles of matter at equal distances from the line ,a ,b1 but on opposite sides of it1 as a1 b1 while the force of the particle at a would tend to draw ,a in the direction of ,a a1 that of b would draw it in the direction of ,a b1 and it would fall in the line ,a ,b1 half way between the two4 ,the same would hold true of any other two corresponding particles of matter on different sides of the earth1 in respect to a body situated in any place without it4 ,illustration ,fig4 #bi4 ,secondly1 all bodies fall towards the earth1 from the same height1 with equal velocities4 ,a musket-ball1 and the finest particle of down1 if let fall from a certain height towards the earth1 tend to descend towards it at the same rate1 and would proceed with equal speed1 were it not for the resistance of the air1 which retards the down more than it does the ball1 and finally stops it4 ,if1 however1 the air be removed out of the way1 as it may be by means of the air-pump1 the two bodies keep side by side in falling from the greatest height at which we can try the experiment4 ,thirdly1 bodies1 in falling towards the earth1 have their rate of motion continually accelerated4 ,suppose we let fall a musket-ball from the top of a high tower1 and watch its progress1 disregarding the resistance of the air3 the first second1 it will pass over sixteen feet and one inch1 but its speed will be constantly increased1 being all the while urged onward by the same force1 and retaining all that it has already acquired2 so that the longer it is in falling1 the swifter its motion becomes4 ,consequently1 when bodies fall from a great height1 they acquire an immense velocity before they reach the earth4 ,thus1 a man falling from a balloon1 or from the mast-head of a ship1 is broken in pieces2 and those meteoric stones1 which sometimes fall from the sky1 bury themselves deep in the earth4 ,on measuring the spaces through which a body falls1 it is found1 that it will fall four times as far in two seconds as in one1 and one hundred times as far in ten seconds as in one2 and universally1 the space described by a falling body is proportioned to the time multiplied into itself2 that is1 to the square of the time4 ,fourthly1 gravity is proportioned to the quantity of matter4 ,a body which has twice as much matter as another exerts a force of attraction twice as great1 and also receives twice as much from the same body as it would do1 if it were only just as heavy as that body4 ,thus the earth1 containing1 as it does1 forty times as much matter as the moon1 exerts upon the moon forty times as much force as it would do1 were its mass the same with that of the moon2 but it is also capable of receiving forty times as much gravity from the moon as it would do1 were its mass the same as the moon's2 so that the power of attracting and that of being attracted are reciprocal2 and it is therefore correct to say1 that the moon attracts the earth just as much as the earth attracts the moon2 and the same may be said of any two bodies1 however different in quantity of matter4 ,fifthly1 gravity1 when acting at a distance from the earth1 is not as intense as it is near the earth4 ,at such a distance as we are accustomed to ascend above the general level of the earth1 no great difference is observed4 ,on the tops of high mountains1 we find bodies falling towards the earth1 with nearly the same speed as they do from the smallest elevations4 ,it is found1 nevertheless1 that there is a real difference2 so that1 in fact1 the weight of a body 7which is nothing more than the measure of its force of gravity7 is not quite so great on the tops of high mountains as at the general level of the sea4 ,thus1 a thousand pounds' weight1 on the top of a mountain half a mile high1 would weigh a quarter of a pound less than at the level of the sea2 and if elevated four thousand miles above the earth1--that is1 twice as far from the centre of the earth as the surface is from the centre1--it would weigh only one fourth as much as before2 if three times as far1 it would weigh only one ninth as much4 ,so that the force of gravity decreases1 as we recede from the earth1 in the same proportion as the square of the distance increases4 ,this fact is generalized by saying1 that the force of gravity1 at different distances from the earth1 is inversely as the square of the distance4 ,were a body to fall from a great distance1--suppose a thousand times that of the radius of the earth1--the force of gravity being one million times less than that at the surface of the earth1 the motion of the body would be exceedingly slow1 carrying it over only the sixth part of an inch in a day4 ,it would be a long time1 therefore1 in making any sensible approaches towards the earth2 but at length1 as it drew near to the earth it would acquire a very great velocity1 and would finally rush towards it with prodigious violence4 ,falling so far1 and being continually accelerated on the way1 we might suppose that it would at length attain a velocity infinitely great2 but it can be demonstrated1 that1 if a body were to fall from an infinite distance1 attracted to the earth only by gravity1 it could never acquire a velocity greater than about seven miles per second4 ,this1 however1 is a speed inconceivably great1 being about eighteen times the greatest velocity that can be given to a cannon-ball1 and more than twenty-five thousand miles per hour4 ,but the phenomena of falling bodies must have long been observed1 and their laws had been fully investigated by ,galileo and others1 before the cause of their falling was understood1 or any such principle as gravity1 inherent in the earth and in all bodies1 was applied to them4 ,the developement of this great principle was the work of ,sir ,isaac ,newton2 and ,i will give you1 in my next ,letter1 some particulars respecting the life and discoveries of this wonderful man4 ,,letter ,,xiv4 ,,sir ,,isaac ,,newton4--,,universal ,,gravitation4--,,figure ,,of ,,the ,,earth',s ,,orbit4--,,precession ,,of ,,the ,,equinoxes4 ,the heavens are all his own2 from the wild rule ,of whirling vortices1 and circling spheres1 ,to their first great simplicity restored4 ,the schools astonished stood2 but found it vain ,to combat long with demonstration clear1 ,and1 unawakened1 dream beneath the blaze ,of truth4 ,at once their pleasing visions fled1 ,with the light shadows of the morning mixed1 ,when ,newton rose1 our philosophic sun4--,thomson's ,elegy4 ,,sir ,,isaac ,,newton was born in ,lincolnshire1 ,england1 in #afdb1 just one year after the death of ,galileo4 ,his father died before he was born1 and he was a helpless infant1 of a diminutive size1 and so feeble a frame1 that his attendants hardly expected his life for a single hour4 ,the family dwelling was of humble architecture1 situated in a retired but beautiful valley1 and was surrounded by a small farm1 which afforded but a scanty living to the widowed mother and her precious charge4 ,the cut on page #add1 ,fig #cj1 represents the modest mansion1 and the emblems of rustic life that first met the eyes of this pride of the ,british nation1 and ornament of human nature4 ,it will probably be found1 that genius has oftener emanated from the cottage than from the palace4 ,illustration ,fig4 #cj4 ,the boyhood of ,newton was distinguished chiefly for his ingenious mechanical contrivances4 ,among other pieces of mechanism1 he constructed a windmill so curious and complete in its workmanship1 as to excite universal admiration4 ,after carrying it a while by the force of the wind1 he resolved to substitute animal power1 and for this purpose he inclosed in it a mouse1 which he called the miller1 and which kept the mill a-going by acting on a tread-wheel4 ,the power of the mouse was brought into action by unavailing attempts to reach a portion of corn placed above the wheel4 ,a water-clock1 a four-wheeled carriage propelled by the rider himself1 and kites of superior workmanship1 were among the productions of the mechanical genius of this gifted boy4 ,at a little later period1 he began to turn his attention to the motions of the heavenly bodies1 and constructed several sun-dials on the walls of the house where he lived4 ,all this was before he had reached his fifteenth year4 ,at this age1 he was sent by his mother1 in company with an old family servant1 to a neighboring market-town1 to dispose of products of their farm1 and to buy articles of merchandise for their family use2 but the young philosopher left all these negotiations to his worthy partner1 occupying himself1 mean-while1 with a collection of old books1 which he had found in a garret4 ,at other times1 he stopped on the road1 and took shelter with his book under a hedge1 until the servant returned4 ,they endeavored to educate him as a farmer2 but the perusal of a book1 the construction of a water-mill1 or some other mechanical or scientific amusement1 absorbed all his thoughts1 when the sheep were going astray1 and the cattle were devouring or treading down the corn4 ,one of his uncles having found him one day under a hedge1 with a book in his hand1 and entirely absorbed in meditation1 took it from him1 and found that it was a mathematical problem which so engrossed his attention4 ,his friends1 therefore1 wisely resolved to favor the bent of his genius1 and removed him from the farm to the school1 to prepare for the university4 ,in the eighteenth year of his age1 ,newton was admitted into ,trinity ,college1 ,cambridge4 ,he made rapid and extraordinary advances in the mathematics1 and soon afforded unequivocal presages of that greatness which afterwards placed him at the head of the human intellect4 ,in #affi1 at the age of twenty-seven1 he became professor of mathematics at ,cambridge1 a post which he occupied for many years afterwards4 ,during the four or five years previous to this he had1 in fact1 made most of those great discoveries which have immortalized his name4 ,we are at present chiefly interested in one of these1 namely1 that of universal gravitation2 and let us see by what steps he was conducted to this greatest of scientific discoveries4 ,in the year #afff1 when ,newton was about twenty-four years of age1 the plague was prevailing at ,cambridge1 and he retired into the country4 ,one day1 while he sat in a garden1 musing on the phenomena of ,nature around him1 an apple chanced to fall to the ground4 ,reflecting on the mysterious power that makes all bodies near the earth fall towards its centre1 and considering that this power remains unimpaired at considerable heights above the earth1 as on the tops of trees and mountains1 he asked himself1--,may not the same force extend its influence to a great distance from the earth1 even as far as the moon8 ,indeed1 may not this be the very reason1 why the moon is drawn away continually from the straight line in which every body tends to move1 and is thus made to circulate around the earth8 ,you will recollect that it was mentioned1 in my ,letter which contained an account of the first law of motion1 that if a body is put in motion by any force1 it will always move forward in a straight line1 unless some other force compels it to turn aside from such a direction2 and that1 when we see a body moving in a curve1 as a circular orbit1 we are authorized to conclude that there is some force existing within the circle1 which continually draws the body away from the direction in which it tends to move4 ,accordingly1 it was a very natural suggestion1 to one so well acquainted with the laws of motion as ,newton1 that the moon should constantly bend towards the earth1 from a tendency to fall towards it1 as any other heavy body would do1 if carried to such a distance from the earth4 ,newton had already proved1 that if such a power as gravity extends from the earth to distant bodies1 it must decrease1 as the square of the distance from the centre of the earth increases2 that is1 at double the distance1 it would be four times less2 at ten times the distance1 one hundred times less2 and so on4 ,now1 it was known that the moon is about sixty times as far from the centre of the earth as the surface of the earth is from the centre1 and consequently1 the force of attraction at the moon must be the square of sixty1 or thirty-six hundred times less than it is at the earth2 so that a body at the distance of the moon would fall towards the earth very slowly1 only one thirty-six hundredth part as far in a given time1 as at the earth4 ,does the moon actually fall towards the earth at this rate2 or1 what is the same thing1 does she depart at this rate continually from the straight line in which she tends to move1 and in which she would move1 if no external force diverted her from it8 ,on making the calculation1 such was found to be the fact4 ,hence gravity1 and no other force than gravity1 acts upon the moon1 and compels her to revolve around the earth4 ,by reasonings equally conclusive1 it was afterwards proved1 that a similar force compels all the planets to circulate around the sun2 and now1 we may ascend from the contemplation of this force1 as we have seen it exemplified in falling bodies1 to that of a universal power whose influence extends to all the material creation4 ,it is in this sense that we recognise the principle of universal gravitation1 the law of which may be thus enunciated2 all bodies in the universe1 whether great or small1 attract each other1 with forces proportioned to their respective quantities of matter1 and inversely as the squares of their distances from each other4 ,this law asserts1 first1 that attraction reigns throughout the material world1 affecting alike the smallest particle of matter and the greatest body2 secondly1 that it acts upon every mass of matter1 precisely in proportion to its quantity2 and1 thirdly1 that its intensity is diminished as the square of the distance is increased4 ,observation has fully confirmed the prevalence of this law throughout the solar system2 and recent discoveries among the fixed stars1 to be more fully detailed hereafter1 indicate that the same law prevails there4 ,the law of universal gravitation is therefore held to be the grand principle which governs all the celestial motions4 ,not only is it consistent with all the observed motions of the heavenly bodies1 even the most irregular of those motions1 but1 when followed out into all its consequences1 it would be competent to assert that such irregularities must take place1 even if they had never been observed4 ,newton first published the doctrine of universal gravitation in the ',principia1' in #afhg4 ,the name implies that the work contains the fundamental principles of natural philosophy and astronomy4 ,being founded upon the immutable basis of mathematics1 its conclusions must of course be true and unalterable1 and thenceforth we may regard the great laws of the universe as traced to their remotest principle4 ,the greatest astronomers and mathematicians have since occupied themselves in following out the plan which ,newton began1 by applying the principles of universal gravitation to all the subordinate as well as to the grand movements of the spheres4 ,this great labor has been especially achieved by ,la ,place1 a ,french mathematician of the highest eminence1 in his profound work1 the ',mecanique ,celeste4' ,of this work1 our distinguished countryman1 ,dr4 ,bowditch1 has given a magnificent translation1 and accompanied it with a commentary1 which both illustrates the original1 and adds a great amount of matter hardly less profound than that4 ,illustration ,fig4 #ca4 ,we have thus far taken the earth's orbit around the sun as a great circle1 such being its projection on the sphere constituting the celestial ecliptic4 ,the real path of the earth around the sun is learned1 as ,i before explained to you1 by the apparent path of the sun around the earth once a year4 ,now1 when a body revolves about the earth at a great distance from us1 as is the case with the sun and moon1 we cannot certainly infer that it moves in a circle because it appears to describe a circle on the face of the sky1 for such might be the appearance of its orbit1 were it ever so irregular a curve4 ,thus1 if ,e1 ,fig4 #ca1 represents the earth1 and ,,acb1 the irregular path of a body revolving about it1 since we should refer the body continually to some place on the celestial sphere1 ,,xyz1 determined by lines drawn from the eye to the concave sphere through the body1 the body1 while moving from ,a to ,b through ,c1 would appear to move from ,x to ,z1 through ,y4 ,hence1 we must determine from other circumstances than the actual appearance1 what is the true figure of the orbit4 ,illustration ,fig4 #cb4 ,were the earth's path a circle1 having the sun in the centre1 the sun would always appear to be at the same distance from us2 that is1 the radius of the orbit1 or radius vector1 7the name given to a line drawn from the centre of the sun to the orbit of any planet17 would always be of the same length4 ,but the earth's distance from the sun is constantly varying1 which shows that its orbit is not a circle4 ,we learn the true figure of the orbit1 by ascertaining the relative distances of the earth from the sun1 at various periods of the year4 ,these distances all being laid down in a diagram1 according to their respective lengths1 the extremities1 on being connected1 give us our first idea of the shape of the orbit1 which appears of an oval form1 and at least resembles an ellipse2 and1 on further trial1 we find that it has the properties of an ellipse4 ,thus1 let ,e1 ,fig4 #cb1 be the place of the earth1 and a1 b1 c1 c41 successive positions of the sun2 the relative lengths of the lines ,e a1 ,e b1 c41 being known1 on connecting the points a1 b1 c1 c41 the resulting figure indicates the true figure of the earth's orbit4 ,these relative distances are found in two different ways2 first1 by changes in the sun's apparent diameter1 and1 secondly1 by variations in his angular velocity4 ,the same object appears to us smaller in proportion as it is more distant2 and if we see a heavenly body varying in size1 at different times1 we infer that it is at different distances from us2 that when largest1 it is nearest to us1 and when smallest1 furthest off4 ,now1 when the sun's diameter is accurately measured by instruments1 it is found to vary from day to day2 being1 when greatest1 more than thirty-two minutes and a half1 and when smallest1 only thirty-one minutes and a half1--differing1 in all1 about seventy-five seconds4 ,when the diameter is greatest1 which happens in ,january1 we know that the sun is nearest to us2 and when the diameter is least1 which occurs in ,july1 we infer that the sun is at the greatest distance from us4 ,the point where the earth1 or any planet1 in its revolution1 is nearest the sun1 is called its perihelion2 the point where it is furthest from the sun1 its aphelion4 ,suppose1 then1 that1 about the first of ,january1 when the diameter of the sun is greatest1 we draw a line1 ,e a1 ,fig4 #cb1 to represent it1 and afterwards1 every ten days1 draw other lines1 ,e b1 ,e c1 c42 increasing in the same ratio as the apparent diameters of the sun decrease4 ,these lines must be drawn at such a distance from each other1 that the triangles1 ,e a b1 ,e b c1 c41 shall be all equal to each other1 for a reason that will be explained hereafter4 ,on connecting the extremities of these lines1 we shall obtain the figure of the earth's orbit4 ,similar conclusions may be drawn from observations on the sun's angular velocity4 ,a body appears to move most rapidly when nearest to us4 ,indeed1 the apparent velocity increases rapidly1 as it approaches us1 and as rapidly diminishes1 when it recedes from us4 ,if it comes twice as near as before1 it appears to move not merely twice as swiftly1 but four times as swiftly2 if it comes ten times nearer1 its apparent velocity is one hundred times as great as before4 ,we say1 therefore1 that the velocity varies inversely as the square of the distance2 for1 as the distance is diminished ten times1 the velocity is increased the square of ten2 that is1 one hundred times4 ,now1 by noting the time it takes the sun1 from day to day1 to cross the central wire of the transit-instrument1 we learn the comparative velocities with which it moves at different times2 and from these we derive the comparative distances of the sun at the corresponding times2 and laying down these relative distances in a diagram1 as before1 we get our first notions of the actual figure of the earth's orbit1 or the path which it describes in its annual revolution around the sun4 ,having now learned the fact1 that the earth moves around the sun1 not in a circular but in an elliptical orbit1 you will desire to know by what forces it is impelled1 to make it describe this figure1 with such uniformity and constancy1 from age to age4 ,it is commonly said1 that gravity causes the earth and the planets to circulate around the sun2 and it is true that it is gravity which turns them aside from the straight line in which1 by the first law of motion1 they tend to move1 and thus causes them to revolve around the sun4 ,but what force is that which gave to them this original impulse1 and impressed upon them such a tendency to move forward in a straight line8 ,the name projectile force is given to it1 because it is the same as though the earth were originally projected into space1 when first created2 and therefore its motion is the result of two forces1 the projectile force1 which would cause it to move forward in a straight line which is a tangent to its orbit1 and gravitation1 which bends it towards the sun4 ,but before you can clearly understand the nature of this motion1 and the action of the two forces that produce it1 ,i must explain to you a few elementary principles upon which this and all the other planetary motions depend4 ,you have already learned1 that when a body is acted on by two forces1 in different directions1 it moves in the direction of neither1 but in some direction between them4 ,if ,i throw a stone horizontally1 the attraction of the earth will continually draw it downward1 out of the line of direction in which it was thrown1 and make it descend to the earth in a curve4 ,the particular form of the curve will depend on the velocity with which it is thrown4 ,it will always begin to move in the line of direction in which it is projected2 but it will soon be turned from that line towards the earth4 ,it will1 however1 continue nearer to the line of projection in proportion as the velocity of projection is greater4 ,thus1 let ,a ,c1 ,fig4 #cc1 be perpendicular to the horizon1 and ,a ,b parallel to it1 and let a stone be thrown from ,a1 in the direction of ,a ,b4 ,it will1 in every case1 commence its motion in the line ,a ,b1 which will therefore be a tangent to the curve it describes2 but1 if it is thrown with a small velocity1 it will soon depart from the tangent1 describing the line ,a ,d2 with a greater velocity1 it will describe a curve nearer the tangent1 as ,a ,e2 and with a still greater velocity1 it will describe the curve ,a ,f4 ,illustration ,fig4 #cc4 ,as an example of a body revolving in an orbit under the influence of two forces1 suppose a body placed at any point1 ,p1 ,fig4 #cd1 above the surface of the earth1 and let ,p ,a be the direction of the earth's centre2 that is1 a line perpendicular to the horizon4 ,if the body were allowed to move1 without receiving any impulse1 it would descend to the earth in the direction ,p ,a with an accelerated motion4 ,but suppose that1 at the moment of its departure from ,p1 it receives a blow in the direction ,p ,b1 which would carry it to ,b in the time the body would fall from ,p to ,a2 then1 under the influence of both forces1 it would descend along the curve ,p ,d4 ,if a stronger blow were given to it in the direction ,p ,b1 it would describe a larger curve1 ,p ,e2 or1 finally1 if the impulse were sufficiently strong1 it would circulate quite around the earth1 and return again to ,p1 describing the circle ,p ,f ,g4 ,with a velocity of projection still greater1 it would describe an ellipse1 ,p ,i ,k2 and if the velocity be increased to a certain degree1 the figure becomes a parabola1 ,l ,p ,m1--a curve which never returns into itself4 ,illustration ,fig4 #cd4 ,in ,fig4 #ce1 page #aed1 suppose the planet to have passed the point ,c1 at the aphelion1 with so small a velocity1 that the attraction of the sun bends its path very much1 and causes it immediately to begin to approach towards the sun4 ,the sun's attraction will increase its velocity1 as it moves through ,d1 ,e1 and ,f1 for the sun's attractive force on the planet1 when at ,d1 is acting in the direction ,d ,s2 and1 on account of the small angle made between ,d ,e and ,d ,s1 the force acting in the line ,d ,s helps the planet forward in the path ,d ,e1 and thus increases its velocity4 ,in like manner1 the velocity of the planet will be continually increasing as it passes through ,d1 ,e1 and ,f2 and though the attractive force1 on account of the planet's nearness1 is so much increased1 and tends1 therefore1 to make the orbit more curved1 yet the velocity is also so much increased1 that the orbit is not more curved than before2 for the same increase of velocity1 occasioned by the planet's approach to the sun1 produces a greater increase of centrifugal force1 which carries it off again4 ,we may see1 also1 the reason why1 when the planet has reached the most distant parts of its orbit1 it does not entirely fly off1 and never return to the sun2 for1 when the planet passes along ,h1 ,k1 ,a1 the sun's attraction retards the planet1 just as gravity retards a ball rolled up hill2 and when it has reached ,c1 its velocity is very small1 and the attraction to the centre of force causes a great deflection from the tangent1 sufficient to give its orbit a great curvature1 and the planet wheels about1 returns to the sun1 and goes over the same orbit again4 ,as the planet recedes from the sun1 its centrifugal force diminishes faster than the force of gravity1 so that the latter finally preponderates4 ,illustration ,fig4 #ce4 ,i shall conclude what ,i have to say at present1 respecting the motion of the earth around the sun1 by adding a few words respecting the precession of the equinoxes4 ,the precession of the equinoxes is a slow but continual shifting of the equinoctial points1 from east to west4 ,suppose that we mark the exact place in the heavens where1 during the present year1 the sun crosses the equator1 and that this point is close to a certain star2 next year1 the sun will cross the equator a little way westward of that star1 and so every year1 a little further westward1 until1 in a long course of ages1 the place of the equinox will occupy successively every part of the ecliptic1 until we come round to the same star again4 ,as1 therefore1 the sun revolving from west to east1 in his apparent orbit1 comes round to the point where it left the equinox1 it meets the equinox before it reaches that point4 ,the appearance is as though the equinox goes forward to meet the sun1 and hence the phenomenon is called the precession of the equinoxes2 and the fact is expressed by saying1 that the equinoxes retrograde on the ecliptic1 until the line of the equinoxes 7a straight line drawn from one equinox to the other7 makes a complete revolution1 from east to west4 ,this is of course a retrograde motion1 since it is contrary to the order of the signs4 ,the equator is conceived as sliding westward on the ecliptic1 always preserving the same inclination to it1 as a ring1 placed at a small angle with another of nearly the same size which remains fixed1 may be slid quite around it1 giving a corresponding motion to the two points of intersection4 ,it must be observed1 however1 that this mode of conceiving of the precession of the equinoxes is purely imaginary1 and is employed merely for the convenience of representation4 ,the amount of precession annually is fifty seconds and one tenth2 whence1 since there are thirty-six hundred seconds in a degree1 and three hundred and sixty degrees in the whole circumference of the ecliptic1 and consequently one million two hundred and ninety-six thousand seconds1 this sum1 divided by fifty seconds and one tenth1 gives twenty-five thousand eight hundred and sixty-eight years for the period of a complete revolution of the equinoxes4 ,suppose we now fix to the centre of each of the two rings1 before mentioned1 a wire representing its axis1 one corresponding to the axis of the ecliptic1 the other to that of the equator1 the extremity of each being the pole of its circle4 ,as the ring denoting the equator turns round on the ecliptic1 which1 with its axis1 remains fixed1 it is easy to conceive that the axis of the equator revolves around that of the ecliptic1 and the pole of the equator around the pole of the ecliptic1 and constantly at a distance equal to the inclination of the two circles4 ,to transfer our conceptions to the celestial sphere1 we may easily see that the axis of the diurnal sphere 7that of the earth produced7 would not have its pole constantly in the same place among the stars1 but that this pole would perform a slow revolution around the pole of the ecliptic1 from east to west1 completing the circuit in about twenty-six thousand years4 ,hence the star which we now call the pole-star has not always enjoyed that distinction1 nor will it always enjoy it1 hereafter4 ,when the earliest catalogues of the stars were made1 this star was twelve degrees from the pole4 ,it is now one degree twenty-four minutes1 and will approach still nearer2 or1 to speak more accurately1 the pole will come still nearer to this star1 after which it will leave it1 and successively pass by others4 ,in about thirteen thousand years1 the bright star ,lyra 7which lies near the circle in which the pole of the equator revolves about the pole of the ecliptic1 on the side opposite to the present pole-star7 will be within five degrees of the pole1 and will constitute the pole-star4 ,as ,lyra now passes near our zenith1 you might suppose that the change of position of the pole among the stars would be attended with a change of altitude of the north pole above the horizon4 ,this mistaken idea is one of the many misapprehensions which result from the habit of considering the horizon as a fixed circle in space4 ,however the pole might shift its position in space1 we should still be at the same distance from it1 and our horizon would always reach the same distance beyond it4 ,the time occupied by the sun1 in passing from the equinoctial point round to the same point again1 is called the tropical year4 ,as the sun does not perform a complete revolution in this interval1 but falls short of it fifty seconds and one tenth1 the tropical year is shorter than the sidereal by twenty minutes and twenty seconds1 in mean solar time1 this being the time of describing an arc of fifty seconds and one tenth1 in the annual revolution4 ,the changes produced by the precession of the equinoxes1 in the apparent places of the circumpolar stars1 have led to some interesting results in chronology4 ,in consequence of the retrograde motion of the equinoctial points1 the signs of the ecliptic do not correspond1 at present1 to the constellations which bear the same names1 but lie about one sign1 or thirty degrees1 westward of them4 ,thus1 that division of the ecliptic which is called the sign ,taurus lies in the constellation ,aries1 and the sign ,gemini1 in the constellation ,taurus4 ,undoubtedly1 however1 when the ecliptic was thus first divided1 and the divisions named1 the several constellations lay in the respective divisions which bear their names4 ,,letter ,,xv4 ,,the ,,moon4 ,soon as the evening shades prevail ,the ,moon takes up the wondrous tale1 ,and nightly to the listening earth ,repeats the story of her birth4--,addison4 ,,having now learned so much of astronomy as relates to the earth and the sun1 and the mutual relations which exist between them1 you are prepared to enter with advantage upon the survey of the other bodies that compose the solar system4 ,this being done1 we shall then have still before us the boundless range of the fixed stars4 ,the moon1 which next claims our notice1 has been studied by astronomers with greater attention than any other of the heavenly bodies1 since her comparative nearness to the earth brings her peculiarly within the range of our telescopes1 and her periodical changes and very irregular motions1 afford curious subjects1 both for observation and speculation4 ,the mild light of the moon also invites our gaze1 while her varying aspects serve barbarous tribes1 especially1 for a kind of dial-plate inscribed on the face of the sky1 for weeks1 and months1 and times1 and seasons4 ,the moon is distant from the earth about two hundred and forty thousand miles2 or1 more exactly1 two hundred and thirty-eight thousand five hundred and forty-five miles4 ,her angular or apparent diameter is about half a degree1 and her real diameter1 two thousand one hundred and sixty miles4 ,she is a companion1 or satellite1 to the earth1 revolving around it every month1 and accompanying us in our annual revolution around the sun4 ,although her nearness to us makes her appear as a large and conspicuous object in the heavens1 yet1 in comparison with most of the other celestial bodies1 she is in fact very small1 being only one forty-ninth part as large as the earth1 and only about one seventy millionth part as large as the sun4 ,the moon shines by light borrowed from the sun1 being itself an opaque body1 like the earth4 ,when the disk1 or any portion of it1 is illuminated1 we can plainly discern1 even with the naked eye1 varieties of light and shade1 indicating inequalities of surface which we imagine to be land and water4 ,i believe it is the common impression1 that the darker portions are land and the lighter portions water2 but if either part is water1 it must be the darker regions4 ,a smooth polished surface1 like water1 would reflect the sun's light like a mirror4 ,it would1 like a convex mirror1 form a diminished image of the sun1 but would not itself appear luminous like an uneven surface1 which multiplies the light by numerous reflections within itself4 ,thus1 from this cause1 high broken mountainous districts appear more luminous than extensive plains4 ,illustration ,figures #cf1 #cg4 ,,telescopic ,,views ,,of ,,the ,,moon4 ,by the aid of the telescope1 we may see undoubted indications of mountains and valleys4 ,indeed1 with a good glass1 we can discover the most decisive evidence that the surface of the moon is exceedingly varied1--one part ascending in lofty peaks1 another clustering in huge mountain groups1 or long ranges1 and another bearing all the marks of deep caverns or valleys4 ,you will not1 indeed1 at the first sight of the moon through a telescope1 recognise all these different objects4 ,if you look at the moon when half her disk is enlightened1 7which is the best time for seeing her varieties of surface17 you will1 at the first glance1 observe a motley appearance1 particularly along the line called the terminator1 which separates the enlightened from the unenlightened part of the disk4 7,fig4 #cg47 ,on one side of the terminator1 within the dark part of the disk1 you will see illuminated points1 and short1 crooked lines1 like rude characters marked with chalk on a black ground4 ,on the other side of the terminator you will see a succession of little circular groups1 appearing like numerous bubbles of oil on the surface of water4 ,the further you carry your eye from the terminator1 on the same side of it1 the more indistinctly formed these bubbles appear1 until towards the edge of the moon they assume quite a different aspect4 ,some persons1 when they look into a telescope for the first time1 having heard that mountains and valleys are to be seen1 and discovering nothing but these unmeaning figures1 break off in disappointment1 and have their faith in these things rather diminished than increased4 ,i would advise you1 therefore1 before you take even your first view of the moon through a telescope1 to form as clear an idea as you can1 how mountains1 and valleys1 and caverns1 situated at such a distance from the eye1 ought to look1 and by what marks they may be recognised4 ,seize1 if possible1 the most favorable period1 7about the time of the first quarter17 and previously learn from drawings and explanations1 how to interpret every thing you see4 ,what1 then1 ought to be the respective appearances of mountains1 valleys1 and deep craters1 or caverns1 in the moon8 ,the sun shines on the moon in the same way as it shines on the earth2 and let1 us reflect1 then1 upon the manner in which it strikes similar objects here4 ,one half the globe is constantly enlightened2 and1 by the revolution of the earth on its axis1 the terminator1 or the line which separates the enlightened from the unenlightened part of the earth1 travels along from east to west1 over different places1 as we see the moon's terminator travel over her disk from new to full moon2 although1 in the case of the earth1 the motion is more rapid1 and depends on a different cause4 ,in the morning1 the sun's light first strikes upon the tops of the mountains1 and1 if they are very high1 they may be brightly illuminated while it is yet night in the valleys below4 ,by degrees1 as the sun rises1 the circle of illumination travels down the mountain1 until at length it reaches the bottom of the valleys2 and these in turn enjoy the full light of day4 ,again1 a mountain casts a shadow opposite to the sun1 which is very long when the sun first rises1 and shortens continually as the sun ascends1 its length at a given time1 however1 being proportioned to the height of the mountain2 so that1 if the shadow be still very long when the sun is far above the horizon1 we infer that the mountain is very lofty4 ,we may1 moreover1 form some judgment of the shape of a mountain1 by observing that of its shadow4 ,now1 the moon is so distant that we could not easily distinguish places simply by their elevations1 since they would be projected into the same imaginary plane which constitutes the apparent disk of the moon2 but the foregoing considerations would enable us to infer their existence4 ,thus1 when you view the moon at any time within her first quarter1 but better near the end of that period1 you will observe1 on the side of the terminator within the dark part of the disk1 the tops of mountains which the light of the sun is just striking1 as the morning sun strikes the tops of mountains on the earth4 ,these you will recognise by those white specks and little crooked lines1 before mentioned1 as is represented in ,fig4 #cg4 ,these bright points and lines you will see altering their figure1 every hour1 as they come more and more into the sun's light2 and1 mean-while1 other bright points1 very minute at first1 will start into view1 which also in turn grow larger as the terminator approaches them1 until they fall into the enlightened part of the disk4 ,as they fall further and further within this part1 you will have additional proofs that they are mountains1 from the shadows which they cast on the plain1 always in a direction opposite to the sun4 ,the mountain itself may entirely disappear1 or become confounded with the other enlightened portions of the surface2 but its position and its shape may still be recognised by the dark line which it projects on the plane4 ,this line will correspond in shape to that of the mountain1 presenting at one time a long serpentine stripe of black1 denoting that the mountain is a continued range2 at another time exhibiting a conical figure tapering to a point1 or a series of such sharp points2 or a serrated1 uneven termination1 indicating1 in each case respectively1 a conical mountain1 or a group of peaks1 or a range with lofty cliffs4 ,all these appearances will indeed be seen in miniature2 but a little familiarity with them will enable you to give them1 in imagination1 their proper dimensions1 as you give to the pictures of known animals their due sizes1 although drawn on a scale far below that of real life4 ,in the next place1 let us see how valleys and deep craters in the moon might be expected to appear4 ,we could not expect to see depressions any more than elevations1 since both would alike be projected on the same imaginary disk4 ,but we may recognise such depressions1 from the manner in which the light of the sun shines into them4 ,when we hold a china tea-cup at some distance from a candle1 in the night1 the candle being elevated but little above the level of the top of the cup1 a luminous crescent will be formed on the side of the cup opposite to the candle1 while the side next to the candle will be covered by a deep shadow4 ,as we gradually elevate the candle1 the crescent enlarges and travels down the side of the cup1 until finally the whole interior becomes illuminated4 ,we observe similar appearances in the moon1 which we recognise as deep depressions4 ,they are those circular spots near the terminator before spoken of1 which look like bubbles of oil floating on water4 ,they are nothing else than circular craters or deep valleys4 ,when they are so situated that the light of the sun is just beginning to shine into them1 you may see1 as in the tea-cup1 a luminous crescent around the side furthest from the sun1 while a deep black shadow is cast on the side next to the sun4 ,as the cavity is turned more and more towards the light1 the crescent enlarges1 until at length the whole interior is illuminated4 ,if the tea-cup be placed on a table1 and a candle be held at some distance from it1 nearly on a level with the top1 but a little above it1 the cup itself will cast a shadow on the table1 like any other elevated object4 ,in like manner1 many of these circular spots on the moon cast deep shadows behind them1 indicating that the tops of the craters are elevated far above the general level of the moon4 ,the regularity of some of these circular spots is very remarkable4 ,the circle1 in some instances1 appears as well formed as could be described by a pair of compasses1 while in the centre there not unfrequently is seen a conical mountain casting its pointed shadow on the bottom of the crater4 ,i hope you will enjoy repeated opportunities to view the moon through a telescope4 ,allow me to recommend to you1 not to rest satisfied with a hasty or even with a single view1 but to verify the preceding remarks by repeated and careful inspection of the lunar disk1 at different ages of the moon4 ,the various places on the moon's disk have received appropriate names4 ,the dusky regions being formerly supposed to be seas1 were named accordingly2 and other remarkable places have each two names1 one derived from some well-known spot on the earth1 and the other from some distinguished personage4 ,thus1 the same bright spot on the surface of the moon is called ,mount ,sinai or ,tycho1 and another1 ,mount ,etna or ,copernicus4 ,the names of individuals1 however1 are more used than the others4 ,the diagram1 ,fig4 #cf1 7see page #aei17 represents rudely1 the telescopic appearance of the full moon4 ,the reality is far more beautiful4 ,a few of the most remarkable points have the following names corresponding to the numbers and letters on the map4 #a4 ,tycho1 #f4 ,eratosthenes1 #b4 ,kepler1 #g4 ,plato1 #c4 ,copernicus1 #h4 ,archimedes1 #d4 ,aristarchus1 #i4 ,eudoxus1 #e4 ,helicon1 #aj4 ,aristotle4 ,a4 ,mare ,humorum1 ,sea of ,humors1 ,b4 ,mare ,nubium1 ,sea of ,clouds1 ,c4 ,mare ,imbrium1 ,sea of ,rains1 ,d4 ,mare ,nectaris1 ,sea of ,nectar1 ,e4 ,mare ,tranquillitatis1 ,sea of ,tranquillity1 ,f4 ,mare ,serenitatis1 ,sea of ,serenity1 ,g4 ,mare ,fecunditatis1 ,sea of ,plenty1 ,h4 ,mare ,crisium1 ,crisian ,sea4 ,the heights of the lunar mountains1 and the depths of the valleys1 can be estimated with a considerable degree of accuracy4 ,some of the mountains are as high as five miles1 and the valleys1 in some instances1 are four miles deep4 ,hence it is inferred1 that the surface of the moon is more broken and irregular than that of the earth1 its mountains being higher and its valleys deeper1 in proportion to its magnitude1 than those of the earth4 ,the varieties of surface in the moon1 as seen by the aid of large telescopes1 have been well described by ,dr4 ,dick1 in his ',celestial ,scenery1' and ,i cannot give you a better idea of them1 than to add a few extracts from his work4 ,the lunar mountains in general exhibit an arrangement and an aspect very different from the mountain scenery of our globe4 ,they may be arranged under the four following varieties3 ,first1 insulated mountains1 which rise from plains nearly level1 shaped like a sugar loaf1 which may be supposed to present an appearance somewhat similar to ,mount ,etna1 or the ,peak of ,teneriffe4 ,the shadows of these mountains1 in certain phases of the moon1 are as distinctly perceived as the shadow of an upright staff1 when placed opposite to the sun2 and these heights can be calculated from the length of their shadows4 ,some of these mountains being elevated in the midst of extensive plains1 would present to a spectator on their summits magnificent views of the surrounding regions4 ,secondly1 mountain ranges1 extending in length two or three hundred miles4 ,these ranges bear a distant resemblance to our ,alps1 ,apennines1 and ,andes2 but they are much less in extent4 ,some of them appear very rugged and precipitous2 and the highest ranges are in some places more than four miles in perpendicular altitude4 ,in some instances1 they are nearly in a straight line from northeast to southwest1 as in the range called the ,apennines2 in other cases1 they assume the form of a semicircle1 or crescent4 ,thirdly1 circular ranges1 which appear on almost every part of the moon's surface1 particularly in its southern regions4 ,this is one grand peculiarity of the lunar ranges1 to which we have nothing similar on the earth4 ,a plain1 and sometimes a large cavity1 is surrounded with a circular ridge of mountains1 which encompasses it like a mighty rampart4 ,these annular ridges and plains are of all dimensions1 from a mile to forty or fifty miles in diameter1 and are to be seen in great numbers over every region of the moon's surface2 they are most conspicuous1 however1 near the upper and lower limbs1 about the time of the half moon4 ,the mountains which form these circular ridges are of different elevations1 from one fifth of a mile to three miles and a half1 and their shadows cover one half of the plain at the base4 ,these plains are sometimes on a level with the general surface of the moon1 and in other cases they are sunk a mile or more below the level of the ground which surrounds the exterior circle of the mountains4 ,fourthly1 central mountains1 or those which are placed in the middle of circular plains4 ,in many of the plains and cavities surrounded by circular ranges of mountains there stands a single insulated mountain1 which rises from the centre of the plain1 and whose shadow sometimes extends1 in the form of a pyramid1 half across the plain to the opposite ridges4 ,these central mountains are generally from half a mile to a mile and a half in perpendicular altitude4 ,in some instances1 they have two1 and sometimes three1 different tops1 whose shadows can be easily distinguished from each other4 ,sometimes they are situated towards one side of the plain1 or cavity2 but in the great majority of instances their position is nearly or exactly central4 ,the lengths of their bases vary from five to about fifteen or sixteen miles4 ,the lunar caverns form a very peculiar and prominent feature of the moon's surface1 and are to be seen throughout almost every region1 but are most numerous in the southwest part of the moon4 ,nearly a hundred of them1 great and small1 may be distinguished in that quarter4 ,they are all nearly of a circular shape1 and appear like a very shallow egg-cup4 ,the smaller cavities appear1 within1 almost like a hollow cone1 with the sides tapering towards the centre2 but the larger ones have1 for the most part1 flat bottoms1 from the centre of which there frequently rises a small1 steep1 conical hill1 which gives them a resemblance to the circular ridges and central mountains before described4 ,in some instances1 their margins are level with the general surface of the moon2 but1 in most cases1 they are encircled with a high annular ridge of mountains1 marked with lofty peaks4 ,some of the larger of these cavities contain smaller cavities of the same kind and form1 particularly in their sides4 ,the mountainous ridges which surround these cavities reflect the greatest quantity of light2 and hence that region of the moon in which they abound appears brighter than any other4 ,from their lying in every possible direction1 they appear1 at and near the time of full moon1 like a number of brilliant streaks1 or radiations4 ,these radiations appear to converge towards a large brilliant spot1 surrounded by a faint shade1 near the lower part of the moon1 which is named ,tycho1--a spot easily distinguished even by a small telescope4 ,the spots named ,kepler and ,copernicus are each composed of a central spot with luminous radiations4#h ,the broken surface and apparent geological structure of the moon has suggested the opinion1 that the moon has been subject to powerful volcanic action4 ,this opinion receives support from certain actual appearances of volcanic fires1 which have at different times been observed4 ,in a total eclipse of the sun1 the moon comes directly between us and that luminary1 and presents her dark side towards us under circumstances very favorable for observation4 ,at such times1 several astronomers1 at different periods1 have noticed bright spots1 which they took to be volcanoes4 ,it must evidently require a large fire to be visible at all1 at such a distance2 and even a burning spark1 or point but just visible in a large telescope1 might be in fact a volcano raging like ,etna or ,vesuvius4 ,still1 as fires might be supposed to exist in the moon from different causes1 we should require some marks peculiar to volcanic fires1 to assure us that such was their origin in a given case4 ,dr4 ,herschel examined this point with great attention1 and with better means of observation than any of his predecessors enjoyed1 and fully embraced the opinion that what he saw were volcanoes4 ,in ,april1 #aghg1 he records his observations as follows3 ,i perceive three volcanoes in different places in the dark part of the moon4 ,two of them are already nearly extinct1 or otherwise in a state of going to break out2 the third shows an eruption of fire or luminous matter4 ,on the next night1 he says3 ,the volcano burns with greater violence than last night2 its diameter cannot be less than three seconds2 and hence the shining or burning matter must be above three miles in diameter4 ,the appearance resembles a small piece of burning charcoal1 when it is covered with a very thin coat of white ashes2 and it has a degree of brightness about as strong as that with which such a coal would be seen to glow in faint daylight4 ,that these were really volcanic fires1 he considered further evident from the fact1 that where a fire1 supposed to have been volcanic1 had been burning1 there was seen1 after its extinction1 an accumulation of matter1 such as would arise from the production of a great quantity of lava1 sufficient to form a mountain4 ,it is probable that the moon has an atmosphere1 although it is difficult to obtain perfectly satisfactory evidence of its existence2 for granting the existence of an atmosphere bearing the same proportion to that planet as our atmosphere bears to the earth1 its dimensions and its density would be so small1 that we could detect its presence only by the most refined observations4 ,as our twilight is owing to the agency of our atmosphere1 so1 could we discern any appearance of twilight in the moon1 we should regard that fact as indicating that she is surrounded by an atmosphere4 ,or1 when the moon covers the sun in a solar eclipse1 could we see around her circumference a faint luminous ring1 indicating that the sunlight shone through an aerial medium1 we might likewise infer the existence of such a medium4 ,such a faint ring of light has sometimes1 as is supposed1 been observed4 ,schroeter1 a ,german astronomer1 distinguished for the acuteness of his vision and his powers of observation in general1 was very confident of having obtained1 from different sources1 clear evidence of a lunar atmosphere4 ,he concluded1 that the inferior or more dense part of the moon's atmosphere is not more than fifteen hundred feet high1 and that the entire height1 at least to the limit where it would be too rare to produce any of the phenomena which are relied on as proofs of its existence1 is not more than a mile4 ,it has been a question1 much agitated among astronomers1 whether there is water in the moon4 ,analogy strongly inclines us to reply in the affirmative4 ,but the analogy between the earth and the moon1 as derived from all the particulars in which we can compare the two bodies1 is too feeble to warrant such a conclusion1 and we must have recourse to other evidence1 before we can decide the point4 ,in the first place1 then1 there is no positive evidence in favor of the existence of water in the moon4 ,those extensive level regions1 before spoken of1 and denominated seas in the geography of this planet1 have no other signs of being water1 except that they are level and dark4 ,but both these particulars would characterize an earthly plain1 like the deserts of ,arabia and ,africa4 ,in the second place1 were those dark regions composed of water1 the terminator would be entirely smooth where it passed over these oceans or seas4 ,it is indeed indented by few inequalities1 compared with those which it exhibits where it passes over the mountainous regions2 but still1 the inequalities are too considerable to permit the conclusion1 that these level spots are such perfect levels as water would form4 ,they do not appear to be more perfect levels than many plain countries on the globe4 ,the deep caverns1 moreover1 seen in those dusky spots which were supposed to be seas1 are unfavorable to the supposition that those regions are covered by water4 ,in the third place1 the face of the moon1 when illuminated by the sun and not obscured by the state of our own atmosphere1 is always serene1 and therefore free from clouds4 ,clouds are objects of great extent2 they frequently intercept light1 like solid bodies2 and did they exist about the moon1 we should certainly see them1 and should lose sight of certain parts of the lunar disk which they covered4 ,but neither position is true2 we neither see any clouds about the moon1 with our best telescopes1 nor do we1 by the intervention of clouds1 ever lose sight of any portion of the moon when our own atmosphere is clear4 ,but the want of clouds in the lunar atmosphere almost necessarily implies the absence of water in the moon4 ,this planet is at the same distance from the sun as our own1 and has1 in this respect1 an equal opportunity to feel the influence of his rays4 ,its days are also twenty-seven times as long as ours1 a circumstance which would augment the solar heat4 ,when the pressure of the atmosphere is diminished on the surface of water1 its tendency to pass into the state of vapor is increased4 ,were the whole pressure of the atmosphere removed from the surface of a lake1 in a ,summer's day1 when the temperature was no higher than seventy-two degrees1 the water would begin to boil4 ,now it is well ascertained1 that if there be any atmosphere about the moon1 it is much lighter than ours1 and presses on the surface of that body with a proportionally small force4 ,this circumstance1 therefore1 would conspire with the other causes mentioned1 to convert all the water of the moon into vapor1 if we could suppose it to have existed at any given time4 ,but those1 who are anxious to furnish the moon and other planets with all the accommodations which they find in our own1 have a subterfuge in readiness1 to which they invariably resort in all cases like the foregoing4 ,there may be1 say they1 some means1 unknown to us1 provided for retaining water on the surface of the moon1 and for preventing its being wasted by evaporation3 perhaps it remains unaltered in quantity1 imparting to the lunar regions perpetual verdure and fertility4 ,to this ,i reply1 that the bare possibility of a thing is but slight evidence of its reality2 nor is such a condition possible1 except by miracle4 ,if they grant that the laws of ,nature are the same in the moon as in the earth1 then1 according to the foregoing reasoning1 there cannot be water in the moon2 but if they say that the laws of ,nature are not the same there as here1 then we cannot reason at all respecting them4 ,one who resorts to a subterfuge of this kind ruins his own cause4 ,he argues the existence of water in the moon1 from the analogy of that planet to this4 ,but if the laws of ,nature are not the same there as here1 what becomes of his analogy8 ,a liquid substance which would not evaporate by such a degree of solar heat as falls on the moon1 which would not evaporate the faster1 in consequence of the diminished atmospheric pressure which prevails there1 could not be water1 for it would not have the properties of water1 and things are known by their properties4 ,whenever we desert the cardinal principle of the ,newtonian philosophy1--that the laws of ,nature are uniform throughout all her realms1--we wander in a labyrinth2 all analogies are made void2 all physical reasonings cease2 and imaginary possibilities or direct miracles take the place of legitimate natural causes4 ,on the supposition that the moon is inhabited1 the question has often been raised1 whether we may hope that our telescopes will ever be so much improved1 and our other means of observation so much augmented1 that we shall be able to discover either the lunar inhabitants or any of their works4 ,the improbability of our ever identifying artificial structures in the moon may be inferred from the fact1 that a space a mile in diameter is the least space that could be distinctly seen4 ,extensive works of art1 as large cities1 or the clearing up of large tracts of country for settlement or tillage1 might indeed afford some varieties of surface2 but they would be merely varieties of light and shade1 and the individual objects that occasioned them would probably never be recognised by their distinctive characters4 ,thus1 a building equal to the great pyramid of ,egypt1 which covers a space less than the fifth of a mile in diameter1 would not be distinguished by its figure2 indeed1 it would be a mere point4 ,still less is it probable that we shall ever discover any inhabitants in the moon4 ,were we to view the moon with a telescope that magnifies ten thousand times1 it would bring the moon apparently ten thousand times nearer1 and present it to the eye like a body twenty-four miles off4 ,but even this is a distance too great for us to see the works of man with distinctness4 ,moreover1 from the nature of the telescope itself1 we can never hope to apply a magnifying power so high as that here supposed4 ,as ,i explained to you1 when speaking of the telescope1 whenever we increase the magnifying power of this instrument we diminish its field of view1 so that with very high magnifiers we can see nothing but a point1 such as a fixed star4 ,we at the same time1 also1 magnify the vapors and smoke of the atmosphere1 and all the imperfections of the medium1 which greatly obscures the object1 and prevents our seeing it distinctly4 ,hence it is generally most satisfactory to view the moon with low powers1 which afford a large field of view and give a clear light4 ,with ,clark's telescope1 belonging to ,yale ,college1 we seldom gain any thing by applying to the moon a higher power than one hundred and eighty1 although the instrument admits of magnifiers as high as four hundred and fifty4 ,some writers1 however1 suppose that possibly we may trace indications of lunar inhabitants in their works1 and that they may in like manner recognise the existence of the inhabitants of our planet4 ,an author1 who has reflected much on subjects of this kind1 reasons as follows3 ,a navigator who approaches within a certain distance of a small island1 although he perceives no human being upon it1 can judge with certainty that it is inhabited1 if he perceives human habitations1 villages1 corn-fields1 or other traces of cultivation4 ,in like manner1 if we could perceive changes or operations in the moon1 which could be traced to the agency of intelligent beings1 we should then obtain satisfactory evidence that such beings exist on that planet2 and it is thought possible that such operations may be traced4 ,a telescope which magnifies twelve hundred times will enable us to perceive1 as a visible point on the surface of the moon1 an object whose diameter is only about three hundred feet4 ,such an object is not larger than many of our public edifices2 and therefore1 were any such edifices rearing in the moon1 or were a town or city extending its boundaries1 or were operations of this description carrying on1 in a district where no such edifices had previously been erected1 such objects and operations might probably be detected by a minute inspection4 ,were a multitude of living creatures moving from place to place1 in a body1 or were they even encamping in an extensive plain1 like a large army1 or like a tribe of ,arabs in the desert1 and afterwards removing1 it is possible such changes might be traced by the difference of shade or color1 which such movements would produce4 ,in order to detect such minute objects and operations1 it would be requisite that the surface of the moon should be distributed among at least a hundred astronomers1 each having a spot or two allotted to him1 as the object of his more particular investigation1 and that the observations be continued for a period of at least thirty or forty years1 during which time certain changes would probably be perceived1 arising either from physical causes1 or from the operations of living agents4#i ,,footnote3 #h ,dick's ',celestial ,scenery1' ,chapter ,,iv ,,letter ,,xvi4 ,,the ,,moon4--,,phases4--,,harvest ,,moon4--,,librations4 ,first to the neighboring ,moon this mighty key ,of nature he applied4 ,behold6 it turned ,the secret wards1 it opened wide the course ,and various aspects of the queen of night3 ,whether she wanes into a scanty orb1 ,or1 waxing broad1 with her pale shadowy light1 ,in a soft deluge overflows the sky4--,thomson's ,elegy4 ,,let us now inquire into the revolutions of the moon around the earth1 and the various changes she undergoes every month1 called her phases1 which depend on the different positions she assumes1 with respect to the earth and the sun1 in the course of her revolution4 ,the moon revolves about the earth from west to east4 ,her apparent orbit1 as traced out on the face of the sky1 is a great circle2 but this fact would not certainly prove that the orbit is really a circle1 since1 if it were an ellipse1 or even a more irregular curve1 the projection of it on the face of the sky would be a circle1 as explained to you before4 7,see page #adh47 ,the moon is comparatively so near to the earth1 that her apparent movements are very rapid1 so that1 by attentively watching her progress in a clear night1 we may see her move from star to star1 changing her place perceptibly1 every few hours4 ,the interval during which she goes through the entire circuit of the heavens1 from any star until she comes round to the same star again1 is called a sidereal month1 and consists of about twenty-seven and one fourth days4 ,the time which intervenes between one new moon and another is called a synodical month1 and consists of nearly twenty-nine and a half days4 ,a new moon occurs when the sun and moon meet in the same part of the heavens2 but the sun as well as the moon is apparently travelling eastward1 and nearly at the rate of one degree a day1 and consequently1 during the twenty-seven days while the moon has been going round the earth1 the sun has been going forward about the same number of degrees in the same direction4 ,hence1 when the moon comes round to the part of the heavens where she passed the sun last1 she does not find him there1 but must go on more than two days1 before she comes up with him again4 ,the moon does not pursue precisely the same track around the earth as the sun does1 in his apparent annual motion1 though she never deviates far from that track4 ,the inclination of her orbit to the ecliptic is only about five degrees1 and of course the moon is never seen further from the ecliptic than about that distance1 and she is commonly much nearer to the ecliptic than five degrees4 ,we may therefore see nearly what is the situation of the ecliptic in our evening sky at any particular time of year1 just by watching the path which the moon pursues1 from night to night1 from new to full moon4 ,the two points where the moon's orbit crosses the ecliptic are called her nodes4 ,they are the intersections of the lunar and solar orbits1 as the equinoxes are the intersections of the equinoctial and ecliptic1 and1 like the latter1 are one hundred and eighty degrees apart4 ,the changes of the moon1 commonly called her phases1 arise from different portions of her illuminated side being turned towards the earth at different times4 ,when the moon is first seen after the setting sun1 her form is that of a bright crescent1 on the side of the disk next to the sun1 while the other portions of the disk shine with a feeble light1 reflected to the moon from the earth4 ,every night1 we observe the moon to be further and further eastward of the sun1 until1 when she has reached an elongation from the sun of ninety degrees1 half her visible disk is enlightened1 and she is said to be in her first quarter4 ,the terminator1 or line which separates the illuminated from the dark part of the moon1 is convex towards the sun from the new to the first quarter1 and the moon is said to be horned4 ,the extremities of the crescent are called cusps4 ,at the first quarter1 the terminator becomes a straight line1 coinciding with the diameter of the disk2 but after passing this point1 the terminator becomes concave towards the sun1 bounding that side of the moon by an elliptical curve1 when the moon is said to be gibbous4 ,when the moon arrives at the distance of one hundred and eighty degrees from the sun1 the entire circle is illuminated1 and the moon is full4 ,she is then in opposition to the sun1 rising about the time the sun sets4 ,for a week after the full1 the moon appears gibbous again1 until1 having arrived within ninety degrees of the sun1 she resumes the same form as at the first quarter1 being then at her third quarter4 ,from this time until new moon1 she exhibits again the form of a crescent before the rising sun1 until1 approaching her conjunction with the sun1 her narrow thread of light is lost in the solar blaze2 and finally1 at the moment of passing the sun1 the dark side is wholly turned towards us1 and for some time we lose sight of the moon4 ,by inspecting ,fig4 #ch1 7where ,t represents the earth1 ,a1 ,b1 ,c1 c41 the moon in her orbit1 and a1 b1 c1 c41 her phases1 as seen in the heavens17 we shall easily see how all these changes occur4 ,illustration ,fig4 #ch4 ,you have doubtless observed1 that the moon appears much further in the south at one time than at another1 when of the same age4 ,this is owing to the fact that the ecliptic1 and of course the moon's path1 which is always very near it1 is differently situated with respect to the horizon1 at a given time of night1 at different seasons of the year4 ,this you will see at once1 by turning to an artificial globe1 and observing how the ecliptic stands with respect to the horizon1 at different periods of the revolution4 ,thus1 if we place the two equinoctial points in the eastern and western horizon1 ,libra being in the west1 it will represent the position of the ecliptic at sunset in the month of ,september1 when the sun is crossing the equator2 and at that season of the year1 the moon's path through our evening sky1 one evening after another1 from new to full1 will be nearly along the same route1 crossing the meridian nearly at right angles4 ,but if we place the ,winter solstice1 or first degree of ,capricorn1 in the western horizon1 and the first degree of ,cancer in the eastern1 then the position of the ecliptic will be very oblique to the meridian1 the ,winter solstice being very far in the southwest1 and the ,summer solstice very far in the northeast2 and the course of the moon from new to full will be nearly along this track4 ,keeping these things in mind1 we may easily see why the moon runs sometimes high and sometimes low4 ,recollect1 also1 that the new moon is always in the same part of the heavens with the sun1 and that the full moon is in the opposite part of the heavens from the sun4 ,now1 when the sun is at the ,winter solstice1 it sets far in the southwest1 and accordingly the new moon runs very low2 but the full moon1 being in the opposite tropic1 which rises far in the northeast1 runs very high1 as is known to be the case in mid-winter4 ,but now take the position of the ecliptic in mid-summer4 ,then1 at sunset1 the tropic of ,cancer is in the northwest1 and the tropic of ,capricorn in the southeast2 consequently1 the new moons run high and the full moons low4 ,it is a natural consequence of this arrangement1 to render the moon's light the most beneficial to us1 by giving it to us in greatest abundance1 when we have least of the sun's light1 and giving it to us most sparingly1 when the sun's light is greatest4 ,thus1 during the long nights of ,winter1 the full moon runs high1 and continues a very long time above the horizon2 while in mid-summer1 the full moon runs low1 and is above the horizon for a much shorter period4 ,this arrangement operates very favorably to the inhabitants of the polar regions4 ,at the season when the sun is absent1 and they have constant night1 then the moon1 during the second and third quarters1 embracing the season of full moon1 is continually above the horizon1 compensating in no small degree for the absence of the sun2 while1 during the ,summer months1 when the sun is constantly above the horizon1 and the light of the moon is not needed1 then she is above the horizon during the first and last quarters1 when her light is least1 affording at that time her greatest light to the inhabitants of the other hemisphere1 from whom the sun is withdrawn4 ,about the time of the ,autumnal equinox1 the moon1 when near her full1 rises about sunset a number of nights in succession4 ,this occasions a remarkable number of brilliant moonlight evenings2 and as this is1 in ,england1 the period of harvest1 the phenomenon is called the harvest moon4 ,its return is celebrated1 particularly among the peasantry1 by festive dances1 and kept as a festival1 called the harvest home1--an occasion often alluded to by the ,british poets4 ,thus ,henry ,kirke ,white3 ,moon of harvest1 herald mild ,of plenty1 rustic labor's child1 ,hail1 ,o hail6 ,i greet thy beam1 ,as soft it trembles o'er the stream1 ,and gilds the straw-thatch'd hamlet wide1 ,where innocence and peace reside2 ',tis thou that glad'st with joy the rustic throng1 ,promptest the tripping dance1 th' exhilarating song4 ,to understand the reason of the harvest moon1 we will1 as before1 consider the moon's orbit as coinciding with the ecliptic1 because we may then take the ecliptic1 as it is drawn on the artificial globe1 to represent that orbit4 ,we will also bear in mind1 7what has been fully illustrated under the last head17 that1 since the ecliptic cuts the meridian obliquely1 while all the circles of diurnal revolution cut it perpendicularly1 different portions of the ecliptic will cut the horizon at different angles4 ,thus1 when the equinoxes are in the horizon1 the ecliptic makes a very small angle with the horizon2 whereas1 when the solstitial points are in the horizon1 the same angle is far greater4 ,in the former case1 a body moving eastward in the ecliptic1 and being at the eastern horizon at sunset1 would descend but a little way below the horizon in moving over many degrees of the ecliptic4 ,now1 this is just the case of the moon at the time of the harvest home1 about the time of the ,autumnal equinox4 ,the sun being then in ,libra1 and the moon1 when full1 being of course opposite to the sun1 or in ,aries2 and moving eastward1 in or near the ecliptic1 at the rate of about thirteen degrees per day1 would descend but a small distance below the horizon for five or six days in succession2 that is for two or three days before1 and the same number of days after1 the full2 and would consequently rise during all these evenings nearly at the same time1 namely1 a little before1 or a little after1 sunset1 so as to afford a remarkable succession of fine moonlight evenings4 ,the moon turns on her axis in the same time in which she revolves around the earth4 ,this is known by the moon's always keeping nearly the same face towards us1 as is indicated by the telescope1 which could not happen unless her revolution on her axis kept pace with her motion in her orbit4 ,take an apple1 to represent the moon2 stick a knittingneedle through it1 in the direction of the stem1 to represent the axis1 in which case the two eyes of the apple will aptly represent the poles4 ,through the poles cut a line around the apple1 dividing it into two hemispheres1 and mark them1 so as to be readily distinguished from each other4 ,now place a candle on the table1 to represent the earth1 and holding the apple by the knittingneedle1 carry it round the candle1 and you will see that1 unless you make the apple turn round on the axis as you carry it about the candle1 it will present different sides towards the candle2 and that1 in order to make it always present the same side1 it will be necessary to make it revolve exactly once on its axis1 while it is going round the circle1--the revolution on its axis always keeping exact pace with the motion in its orbit4 ,the same thing will be observed1 if you walk around a tree1 always keeping your face towards the tree4 ,if you have your face towards the tree when you set out1 and walk round without turning1 when you have reached the opposite side of the tree1 your back will be towards it1 and you will find that1 in order to keep your face constantly towards the tree1 it will be necessary to turn yourself round on your heel at the same rate as you go forward4 ,since1 however1 the motion of the moon on its axis is uniform1 while the motion in its orbit is unequal1 the moon does in fact reveal to us a little sometimes of one side and sometimes of the other4 ,thus if1 while carrying the apple round the candle1 you carry it forward a little faster than the rate at which it turns on its axis1 a portion of the hemisphere usually out of sight is brought into view on one side2 or if the apple is moved forward slower than it is turned on its axis1 a portion of the same hemisphere comes into view on the other side4 ,these appearances are called the moon's librations in longitude4 ,the moon has also a libration in latitude2--so called1 because in one part of her revolution more of the region around one of the poles comes into view1 and1 in another part of the revolution1 more of the region around the other pole1 which gives the appearance of a tilting motion to the moon's axis4 ,this is owing to the fact1 that the moon's axis is inclined to the plane of her orbit4 ,if1 in the experiment with the apple1 you hold the knittingneedle parallel to the candle1 7in which case the axis will be perpendicular to the plane of revolution17 the candle will shine upon both poles during the whole circuit1 and an eye situated where the candle is would constantly see both poles2 but now incline the needle towards the plane of revolution1 and carry it round1 always keeping it parallel to itself1 and you will observe that the two poles will be alternately in and out of sight4 ,the moon exhibits another appearance of this kind1 called her diurnal libration1 depending on the daily rotation of the spectator4 ,she turns the same face towards the centre of the earth only1 whereas we view her from the surface4 ,when she is on the meridian1 we view her disk nearly as though we viewed it from the centre of the earth1 and hence1 in this situation1 it is subject to little change2 but when she is near the horizon1 our circle of vision takes in more of the upper limb than would be presented to a spectator at the centre of the earth4 ,hence1 from this cause1 we see a portion of one limb while the moon is rising1 which is gradually lost sight of1 and we see a portion of the opposite limb1 as the moon declines to the west4 ,you will remark that neither of the foregoing changes implies any actual motion in the moon1 but that each arises from a change of position in the spectator4 ,since the succession of day and night depends on the revolution of a planet on its own axis1 and it takes the moon twenty-nine and a half days to perform this revolution1 so that the sun shall go from the meridian of any place and return to the same meridian again1 of course the lunar day occupies this long period4 ,so protracted an exposure to the sun's rays1 especially in the equatorial regions of the moon1 must occasion an excessive accumulation of heat2 and so long an absence of the sun must occasion a corresponding degree of cold4 ,a spectator on the side of the moon which is opposite to us would never see the earth1 but one on the side next to us would see the earth constantly in his firmament1 undergoing a gradual succession of changes1 corresponding to those which the moon exhibits to the earth1 but in the reverse order4 ,thus1 when it is full moon to us1 the earth1 as seen from the moon1 is then in conjunction with the sun1 and of course presents her dark side to the moon4 ,soon after this1 an inhabitant of the moon would see a crescent1 resembling our new moon1 which would in like manner increase and go through all the changes1 from new to full1 and from full to new1 as we see them in the moon4 ,there are1 however1 in the two cases1 several striking points of difference4 ,in the first place1 instead of twenty-nine and a half days1 all these changes occur in one lunar day and night4 ,during the first and last quarters1 the changes would occur in the day-time2 but during the second and third quarters1 during the night4 ,by this arrangement1 the lunarians would enjoy the greatest possible benefit from the light afforded by the earth1 since in the half of her revolution where she appears to them as full1 she would be present while the sun was absent1 and would afford her least light while the sun was present4 ,in the second place1 the earth would appear thirteen times as large to a spectator on the moon as the moon appears to us1 and would afford nearly the same proportion of light1 so that their long nights must be continually cheered by an extraordinary degree of light derived from this source2 and if the full moon is hailed by our poets as refulgent lamp of night1#aj with how much more reason might a lunarian exult thus1 in view of the splendid orb that adorns his nocturnal sky6 ,in the third place1 the earth1 as viewed from any particular place on the moon1 would occupy invariably the same part of the heavens4 ,for while the rotation of the moon on her axis from west to east would appear to make the earth 7as the moon does to us7 revolve from east to west1 the corresponding progress of the moon in her orbit would make the earth appear to revolve from west to east2 and as these two motions are equal1 their united effect would be to keep the moon apparently stationary in the sky4 ,thus1 a spectator at ,e1 ,fig4 #ch1 page #age1 in the middle of the disk that is turned towards the earth1 would have the earth constantly on his meridian1 and at ,e1 the conjunction of the earth and sun would occur at mid-day2 but when the moon arrived at ,g1 the same place would be on the margin of the circle of illumination1 and will have the sun in the horizon2 but the earth would still be on his meridian and in quadrature4 ,in like manner1 a place situated on the margin of the circle of illumination1 when the moon is at ,e1 would have the earth in the horizon2 and the same place would always see the earth in the horizon1 except the slight variations that would occur from the librations of the moon4 ,in the fourth place1 the earth would present to a spectator on the moon none of that uniformity of aspect which the moon presents to us1 but would exhibit an appearance exceedingly diversified4 ,the comparatively rapid rotation of the earth1 repeated fifteen times during a lunar night1 would present1 in rapid succession1 a view of our seas1 oceans1 continents1 and mountains1 all diversified by our clouds1 storms1 and volcanoes4 ,,footnotes3 #i ,dick's ',celestial ,scenery4' #aj ,as when the moon1 refulgent lamp of night1 ,o'er heaven's clear azure sheds her sacred light1 ,when not a breath disturbs the deep serene1 ,and not a cloud o'ercasts the solemn scene1 ,around her throne the vivid planets roll1 ,and stars unnumbered gild the glowing pole2 ,o'er the dark trees a yellower verdure shed1 ,and tip with silver every mountain's head2 ,then shine the vales1 the rocks in prospect rise1 ,a flood of glory bursts from all the skies2 ,the conscious swains1 rejoicing in the sight1 ,eye the blue vault1 and bless the useful light4 ,pope's ,homer4 ,,letter ,,xvii4 ,,moon',s ,,orbit4--,,her ,,irregularities4 ,some say the zodiac constellations ,have long since left their antique stations1 ,above a sign1 and prove the same ,in ,taurus now1 once in the ,ram2 ,that in twelve hundred years and odd1 ,the sun has left his ancient road1 ,and nearer to the earth is come1 ',bove fifty thousand miles from home4--,hudibras4 ,,we have thus far contemplated the revolution of the moon around the earth as though the earth were at rest4 ,but in order to have just ideas respecting the moon's motions1 we must recollect that the moon likewise revolves along with the earth around the sun4 ,it is sometimes said that the earth carries the moon along with her1 in her annual revolution4 ,this language may convey an erroneous idea2 for the moon1 as well as the earth1 revolves around the sun under the influence of two forces1 which are independent of the earth1 and would continue her motion around the sun1 were the earth removed out of the way4 ,indeed1 the moon is attracted towards the sun two and one fifth times more than towards the earth1 and would abandon the earth1 were not the latter also carried along with her by the same forces4 ,so far as the sun acts equally on both bodies1 the motion with respect to each other would not be disturbed4 ,because the gravity of the moon towards the sun is found to be greater1 at the conjunction1 than her gravity towards the earth1 some have apprehended that1 if the doctrine of universal gravitation is true1 the moon ought necessarily to abandon the earth4 ,in order to understand the reason why it does not do thus1 we must reflect1 that1 when a body is revolving in its orbit under the influence of the projectile force and gravity1 whatever diminishes the force of gravity1 while that of projection remains the same1 causes the body to approach nearer to the tangent of her orbit1 and of course to recede from the centre2 and whatever increases the amount of gravity1 carries the body towards the centre4 ,thus1 in ,fig4 #cc1 page #aeb1 if1 with a certain force of projection acting in the direction ,a ,b1 and of attraction1 in the direction ,a ,c1 the attraction which caused a body to move in the line ,a ,d were diminished1 it would move nearer to the tangent1 as in ,a ,e1 or ,a ,f4 ,now1 when the moon is in conjunction1 her gravity towards the earth acts in opposition to that towards the sun1 7see ,fig4 #ch1 page #age17 while her velocity remains too great to carry her with what force remains1 in a circle about the sun1 and she therefore recedes from the sun1 and commences her revolution around the earth4 ,on arriving at the opposition1 the gravity of the earth conspires with that of the sun1 and the moon's projectile force being less than that required to make her revolve in a circular orbit1 when attracted towards the sun by the sum of these forces1 she accordingly begins to approach the sun1 and descends again to the conjunction4 ,the attraction of the sun1 however1 being every where greater than that of the earth1 the actual path of the moon around the sun is every where concave towards the latter4 ,still1 the elliptical path of the moon around the earth is to be conceived of1 in the same way as though both bodies were at rest with respect to the sun4 ,thus1 while a steam-boat is passing swiftly around an island1 and a man is walking slowly around a post in the cabin1 the line which he describes in space between the forward motion of the boat and his circular motion around the post1 may be every where concave towards the island1 while his path around the post will still be the same as though both were at rest4 ,a nail in the rim of a coach-wheel will turn around the axis of the wheel1 when the coach has a forward motion1 in the same manner as when the coach is at rest1 although the line actually described by the nail will be the resultant of both motions1 and very different from either4 ,we have hitherto regarded the moon as describing a great circle on the face of the sky1 such being the visible orbit1 as seen by projection4 ,but1 on a more exact investigation1 it is found that her orbit is not a circle1 and that her motions are subject to very numerous irregularities4 ,these will be best understood in connexion with the causes on which they depend4 ,the law of universal gravitation has been applied with wonderful success to their developement1 and its results have conspired with those of long-continued observation1 to furnish the means of ascertaining with great exactness the place of the moon in the heavens1 at any given instant of time1 past or future1 and thus to enable astronomers to determine longitudes1 to calculate eclipses1 and to solve other problems of the highest interest4 ,the whole number of irregularities to which the moon is subject is not less than sixty1 but the greater part are so small as to be hardly deserving of attention2 but as many as thirty require to be estimated and allowed for1 before we can ascertain the exact place of the moon at any given time4 ,you will be able to understand something of the cause of these irregularities1 if you first gain a distinct idea of the mutual actions of the sun1 the moon1 and the earth4 ,the irregularities in the moon's motions are due chiefly to the disturbing influence of the sun1 which operates in two ways2 first1 by acting unequally on the earth and moon2 and secondly1 by acting obliquely on the moon1 on account of the inclination of her orbit to the ecliptic4 ,if the sun acted equally on the earth and moon1 and always in parallel lines1 this action would serve only to restrain them in their annual motions around the sun1 and would not affect their actions on each other1 or their motions about their common centre of gravity4 ,in that case1 if they were allowed to fall towards the sun1 they would fall equally1 and their respective situations would not be affected by their descending equally towards it4 ,but1 because the moon is nearer the sun in one half of her orbit than the earth is1 and in the other half of her orbit is at a greater distance than the earth from the sun1 while the power of gravity is always greater at a less distance2 it follows1 that in one half of her orbit the moon is more attracted than the earth towards the sun1 and1 in the other half1 less attracted than the earth4 ,to see the effects of this process1 let us suppose that the projectile motions of the earth and moon were destroyed1 and that they were allowed to fall freely towards the sun4 7,see ,fig4 #ch1 page #age47 ,if the moon was in conjunction with the sun1 or in that part of her orbit which is nearest to him1 the moon would be more attracted than the earth1 and fall with greater velocity towards the sun2 so that the distance of the moon from the earth would be increased by the fall4 ,if the moon was in opposition1 or in the part of her orbit which is furthest from the sun1 she would be less attracted than the earth by the sun1 and would fall with a less velocity1 and be left behind2 so that the distance of the moon from the earth would be increased in this case1 also4 ,if the moon was in one of the quarters1 then the earth and the moon being both attracted towards the centre of the sun1 they would both descend directly towards that centre1 and1 by approaching it1 they would necessarily at the same time approach each other1 and in this case their distance from each other would be diminished4 ,now1 whenever the action of the sun would increase their distance1 if they were allowed to fall towards the sun1 then the sun's action1 by endeavoring to separate them1 diminishes their gravity to each other2 whenever the sun's action would diminish the distance1 then it increases their mutual gravitation4 ,hence1 in the conjunction and opposition1 their gravity towards each other is diminished by the action of the sun1 while in the quadratures it is increased4 ,but it must be remembered1 that it is not the total action of the sun on them that disturbs their motions1 but only that part of it which tends at one time to separate them1 and at another time to bring them nearer together4 ,the other and far greater part has no other effect than to retain them in their annual course around the sun4 ,the cause of the lunar irregularities was first investigated by ,sir ,isaac ,newton1 in conformity with his doctrine of universal gravitation1 and the explanation was first published in the ',principia2' but1 as it was given in a mathematical dress1 there were at that age very few persons capable of reading or understanding it4 ,several eminent individuals1 therefore1 undertook to give a popular explanation of these difficult points4 ,among ,newton's contemporaries1 the best commentator was ,m',laurin1 a ,scottish astronomer1 who published a large work entitled ',m',laurin's ,account of ,sir ,isaac ,newton's ,discoveries4' ,no writer of his own day1 and1 in my opinion1 no later commentator1 has equalled ,m',laurin1 in reducing to common apprehension the leading principles of the doctrine of gravitation1 and the explanation it affords of the motions of the heavenly bodies4 ,to this writer ,i am indebted for the preceding easy explanation of the irregularities of the moon's motions1 as well as for several other illustrations of the same sublime doctrine4 ,the figure of the moon's orbit is an ellipse4 ,we have before seen1 that the earth's orbit around the sun is of the same figure2 and we shall hereafter see this to be true of all the planetary orbits4 ,the path of the earth1 however1 departs very little from a circle2 that of the moon differs materially from a circle1 being considerably longer one way than the other4 ,were the orbit a circle having the earth in the centre1 then the radius vector1 or line drawn from the centre of the moon to the centre of the earth1 would always be of the same length2 but it is found that the length of the radius vector is only fifty-six times the radius of the earth when the moon is nearest to us1 while it is sixty-four times that radius when the moon is furthest from us4 ,the point in the moon's orbit nearest the earth is called her perigee2 the point furthest from the earth1 her apogee4 ,we always know when the moon is at one of these points1 by her apparent diameter or apparent velocity2 for1 when at the perigee1 her diameter is greater than at any time1 and her motion most rapid2 and1 on the other hand1 her diameter is least1 and her motion slowest1 when she is at her apogee4 ,the moon's nodes constantly shift their positions in the ecliptic1 from east to west1 at the rate of about nineteen and a half degrees every year1 returning to the same points once in eighteen and a half years4 ,in order to understand what is meant by this backward motion of the nodes1 you must have very distinctly in mind the meaning of the terms themselves2 and if1 at any time1 you should be at a loss about the signification of any word that is used in expressing an astronomical proposition1 ,i would advise you to turn back to the previous definition of that term1 and revive its meaning clearly in the mind1 before you proceed any further4 ,in the present case1 you will recollect that the moon's nodes are the two points where her orbit cuts the plane of the ecliptic4 ,suppose the great circle of the ecliptic marked out on the face of the sky in a distinct line1 and let us observe1 at any given time1 the exact moment when the moon crosses this line1 which we will suppose to be close to a certain star2 then1 on its next return to that part of the heavens1 we shall find that it crosses the ecliptic sensibly to the westward of that star1 and so on1 further and further to the westward1 every time it crosses the ecliptic at either node4 ,this fact is expressed by saying that the nodes retrograde on the ecliptic2 since any motion from east to west1 being contrary to the order of the signs1 is called retrograde4 ,the line which joins these two points1 or the line of the nodes1 is also said to have a retrograde motion1 or to revolve from east to west once in eighteen and a half years4 ,the line of the apsides of the moon's orbit revolves from west to east1 through her whole course1 in about nine years4 ,you will recollect that the apsides of an elliptical orbit are the two extremities of the longer axis of the ellipse2 corresponding to the perihelion and aphelion of bodies revolving about the sun1 or to the perigee and apogee of a body revolving about the earth4 ,if1 in any revolution of the moon1 we should accurately mark the place in the heavens where the moon is nearest the earth1 7which may be known by the moon's apparent diameter being then greatest17 we should find that1 at the next revolution1 it would come to its perigee a little further eastward than before1 and so on1 at every revolution1 until1 after nine years1 it would come to its perigee nearly at the same point as at first4 ,this fact is expressed by saying1 that the perigee1 and of course the apogee1 revolves1 and that the line which joins these two points1 or the line of the apsides1 also revolves4 ,these are only a few of the irregularities that attend the motions of the moon4 ,these and a few others were first discovered by actual observation and have been long known2 but a far greater number of lunar irregularities have been made known by following out all the consequences of the law of universal gravitation4 ,the moon may be regarded as a body endeavoring to make its way around the earth1 but as subject to be continually impeded1 or diverted from its main course1 by the action of the sun and of the earth2 sometimes acting in concert and sometimes in opposition to each other4 ,now1 by exactly estimating the amount of these respective forces1 and ascertaining their resultant or combined effect1 in any given case1 the direction and velocity of the moon's motion may be accurately determined4 ,but to do this has required the highest powers of the human mind1 aided by all the wonderful resources of mathematics4 ,yet1 so consistent is truth with itself1 that1 where some minute inequality in the moon's motions is developed at the end of a long and intricate mathematical process1 it invariably happens1 that1 on pointing the telescope to the moon1 and watching its progress through the skies1 we may actually see her commit the same irregularities1 unless 7as is the case with many of them7 they are too minute to be matters of observation1 being beyond the powers of our vision1 even when aided by the best telescopes4 ,but the truth of the law of gravitation1 and of the results it gives1 when followed out by a chain of mathematical reasoning1 is fully confirmed1 even in these minutest matters1 by the fact that the moon's place in the heavens1 when thus determined1 always corresponds1 with wonderful exactness1 to the place which she is actually observed to occupy at that time4 ,the mind1 that was first able to elicit from the operations of ,nature the law of universal gravitation1 and afterwards to apply it to the complete explanation of all the irregular wanderings of the moon1 must have given evidence of intellectual powers far elevated above those of the majority of the human race4 ,we need not wonder1 therefore1 that such homage is now paid to the genius of ,newton1--an admiration which has been continually increasing1 as new discoveries have been made by tracing out new consequences of the law of universal gravitation4 ,the chief object of astronomical tables is to give the amount of all the irregularities that attend the motions of the heavenly bodies1 by estimating the separate value of each1 under all the different circumstances in which a body can be placed4 ,thus1 with respect to the moon1 before we can determine accurately the distance of the moon from the vernal equinox1 that is1 her longitude at any given moment1 we must be able to make exact allowances for all her irregularities which would affect her longitude4 ,these are in all no less than sixty1 though most of them are so exceedingly minute1 that it is not common to take into the account more than twenty-eight or thirty4 ,the values of these are all given in the lunar tables2 and in finding the moon's place1 at any given time1 we proceed as follows3 ,we first find what her place would be on the supposition that she moves uniformly in a circle4 ,this gives her mean place4 ,we next apply the various corrections for her irregular motions2 that is1 we apply the equations1 subtracting some and adding others1 and thus we find her true place4 ,the astronomical tables have been carried to such an astonishing degree of accuracy1 that it is said1 by the highest authority1 that an astronomer could now predict1 for a thousand years to come1 the precise moment of the passage of any one of the stars over the meridian wire of the telescope of his transit-instrument1 with such a degree of accuracy1 that the error would not be so great as to remove the object through an angular space corresponding to the semidiameter of the finest wire that could be made2 and a body which1 by the tables1 ought to appear in the transit-instrument in the middle of that wire1 would in no case be removed to its outer edge4 ,the astronomer1 the mathematician1 and the artist1 have united their powers to produce this great result4 ,the astronomer has collected the data1 by long-continued and most accurate observations on the actual motions of the heavenly bodies1 from night to night1 and from year to year2 the mathematician has taken these data1 and applied to them the boundless resources of geometry and the calculus2 and1 finally1 the instrument-maker has furnished the means1 not only of verifying these conclusions1 but of discovering new truths1 as the foundation of future reasonings4 ,since the points where the moon crosses the ecliptic1 or the moon's nodes1 constantly shift their positions about nineteen and a half degrees to the westward1 every year1 the sun1 in his annual progress in the ecliptic1 will go from the node round to the same node again in less time than a year1 since the node goes to meet him nineteen and a half degrees to the west of the point where they met before4 ,it would have taken the sun about nineteen days to have passed over this arc2 and consequently1 the interval between two successive conjunctions between the sun and the moon's node is about nineteen days shorter than the solar year of three hundred and sixty-five days2 that is1 it is about three hundred and forty-six days2 or1 more exactly1 it is #cdf4faihea days4 ,the time from one new moon to another is #bi4ecjehhg days4 ,now1 nineteen of the former periods are almost exactly equal to two hundred and twenty-three of the latter3 ,for #cdf4faihea #aifehe4gh days#ah y4 #aj d4 ,and #bi4ecjehhg #bbcfehe4cb ,hence1 if the sun and moon were to leave the moon's node together1 after the sun had been round to the same node nineteen times1 the moon would have made very nearly two hundred and twenty-three conjunctions with the sun4 ,if1 therefore1 she was in conjunction with the sun at the beginning of this period1 she would be in conjunction again at the end of it2 and all things relating to the sun1 the moon1 and the node1 would be restored to the same relative situation as before1 and the sun and moon would start again1 to repeat the same phenomena1 arising out of these relations1 as occurred in the preceding period1 and in the same order4 ,now1 when the sun and moon meet at the moon's node1 an eclipse of the sun happens2 and during the entire period of eighteen and a half years eclipses will happen1 nearly in the same manner as they did at corresponding times in the preceding period4 ,thus1 if there was a great eclipse of the sun on the fifth year of one of these periods1 a similar eclipse 7usually differing somewhat in magnitude7 might be expected on the fifth year of the next period4 ,hence this period1 consisting of about eighteen years and ten days1 under the name of the ,saros1 was used by the ,chaldeans1 and other ancient nations1 in predicting eclipses4 ,it was probably by this means that ,thales1 a ,grecian astronomer who flourished six hundred years before the ,christian era1 predicted an eclipse of the sun4 ,herodotus1 the old historian of ,greece1 relates that the day was suddenly changed into night1 and that ,thales of ,miletus had foretold that a great eclipse was to happen this year4 ,it was therefore1 at that age1 considered as a distinguished feat to predict even the year in which an eclipse was to happen4 ,this eclipse is memorable in ancient history1 from its having terminated the war between the ,lydians and the ,medes1 both parties being smitten with such indications of the wrath of the gods4 ,the ,metonic ,cycle has sometimes been confounded with the ,saros1 but it is not the same with it1 nor was the period used1 like the ,saros1 for foretelling eclipses1 but for ascertaining the age of the moon at any given period4 ,it consisted of nineteen tropical years1 during which time there are exactly two hundred and thirty-five new moons2 so that1 at the end of this period1 the new moons will recur at seasons of the year corresponding exactly to those of the preceding cycle4 ,if1 for example1 a new moon fell at the time of the vernal equinox1 in one cycle1 nineteen years afterwards it would occur again at the same equinox2 or1 if it had happened ten days after the equinox1 in one cycle1 it would also happen ten days after the equinox1 nineteen years afterwards4 ,by registering1 therefore1 the exact days of any cycle at which the new or full moons occurred1 such a calendar would show on what days these events would occur in any other cycle2 and1 since the regulation of games1 feasts1 and fasts1 has been made very extensively1 both in ancient and modern times1 according to new or full moons1 such a calendar becomes very convenient for finding the day on which the new or full moon required takes place4 ,suppose1 for example1 it were decreed that a festival should be held on the day of the first full moon after the ,vernal equinox4 ,then1 to find on what day that would happen1 in any given year1 we have only to see what year it is of the lunar cycle2 for the day will be the same as it was in the corresponding year of the calendar which records all the full moons of the cycle for each year1 and the respective days on which they happen4 ,the ,athenians adopted the metonic cycle four hundred and thirty-three years before the ,christian era1 for the regulation of their calendars1 and had it inscribed in letters of gold on the walls of the temple of ,minerva4 ,hence the term golden number1 still found in our almanacs1 which denotes the year of the lunar cycle4 ,thus1 fourteen was the golden number for #ahcg1 being the fourteenth year of the lunar cycle4 ,the inequalities of the moon's motions are divided into periodical and secular4 ,periodical inequalities are those which are completed in comparatively short periods4 ,secular inequalities are those which are completed only in very long periods1 such as centuries or ages4 ,hence the corresponding terms periodical equations and secular equations4 ,as an example of a secular inequality1 we may mention the acceleration of the moon's mean motion4 ,it is discovered that the moon actually revolves around the earth in a less period now than she did in ancient times4 ,the difference1 however1 is exceedingly small1 being only about ten seconds in a century4 ,in a lunar eclipse1 the moon's longitude differs from that of the sun1 at the middle of the eclipse1 by exactly one hundred and eighty degrees2 and since the sun's longitude at any given time of the year is known1 if we can learn the day and hour when an eclipse occurred at any period of the world1 we of course know the longitude of the sun and moon at that period4 ,now1 in the year #gba1 before the ,christian era1 ,ptolemy records a lunar eclipse to have happened1 and to have been observed by the ,chaldeans4 ,the moon's longitude1 therefore1 for that time1 is known2 and as we know the mean motions of the moon1 at present1 starting from that epoch1 and computing1 as may easily be done1 the place which the moon ought to occupy at present1 at any given time1 she is found to be actually nearly a degree and a half in advance of that place4 ,moreover1 the same conclusion is derived from a comparison of the ,chaldean observations with those made by an ,arabian astronomer of the tenth century4 ,this phenomenon at first led astronomers to apprehend that the moon encountered a resisting medium1 which1 by destroying at every revolution a small portion of her projectile force1 would have the effect to bring her nearer and nearer to the earth1 and thus to augment her velocity4 ,but1 in #aghf1 ,la ,place demonstrated that this acceleration is one of the legitimate effects of the sun's disturbing force1 and is so connected with changes in the eccentricity of the earth's orbit1 that the moon will continue to be accelerated while that eccentricity diminishes2 but when the eccentricity has reached its minimum1 or lowest point1 7as it will do1 after many ages17 and begins to increase1 then the moon's motions will begin to be retarded1 and thus her mean motions will oscillate for ever about a mean value4 ,,letter ,,xviii4 ,,eclipses4 ----,as when the sun1 new risen1 ,looks through the horizontal misty air1 ,shorn of his beams1 or from behind the moon1 ,in dim eclipse1 disastrous twilight sheds ,on half the nations1 and with fear of change ,perplexes monarchs3 darkened so1 yet shone1 ,above them all1 the ,archangel4--,milton4 ,,having now learned various particulars respecting the earth1 the sun1 and the moon1 you are prepared to understand the explanation of solar and lunar eclipses1 which have in all ages excited a high degree of interest4 ,indeed1 what is more admirable1 than that astronomers should be able to tell us1 years beforehand1 the exact instant of the commencement and termination of an eclipse1 and describe all the attendant circumstances with the greatest fidelity4 ,you have doubtless1 my dear friend1 participated in this admiration1 and felt a strong desire to learn how it is that astronomers are able to look so far into futurity4 ,i will endeavor1 in this ,letter1 to explain to you the leading principles of the calculation of eclipses1 with as much plainness as possible4 ,an eclipse of the moon happens when the moon1 in its revolution around the earth1 falls into the earth's shadow4 ,an eclipse of the sun happens when the moon1 coming between the earth and the sun1 covers either a part or the whole of the solar disk4 ,the earth and the moon being both opaque1 globular bodies1 exposed to the sun's light1 they cast shadows opposite to the sun1 like any other bodies on which the sun shines4 ,were the sun of the same size with the earth and the moon1 then the lines drawn touching the surface of the sun and the surface of the earth or moon 7which lines form the boundaries of the shadow7 would be parallel to each other1 and the shadow would be a cylinder infinite in length2 and were the sun less than the earth or the moon1 the shadow would be an increasing cone1 its narrower end resting on the earth2 but as the sun is vastly greater than either of these bodies1 the shadow of each is a cone whose base rests on the body itself1 and which comes to a point1 or vertex1 at a certain distance behind the body4 ,these several cases are represented in the following diagrams1 ,figs4 #ci1 #dj1 #da4 ,illustration ,figs4 #ci1 #dj1 #da4 ,it is found1 by calculation1 that the length of the moon's shadow1 on an average1 is just about sufficient to reach to the earth2 but the moon is sometimes further from the earth than at others1 and when she is nearer than usual1 the shadow reaches considerably beyond the surface of the earth4 ,also1 the moon1 as well as the earth1 is at different distances from the sun at different times1 and its shadow is longest when it is furthest from the sun4 ,now1 when both these circumstances conspire1 that is1 when the moon is in her perigee and along with the earth in her aphelion1 her shadow extends nearly fifteen thousand miles beyond the centre of the earth1 and covers a space on the surface one hundred and seventy miles broad4 ,the earth's shadow is nearly a million of miles in length1 and consequently more than three and a half times as long as the distance of the earth from the moon2 and it is also1 at the distance of the moon1 three times as broad as the moon itself4 ,an eclipse of the sun can take place only at new moon1 when the sun and moon meet in the same part of the heavens1 for then only can the moon come between us and the sun2 and an eclipse of the moon can occur only when the sun and moon are in opposite parts of the heavens1 or at full moon2 for then only can the moon fall into the shadow of the earth4 ,illustration ,fig4 #db4 ,the nature of eclipses will be clearly understood from the following representation4 ,the diagram1 ,fig4 #db1 exhibits the relative position of the sun1 the earth1 and the moon1 both in a solar and in a lunar eclipse4 ,here1 the moon is first represented1 while revolving round the earth1 as passing between the earth and the sun1 and casting its shadow on the earth4 ,as the moon is here supposed to be at her average distance from the earth1 the shadow but just reaches the earth's surface4 ,were the moon 7as is sometimes the case7 nearer the earth her shadow would not terminate in a point1 as is represented in the figure1 but at a greater or less distance nearer the base of the cone1 so as to cover a considerable space1 which1 as ,i have already mentioned1 sometimes extends to one hundred and seventy miles in breadth1 but is commonly much less than this4 ,on the other side of the earth1 the moon is represented as traversing the earth's shadow1 as is the case in a lunar eclipse4 ,as the moon is sometimes nearer the earth and sometimes further off1 it is evident that it will traverse the shadow at a broader or a narrower part1 accordingly4 ,the figure1 however1 represents the moon as passing the shadow further from the earth than is ever actually the case1 since the distance from the earth is never so much as one third of the whole length of the shadow4 ,it is evident from the figure1 that if a spectator were situated where the moon's shadow strikes the earth1 the moon would cut off from him the view of the sun1 or the sun would be totally eclipsed4 ,or1 if he were within a certain distance of the shadow on either side1 the moon would be partly between him and the sun1 and would intercept from him more or less of the sun's light1 according as he was nearer to the shadow or further from it4 ,if he were at c or d1 he would just see the moon entering upon the sun's disk2 if he were nearer the shadow than either of these points1 he would have a portion of this light cut off from his view1 and more1 in proportion as he drew nearer the shadow2 and the moment he entered the shadow1 he would lose sight of the sun4 ,to all places between a or b and the shadow1 the sun would cast a partial shadow of the moon1 growing deeper and deeper1 as it approached the true shadow4 ,this partial shadow is called the moon's penumbra4 ,in like manner1 as the moon approaches the earth's shadow1 in a lunar eclipse1 as soon as she arrives at a1 the earth begins to intercept from her a portion of the sun's light1 or she falls in the earth's penumbra4 ,she continues to lose more and more of the sun's light1 as she draws near to the shadow1 and hence her disk becomes gradually obscured1 until it enters the shadow1 when the sun's light is entirely lost4 ,as the sun and earth are both situated in the plane of the ecliptic1 if the moon also revolved around the earth in this plane1 we should have a solar eclipse at every new moon1 and a lunar eclipse at every full moon2 for1 in the former case1 the moon would come directly between us and the sun1 and in the latter case1 the earth would come directly between the sun and the moon4 ,but the moon is inclined to the ecliptic about five degrees1 and the centre of the moon may be all this distance from the centre of the sun at new moon1 and the same distance from the centre of the earth's shadow at full moon4 ,it is true1 the moon extends across her path1 one half her breadth lying on each side of it1 and the sun likewise reaches from the ecliptic a distance equal to half his breadth4 ,but these luminaries together make but little more than a degree1 and consequently1 their two semidiameters would occupy only about half a degree of the five degrees from one orbit to the other where they are furthest apart4 ,also1 the earth's shadow1 where the moon crosses it1 extends from the ecliptic less than three fourths of a degree1 so that the semidiameter of the moon and of the earth's shadow would together reach but little way across the space that may1 in certain cases1 separate the two luminaries from each other when they are in opposition4 ,thus1 suppose we could take hold of the circle in the figure that represents the moon's orbit1 7,fig4 #db1 page #aig17 and lift the moon up five degrees above the plane of the paper1 it is evident that the moon1 as seen from the earth1 would appear in the heavens five degrees above the sun1 and of course would cut off none of his light2 and it is also plain that the moon1 at the full1 would pass the shadow of the earth five degrees below it1 and would suffer no eclipse4 ,but in the course of the sun's apparent revolution round the earth once a year he is successively in every part of the ecliptic2 consequently1 the conjunctions and oppositions of the sun and moon may occur at any part of the ecliptic1 and of course at the two points where the moon's orbit crosses the ecliptic1--that is1 at the nodes2 for the sun must necessarily come to each of these nodes once a year4 ,if1 then1 the moon overtakes the sun just as she is crossing his path1 she will hide more or less of his disk from us4 ,since1 also1 the earth's shadow is always directly opposite to the sun1 if the sun is at one of the nodes1 the shadow must extend in the direction of the other node1 so as to lie directly across the moon's path2 and if the moon overtakes it there1 she will pass through it1 and be eclipsed4 ,thus1 in ,fig4 #dc1 let ,,bn represent the sun's path1 and ,,an1 the moon's1--,n being the place of the node2 then it is evident1 that if the two luminaries at new moon be so far from the node1 that the distances between their centres is greater than their semidiameters1 no eclipse can happen2 but if that distance is less than this sum1 as at ,e1 ,f1 then an eclipse will take place2 but if the position be as at ,c1 ,d1 the two bodies will just touch one another4 ,if ,a denotes the earth's shadow1 instead of the sun1 the same illustration will apply to an eclipse of the moon4 ,illustration ,fig4 #dc4 ,since bodies are defined to be in conjunction when they are in the same part of the heavens1 and to be in opposition when they are in opposite parts of the heavens1 it may not appear how the sun and moon can be in conjunction1 as at ,a and ,b1 when they are still at some distance from each other4 ,but it must be recollected that bodies are in conjunction when they have the same longitude1 in which case they are situated in the same great circle perpendicular to the ecliptic1--that is1 in the same secondary to the ecliptic4 ,one of these bodies may be much further from the ecliptic than the other2 still1 if the same secondary to the ecliptic passes through them both1 they will be in conjunction or opposition4 ,in a total eclipse of the moon1 its disk is still visible1 shining with a dull1 red light4 ,this light cannot be derived directly from the sun1 since the view of the sun is completely hidden from the moon2 nor by reflection from the earth1 since the illuminated side of the earth is wholly turned from the moon2 but it is owing to refraction from the earth's atmosphere1 by which a few scattered rays of the sun are bent round into the earth's shadow and conveyed to the moon1 sufficient in number to afford the feeble light in question4 ,it is impossible fully to understand the method of calculating eclipses1 without a knowledge of trigonometry2 still it is not difficult to form some general notion of the process4 ,it may be readily conceived that1 by long-continued observations on the sun and moon1 the laws of their revolution may be so well understood1 that the exact places which they will occupy in the heavens at any future times may be foreseen and laid down in tables of the sun and moon's motions2 that we may thus ascertain1 by inspecting the tables1 the instant when these two bodies will be together in the heavens1 or be in conjunction1 and when they will be one hundred and eighty degrees apart1 or in opposition4 ,moreover1 since the exact place of the moon's node among the stars at any particular time is known to astronomers1 it cannot be difficult to determine when the new or full moon occurs in the same part of the heavens as that where the node is projected1 as seen from the earth4 ,in short1 as astronomers can easily determine what will be the relative position of the sun1 the moon1 and the moon's nodes1 for any given time1 they can tell when these luminaries will meet so near the node as to produce an eclipse of the sun1 or when they will be in opposition so near the node as to produce an eclipse of the moon4 ,a little reflection will enable you to form a clear idea of the situation of the sun1 the moon1 and the earth1 at the time of a solar eclipse4 ,first1 suppose the conjunction to take place at the node2 that is1 imagine the moon to come directly between the earth and the sun1 as she will of course do1 if she comes between the earth and the sun the moment she is crossing the ecliptic2 for then the three bodies will all lie in one and the same straight line4 ,but when the moon is in the ecliptic1 her shadow1 or at least the axis1 or central line1 of the shadow1 must coincide with the line that joins the centres of the sun and earth1 and reach along the plane of the ecliptic towards the earth4 ,the moon's shadow1 at her average distance from the earth1 is just about long enough to reach the surface of the earth2 but when the moon1 at the new1 is in her apogee1 or at her greatest distance from the earth1 the shadow is not long enough to reach the earth4 ,on the contrary1 when the moon is nearer to us than her average distance1 her shadow is long enough to reach beyond the earth1 extending1 when the moon is in her perigee1 more than fourteen thousand miles beyond the centre of the earth4 ,now1 as during the eclipse the moon moves nearly in the plane of the ecliptic1 her shadow which accompanies her must also move nearly in the same plane1 and must therefore traverse the earth across its central regions1 along the terrestrial ecliptic1 since this is nothing more than the intersection of the plane of the celestial ecliptic with the earth's surface4 ,the motion of the earth1 too1 on its axis1 in the same direction1 will carry a place along with the shadow1 though with a less velocity by more than one half2 so that the actual velocity of the shadow1 in respect to places over which it passes on the earth1 will only equal the difference between its own rate and that of the places1 as they are carried forward in the diurnal revolution4 ,we have thus far supposed that the moon comes to her conjunction precisely at the node1 or at the moment when she is crossing the ecliptic4 ,but1 secondly1 suppose she is on the north side of the ecliptic at the time of conjunction1 and moving towards her descending node1 and that the conjunction takes place as far from the node as an eclipse can happen4 ,the shadow will not fall in the plane of the ecliptic1 but a little northward of it1 so as just to graze the earth near the pole of the ecliptic4 ,the nearer the conjunction comes to the node1 the further the shadow will fall from the polar towards the equatorial regions4 ,in a solar eclipse1 the shadow of the moon travels over a portion of the earth1 as the shadow of a small cloud1 seen from an eminence in a clear day1 rides along over hills and plains4 ,let us imagine ourselves standing on the moon2 then we shall see the earth partially eclipsed by the moon's shadow1 in the same manner as we now see the moon eclipsed by the shadow of the earth2 and we might calculate the various circumstances of the eclipse1--its commencement1 duration1 and quantity1--in the same manner as we calculate these elements in an eclipse of the moon1 as seen from the earth4 ,but although the general characters of a solar eclipse might be investigated on these principles1 so far as respects the earth at large1 yet1 as the appearances of the same eclipse of the sun are very different at different places on the earth's surface1 it is necessary to calculate its peculiar aspects for each place separately1 a circumstance which makes the calculation of a solar eclipse much more complicated and tedious than that of an eclipse of the moon4 ,the moon1 when she enters the shadow of the earth1 is deprived of the light of the part immersed1 and the effect upon its appearance is the same as though that part were painted black1 in which case it would be black alike to all places where the moon was above the horizon4 ,but it not so with a solar eclipse4 ,we do not see this by the shadow cast on the earth1 as we should do1 if we stood on the moon1 but by the interposition of the moon between us and the sun2 and the sun may be hidden from one observer1 while he is in full view of another only a few miles distant4 ,thus1 a small insulated cloud sailing in a clear sky will1 for a few moments1 hide the sun from us1 and from a certain space near us1 while all the region around is illuminated4 ,but although the analogy between the motions of the shadow of a small cloud and of the moon in a solar eclipse holds good in many particulars1 yet the velocity of the lunar shadow is far greater than that of the cloud1 being no less than two thousand two hundred and eighty miles per hour4 ,the moon's shadow can never cover a space on the earth more than one hundred and seventy miles broad1 and the space actually covered commonly falls much short of that4 ,the portion of the earth's surface ever covered by the moon's penumbra is about four thousand three hundred and ninety-three miles4 ,the apparent diameter of the moon varies materially at different times1 being greatest when the moon is nearest to us1 and least when she is furthest off2 while the sun's apparent dimensions remain nearly the same4 ,when the moon is at her average distance from the earth1 she is just about large enough to cover the sun's disk2 consequently1 if1 in a central eclipse of the sun1 the moon is at her mean distance1 she covers the sun but for an instant1 producing only a momentary eclipse4 ,if she is nearer than her average distance1 then the eclipse may continue total some time1 though never more than eight minutes1 and seldom so long as that2 but if she is further off than usual1 or towards her apogee1 then she is not large enough to cover the whole solar disk1 but we see a ring of the sun encircling the moon1 constituting an annular eclipse1 as seen in ,fig4 #dd4 ,even the elevation of the moon above the horizon will sometimes sensibly affect the dimensions of the eclipse4 ,you will recollect that the moon is nearer to us when on the meridian than when in the horizon by nearly four thousand miles1 or by nearly the radius of the earth2 and consequently1 her apparent diameter is largest when on the meridian4 ,the difference is so considerable1 that the same eclipse will appear total to a spectator who views it near his meridian1 while1 at the same moment1 it appears annular to one who has the moon near his horizon4 ,an annular eclipse may last1 at most1 twelve minutes and twenty-four seconds4 ,illustration ,fig4 #dd4 ,eclipses of the sun are more frequent than those of the moon4 ,yet lunar eclipses being visible to every part of the terrestrial hemisphere opposite to the sun1 while those of the sun are visible only to a small portion of the hemisphere on which the moon's shadow falls1 it happens that1 for any particular place on the earth1 lunar eclipses are more frequently visible than solar4 ,in any year1 the number of eclipses of both luminaries cannot be less than two nor more than seven3 the most usual number is four1 and it is very rare to have more than six4 ,a total eclipse of the moon frequently happens at the next full moon after an eclipse of the sun4 ,for since1 in a solar eclipse1 the sun is at or near one of the moon's nodes1--that is1 is projected to the place in the sky where the moon crosses the ecliptic1--the earth's shadow1 which is of course directly opposite to the sun1 must be at or near the other node1 and may not have passed too far from the node before the moon comes round to the opposition and overtakes it4 ,in total eclipses of the sun1 there has sometimes been observed a remarkable radiation of light from the margin of the sun1 which is thought to be owing to the zodiacal light1 which is of such dimensions as to extend far beyond the solar orb4 ,a striking appearance of this kind was exhibited in the total eclipse of the sun which occurred in ,june1 #ahjf4 ,a total eclipse of the sun is one of the most sublime and impressive phenomena of ,nature4 ,among barbarous tribes it is ever contemplated with fear and astonishment1 and as strongly indicative of the displeasure of the gods4 ,two ancient nations1 the ,lydians and ,medes1 alluded to before1 who were engaged in a bloody war1 about six hundred years before ,christ1 were smitten with such awe1 on the appearance of a total eclipse of the sun1 just on the eve of a battle1 that they threw down their arms1 and made peace4 ,when ,columbus first discovered ,america1 and was in danger of hostility from the ,natives1 he awed them into submission by telling them that the sun would be darkened on a certain day1 in token of the anger of the gods at them1 for their treatment of him4 ,among cultivated nations1 a total eclipse of the sun is recognised1 from the exactness with which the time of occurrence and the various appearances answer to the prediction1 as affording one of the proudest triumphs of astronomy4 ,by astronomers themselves1 it is of course viewed with the highest interest1 not only as verifying their calculations1 but as contributing to establish1 beyond all doubt1 the certainty of those grand laws1 the truth of which is involved in the result4 ,i had the good fortune to witness the total eclipse of the sun of ,june1 #ahjf1 which was one of the most remarkable on record4 ,to the wondering gaze of childhood it presented a spectacle that can never be forgotten4 ,a bright and beautiful morning inspired universal joy1 for the sky was entirely cloudless4 ,every one was busily occupied in preparing smoked glass1 in readiness for the great sight1 which was to be first seen about ten o'clock4 ,a thrill of mingled wonder and delight struck every mind when1 at the appointed moment1 a little black indentation appeared on the limb of the sun4 ,this gradually expanded1 covering more and more of the solar disk1 until an increasing gloom was spread over the face of ,nature2 and when the sun was wholly lost1 near mid-day1 a feeling of horror pervaded almost every beholder4 ,the darkness was wholly unlike that of twilight or night4 ,a thick curtain1 very different from clouds1 hung upon the face of the sky1 producing a strange and indescribably gloomy appearance1 which was reflected from all things on the earth1 in hues equally strange and unnatural4 ,some of the planets1 and the largest of the fixed stars1 shone out through the gloom1 yet with their usual brightness4 ,the temperature of the air rapidly declined1 and so sudden a chill came over the earth1 that many persons caught severe colds from their exposure4 ,even the animal tribes exhibited tokens of fear and agitation4 ,birds1 especially1 fluttered and flew swiftly about1 and domestic fowls went to rest4 ,indeed1 the word eclipse is derived from a ,greek word1 7 ekleipsis1 ekleipsis17 which signifies to fail1 to faint or swoon away2 since the moon1 at the period of her greatest brightness1 falling into the shadow of the earth1 was imagined by the ancients to sicken and swoon1 as if she were going to die4 ,by some very ancient nations she was supposed1 at such times1 to be in pain2 and1 in order to relieve her fancied distress1 they lifted torches high in the atmosphere1 blew horns and trumpets1 beat upon brazen vessels1 and even1 after the eclipse was over1 they offered sacrifices to the moon4 ,the opinion also extensively prevailed1 that it was in the power of witches1 by their spells and charms1 not only to darken the moon1 but to bring her down from her orbit1 and to compel her to shed her baleful influences upon the earth4 ,in solar eclipses1 also1 especially when total1 the sun was supposed to turn away his face in abhorrence of some atrocious crime1 that either had been perpetrated or was about to be perpetrated1 and to threaten mankind with everlasting night1 and the destruction of the world4 ,to such superstitions ,milton alludes1 in the passage which ,i have taken for the motto of this ,letter4 ,the ,chinese1 who1 from a very high period of antiquity1 have been great observers of eclipses1 although they did not take much notice of those of the moon1 regarded eclipses of the sun in general as unfortunate1 but especially such as occurred on the first day of the year4 ,these were thought to forebode the greatest calamities to the emperor1 who on such occasions did not receive the usual compliments of the season4 ,when1 from the predictions of their astronomers1 an eclipse of the sun was expected1 they made great preparation at court for observing it2 and as soon as it commenced1 a blind man beat a drum1 a great concourse assembled1 and the mandarins1 or nobility1 appeared in state4 ,,letter ,,xix4 ,,longitude4--,,tides4 ,first in his east1 the glorious lamp was seen1 ,regent of day1 and all the horizon round ,invested with bright rays1 jocund to run ,his longitude through heaven's high road2 the gray ,dawn and the ,pleiades before him danced1 ,shedding sweet influence4--,milton4 ,,the ancients studied astronomy chiefly as subsidiary to astrology1 with the vain hope of thus penetrating the veil of futurity1 and reading their destinies among the stars4 ,the moderns1 on the other hand1 have in view1 as the great practical object of this study1 the perfecting of the art of navigation4 ,when we reflect on the vast interests embarked on the ocean1 both of property and life1 and upon the immense benefits that accrue to society from a safe and speedy intercourse between the different nations of the earth1 we cannot but see that whatever tends to enable the mariner to find his way on the pathless ocean1 and to secure him against its multiplied dangers1 must confer a signal benefit on society4 ,in ancient times1 to venture out of sight of land was deemed an act of extreme audacity2 and ,horace1 the ,roman poet1 pronounces him who first ventured to trust his frail bark to the stormy ocean1 endued with a heart of oak1 and girt with triple folds of brass4 ,but now1 the navigator who fully avails himself of all the resources of science1 and especially of astronomy1 may launch fearlessly on the deep1 and almost bid defiance to rocks and tempests4 ,by enabling the navigator to find his place on the ocean with almost absolute precision1 however he may have been driven about by the winds1 and however long he may have been out of sight of land1 astronomers must be held as great benefactors to all who commit either their lives or their fortunes to the sea4 ,nor have they secured to the art of navigation such benefits without incredible study and toil1 in watching the motions of the heavenly bodies1 in investigating the laws by which their movements are governed1 and in reducing all their discoveries to a form easily available to the navigator1 so that1 by some simple observation on one or two of the heavenly bodies1 with instruments which the astronomer has invented1 and prepared for his use1 and by looking out a few numbers in tables which have been compiled for him1 with immense labor1 he may ascertain the exact place he occupies on the surface of the globe1 thousands of miles from land4 ,the situation of any place is known by its latitude and longitude4 ,as charts of every ocean and sea are furnished to the sailor1 in which are laid down the latitudes and longitudes of every point of land1 whether on the shores of islands or the main1 he has1 therefore1 only to ascertain his latitude and longitude at any particular place on the ocean1 in order to find where he is1 with respect to the nearest point of land1 although this may be1 and may always have been1 entirely out of sight to him4 ,to determine the latitude of a place is comparatively an easy matter1 whenever we can see either the sun or the stars4 ,the distance of the sun from the zenith1 when on the meridian1 on a given day of the year1 7which distance we may easily take with the sextant17 enables us1 with the aid of the tables1 to find the latitude of the place2 or1 by taking the altitude of the north star1 we at once obtain the latitude4 ,the longitude of a place may be found by any method1 by which we may ascertain how much its time of day differs from that of ,greenwich at the same moment4 ,a place that lies eastward of another comes to the meridian an hour earlier for every fifteen degrees of longitude1 and of course has the hour of the day so much in advance of the other1 so that it counts one o'clock when the other place counts twelve4 ,on the other hand1 a place lying westward of another comes to the meridian later by one hour for every fifteen degrees1 so that it counts only eleven o'clock when the other place counts twelve4 ,keeping these principles in view1 it is easy to see that a comparison of the difference of time between two places at the same moment1 allowing fifteen degrees for an hour1 sixty minutes for every four minutes of time1 and sixty seconds for every four seconds of time1 affords us an accurate mode of finding the difference of longitude between the two places4 ,this comparison may be made by means of a chronometer1 or from solar or lunar eclipses1 or by what is called the lunar method of finding the longitude4 ,chronometers are distinguished from clocks1 by being regulated by means of a balance-wheel instead of a pendulum4 ,a watch1 therefore1 comes under the general definition of a chronometer2 but the name is more commonly applied to larger timepieces1 too large to be carried about the person1 and constructed with the greatest possible accuracy1 with special reference to finding the longitude4 ,suppose1 then1 we are furnished with a chronometer set to ,greenwich time4 ,we arrive at ,new ,york1 for example1 and compare it with the time there4 ,we find it is five hours in advance of the ,new-,york time1 indicating five o'clock1 ,p4,m41 when it is noon at ,new ,york4 ,hence we find that the longitude of ,new ,york is #eaege degrees4#aa ,the time at ,new ,york1 or any individual place1 can be known by observations with the transit-instrument1 which gives us the precise moment when the sun is on the meridian4 ,it would not be necessary to resort to ,greenwich1 for the purpose of setting our chronometer to ,greenwich time1 as it might be set at any place whose longitude is known1 having been previously determined4 ,thus1 if we know that the longitude of a certain place is exactly sixty degrees east of ,greenwich1 we have only to set our chronometer four hours behind the time at that place1 and it will be regulated to ,greenwich time4 ,hence it is a matter of the greatest importance to navigation1 that the longitude of numerous ports1 in different parts of the earth1 should be accurately determined1 so that when a ship arrives at any such port1 it may have the means of setting or verifying its chronometer4 ,this method of taking the longitude seems so easy1 that you will perhaps ask1 why it is not sufficient for all purposes1 and accordingly1 why it does not supersede the move complicated and laborious methods8 why every sailor does not provide himself with a chronometer1 instead of finding his longitude at sea by tedious and oft-repeated calculations1 as he is in the habit of doing8 ,i answer1 it is only in a few extraordinary cases that chronometers have been constructed of such accuracy as to afford results as exact as those obtained by the other methods1 to be described shortly2 and instruments of such perfection are too expensive for general use among sailors4 ,indeed1 the more common chronometers cost too much to come within the means of a great majority of sea-faring men4 ,moreover1 by being transported from place to place1 chronometers are liable to change their rate4 ,by the rate of any timepiece is meant its deviation from perfect accuracy4 ,thus1 if a clock should gain one second per day1 one day with another1 and we should find it impossible to bring it nearer to the truth1 we may reckon this as its rate1 and allow for it in our estimate of the time of any particular observation4 ,if the error was not uniform1 but sometimes greater and sometimes less than one second per day1 then the amount of such deviation is called its variation from its mean rate4 ,i introduce these minute statements1 7which are more precise than ,i usually deem necessary17 to show you to what an astonishing degree of accuracy chronometers have in some instances been brought4 ,they have been carried from ,london to ,baffin's ,bay1 and brought back1 after a three years' voyage1 and found to have varied from their mean rate1 during the whole time1 only a second or two1 while the extreme variation of several chronometers1 tried at the ,royal ,observatory at ,greenwich1 never exceeded a second and a half4 ,could chronometers always be depended on to such a degree of accuracy as this1 we should hardly desire any thing better for determining the longitude of different places on the earth4 ,a recent determination of the longitude of the ,city ,hall in ,new ,york1 by means of three chronometers1 sent out from ,london expressly for that purpose1 did not differ from the longitude as found by a solar eclipse 7which is one of the best methods7 but a second and a quarter4 ,eclipses of the sun and moon furnish the means of ascertaining the longitude of a place1 because the entrance of the moon into the earth's shadow in a lunar eclipse1 and the entrance of the moon upon the disk of the sun in a solar eclipse1 are severally examples of one of those instantaneous occurrences in the heavens1 which afford the means of comparing the times of different places1 and of thus determining their differences of longitude4 ,thus1 if the commencement of a lunar eclipse was seen at one place an hour sooner than at another1 the two places would be fifteen degrees apart1 in longitude2 and if the longitude of one of the places was known1 that of the other would become known also4 ,the exact instant of the moon's entering into the shadow of the earth1 however1 cannot be determined with very great precision1 since the moon1 in passing through the earth's penumbra1 loses its light gradually1 so that the moment when it leaves the penumbra and enters into the shadow cannot be very accurately defined4 ,the first contact of the moon with the sun's disk1 in a solar eclipse1 or the moment of leaving it1--that is1 the beginning and end of the eclipse1--are instants that can be determined with much precision1 and accordingly they are much relied on for an accurate determination of the longitude4 ,but1 on account of the complicated and laborious nature of the calculation of the longitude from an eclipse of the sun1 7since the beginning and end are not seen at different places1 at the same moment17 this method of finding the longitude is not adapted to common use1 nor available at sea4 ,it is useful1 however1 for determining the longitude of fixed observatories4 ,the lunar method of finding the longitude is the most refined and accurate of all the modes practised at sea4 ,the motion of the moon through the heavens is so rapid1 that she perceptibly alters her distance from any star every minute2 consequently1 the moment when that distance is a certain number of degrees and minutes is one of those instantaneous events1 which may be taken advantage of for comparing the times of different places1 and thus determining their difference of longitude4 ,now1 in a work called the ',nautical ,almanac1' printed in ,london1 annually1 for the use of navigators1 the distance of the moon from the sun by day1 or from known fixed stars by night1 for every day and night in the year1 is calculated beforehand4 ,if1 therefore1 a sailor wishes to ascertain his longitude1 he may take with his sextant the distance of the moon from one of these stars at any time1--suppose nine o'clock1 at night1--and then turn to the ',nautical ,almanac1' and see what time it was at ,greenwich when the distance between the moon and that star was the same4 ,let it be twelve o'clock1 or three hours in advance of his time3 his longitude1 of course1 is forty-five degrees west4 ,this method requires more skill and accuracy than are possessed by the majority of seafaring men2 but1 when practised with the requisite degree of skill1 its results are very satisfactory4 ,captain ,basil ,hall1 one of the most scientific commanders in the ,british navy1 relates the following incident1 to show the excellence of this method4 ,he sailed from ,san ,blas1 on the west coast of ,mexico1 and1 after a voyage of eight thousand miles1 occupying eighty-nine days1 arrived off ,rio de ,janeiro1 having1 in this interval1 passed through the ,pacific ,ocean1 rounded ,cape ,horn1 and crossed the ,south ,atlantic1 without making any land1 or even seeing a single sail1 with the exception of an ,american whaler off ,cape ,horn4 ,when within a week's sail of ,rio1 he set seriously about determining1 by lunar observations1 the precise line of the ship's course1 and its situation at a determinate moment2 and having ascertained this within from five to ten miles1 ran the rest of the way by those more ready and compendious methods1 known to navigators1 which can be safely employed for short trips between one known point and another1 but which cannot be trusted in long voyages1 where the moon is the only sure guide4 ,they steered towards ,rio ,janeiro for some days after taking the lunars1 and1 having arrived within fifteen or twenty miles of the coast1 they hove to1 at four in the morning1 till the day should break1 and then bore up1 proceeding cautiously1 on account of a thick fog which enveloped them4 ,as this cleared away1 they had the satisfaction of seeing the great ,sugar-,loaf ,rock1 which stands on one side of the harbor's mouth1 so nearly right ahead1 that they had not to alter their course above a point1 in order to hit the entrance of the harbor4 ,this was the first land they had seen for three months1 after crossing so many seas1 and being set backwards and forwards by innumerable currents and foul winds4 ,the effect on all on board was electric2 and the admiration of the sailors was unbounded4 ,indeed1 what could be more admirable than that a man on the deck of a vessel1 by measuring the distance between the moon and a star1 with a little instrument which he held in his hand1 could determine his exact place on the earth's surface in the midst of a vast ocean1 after having traversed it in all directions1 for three months1 crossing his track many times1 and all the while out of sight of land8 ,the lunar method of finding the longitude could never have been susceptible of sufficient accuracy1 had not the motions of the moon1 with all their irregularities1 been studied and investigated by the most laborious and profound researches4 ,hence ,newton1 while wrapt in those meditations which1 to superficial minds1 would perhaps have appeared rather curious than useful1 inasmuch as they respected distant bodies of the universe which seemed to have little connexion with the affairs of this world1 was laboring night and day for the benefit of the sailor and the merchant4 ,he was guiding the vessel of the one1 and securing the merchandise of the other2 and thus he contributed a large share to promote the happiness of his fellow-men1 not only in exalting the powers of the human intellect1 but also in preserving the lives and fortunes of those engaged in navigation and commerce4 ,principles in science are rules in art2 and the philosopher who is engaged in the investigation of these principles1 although his pursuits may be thought less practically useful than those of the artisan who carries out those principles into real life1 yet1 without the knowledge of the principles1 the rules would have never been known4 ,studies1 therefore1 the most abstruse1 are1 when viewed as furnishing rules to act1 often productive of the highest practical utility4 ,since the tides are occasioned by the influence of the sun and moon1 ,i will conclude this ,letter with a few remarks on this curious phenomenon4 ,by the tides are meant the alternate rising and falling of the waters of the ocean4 ,its greatest and least elevations are called high and low water2 its rising and falling are called flood and ebb2 and the extraordinary high and low tides that occur twice every month are called spring and neap tides4 ,it is high or low tide on opposite sides of the globe at the same time4 ,if1 for example1 we have high water at noon1 it is also high water to those who live on the meridian below us1 where it is midnight4 ,in like manner1 low water occurs simultaneously on opposite sides of the meridian4 ,the average amount of the tides for the whole globe is about two and a half feet2 but their actual height at different places is very various1 sometimes being scarcely perceptible1 and sometimes rising to sixty or seventy feet4 ,at the same place1 also1 the phenomena of the tides are very different at different times4 ,in the ,bay of ,fundy1 where the tide rises seventy feet1 it comes in a mighty wave1 seen thirty miles off1 and roaring with a loud noise4 ,at the mouth of the ,severn1 in ,england1 the flood comes up in one head about ten feet high1 bringing certain destruction to any small craft that has been unfortunately left by the ebbing waters on the flats and as it passes the mouth of the ,avon1 it sends up that small river a vast body of water1 rising1 at ,bristol1 forty or fifty feet4 ,tides are caused by the unequal attractions of the sun and moon upon different parts of the earth4 ,suppose the projectile force by which the earth is carried forward in her orbit to be suspended1 and the earth to fall towards one of these bodies1--the moon1 for example1--in consequence of their mutual attraction4 ,then1 if all parts of the earth fell equally towards the moon1 no derangement of its different parts would result1 any more than of the particles of a drop of water1 in its descent to the ground4 ,but if one part fell faster than another1 the different portions would evidently be separated from each other4 ,now1 this is precisely what takes place with respect to the earth1 in its fall towards the moon4 ,the portions of the earth in the hemisphere next to the moon1 on account of being nearer to the centre of attraction1 fall faster than those in the opposite hemisphere1 and consequently leave them behind4 ,the solid earth1 on account of its cohesion1 cannot obey this impulse1 since all its different portions constitute one mass1 which is acted on in the same manner as though it were all collected in the centre2 but the waters on the surface1 moving freely under this impulse1 endeavor to desert the solid mass and fall towards the moon4 ,for a similar reason1 the waters in the opposite hemisphere1 falling less towards the moon than the solid earth does1 are left behind1 or appear to rise4 ,illustration ,fig4 #df4 ,but if the moon draws the waters of the earth into an oval form towards herself1 raising them simultaneously on the opposite sides of the earth1 they must obviously be drawn away from the intermediate parts of the earth1 where it must at the same time be low water4 ,thus1 in ,fig4 #df1 the moon1 ,m1 raises the waters beneath itself at ,z and ,n1 at which places it is high water1 but at the same time depresses the waters at ,h and ,r1 at which places it is low water4 ,hence1 the interval between the high and low tide1 on successive days1 is about fifty minutes1 corresponding to the progress of the moon in her orbit from west to east1 which causes her to come to the meridian about fifty minutes later every day4 ,there occurs1 however1 an intermediate tide1 when the moon is on the lower meridian1 so that the interval between two high tides is about twelve hours1 and twenty-five minutes4 ,were it not for the impediments which prevent the force from producing its full effects1 we might expect to see the great tide-wave1 as the elevated crest is called1 always directly beneath the moon1 attending it regularly around the globe4 ,but the inertia of the waters prevents their instantly obeying the moon's attraction1 and the friction of the waters on the bottom of the ocean still further retards its progress4 ,it is not1 therefore1 until several hours 7differing at different places7 after the moon has passed the meridian of a place1 that it is high tide at that place4 ,the sun has an action similar to that of the moon1 but only one third as great4 ,on account of the great mass of the sun1 compared with that of the moon1 we might suppose that his action in raising the tides would be greater than the moon's2 but the nearness of the moon to the earth more than compensates for the sun's greater quantity of matter4 ,as1 however1 wrong views are frequently entertained on this subject1 let us endeavor to form a correct idea of the advantage which the moon derives from her proximity4 ,it is not that her actual amount of attraction is thus rendered greater than that of the sun2 but it is that her attraction for the different parts of the earth is very unequal1 while that of the sun is nearly uniform4 ,it is the inequality of this action1 and not the absolute force1 that produces the tides4 ,the sun being ninety-five millions of miles from the earth1 while the diameter of the earth is only one twelve thousandth part of this distance1 the effects of the sun's attraction will be nearly the same on all parts of the earth1 and therefore will not1 as was explained of the moon1 tend to separate the waters from the earth on the nearest side1 or the earth from the waters on the remotest side1 but in a degree proportionally smaller4 ,but the diameter of the earth is one thirtieth the distance of the moon1 and therefore the moon acts with considerably greater power on one part of the earth than on another4 ,as the sun and moon both contribute to produce the tides1 and as they sometimes act together and sometimes in opposition to each other1 so corresponding variations occur in the height of the tide4 ,the spring tides1 or those which rise to an unusual height twice a month1 are produced by the sun and moon's acting together2 and the neap tides1 or those which are unusually low twice a month1 are produced by the sun and moon's acting in opposition to each other4 ,the spring tides occur at the syzygies3 the neap tides at the quadratures4 ,at the time of new moon1 the sun and moon both being on the same side of the earth1 and acting upon it in the same line1 their actions conspire1 and the sun may be considered as adding so much to the force of the moon4 ,we have already seen how the moon contributes to raise a tide on the opposite side of the earth4 ,but the sun1 as well as the moon1 raises its own tide-wave1 which at new moon coincides with the lunar tide-wave4 ,this will be plain on inspecting the diagram1 ,fig4 #dg1 on page #bbj1 where ,s represents the sun1 ,c1 the moon in conjunction1 ,o1 the moon in opposition1 and ,z1 ,n1 the tide-wave4 ,since the sun and moon severally raise a tide-wave1 and the two here coincide1 it is evident that a peculiarly high tide must occur when the two bodies are in conjunction1 or at new moon4 ,at full moon1 also1 the two luminaries conspire in the same way to raise the tide2 for we must recollect that each body contributes to raise a tide on the opposite side4 ,thus1 when the sun is at ,s and the moon at ,o1 the sun draws the waters on the side next to it away from the earth1 and the moon draws the earth away from the waters on that side2 their united actions1 therefore1 conspire1 and an unusually high tide is the result4 ,on the side next to ,o1 the two forces likewise conspire3 for while the moon draws the waters away from the earth1 the sun draws the earth away from the waters4 ,in both cases an unusually low tide is produced2 for the more the water is elevated at ,z and ,n1 the more it will be depressed at ,h and ,r1 the places of low tide4 ,illustration ,fig4 #dg4 ,twice a month1 also1 namely1 at the quadratures of the moon1 the tides neither rise so high nor fall so low as at other times1 because then the sun and moon act against each other4 ,thus1 in ,fig4 #dh1 while ,f tends to raise the water at ,z1 ,s tends to depress it1 and consequently the high tide is less than usual4 ,again1 while ,f tends to depress the water at ,r1 ,s tends to elevate it1 and therefore the low tide is less than usual4 ,hence the difference between high and low water is only half as great at neap as at spring tide4 ,in the diagrams1 the elevation and depression of the waters is represented1 for the sake of illustration1 as far greater than it really is2 for you must recollect that the average height of the tides for the whole globe is only about two and a half feet1 a quantity so small1 in comparison with the diameter of the earth1 that were the due proportions preserved in the figures1 the effect would be wholly insensible4 ,illustration ,fig4 #dh4 ,the variations of distance in the sun are not great enough to influence the tides very materially1 but the variations in the moon's distances have a striking effect4 ,the tides which happen1 when the moon is in perigee1 are considerably greater than when she is in apogee2 and if she happens to be in perigee at the time of the syzygies1 the spring tides are unusually high4 ,the motion of the tide-wave is not a progressive motion1 but a mere undulation1 and is to be carefully distinguished from the currents to which it gives rise4 ,if the ocean completely covered the earth1 the sun and moon being in the equator1 the tide-wave would travel at the same rate as the earth revolves on its axis4 ,indeed1 the correct way of conceiving of the tide-wave1 is to consider the moon at rest1 and the earth1 in its rotation from west to east1 as bringing successive portions of water under the moon1 which portions being elevated successively1 at the same rate as the earth revolves on its axis1 have a relative motion westward1 at the same rate4 ,the tides of rivers1 narrow bays1 and shores far from the main body of the ocean1 are not produced in those places by the direct action of the sun and moon1 but are subordinate waves propagated from the great tide-wave1 and are called derivative tides1 while those raised directly by the sun and moon are called primitive tides4 ,illustration ,fig4 #di4 ,the velocity with which the tide moves will depend on various circumstances1 but principally on the depth1 and probably on the regularity1 of the channel4 ,if the depth is nearly uniform the tides will be regular2 but if some parts of the channel are deep while others are shallow1 the waters will be detained by the greater friction of the shallow places1 and the tides will be irregular4 ,the direction1 also1 of the derivative tide may be totally different from that of the primitive4 ,thus1 in ,fig4 #di1 if the great tide-wave1 moving from east to west1 is represented by the lines #a1 #b1 #c1 #d1 the derivative tide1 which is propagated up a river or bay1 will be represented by the lines #c1 #d1 #e1 #f1 #g4 ,advancing faster in the channel than next the bank1 the tides will lag behind towards the shores1 and the tide-wave will take the form of curves1 as represented in the diagram4 ,on account of the retarding influence of shoals1 and an uneven1 indented coast1 the tide-wave travels more slowly along the shores of an island than in the neighboring sea1 assuming convex figures at a little distance from the island1 and on opposite sides of it4 ,these convex lines sometimes meet1 and become blended in such a way1 as to create singular anomalies in a sea much broken by islands1 as well as on coasts indented with numerous bays and rivers4 ,peculiar phenomena are also produced1 when the tide flows in at opposite extremities of a reef or island1 as into the two opposite ends of ,long-,island ,sound4 ,in certain cases1 a tide-wave is forced into a narrow arm of the sea1 and produces very remarkable tides4 ,the tides of the ,bay of ,fundy 7the highest in the world7 are ascribed to this cause4 ,the tides on the coast of ,north ,america are derived from the great tide-wave of the ,south ,atlantic1 which runs steadily northward along the coast to the mouth of the ,bay of ,fundy1 where it meets the northern tide-wave flowing in the opposite direction4 ,this accumulated wave being forced into the narrow space occupied by the ,bay1 produces the remarkable tide of that place4 ,the largest lakes and inland seas have no perceptible tides4 ,this is asserted by all writers respecting the ,caspian and ,euxine2 and the same is found to be true of the largest of the ,north-,american lakes1 ,lake ,superior4 ,although these several tracts of water appear large1 when taken by themselves1 yet they occupy but small portions of the surface of the globe1 as will appear evident from the delineation of them on the artificial globe4 ,now1 we must recollect that the primitive tides are produced by the unequal action of the sun and moon upon the different parts of the earth2 and that it is only at points whose distance from each other bears a considerable ratio to the whole distance of the sun or moon1 that the inequality of action becomes manifest4 ,the space required to make the effect sensible is larger than either of these tracts of water4 ,it is obvious1 also1 that they have no opportunity to be subject to a derivative tide4 ,although all must admit that the tides have some connexion with the sun and the moon1 yet there are so many seeming anomalies1 which at first appear irreconcilable with the theory of gravitation1 that some are unwilling to admit the explanation given by this theory4 ,thus1 the height of the tide is so various1 that at some places on the earth there is scarcely any tide at all1 while at other places it rises to seventy feet4 ,the time of occurrence is also at many places wholly unconformable to the motions of the moon1 as is required by the theory1 being low water where it should be high water2 or1 instead of appearing just beneath the moon1 as the theory would lead us to expect1 following it at the distance of six1 ten1 or even fifteen1 hours2 and finally1 the moon sometimes appears to have no part at all in producing the tide1 but it happens uniformly at noon and midnight1 7as is said to be the case at the ,society ,islands17 and therefore seems wholly dependent on the sun4 ,notwithstanding these seeming inconsistencies with the law of universal gravitation1 to which the explanation of the tides is referred1 the correspondence of the tides to the motions of the sun and moon1 in obedience to the law of attraction1 is in general such as to warrant the application of that law to them1 while in a great majority of the cases which appear to be exceptions to the operation of that law1 local causes and impediments have been discovered1 which modified or overruled the uniform operation of the law of gravitation4 ,thus it does not disprove the reality of the existence of a force which carries bodies near the surface of the earth towards its centre1 that we see them sometimes compelled1 by the operation of local causes1 to move in the opposite direction4 ,a ball shot from a cannon is still subject to the law of gravitation1 although1 for a certain time1 in obedience to the impulse given it1 it may proceed in a line contrary to that in which gravity alone would carry it4 ,the fact that water may be made to run up hill does not disprove the fact that it usually runs down hill by the force of gravity1 or that it is still subject to this force1 although1 from the action of modifying or superior forces1 it may be proceeding in a direction contrary to that given by gravity4 ,indeed1 those who have studied the doctrine of the tides most profoundly consider them as affording a striking and palpable exhibition of the truth of the doctrine of universal gravitation4 ,,footnote3 #aa ,the exact longitude of the ,city ,hall1 in the city of ,new ,york1 is #d;h4 #efm4 #cc4es4 ,,letter ,,xx4 ,,planets4--,,mercury ,,and ,,venus4 ,first1 ,mercury1 amidst full tides of light1 ,rolls next the sun1 through his small circle bright2 ,our earth would blaze beneath so fierce a ray1 ,and all its marble mountains melt away4 ,fair ,venus next fulfils her larger round1 ,with softer beams1 and milder glory crowned2 ,friend to mankind1 she glitters from afar1 ,now the bright evening1 now the morning1 star4--,baker4 ,,there is no study in which more is to be hoped for from a lucid arrangement1 than in the study of astronomy4 ,some subjects involved in this study appear very difficult and perplexing to the learner1 before he has fully learned the doctrine of the sphere1 and gained a certain familiarity with astronomical doctrines1 which would seem very easy to him after he had made such attainments4 ,such an order ought to be observed1 as shall bring out the facts and doctrines of the science just in the place where the mind of the learner is prepared to receive them4 ,some writers on astronomy introduce their readers at once to the most perplexing part of the whole subject1--the planetary motions4 ,i have thought a different course advisable1 and have therefore commenced these ,letters with an account of those bodies which are most familiarly known to us1 the earth1 the sun1 and the moon4 ,in connexion with the earth1 we are able to acquire a good knowledge of the artificial divisions and points of reference that are established on the earth and in the heavens1 constituting the doctrine of the sphere4 ,you thus became familiar with many terms and definitions which are used in astronomy4 ,these ought to be always very clearly borne in mind2 and if you now meet with any term1 the definition of which you have either partially or wholly forgotten1 let me strongly recommend to you1 to turn back and review it1 until it becomes as familiar to you as household words4 ,indeed1 you will find it much to your advantage to go back frequently1 and reiterate the earlier parts of the subject1 before you advance to subjects of a more intricate nature4 ,if this process should appear to you a little tedious1 still you will find yourself fully compensated by the clear light in which all the succeeding subjects will appear4 ,this clear and distinct perception of the ground we have been over shows us just where we are on our journey1 and helps us to find the remainder of the way with far greater ease than we could otherwise do4 ,i do not1 however1 propose by any devices to relieve you from the trouble of thinking4 ,those who are not willing to incur this trouble can never learn much of astronomy4 ,in introducing you to the planets1 7which next claim our attention17 ,i will1 in the first place1 endeavor to convey to you some clear views of these bodies individually1 and afterwards help you to form as correct a notion as possible of their motions and mutual relations4 ,the name planet is derived from a ,greek word1 7 plants1 planetes17 which signifies a wanderer1 and is applied to this class of bodies1 because they shift their positions in the heavens1 whereas the fixed stars constantly maintain the same places with respect to each other4 ,the planets known from a high antiquity are1 ,mercury1 ,venus1 ,earth1 ,mars1 ,jupiter1 and ,saturn4 ,to these1 in #agha1 was added ,uranus1 7or ,herschel1 as it is sometimes called1 from the name of its discoverer27 and1 as late as the commencement of the present century1 four more were added1 namely1 ,ceres1 ,pallas1 ,juno1 and ,vesta4 ,these bodies are designated by the following characters3 #a4 ,mercury1 ,planet3 ,mercury #b4 ,venus1 ,planet3 ,venus #c4 ,earth1 ,planet3 ,earth #d4 ,mars1 ,planet3 ,mars #e4 ,vesta1 ,planet3 ,vesta #f4 ,juno1 ,planet3 ,juno #g4 ,ceres1 ,planet3 ,ceres #h4 ,pallas1 ,planet3 ,pallas #i4 ,jupiter1 ,planet3 ,jupiter #aj4 ,saturn1 ,planet3 ,saturn #aa4 ,uranus1 ,planet3 ,uranus ,the foregoing are called the primary planets4 ,several of these have one or more attendants1 or satellites1 which revolve around them as they revolve around the sun4 ,the ,earth has one satellite1 namely1 the ,moon2 ,jupiter has four2 ,saturn1 seven2 and ,uranus1 six4 ,these bodies are also planets1 but1 in distinction from the others1 they are called secondary planets4 ,hence1 the whole number of planets are twenty-nine1 namely1 eleven primary1 and eighteen secondary1 planets4 ,you need never look for a planet either very far in the north or very far in the south1 since they are always near the ecliptic4 ,mercury1 which deviates furthest from that great circle1 never is seen more than seven degrees from it2 and you will hardly ever see one of the planets so far from it as this1 but they all pursue nearly the same great route through the skies1 in their revolutions around the sun4 ,the new planets1 however1 make wider excursions from the plane of the ecliptic1 amounting1 in the case of ,pallas1 to thirty-four and a half degrees4 ,mercury and ,venus are called inferior planets1 because they have their orbits nearer to the sun than that of the earth2 while all the others1 being more distant from the sun than the earth1 are called superior planets4 ,the planets present great diversities among themselves1 in respect to distance from the sun1 magnitude1 time of revolution1 and density4 ,they differ1 also1 in regard to satellites1 of which1 as we have seen1 three have respectively four1 six1 and seven1 while more than half have none at all4 ,it will aid the memory1 and render our view of the planetary system more clear and comprehensive1 if we classify1 as far as possible1 the various particulars comprehended under the foregoing heads4 ,as you have had an opportunity1 in preceding ,letters1 of learning something respecting the means which astronomers have of ascertaining the distances and magnitudes of these bodies1 you will not doubt that they are really as great as they are represented2 but when you attempt to conceive of spaces so vast1 you will find the mind wholly inadequate to the task4 ,it is indeed but a comparatively small space that we can fully comprehend at one grasp4 ,still1 by continual and repeated efforts1 we may1 from time to time1 somewhat enlarge the boundaries of our mental vision4 ,let us begin with some known and familiar space1 as the distance between two places we are accustomed to traverse4 ,suppose this to be one hundred miles4 ,taking this as our measure1 let us apply it to some greater distance1 as that across the ,atlantic ,ocean1--say three thousand miles4 ,from this step we may advance to some faint conception of the diameter of the earth2 and taking that as a new measure1 we may apply it to such greater spaces as the distance of the planets from the sun4 ,i hope you will make trial of this method on the following comparative statements respecting the planets4 ,distances from the ,sun1 in miles4 #a4 ,mercury1 #cg1jjj1jjj #b4 ,venus1 #fh1jjj1jjj #c4 ,earth1 #ie1jjj1jjj #d4 ,mars1 #adb1jjj1jjj #e4 ,vesta1 #bbe1jjj1jjj #f4 ,juno1 #g4 ,ceres1 #bfa1jjj1jjj #h4 ,pallas1 #i4 ,jupiter1 #dhe1jjj1jjj #aj4 ,saturn1 #hij1jjj1jjj #aa4 ,uranus1 or ,herschel1 #ahjj1jjj1jjj ,the dimensions of the planetary system are seen from this table to be vast1 comprehending a circular space thirty-six hundred millions of miles in diameter4 ,a rail-way car1 travelling constantly at the rate of twenty miles an hour1 would require more than twenty thousand years to cross the orbit of ,uranus4 ,magnitudes4 ,diam4 in miles4 #a4 ,mercury1 #cadj #b4 ,venus1 #ggjj #c4 ,earth1 #giab #d4 ,mars1 #dbjj #e4 ,ceres1 #afj #f4 ,jupiter1 #hi1jjj #g4 ,saturn1 #gi1jjj #h4 ,uranus1 #ce1jjj ,we remark here a great diversity in regard to magnitude1--a diversity which does not appear to be subject to any definite law4 ,while ,venus1 an inferior planet1 is nine tenths as large as the earth1 ,mars1 a superior planet1 is only one seventh1 while ,jupiter is twelve hundred and eighty-one times as large4 ,although several of the planets1 when nearest to us1 appear brilliant and large1 when compared with most of the fixed stars1 yet the angle which they subtend is very small1--that of ,venus1 the greatest of all1 never exceeding about one minute1 which is less than one thirtieth the apparent diameter of the sun or moon4 ,jupiter1 also1 by his superior brightness1 sometimes makes a striking figure among the stars2 yet his greatest apparent diameter is less than one fortieth that of the sun4 ,periodic ,times4 ,mercury revolves around the sun in nearly #c months4 ,venus1 #g-a_/b ,earth1 #a year4 ,mars1 #b years4 ,ceres1 #d-b_/c ,jupiter1 #ab ,saturn1 #bi ,uranus1 #hd ,from this view1 it appears that the planets nearest the sun move most rapidly4 ,thus1 ,mercury performs nearly three hundred and fifty revolutions while ,uranus performs one4 ,the apparent progress of the most distant planets around the sun is exceedingly slow4 ,uranus advances only a little more than four degrees in a whole year2 so that we find this planet occupying the same sign1 and of course remaining nearly in the same part of the heavens1 for several years in succession4 ,after this comparative view of the planets in general1 let us now look at them individually2 and first1 of the inferior planets1 ,mercury and ,venus4 ,,mercury and ,,venus1 having their orbits so far within that of the earth1 appear to us as attendants upon the sun4 ,mercury never appears further from the sun than twenty-nine degrees1 and seldom so far2 and ,venus1 never more than about forty-seven degrees4 ,both planets1 therefore1 appear either in the west soon after sunset1 or in the east a little before sunrise4 ,in high latitudes1 where the twilight is long1 ,mercury can seldom be seen with the naked eye1 and then only when its angular distance from the sun is greatest4 ,copernicus1 the great ,prussian astronomer1 7who first distinctly established the order of the solar system1 as at present received17 lamented1 on his death-bed1 that he had never been able to obtain a sight of ,mercury2 and ,delambre1 a distinguished astronomer of ,france1 saw it but twice4 ,in our latitude1 however1 we may see this planet for several evenings and mornings1 if we will watch the time 7as usually given in the almanac7 when it is at its greatest elongations from the sun4 ,it will not1 however1 remain long for our gaze1 but will soon run back to the sun4 ,the reason of this will be readily understood from the following diagram1 ,fig4 #ej4 ,let ,s represent the sun1 ,e1 the earth1 and ,m1 ,n1 ,mercury at its greatest elongations from the sun1 and ,o ,z ,p1 a portion of the sky4 ,then1 since we refer all distant bodies to the same concave sphere of the heavens1 it is evident that we should see the sun at ,z1 and ,mercury at ,o1 when at its greatest eastern elongation1 and at ,p1 when at its greatest western elongation2 and while passing from ,m to ,n through ,q1 it would appear to describe the arc ,o ,p2 and while passing from ,n to ,m through ,r1 it would appear to run back across the sun on the same arc4 ,it is further evident that it would be visible only when at or near one of its greatest elongations2 being at all other times so near the sun as to be lost in his light4 ,illustration ,fig4 #ej4 ,a planet is said to be in conjunction with the sun when it is seen in the same part of the heavens with the sun4 ,mercury and ,venus have each two conjunctions1 the inferior and the superior conjunction4 ,the inferior conjunction is its position when in conjunction on the same side of the sun with the earth1 as at ,q1 in the figure2 the superior conjunction is its position when on the side of the sun most distant from the earth1 as at ,r4 ,the time which a planet occupies in making one entire circuit of the heavens1 from any star1 until it comes round to the same star again1 is called its sidereal revolution4 ,the period occupied by a planet between two successive conjunctions with the earth is called its synodical revolution4 ,both the planet and the earth being in motion1 the time of the synodical revolution of ,mercury or ,venus exceeds that of the sidereal2 for when the planet comes round to the place where it before overtook the earth1 it does not find the earth at that point1 but far in advance of it4 ,thus1 let ,mercury come into inferior conjunction with the earth at ,c1 ,fig4 #ea4 ,in about eighty-eight days1 the planet will come round to the same point again2 but1 mean-while1 the earth has moved forward through the arc ,e ,e1 and will continue to move while the planet is moving more rapidly to overtake her2 the case being analogous to that of the hour and minute hand of a clock4 ,illustration ,fig4 #ea4 ,the synodical period of ,mercury is one hundred and sixteen days1 and that of ,venus five hundred and eighty-four days4 ,the former is increased twenty-eight days1 and the latter1 three hundred and sixty days1 by the motion of the earth2 so that ,venus1 after being in conjunction with the earth1 goes more than twice round the sun before she comes into conjunction again4 ,for1 since the earth is likewise in motion1 and moves more than half as fast as ,venus1 by the time the latter has gone round and returned to the place where the two bodies were together1 the earth is more than half way round1 and continues moving1 so that it will be a long time before ,venus comes up with it4 ,the motion of an inferior planet is direct in passing through its superior conjunction1 and retrograde in passing through its inferior conjunction4 ,you will recollect that the motion of a heavenly body is said to be direct when it is in the order of the signs from west to east1 and retrograde when it is contrary to the order of the signs1 or from east to west4 ,now ,venus1 while going from ,b through ,d to ,a1 7,fig4 #ea17 moves from west to east1 and would appear to traverse the celestial vault ,b ,s ,a1 from right to left2 but in passing from ,a through ,c to ,b1 her course would be retrograde1 returning on the same arc from left to right4 ,if the earth were at rest1 therefore1 7and the sun1 of course1 at rest17 the inferior planets would appear to oscillate backwards and forwards across the sun4 ,but it must be recollected that the earth is moving in the same direction with the planet1 as respects the signs1 but with a slower motion4 ,this modifies the motions of the planet1 accelerating it in the superior1 and retarding it in the inferior1 conjunction4 ,thus1 in ,fig4 #ea1 ,venus1 while moving through ,b ,d ,a1 would seem to move in the heavens from ,b to ,a1 were the earth at rest2 but1 mean-while1 the earth changes its position from ,e to ,e1 on which account the planet is not seen at ,a1 but at ,a1 being accelerated by the arc ,a ,a1 in consequence of the earth's motion4 ,on the other hand1 when the planet is passing through its inferior conjunction ,a ,c ,b1 it appears to move backwards in the heavens from ,a to ,b1 if the earth is at rest1 but from ,a to ,b1 if the earth has in the mean time moved from ,e to ,e1 being retarded by the arc ,b ,b4 ,although the motions of the earth have the effect to accelerate the planet in the superior conjunction1 and to retard it in the inferior1 yet1 on account of the greater distance1 the apparent motion of the planet is much slower in the superior than in the inferior conjunction1 ,venus being the whole breadth of her orbit1 or one hundred and thirty-six millions of miles further from us when at her greatest1 than when at her least1 distance1 as is evident from ,fig4 #ea4 ,when passing from the superior to the inferior conjunction1 or from the inferior to the superior1 through the greatest elongations1 the inferior planets are stationary4 ,thus1 7,fig4 #ea17 when the planet is at ,a1 the earth being at ,e1 as the planet's motion is directly towards the spectator1 he would constantly project it at the same point in the heavens1 namely1 ,a2 consequently1 it would appear to stand still4 ,or1 when at its greatest elongation on the other side1 at ,b1 as its motion would be directly from the spectator1 it would be seen constantly at ,b4 ,if the earth were at rest1 the stationary points would be at the greatest elongations1 as at ,a and ,b2 but the earth itself is moving nearly at right angles to the planet's motion1 which makes the planet appear to move in the opposite direction4 ,its direct motion will therefore continue longer on the one side1 and its retrograde motion longer on the other side1 than would be the case1 were it not for the motion of the earth4 ,mercury1 whose greatest angular distance from the sun is nearly twenty-nine degrees1 is stationary at an elongation of from fifteen to twenty degrees2 and ,venus1 at about twenty-nine degrees1 although her greatest elongation is about forty-seven degrees4 ,mercury and ,venus exhibit to the telescope phases similar to those of the moon4 ,when on the side of their inferior conjunction1 as from ,b to ,c through ,d1 ,fig4 #eb1 less than half their enlightened disk is turned towards us1 and they appear horned1 like the moon in her first and last quarters2 and when on the side of the superior conjunction1 as from ,c to ,b through ,a1 more than half the enlightened disk is turned towards us1 and they appear gibbous4 ,at the moment of superior conjunction1 the whole enlightened orb of the planet is turned towards the earth1 and the appearance would be that of the full moon2 but the planet is too near the sun to be commonly visible4 ,illustration ,fig4 #eb4 ,we should at first thought expect1 that each of these planets would be largest and brightest near their inferior conjunction1 being then so much nearer to us than at other times2 but we must recollect that1 when in this situation1 only a small part of the enlightened disk is turned toward us4 ,still1 the period of greatest brilliancy cannot be when most of the illuminated side is turned towards us1 for then1 being at the superior conjunction1 its light will be diminished1 both by its great distance1 and by its being so near the sun as to be partially lost in the twilight4 ,hence1 when ,venus is a little within her place of greatest elongation1 about forty degrees from the sun1 although less than half her disk is enlightened1 yet1 being comparatively near to us1 and shining at a considerable altitude after the evening or before the morning twilight1 she then appears in greatest splendor1 and presents an object admired for its beauty in all ages4 ,thus ,milton1 ,fairest of stars1 last in the train of night1 ,if better thou belong not to the dawn1 ,sure pledge of day that crown'st the smiling morn ,with thy bright circlet4 ,mercury and ,venus both revolve on their axes in nearly the same time with the earth4 ,the diurnal period of ,mercury is a little greater1 and that of ,venus a little less1 than twenty-four hours4 ,these revolutions have been determined by means of some spot or mark seen by the telescope1 as the revolution of the sun on his axis is ascertained by means of his spots4 ,mercury owes most of its peculiarities to its proximity to the sun4 ,its light and heat1 derived from the sun1 are estimated to be neatly seven times as great as on the earth1 and the apparent magnitude of the sun to a spectator on ,mercury would be seven times greater than to us4 ,hence the sun would present to an inhabitant of that planet1 with eyes like ours1 an object of insufferable brightness2 and all objects on the surface would be arrayed in a light more glorious than we can well imagine4 7,see ,fig4 #ec47 ,the average heat on the greater portion of this planet would exceed that of boiling water1 and therefore be incompatible with the existence both of an animal and a vegetable kingdom constituted like ours4 ,the motion of ,mercury1 in his revolution round the sun1 is swifter than that of any other planet1 being more than one hundred thousand miles every hour2 whereas that of the earth is less than seventy thousand4 ,eighteen hundred miles every minute1--crossing the ,atlantic ocean in less than two minutes1--this is a velocity of which we can form but a very inadequate conception1 although1 as we shall see hereafter1 it is far less than comets sometimes exhibit4 ,venus is regarded as the most beautiful of the planets1 and is well known as the morning and evening star4 ,the most ancient nations1 indeed1 did not recognise the morning and evening star as one and the same body1 but supposed they were different planets1 and accordingly gave them different names1 calling the morning star ,lucifer1 and the evening star ,hesperus4 ,at her period of greatest splendor1 ,venus casts a shadow1 and is sometimes visible in broad daylight4 ,her light is then estimated as equal to that of twenty stars of the first magnitude4 ,in the equatorial regions of the earth1 where the twilight is short1 and ,venus1 at her greatest elongation1 appears very high above the horizon1 her splendors are said to be far more conspicuous than in our latitude4 ,illustration ,fig4 #ec4 ,,apparent ,,magnitudes ,,of ,,the ,,sun1 ,,as ,,seen ,,from ,,the ,,different ,,planets4 ,illustration ,figures #ed1 #ee1 #ef4 ,,venus ,,and ,,mars4 ,every eight years1 ,venus forms her conjunction with the sun in the same part of the heavens4 ,whatever appearances1 therefore1 arise from her position with respect to the earth and the sun1 they are repeated every eight years1 in nearly the same form4 ,thus1 every eight years1 ,venus is remarkably conspicuous1 so as to be visible in the day-time1 being then most favorably situated1 on several accounts2 namely1 being nearest the earth1 and at the point in her orbit where she gives her greatest brilliancy1 that is1 a little within the place of greatest elongation4 ,this is the period for obtaining fine telescopic views of ,venus1 when she is seen with spots on her disk4 ,thus two figures of the annexed diagram 7,fig4 #ed7 represent ,venus as seen near her inferior conjunction1 and at the period of maximum brilliancy4 ,the former situation is favorable for viewing her inequalities of surface1 as indicated by the roughness of the line which separates the enlightened from the unenlightened part1 7the terminator47 ,according to ,schroeter1 a ,german astronomer1 ,venus has mountains twenty-two miles high4 ,her mountains1 however1 are much more difficult to be seen than those of the moon4 ,the sun would appear1 as seen from ,venus1 twice as large as on the earth1 and its light and heat would be augmented in the same proportion4 7,see ,fig4 #ec47 ,in many respects1 however1 the phenomena of this planet are similar to those of our own2 and the general likeness between ,venus and the earth1 in regard to dimensions1 revolutions1 and seasons1 is greater than exists between any other two bodies of the system4 ,i will only add to the present ,letter a few words on the transits of the inferior planets4 ,the transit of ,mercury or ,venus is its passage across the sun's disk1 as the moon passes over it in a solar eclipse4 ,the planet is seen projected on the sun's disk in a small1 black1 round spot1 moving slowly over the face of the sun4 ,as the transit takes place only when the planet is in inferior conjunction1 at which time her motion is retrograde1 it is always from left to right2 and1 on account of its motion being retarded by the motion of the earth1 7as was explained by ,fig4 #ea1 page #bcb17 it remains sometimes a long time on the solar disk4 ,mercury1 when it makes its transit across the sun's centre1 may remain on the sun from five to seven hours4 ,you may ask1 why we do not observe this appearance every time one of the inferior planets comes into inferior conjunction1 for then1 of course1 it passes between us and the sun4 ,it must1 indeed1 at this time1 cross the meridian at the same time with the sun2 but1 because its orbit is inclined to that of the sun1 it may cross it 7and generally does7 a little above or a little below the sun4 ,it is only when the conjunction takes place at or very near the point where the two orbits cross one another1 that is1 near the node1 that a transit can occur4 ,thus1 if the orbit of ,mercury1 ,n ,m ,r1 ,fig4 #ej1 7page #bca17 were in the same plane with the earth's orbit1 7and of course with the sun's apparent orbit17 then1 when the planet was at ,q1 in its inferior conjunction1 the earth being at ,e1 it would always be projected on the sun's disk at ,z1 on the concave sphere of the heavens1 and a transit would happen at every inferior conjunction4 ,but now let us take hold of the point ,r1 and lift the circle which represents the orbit of ,mercury upwards seven degrees1 letting it turn upon the diameter d b2 then1 we may easily see that a spectator at ,e would project the planet higher in the heavens than the sun2 and such would always be the case1 except when the conjunction takes place at the node4 ,then the point of intersection of the two orbits being in one and the same plane1 both bodies would be referred to the same point on the celestial sphere4 ,as the sun1 in his apparent revolution around the earth every year1 passes through every point in the ecliptic1 of course he must every year be at each of the points where the orbit of ,mercury or ,venus crosses the ecliptic1 that is1 at each of the nodes of one of these planets2#ab and as these nodes are on opposite sides of the ecliptic1 consequently1 the sun will pass through them at opposite seasons of the year1 as in ,january and ,july1 ,february and ,august4 ,now1 should ,mercury or ,venus happen to come between us and the sun1 just as the sun is passing one of the planet's nodes1 a transit would happen4 ,hence the transits of ,mercury take place in ,may and ,november1 and those of ,venus1 in ,june and ,december4 ,transits of ,mercury occur more frequently than those of ,venus4 ,the periodic times of ,mercury and the earth are so adjusted to each other1 that ,mercury performs nearly twenty-nine revolutions while the earth performs seven4 ,if1 therefore1 the two bodies meet at the node in any given year1 seven years afterwards they will meet nearly at the same node1 and a transit may take place1 accordingly1 at intervals of seven years4 ,but fifty-four revolutions of ,mercury correspond still nearer to thirteen revolutions of the earth2 and therefore a transit is still more probable after intervals of thirteen years4 ,at intervals of thirty-three years1 transits of ,mercury are exceedingly probable1 because in that time ,mercury makes almost exactly one hundred and thirty-seven revolutions4 ,intermediate transits1 however1 may occur at the other node4 ,thus1 transits of ,mercury happened at the ascending node in #ahae1 and #ahbb1 at intervals of seven years2 and at the descending node in #ahcb1 which will return in #ahde1 after thirteen years4 ,transits of ,venus are events of very unfrequent occurrence4 ,eight revolutions of the earth are completed in nearly the same time as thirteen revolutions of ,venus2 and hence two transits of ,venus may occur after an interval of eight years1 as was the case at the last return of the phenomenon1 one transit having occurred in #agfa1 and another in #agfi4 ,but if a transit does not happen after eight years1 it will not happen at the same node1 until an interval of two hundred and thirty-five years3 but intermediate transits may occur at the other node4 ,the next transit of ,venus will take place in #ahgd1 being two hundred and thirty-five years after the first that was ever observed1 which occurred in #afci4 ,this was seen1 for the first time by mortal eyes1 by two youthful ,english astronomers1 ,horrox and ,crabtree4 ,horrox was a young man of extraordinary promise1 and indicated early talents for practical astronomy1 which augured the highest eminence2 but he died in the twenty-third year of his age4 ,he was only twenty when the transit appeared1 and he had made the calculations and observations1 by which he was enabled to anticipate its arrival several years before4 ,at the approach of the desired time for observing the transit1 he received the sun's image through a telescope in a dark room upon a white piece of paper1 and after waiting many hours with great impatience1 7as his calculation did not lead him to a knowledge of the precise time of the occurrence17 at last1 on the twenty-fourth of ,november1 #afci1 old style1 at three and a quarter hours past twelve1 just as he returned from church1 he had the pleasure to find a large round spot near the limb of the sun's image4 ,it moved slowly across the sun's disk1 but had not entirely left it when the sun set4 ,the great interest attached by astronomers to a transit of ,venus arises from its furnishing the most accurate means in our power of determining the sun's horizontal parallax1--an element of great importance1 since it leads us to a knowledge of the distance of the earth from the sun1 which again affords the means of estimating the distances of all the other planets1 and possibly1 of the fixed stars4 ,hence1 in #agfi1 great efforts were made throughout the civilized world1 under the patronage of different governments1 to observe this phenomenon under circumstances the most favorable for determining the parallax of the sun4 ,the common methods of finding the parallax of a heavenly body cannot be relied on to a greater degree of accuracy than four seconds4 ,in the case of the moon1 whose greatest parallax amounts to about one degree1 this deviation from absolute accuracy is not very material2 but it amounts to nearly half the entire parallax of the sun4 ,if the sun and ,venus were equally distant from us1 they would be equally affected by parallax1 as viewed by spectators in different parts of the earth1 and hence their relative situation would not be altered by it2 but since ,venus1 at the inferior conjunction1 is only about one third as far off as the sun1 her parallax is proportionally greater1 and therefore spectators at distant points will see ,venus projected on different parts of the solar disk1 as the planet traverses the disk4 ,astronomers avail themselves of this circumstance to ascertain the sun's horizontal parallax1 which they are enabled to do by comparing it with that of ,venus1 in a manner which1 without a knowledge of trigonometry1 you will not fully understand4 ,in order to make the difference in the apparent places of ,venus on the sun's disk as great as possible1 very distant places are selected for observation4 ,thus1 in the transits of #agfa and #agfi1 several of the ,european governments fitted out expensive expeditions to parts of the earth remote from each other4 ,for this purpose1 the celebrated ,captain ,cook1 in #agfi1 went to the ,south ,pacific ,ocean1 and observed the transit at the island of ,otaheite1 while others went to ,lapland1 for the same purpose1 and others still1 to many other parts of the globe4 ,thus1 suppose two observers took their stations on opposite sides of the earth1 as at ,a1 and ,b1 ,fig4 #eg1 page #bdb2 at ,a1 the planet ,v would be seen on the sun's disk at a1 while at ,b1 it would be seen at b4 ,the appearance of ,venus on the sun's disk being that of a well-defined black spot1 and the exactness with which the moment of external or internal contact may be determined1 are circumstances favorable to the exactness of the result2 and astronomers repose so much confidence in the estimation of the sun's horizontal parallax1 as derived from observations on the transit of #agfi1 that this important element is thought to be ascertained within one tenth of a second4 ,the general result of all these observations gives the sun's horizontal parallax eight seconds and six tenths1--a result which shows at once that the sun must be a great way off1 since the semidiameter of the earth1 a line nearly four thousand miles in length1 would appear at the sun under an angle less than one four hundredth of a degree4 ,during the transits of ,venus over the sun's disk1 in #agfa and #agfi1 a sort of penumbral light was observed around the planet1 by several astronomers1 which was thought to indicate an atmosphere4 ,this appearance was particularly observable while the planet was coming on or going off the solar disk4 ,the total immersion and emersion were not instantaneous2 but as two drops of water1 when about to separate1 form a ligament between them1 so there was a dark shade stretched out between ,venus and the sun2 and when the ligament broke1 the planet seemed to have got about an eighth part of her diameter from the limb of the sun4 ,the various accounts of the two transits abound with remarks like these1 which indicate the existence of an atmosphere about ,venus of nearly the density and extent of the earth's atmosphere4 ,similar proofs of the existence of an atmosphere around this planet are derived from appearances of twilight4 ,illustration ,fig4 #eg4 ,the elder astronomers imagined that they had discovered a satellite accompanying ,venus in her transit4 ,if ,venus had in reality any satellite1 the fact would be obvious at her transits1 as1 in some of them at least1 it is probable that the satellite would be projected near the primary on the sun's disk2 but later astronomers have searched in vain for any appearances of the kind1 and the inference is1 that former astronomers were deceived by some optical illusion4 ,,footnote3 #ab ,you will recollect that the sun is said to be at the node1 when the places of the node and the sun are both projected1 by a spectator on the earth1 upon the same part of the heavens4 ,,letter ,,xxi4 ,,superior ,,planets3 ,,mars1 ,,jupiter1 ,,saturn1 ,,and ,,uranus4 ,with what an awful1 world-revolving power1 ,were first the unwieldy planets launched along ,the illimitable void6 ,there to remain ,amidst the flux of many thousand years1 ,that oft has swept the toiling race of men1 ,and all their labored monuments1 away4--,thomson4 ,,mercury ,,and ,,venus1 as we have seen1 are always observed near the sun1 and from this circumstance1 as well as from the changes of magnitude and form which they undergo1 we know that they have their orbits within that of the earth1 and hence we call them inferior planets4 ,on the other hand1 ,mars1 ,jupiter1 ,saturn1 and ,uranus1 exhibit such appearances1 at different times1 as show that they revolve around the sun at a greater distance than the earth1 and hence we denominate them superior planets4 ,we know that they never come between us and the sun1 because they never undergo those changes which ,mercury and ,venus1 as well as the moon1 sustain1 in consequence of their coming into such a position4 ,they1 however1 wander to the greatest angular distance from the sun1 being sometimes seen one hundred and eighty degrees from him1 so as to rise when the sun sets4 ,all these different appearances must naturally result from their orbits' being exterior to that of the earth1 as will be evident from the following representation4 ,let ,e1 ,fig4 #eh1 page #bdd1 be the earth1 and ,m1 one of the superior planets1 ,mars1 for example1 each body being seen in its path around the sun4 ,at ,m1 the planet would be in opposition to the sun1 like the moon at the full2 at ,q and ,q1 it would be seen ninety degrees off1 or in quadrature2 and at ,m1 in conjunction4 ,we know1 however1 that this must be a superior and not an inferior conjunction1 for the illuminated disk is still turned towards us2 whereas1 if it came between us and the sun1 like ,mercury1 or ,venus1 in its inferior conjunction1 its dark side would be presented to us4 ,illustration ,fig4 #eh4 ,the superior planets do not exhibit to the telescope different phases1 but1 with a single exception1 they always present the side that is turned towards the earth fully enlightened4 ,this is owing to their great distance from the earth2 for were the spectator to stand upon the sun1 he would of course always have the illuminated side of each of the planets turned towards him2 but so distant are all the superior planets1 except ,mars1 that they are viewed by us very nearly1 in the same manner as they would be if we actually stood on the sun4 ,mars1 however1 is sufficiently near to appear somewhat gibbous when at or near one of its quadratures4 ,thus1 when the planet is at ,q1 it is plain that1 of the hemisphere that is turned towards the earth1 a small part is unilluminated4 ,mars is a small planet1 his diameter being only about half that of the earth1 or four thousand two hundred miles4 ,he also1 at times1 comes nearer to the earth than any other planet1 except ,venus4 ,his mean distance from the sun is one hundred and forty-two millions of miles2 but his orbit is so elliptical1 that his distance varies much in different parts of his revolution4 ,mars is always very near the ecliptic1 never varying from it more than two degrees4 ,he is distinguished from all the planets by his deep red color1 and fiery aspect2 but his brightness and apparent magnitude vary much1 at different times1 being sometimes nearer to us than at others by the whole diameter of the earth's orbit2 that is1 by about one hundred and ninety millions of miles4 ,when ,mars is on the same side of the sun with the earth1 or at his opposition1 he comes within forty-seven millions of miles of the earth1 and1 rising about the time the sun sets1 surprises us by his magnitude and splendor2 but when he passes to the other side of the sun1 to his superior conjunction1 he dwindles to the appearance of a small star1 being then two hundred and thirty-seven millions of miles from us4 ,thus1 let ,m1 ,fig1 #eh1 represent ,mars in opposition1 and ,m1 in the superior conjunction1 while ,e represents the earth4 ,it is obvious that1 in the former situation1 the planet must be nearer to the earth than in the latter1 by the whole diameter of the earth's orbit4 ,when viewed with a powerful telescope1 the surface of ,mars appears diversified with numerous varieties of light and shade4 ,the region around the poles is marked by white spots1 7see ,fig4 #ef1 page #bcg17 which vary their appearances with the changes of seasons in the planet4 ,hence ,dr4 ,herschel conjectured that they were owing to ice and snow1 which alternately accumulate and melt away1 according as it is ,winter or ,summer1 in that region4 ,they are greatest and most conspicuous when that part of the planet has just emerged from a long ,winter1 and they gradually waste away1 as they are exposed to the solar heat4 ,fig4 #ef1 represents the planet1 as exhibited1 under the most favorable circumstances1 to a powerful telescope1 at the time when its gibbous form is strikingly obvious4 ,it has been common to ascribe the ruddy light of ,mars to an extensive and dense atmosphere1 which was said to be distinctly indicated by the gradual diminution of light observed in a star1 as it approaches very near to the planet1 in undergoing an occultation2 but more recent observations afford no such evidence of an atmosphere4 ,by observations on the spots1 we learn that ,mars revolves on his axis in very nearly the same time with the earth1 7twenty-four hours thirty-nine minutes twenty-one seconds and three tenths17 and that the inclination of his axis to that of his orbit is also nearly the same1 being thirty degrees eighteen minutes ten seconds and eight tenths4 ,hence the changes of day and night must be nearly the same there as here1 and the seasons also very similar to ours4 ,since1 however1 the distance of ,mars from the sun is one hundred and forty-two while that of the earth is only ninety-five millions of miles1 the sun will appear more than twice as small on that planet as on ours1 7see ,fig4 #ec1 page #bcf17 and its light and heat will be diminished in the same proportion4 ,only the equatorial regions1 therefore1 will be suitable for the existence of animals and vegetables4 ,the earth will be seen from ,mars as an inferior planet1 always near the sun1 presenting appearances similar1 in many respects1 to those which ,venus presents to us4 ,it will be to that planet the evening and morning star1 sung by their poets 7if poets they have7 with a like enthusiasm4 ,the moon will attend the earth as a little star1 being never seen further from her side than about the diameter under which we view the moon4 ,to the telescope1 the earth will exhibit phases similar to those of ,venus2 and1 finally1 she will1 at long intervals1 make her transits over the solar disk4 ,mean-while1 ,venus will stand to ,mars in a relation similar to that of ,mercury ,illustration ,figures #ei1 #fj4 ,,jupiter ,,and ,,saturn4 to us1 revealing herself only when at the periods of her greatest elongation1 and at all other times hiding herself within the solar blaze4 ,mercury will never be visible to an inhabitant of ,mars4 ,jupiter is distinguished from all the other planets by his great magnitude4 ,his diameter is eighty-nine thousand miles1 and his volume one thousand two hundred and eighty times that of the earth4 ,his figure is strikingly spheroidal1 the equatorial being more than six thousand miles longer than the polar diameter4 ,such a figure might naturally be expected from the rapidity of his diurnal rotation1 which is accomplished in about ten hours4 ,a place on the equator of ,jupiter must turn twenty-seven times as fast as on the terrestrial equator4 ,the distance of ,jupiter from the sun is nearly four hundred and ninety millions of miles1 and his revolution around the sun occupies nearly twelve years4 ,every thing appertaining to ,jupiter is on a grand scale4 ,a world in itself1 equal in dimensions to twelve hundred and eighty of ours2 the whole firmament rolling round it in the short space of ten hours1 a movement so rapid that the eye could probably perceive the heavenly bodies to change their places every moment2 its year dragging out a length of more than four thousand days1 and more than ten thousand of its own days1 while its nocturnal skies are lighted up with four brilliant moons2--these are some of the peculiarities which characterize this magnificent planet4 ,the view of ,jupiter through a good telescope is one of the most splendid and interesting spectacles in astronomy4 ,the disk expands into a large and bright orb1 like the full moon2 the spheroidal figure which theory assigns to revolving spheres1 especially to those which turn with great velocity1 is here palpably exhibited to the eye2 across the disk1 arranged in parallel stripes1 are discerned several dusky bands1 called belts2 and four bright satellites1 always in attendance1 and ever varying their positions1 compose a splendid retinue4 ,indeed1 astronomers gaze with peculiar interest on ,jupiter and his moons1 as affording a miniature representation of the whole solar system1 repeating1 on a smaller scale1 the same revolutions1 and exemplifying more within the compass of our observation1 the same laws as regulate the entire assemblage of sun and planets4 ,figure #ei1 facing page #bdg1 gives a correct view of ,jupiter1 as exhibited to a powerful telescope in a clear evening4 ,you will remark his flattened or spheroidal figure1 the belts which appear in parallel stripes across his disk1 and the four satellites1 that are seen like little stars in a straight line with the equator of the planet4 ,the belts of ,jupiter are variable in their number and dimensions4 ,with the smaller telescopes only one or two are seen1 and those across the equatorial regions2 but with more powerful instruments1 the number is increased1 covering a large part of the entire disk4 ,different opinions have been entertained by astronomers respecting the cause of these belts2 but they have generally been regarded as clouds formed in the atmosphere of the planet1 agitated by winds1 as is indicated by their frequent changes1 and made to assume the form of belts parallel to the equator1 like currents that circulate around our globe4 ,sir ,john ,herschel supposes that the belts are not ranges of clouds1 but portions of the planet itself1 brought into view by the removal of clouds and mists1 that exist in the atmosphere of the planet1 through which are openings made by currents circulating around ,jupiter4 ,the satellites of ,jupiter may be seen with a telescope of very moderate powers4 ,even a common spyglass will enable us to discern them4 ,indeed1 one or two of them have been occasionally seen with the naked eye4 ,in the largest telescopes they severally appear as bright as ,sirius4 ,with such an instrument1 the view of ,jupiter1 with his moons and belts1 is truly a magnificent spectacle4 ,as the orbits of the satellites do not deviate far from the plane of the ecliptic1 and but little from the equator of the planet1 they are usually seen in nearly a straight line with each other1 extending across the central part of the disk4 7,see ,fig4 #ei1 facing page #bdg47 ,jupiter and his satellites exhibit in miniature all the phenomena of the solar system4 ,the satellites perform1 around their primary1 revolutions very analogous to those which the planets perform around the sun1 having1 in like manner1 motions alternately direct1 stationary1 and retrograde4 ,they are all1 with one exception1 a little larger than the moon2 and the second satellite1 which is the smallest1 is nearly as large as the moon1 being two thousand and sixty-eight miles in diameter4 ,they are all very small compared with the primary1 the largest being only one twenty-sixth part of the primary4 ,the outermost satellite extends to the distance from the planet of fourteen times his diameter4 ,the whole system1 therefore1 occupies a region of space more than one million miles in breadth4 ,rapidity of motion1 as well as greatness of dimensions1 is characteristic of the system of ,jupiter4 ,i have already mentioned that the planet itself has a motion on its own axis much swifter than that of the earth1 and the motions of the satellites are also much more rapid than that of the moon4 ,the innermost1 which is a little further off than the moon is from the earth1 goes round its primary in about a day and three quarters2 and the outermost occupies less than seventeen days4 ,the orbits of the satellites are nearly or quite circular1 and deviate but little from the plane of the planet's equator1 and of course are but slightly inclined to the plane of his orbit4 ,they are therefore in a similar situation with respect to ,jupiter1 as the moon would be with respect to the earth1 if her orbit nearly coincided with the ecliptic1 in which case1 she would undergo an eclipse at every opposition4 ,the eclipses of ,jupiter's satellites1 in their general circumstances1 are perfectly analogous to those of the moon1 but in their details they differ in several particulars4 ,owing to the much greater distance of ,jupiter from the sun1 and its greater magnitude1 the cone of its shadow is much longer and larger than that of the earth4 ,on this account1 as well as on account of the little inclination of their orbit to that of the primary1 the three inner satellites of ,jupiter pass through his shadow1 and are totally eclipsed1 at every revolution4 ,the fourth satellite1 owing to the greater inclination of its orbit1 sometimes1 though rarely1 escapes eclipse1 and sometimes merely grazes the limits of the shadow1 or suffers a partial eclipse4 ,these eclipses1 moreover1 are not seen1 as is the case with those of the moon1 from the centre of their motion1 but from a remote station1 and one whose situation with respect to the line of the shadow is variable4 ,this makes no difference in the times of the eclipses1 but it makes a very great one in their visibility1 and in their apparent situations with respect to the planet at the moment of their entering or quitting the shadow4 ,illustration ,fig4 #fa4 ,the eclipses of ,jupiter's satellites present some curious phenomena1 which you will easily understand by studying the following diagram4 ,let ,a1 ,b1 ,c1 ,d1 ,fig4 #fa1 represent the earth in different parts of its orbit2 ,j1 ,jupiter1 in his orbit1 surrounded by his four satellites1 the orbits of which are marked #a1 #b1 #c1 #d4 ,at a1 the first satellite enters the shadow of the planet1 emerges from it at b1 and advances to its greatest elongation at c4 ,the other satellites traverse the shadow in a similar manner4 ,the apparent place1 with respect to the planet1 at which these eclipses will be seen to occur1 will be altered by the position the earth happens at that moment to have in its orbit2 but their appearances for any given night1 as exhibited at ,greenwich1 are calculated and accurately laid down in the ,nautical ,almanac4 ,when one of the satellites is passing between ,jupiter and the sun1 it casts its shadow on the primary1 as the moon casts its shadow on the earth in a solar eclipse4 ,we see with the telescope the shadow traversing the disk4 ,sometimes1 the satellite itself is seen projected on the disk2 but1 being illuminated as well as the primary1 it is not so easily distinguished as ,venus or ,mercury1 when seen on the sun's disk in one of their transits1 since these bodies have their dark sides turned towards us2 but the satellite is illuminated by the sun1 as well as the primary1 and therefore is not easily distinguishable from it4 ,the eclipses of ,jupiter's satellites have been studied with great attention by astronomers1 on account of their affording one of the easiest methods of determining the longitude4 ,on this subject1 ,sir ,john ,herschel remarks3 ,the discovery of ,jupiter's satellites by ,galileo1 which was one of the first fruits of the invention of the telescope1 forms one of the most memorable epochs in the history of astronomy4 ,the first astronomical solution of the problem of 'the longitude1'--the most important problem for the interests of mankind that has ever been brought under the dominion of strict scientific principles1--dates immediately from this discovery4 ,the final and conclusive establishment of the ,copernican system of astronomy may also be considered as referable to the discovery and study of this exquisite miniature system1 in which the laws of the planetary motions1 as ascertained by ,kepler1 and especially that which connects their periods and distances1 were speedily traced1 and found to be satisfactorily maintained4 ,the entrance of one of ,jupiter's satellites into the shadow of the primary1 being seen like the entrance of the moon into the earth's shadow at the same moment of absolute time1 at all places where the planet is visible1 and being wholly independent of parallax1 that is1 presenting the same phenomenon to places remote from each other2 being1 moreover1 predicted beforehand1 with great accuracy1 for the instant of its occurrence at ,greenwich1 and given in the ,nautical ,almanac2 this would seem to be one of those events which are peculiarly adapted for finding the longitude4 ,for you will recollect1 that any instantaneous appearance in the heavens1 visible at the same moment of absolute time at any two places1 may be employed for determining the difference of longitude between those places2 for the difference in their local times1 as indicated by clocks or chronometers1 allowing fifteen degrees for every hour1 will show their difference of longitude4 ,with respect to the method by the eclipses of ,jupiter's satellites1 it must be remarked1 that the extinction of light in the satellite1 at its immersion1 and the recovery of its light at its emersion1 are not instantaneous1 but gradual2 for the satellite1 like the moon1 occupies some time in entering into the shadow1 or in emerging from it1 which occasions a progressive diminution or increase of light4 ,two observers in the same room1 observing with different telescopes the same eclipse1 will frequently disagree1 in noting its time1 to the amount of fifteen or twenty seconds4 ,better methods1 therefore1 of finding the longitude1 are now employed1 although the facility with which the necessary observations can be made1 and the little calculation required1 still render this method eligible in many cases where extreme accuracy is not important4 ,as a telescope is essential for observing an eclipse of one of the satellites1 it is obvious that this method cannot be practised at sea1 since the telescope cannot be used on board of ship1 for want of the requisite steadiness4 ,the grand discovery of the progressive motion of light was first made by observations on the eclipses of ,jupiter's satellites4 ,in the year #afge1 it was remarked by ,roemer1 a ,danish astronomer1 on comparing together observations of these eclipses during many successive years1 that they take place sooner by about sixteen minutes1 when the earth is on the same side of the sun with the planet1 than when she is on the opposite side4 ,the difference he ascribes to the progressive motion of light1 which takes that time to pass through the diameter of the earth's orbit1 making the velocity of light about one hundred and ninety-two thousand miles per second4 ,so great a velocity startled astronomers at first1 and produced some degree of distrust of this explanation of the phenomenon2 but the subsequent discovery of what is called the aberration of light1 led to an independent estimation of the velocity of light1 with almost precisely the same result4 ,few greater feats have ever been performed by the human mind1 than to measure the speed of light1--a speed so great1 as would carry it across the ,atlantic ,ocean in the sixty-fourth part of a second1 and around the globe in less than the seventh part of a second6 ,thus has man applied his scale to the motions of an element1 that literally leaps from world to world in the twinkling of an eye4 ,this is one example of the great power which the invention of the telescope conferred on man4 ,could we plant ourselves on the surface of this vast planet1 we should see the same starry firmament expanding over our heads as we see now2 and the same would be true if we could fly from one planetary world to another1 until we made the circuit of them all2 but the sun and the planetary system would present themselves to us under new and strange aspects4 ,the sun himself would dwindle to one twenty-seventh of his present surface1 7,fig4 #ec1 facing page #bcf17 and afford a degree of light and heat proportionally diminished2 ,mercury1 ,venus1 and even the ,earth1 would all disappear1 being too near the sun to be visible2 ,mars would be as seldom seen as ,mercury is by us1 and constitute the only inferior planet4 ,on the other hand1 ,saturn would shine with greatly augmented size and splendor4 ,when in opposition to the sun1 7at which time it comes nearest to ,jupiter17 it would be a grand object1 appearing larger than either ,venus or ,jupiter does to us4 ,when1 however1 passing to the other side of the sun1 through its superior conjunction1 it would gradually diminish in size and brightness1 and at length become much less than it ever appears to us1 since it would then be four hundred millions of miles further from ,jupiter than it ever is from us4 ,although ,jupiter comes four hundred millions of miles nearer to ,uranus than the earth does1 yet it is still thirteen hundred millions of miles distant from that planet4 ,hence the augmentation of the magnitude and light of ,uranus would be barely sufficient to render it distinguishable by the naked eye4 ,it appears1 therefore1 that ,saturn is the peculiar ornament of the firmament of ,jupiter1 and would present to the telescope most interesting and sublime phenomena4 ,as we owe the revelation of the system of ,jupiter and his attendant worlds wholly to the telescope1 and as the discovery and observation of them constituted a large portion of the glory of ,galileo1 ,i am now forcibly reminded of his labors1 and will recur to his history1 and finish the sketch which ,i commenced in a previous ,letter4 ,,letter ,,xxii4 ,,copernicus4--,,galileo4 ,they leave at length the nether gloom1 and stand ,before the portals of a better land2 ,to happier plains they come1 and fairer groves1 ,the seats of those whom ,heaven1 benignant1 loves2 ,a brighter day1 a bluer ether1 spreads ,its lucid depths above their favored heads2 ,and1 purged from mists that veil our earthly skies1 ,shine suns and stars unseen by mortal eyes4--,virgil4 ,,in order to appreciate the value of the contributions which ,galileo made to astronomy1 soon after the invention of the telescope1 it is necessary to glance at the state of the science when he commenced his discoveries ,for many centuries1 during the middle ages1 a dark night had hung over astronomy1 through which hardly a ray of light penetrated1 when1 in the eastern part of civilized ,europe1 a luminary appeared1 that proved the harbinger of a bright and glorious day4 ,this was ,copernicus1 a native of ,thorn1 in ,prussia4 ,he was born in #adgc4 ,though destined for the profession of medicine1 from his earliest years he displayed a great fondness and genius for mathematical studies1 and pursued them with distinguished success in the ,university of ,cracow4 ,at the age of twenty-five years1 he resorted to ,italy1 for the purpose of studying astronomy1 where he resided a number of years4 ,thus prepared1 he returned to his native country1 and1 having acquired an ecclesiastical living that was adequate to his support in his frugal mode of life1 he established himself at ,frauenberg1 a small town near the mouth of the ,vistula1 where he spent nearly forty years in observing the heavens1 and meditating on the celestial motions4 ,he occupied the upper part of a humble farm-house1 through the roof of which he could find access to an unobstructed sky1 and there he carried on his observations4 ,his instruments1 however1 were few and imperfect1 and it does not appear that he added any thing to the art of practical astronomy4 ,this was reserved for ,tycho ,brahe1 who came a half a century after him4 ,nor did ,copernicus enrich the science with any important discoveries4 ,it was not so much his genius or taste to search for new bodies1 or new phenomena among the stars1 as it was to explain the reasons of the most obvious and well-known appearances and motions of the heavenly bodies4 ,with this view1 he gave his mind to long-continued and profound meditation4 ,copernicus tells us that he was first led to think that the apparent motions of the heavenly bodies1 in their diurnal revolution1 were owing to the real motion of the earth in the opposite direction1 from observing instances of the same kind among terrestrial objects2 as when the shore seems to the mariner to recede1 as he rapidly sails from it2 and as trees and other objects seem to glide by us1 when1 on riding swiftly past them1 we lose the consciousness of our own motion4 ,he was also smitten with the simplicity prevalent in all the works and operations of ,nature1 which is more and more conspicuous the more they are understood2 and he hence concluded that the planets do not move in the complicated paths which most preceding astronomers assigned to them4 ,i shall explain to you1 hereafter1 the details of his system4 ,i need only at present remind you that the hypothesis which he espoused and defended1 7being substantially the same as that proposed by ,pythagoras1 five hundred years before the ,christian era17 supposes1 first1 that the apparent movements of the sun by day1 and of the moon and stars by night1 from east to west1 result from the actual revolution of the earth on its own axis from west to east2 and1 secondly1 that the earth and all the planets revolve about the sun in circular orbits4 ,this hypothesis1 when he first assumed it1 was with him1 as it had been with ,pythagoras1 little more than mere conjecture4 ,the arguments by which its truth was to be finally established were not yet developed1 and could not be1 without the aid of the telescope1 which was not yet invented4 ,upon this hypothesis1 however1 he set out to explain all the phenomena of the visible heavens1--as the diurnal revolutions of the sun1 moon1 and stars1 the slow progress of the planets through the signs of the zodiac1 and the numerous irregularities to which the planetary motions are subject4 ,these last are apparently so capricious1--being for some time forward1 then stationary1 then backward1 then stationary again1 and finally direct1 a second time1 in the order of the signs1 and constantly varying in the velocity of their movements1--that nothing but long-continued and severe meditation could have solved all these appearances1 in conformity with the idea that each planet is pursuing its simple way all the while in a circle around the sun4 ,although1 therefore1 ,pythagoras fathomed the profound doctrine that the sun is the centre around which the earth and all the planets revolve1 yet we have no evidence that he ever solved the irregular motions of the planets in conformity with his hypothesis1 although the explanation of the diurnal revolution of the heavens1 by that hypothesis1 involved no difficulty4 ,ignorant as ,copernicus was of the principle of gravitation1 and of most of the laws of motion1 he could go but little way in following out the consequences of his own hypothesis2 and all that can be claimed for him is1 that he solved1 by means of it1 most of the common phenomena of the celestial motions4 ,he indeed got upon the road to truth1 and advanced some way in its sure path2 but he was able to adduce but few independent proofs1 to show that it was the truth4 ,it was only quite at the close of his life that he published his system to the world1 and that only at the urgent request of his friends2 anticipating1 perhaps1 the opposition of a bigoted priesthood1 whose fury was afterwards poured upon the head of ,galileo1 for maintaining the same doctrines4 ,although1 therefore1 the system of ,copernicus afforded an explanation of the celestial motions1 far more simple and rational than the previous systems which made the earth the centre of those motions1 yet this fact alone was not sufficient to compel the assent of astronomers2 for the greater part1 to say the least1 of the same phenomena1 could be explained on either hypothesis4 ,with the old doctrine astronomers were already familiar1 a circumstance which made it seem easier2 while the new doctrines would seem more difficult1 from their being imperfectly understood4 ,accordingly1 for nearly a century after the publication of the system of ,copernicus1 he gained few disciples4 ,tycho ,brahe rejected it1 and proposed one of his own1 of which ,i shall hereafter give you some account2 and it would probably have fallen quite into oblivion1 had not the observations of ,galileo1 with his newly-invented telescope1 brought to light innumerable proofs of its truth1 far more cogent than any which ,copernicus himself had been able to devise4 ,galileo no sooner had completed his telescope1 and directed it to the heavens1 than a world of wonders suddenly burst upon his enraptured sight4 ,pointing it to the moon1 he was presented with a sight of her mottled disk1 and of her mountains and valleys4 ,the sun exhibited his spots2 ,venus1 her phases2 and ,jupiter1 his expanded orb1 and his retinue of moons4 ,these last he named1 in honor of his patron1 ,cosmo d',medici1 ,medicean stars4 ,so great was this honor deemed of associating one's name with the stars1 that express application was made to ,galileo1 by the court of ,france1 to award this distinction to the reigning ,monarch1 ,henry the ,fourth1 with plain intimations1 that by so doing he would render himself and his family rich and powerful for ever4 ,galileo published the result of his discoveries in a paper1 denominated ',nuncius ,sidereus1' the ',messenger of the ,stars4' ,in that ignorant and marvellous age1 this publication produced a wonderful excitement4 ,many doubted1 many positively refused to believe1 so novel an announcement2 all were struck with the greatest astonishment1 according to their respective opinions1 either at the new view of the universe thus offered to them1 or at the high audacity of ,galileo1 in inventing such fables4 ,even ,kepler1 the great ,german astronomer1 of whom ,i shall tell you more by and by1 wrote to ,galileo1 and desired him to supply him with arguments1 by which he might answer the objections to these pretended discoveries with which he was continually assailed4 ,galileo answered him as follows3 ,in the first place1 ,i return you my thanks that you first1 and almost alone1 before the question had been sifted1 7such is your candor1 and the loftiness of your mind17 put faith in my assertions4 ,you tell me you have some telescopes1 but not sufficiently good to magnify distant objects with clearness1 and that you anxiously expect a sight of mine1 which magnifies images more than a thousand times4 ,it is mine no longer1 for the ,grand ,duke of ,tuscany has asked it of me1 and intends to lay it up in his museum1 among his most rare and precious curiosities1 in eternal remembrance of the invention4 ,you ask1 my dear ,kepler1 for other testimonies4 ,i produce1 for one1 the ,grand ,duke1 who1 after observing the ,medicean planets several times with me at ,pisa1 during the last months1 made me a present1 at parting1 of more than a thousand florins1 and has now invited me to attach myself to him1 with the annual salary of one thousand florins1 and with the title of ',philosopher and ,principal ,mathematician to ,his ,highness2' without the duties of any office to perform1 but with the most complete leisure4 ,i produce1 for another witness1 myself1 who1 although already endowed in this ,college with the noble salary of one thousand florins1 such as no professor of mathematics ever before received1 and which ,i might securely enjoy during my life1 even if these planets should deceive me and should disappear1 yet quit this situation1 and take me where want and disgrace will be my punishment1 should ,i prove to have been mistaken4 ,the learned professors in the universities1 who1 in those days1 were unaccustomed to employ their senses in inquiring into the phenomena of ,nature1 but satisfied themselves with the authority of ,aristotle1 on all subjects1 were among the most incredulous with respect to the discoveries of ,galileo4 ,oh1 my dear ,kepler1 says ,galileo1 how ,i wish that we could have one hearty laugh together4 ,here1 at ,padua1 is the principal ,professor of ,philosophy1 whom ,i have repeatedly and urgently requested to look at the moon and planets through my glass1 which he pertinaciously refuses to do4 ,why are you not here8 ,what shouts of laughter we should have at this glorious folly1 and to hear the ,professor of ,philosophy at ,pisa laboring before the ,grand ,duke1 with logical arguments1 as if with magical incantations1 to charm the new planets out of the sky4 ,the following argument by ,sizzi1 a contemporary astronomer of some note1 to prove that there can be only seven planets1 is a specimen of the logic with which ,galileo was assailed4 ,there are seven windows given to animals in the domicile of the head1 through which the air is admitted to the tabernacle of the body1 to enlighten1 to warm1 and to nourish it2 which windows are the principal parts of the microcosm1 or little world1--two nostrils1 two eyes1 two ears1 and one mouth4 ,so in the heavens1 as in a macrocosm1 or great world1 there are two favorable stars1 ,jupiter and ,venus2 two unpropitious1 ,mars and ,saturn2 two luminaries1 the ,sun and ,moon2 and ,mercury alone1 undecided and indifferent4 ,from which1 and from many other phenomena of ,nature1 such as the seven metals1 c41 which it were tedious to enumerate1 we gather that the number of planets is necessarily seven4 ,moreover1 the satellites are invisible to the naked eye1 and therefore can exercise no influence over the earth1 and therefore would be useless1 and therefore do not exist4 ,besides1 as well the ,jews and other ancient nations1 as modern ,europeans1 have adopted the division of the week into seven days1 and have named them from the seven planets4 ,now1 if we increase the number of planets1 this whole system falls to the ground4 ,when1 at length1 the astronomers of the schools found it useless to deny the fact that ,jupiter is attended by smaller bodies1 which revolve around him1 they shifted their ground of warfare1 and asserted that ,galileo had not told the whole truth2 that there were not merely four satellites1 but a still greater number2 one said five2 another1 nine2 and another1 twelve2 but1 in a little time1 ,jupiter moved forward in his orbit1 and left all behind him1 save the four ,medicean stars4 ,it had been objected to the ,copernican system1 that were ,venus a body which revolved around the sun in an orbit interior to that of the earth1 she would undergo changes similar to those of the moon4 ,as no such changes could be detected by the naked eye1 no satisfactory answer could be given to this objection2 but the telescope set all right1 by showing1 in fact1 the phases of ,venus4 ,the same instrument1 disclosed1 also1 in the system of ,jupiter and his moons1 a miniature exhibition of the solar system itself4 ,it showed the actual existence of the motion of a number of bodies around one central orb1 exactly similar to that which was predicated of the sun and planets4 ,every one1 therefore1 of these new and interesting discoveries1 helped to confirm the truth of the system of ,copernicus4 ,but a fearful cloud was now rising over ,galileo1 which spread itself1 and grew darker every hour4 ,the ,church of ,rome had taken alarm at the new doctrines respecting the earth's motion1 as contrary to the declarations of the ,bible1 and a formidable difficulty presented itself1 namely1 how to publish and defend these doctrines1 without invoking the terrible punishments inflicted by the ,inquisition on heretics4 ,no work could be printed without license from the court of ,rome2 and any opinions supposed to be held and much more known to be taught by any one1 which1 by an ignorant and superstitious priesthood1 could be interpreted as contrary to ,scripture1 would expose the offender to the severest punishments1 even to imprisonment1 scourging1 and death4 ,we1 who live in an age so distinguished for freedom of thought and opinion1 can form but a very inadequate conception of the bondage in which the minds of men were held by the chains of the ,inquisition4 ,it was necessary1 therefore1 for ,galileo to proceed with the greatest caution in promulgating truths which his own discoveries had confirmed4 ,he did not1 like the ,christian martyrs1 proclaim the truth in the face of persecutions and tortures2 but while he sought to give currency to the ,copernican doctrines1 he labored1 at the same time1 by cunning artifices1 to blind the ecclesiastics to his real designs1 and thus to escape the effects of their hostility4 ,before ,galileo published his doctrines in form1 he had expressed himself so freely1 as to have excited much alarm among the ecclesiastics4 ,one of them preached publicly against him1 taking for his text1 the passage1 ,ye men of ,galilee1 why stand ye here gazing up into heaven8 ,he therefore thought it prudent to resort to ,rome1 and confront his enemies face to face4 ,a contemporary describes his appearance there in the following terms1 in a letter addressed to a ,romish ,cardinal3 ,your ,eminence would be delighted with ,galileo1 if you heard him holding forth1 as he often does1 in the midst of fifteen or twenty1 all violently attacking him1 sometimes in one house1 sometimes in another4 ,but he is armed after such fashion1 that he laughs all of them to scorn2 and even if the novelty of his opinions prevents entire persuasion1 at least he convicts of emptiness most of the arguments with which his adversaries endeavor to overwhelm him4 ,in #afaf1 ,galileo1 as he himself states1 had a most gracious audience of the ,pope1 ,paul the ,fifth1 which lasted for nearly an hour1 at the end of which his ,holiness assured him1 that the ,congregation were no longer in a humor to listen lightly to calumnies against him1 and that so long as he occupied the ,papal chair1 ,galileo might think himself out of all danger4 ,nevertheless1 he was not allowed to return home1 without receiving formal notice not to teach the opinions of ,copernicus1 that the sun is in the centre of the system1 and that the earth moves about it1 from that time forward1 in any manner4 ,galileo had a most sarcastic vein1 and often rallied his persecutors with the keenest irony4 ,this he exhibited1 some time after quitting ,rome1 in an epistle which he sent to the ,arch ,duke ,leopold1 accompanying his ',theory of the ,tides4' ,this theory1 says he1 occurred to me when in ,rome1 whilst the theologians were debating on the prohibition of ,copernicus's book1 and of the opinion maintained in it of the motion of the earth1 which ,i at that time believed2 until it pleased those gentlemen to suspend the book1 and to declare the opinion false and repugnant to the ,holy ,scriptures4 ,now1 as ,i know how well it becomes me to obey and believe the decisions of my superiors1 which proceed out of more profound knowledge than the weakness of my intellect can attain to1 this theory1 which ,i send you1 which is founded on the motion of the earth1 ,i now look upon as a fiction and a dream1 and beg your ,highness to receive it as such4 ,but1 as poets often learn to prize the creations of their fancy1 so1 in like manner1 do ,i set some value on this absurdity of mine4 ,it is true1 that when ,i sketched this little work1 ,i did hope that ,copernicus would not1 after eighty years1 be convicted of error2 and ,i had intended to develope and amplify it further2 but a voice from heaven suddenly awakened me1 and at once annihilated all my confused and entangled fancies4 ,it is difficult1 however1 sometimes to decide whether the language of ,galileo is ironical1 or whether he uses it with subtlety1 with the hope of evading the anathemas of the ,inquisition4 ,thus he ends one of his writings with the following passage3 ,in conclusion1 since the motion attributed to the earth1 which ,i1 as a pious and ,catholic person1 consider most false1 and not to exist1 accommodates itself so well to explain so many and such different phenomena1 ,i shall not feel sure that1 false as it is1 it may not just as deludingly correspond with the phenomena of comets4 ,in the year #afbd1 soon after the accession of ,urban the ,eighth to the ,pontifical chair1 ,galileo went to ,rome again1 to offer his congratulations to the new ,pope1 as well as to propitiate his favor4 ,he seems to have been received with unexpected cordiality2 and1 on his departure1 the ,pope commended him to the good graces of ,ferdinand1 ,grand ,duke of ,tuscany1 in the following terms3 ,we find in him not only literary distinction1 but also the love of piety1 and he is strong in those qualities by which ,pontifical good-will is easily obtained4 ,and now1 when he has been brought to this city1 to congratulate ,us on ,our elevation1 ,we have lovingly embraced him2 nor can ,we suffer him to return to the country whither your liberality recalls him1 without an ample provision of ,pontifical love4 ,and that you may know how dear he is to ,us1 we have willed to give him this honorable testimonial of virtue and piety4 ,and ,we further signify1 that every benefit which you shall confer upon him will conduce to ,our gratification4 ,in the year #afcj1 ,galileo finished a great work1 on which he had been long engaged1 entitled1 ',the ,dialogue on the ,ptolemaic and ,copernican ,systems4' ,from the notion which prevailed1 that he still countenanced the ,copernican doctrine of the earth's motion1 which had been condemned as heretical1 it was some time before he could obtain permission from the ,inquisitors 7whose license was necessary to every book7 to publish it4 ,this he was able to do1 only by employing again that duplicity or artifice which would throw dust in the eyes of the vain and superstitious priesthood4 ,in #afcb1 the work appeared under the following title3 ',a ,dialogue1 by ,galileo ,galilei1 ,extraordinary ,mathematician of the ,university of ,pisa1 and ,principal ,philosopher and ,mathematician of the ,most ,serene ,grand ,duke of ,tuscany2 in which1 in a ,conversation of four days1 are discussed the two principal ,systems of the ,world1 the ,ptolemaic and ,copernican1 indeterminately proposing the ,philosophical ,arguments as well on one side as on the other4' ,the subtle disguise which he wore1 may be seen from the following extract from his ',introduction1' addressed ',to the discreet ,reader4' ,some years ago1 a salutary edict was promulgated at ,rome1 which1 in order to obviate the perilous scandals of the present age1 enjoined an opportune silence on the ,pythagorean opinion of the earth's motion4 ,some were not wanting1 who rashly asserted that this decree originated1 not in a judicious examination1 but in ill-informed passion2 and complaints were heard1 that counsellors totally inexperienced in astronomical observations ought not1 by hasty prohibitions1 to clip the wings of speculative minds4 ,my zeal could not keep silence when ,i heard these rash lamentations1 and ,i thought it proper1 as being fully informed with regard to that most prudent determination1 to appear publicly on the theatre of the world1 as a witness of the actual truth4 ,i happened at that time to be in ,rome3 ,i was admitted to the audiences1 and enjoyed the approbation1 of the most eminent prelates of that court2 nor did the publication of that decree occur without my receiving some prior intimation of it4 ,wherefore1 it is my intention1 in this present work1 to show to foreign nations1 that as much is known of this matter in ,italy1 and particularly in ,rome1 as ultramontane diligence can ever have formed any notion of1 and collecting together all my own speculations on the ,copernican system1 to give them to understand that the knowledge of all these preceded the ,roman censures2 and that from this country proceed not only dogmas for the salvation of the soul1 but also ingenious discoveries for the gratification of the understanding4 ,with this object1 ,i have taken up in the ',dialogue' the ,copernican side of the question1 treating it as a pure mathematical hypothesis2 and endeavoring1 in every artificial manner1 to represent it as having the advantage1 not over the opinion of the stability of the earth absolutely1 but according to the manner in which that opinion is defended by some1 who indeed profess to be ,aristotelians1 but retain only the name1 and are contented1 without improvement1 to worship shadows1 not philosophizing with their own reason1 but only from the recollection of the four principles imperfectly understood4 ,although the ,pope himself1 as well as the ,inquisitors1 had examined ,galileo's manuscript1 and1 not having the sagacity to detect the real motives of the author1 had consented to its publication1 yet1 when the book was out1 the enemies of ,galileo found means to alarm the court of ,rome1 and ,galileo was summoned to appear before the ,inquisition4 ,the philosopher was then seventy years old1 and very infirm1 and it was with great difficulty that he performed the journey4 ,his unequalled dignity and celebrity1 however1 commanded the involuntary respect of the tribunal before which he was summoned1 which they manifested by permitting him to reside at the palace of his friend1 the ,tuscan ,ambassador2 and when it became necessary1 in the course of the inquiry1 to examine him in person1 although his removal to the ,holy ,office was then insisted upon1 yet he was not1 like other heretics1 committed to close and solitary confinement4 ,on the contrary1 he was lodged in the apartments of the ,head of the ,inquisition1 where he was allowed the attendance of his own servant1 who was also permitted to sleep in an adjoining room1 and to come and go at pleasure4 ,these were deemed extraordinary indulgences in an age when the punishment of heretics usually began before their trial4 ,about four months after ,galileo's arrival in ,rome1 he was summoned to the ,holy ,office4 ,he was detained there during the whole of that day2 and on the next day was conducted1 in a penitential dress1 to the ,convent of ,minerva1 where the ,cardinals and ,prelates1 his judges1 were assembled for the purpose of passing judgement upon him1 by which this venerable old man was solemnly called upon to renounce and abjure1 as impious and heretical1 the opinions which his whole existence had been consecrated to form and strengthen4 ,probably there is not a more curious document in the history of science1 than that which contains the sentence of the ,inquisition on ,galileo1 and his consequent abjuration4 ,it teaches us so much1 both of the darkness and bigotry of the terrible ,inquisition1 and of the sufferings encountered by those early martyrs of science1 that ,i will transcribe for your perusal1 from the excellent ',life of ,galileo' in the ',library of ,useful ,knowledge1' 7from which ,i have borrowed much already17 the entire record of this transaction4 ,the sentence of the ,inquisition is as follows3 ,we1 the undersigned1 by the grace of ,god1 ,cardinals of the ,holy ,roman ,church1 ,inquisitors ,general throughout the whole ,christian ,republic1 ,special ,deputies of the ,holy ,apostolical ,chair against heretical depravity3 ,whereas1 you1 ,galileo1 son of the late ,vincenzo ,galilei of ,florence1 aged seventy years1 were denounced in #afae1 to this ,holy ,office1 for holding as true a false doctrine taught by many1 namely1 that the sun is immovable in the centre of the world1 and that the earth moves1 and also with a diurnal motion2 also1 for having pupils which you instructed in the same opinions2 also1 for maintaining a correspondence on the same with some ,german mathematicians2 also1 for publishing certain letters on the solar spots1 in which you developed the same doctrine as true2 also1 for answering the objections which were continually produced from the ,holy ,scriptures1 by glozing the said ,scriptures1 according to your own meaning2 and whereas1 thereupon was produced the copy of a writing1 in form of a letter1 professedly written by you to a person formerly your pupil1 in which1 following the hypothesis of ,copernicus1 you include several propositions contrary to the true sense and authority of the ,holy ,scriptures3 therefore1 this ,holy ,tribunal1 being desirous of providing against the disorder and mischief which was thence proceeding and increasing1 to the detriment of the holy faith1 by the desire of ,his ,holiness1 and of the ,most ,eminent ,lords ,cardinals of this supreme and universal ,inquisition1 the two propositions of the stability of the sun1 and motion of the earth1 were qualified by the ,theological ,qualifiers1 as follows3 #a4 ,the proposition that the sun is in the centre of the world1 and immovable from its place1 is absurd1 philosophically false1 and formally heretical2 because it is expressly contrary to the ,holy ,scriptures4 #b4 ,the proposition that the earth is not the centre of the world1 nor immovable1 but that it moves1 and also with a diurnal motion1 is also absurd1 philosophically false1 and1 theologically considered1 equally erroneous in faith4 ,but whereas1 being pleased at that time to deal mildly with you1 it was decreed in the ,holy ,congregation1 held before ,his ,holiness on the twenty-fifth day of ,february1 #afaf1 that ,his ,eminence the ,lord ,cardinal ,bellarmine should enjoin you to give up altogether the said false doctrine2 if you should refuse1 that you should be ordered by the ,commissary of the ,holy ,office to relinquish it1 not to teach it to others1 nor to defend it1 and in default of the acquiescence1 that you should be imprisoned2 and in execution of this decree1 on the following day1 at the palace1 in presence of ,his ,eminence the said ,lord ,cardinal ,bellarmine1 after you had been mildly admonished by the said ,lord ,cardinal1 you were commanded by the acting ,commissary of the ,holy ,office1 before a notary and witnesses1 to relinquish altogether the said false opinion1 and in future neither to defend nor teach it in any manner1 neither verbally nor in writing1 and upon your promising obedience1 you were dismissed4 ,and1 in order that so pernicious a doctrine might be altogether rooted out1 nor insinuate itself further to the heavy detriment of the ,catholic truth1 a decree emanated from the ,holy ,congregation of the ,index1 prohibiting the books which treat of this doctrine2 and it was declared false1 and altogether contrary to the ,holy and ,divine ,scripture4 ,and whereas1 a book has since appeared1 published at ,florence last year1 the title of which showed that you were the author1 which title is1 ',the ,dialogue of ,galileo ,galilei1 on the two principal ,systems of the ,world1 the ,ptolemaic and ,copernican2' and whereas1 the ,holy ,congregation has heard that1 in consequence of printing the said book1 the false opinion of the earth's motion and stability of the sun is daily gaining ground2 the said book has been taken into careful consideration1 and in it has been detected a glaring violation of the said order1 which had been intimated to you2 inasmuch as in this book you have defended the said opinion1 already1 and in your presence1 condemned2 although in the said book you labor1 with many circumlocutions1 to induce the belief that it is left by you undecided1 and in express terms probable2 which is equally a very grave error1 since an opinion can in no way be probable which has been already declared and finally determined contrary to the ,divine ,scripture4 ,therefore1 by ,our order1 you have been cited to this ,holy ,office1 where1 on your examination upon oath1 you have acknowledged the said book as written and printed by you4 ,you also confessed that you began to write the said book ten or twelve years ago1 after the order aforesaid had been given4 ,also1 that you demanded license to publish it1 but without signifying to those who granted you this permission1 that you had been commanded not to hold1 defend1 or teach1 the said doctrine in any manner4 ,you also confessed1 that the style of said book was1 in many places1 so composed1 that the reader might think the arguments adduced on the false side to be so worded1 as more effectually to entangle the understanding than to be easily solved1 alleging1 in excuse1 that you have thus run into an error1 foreign 7as you say7 to your intention1 from writing in the form of a dialogue1 and in consequence of the natural complacency which every one feels with regard to his own subtilties1 and in showing himself more skilful than the generality of mankind in contriving1 even in favor of false propositions1 ingenious and apparently probable arguments4 ,and1 upon a convenient time being given you for making your defence1 you produced a certificate in the handwriting of ,his ,eminence1 the ,lord ,cardinal ,bellarmine1 procured1 as you said1 by yourself1 that you might defend yourself against the calumnies of your enemies1 who reported that you had abjured your opinions1 and had been punished by the ,holy ,office2 in which certificate it is declared1 that you had not abjured1 nor had been punished1 but merely that the declaration made by his ,holiness1 and promulgated by the ,holy ,congregation of the ,index1 had been announced to you1 which declares that the opinion of the motion of the earth1 and stability of the sun1 is contrary to the ,holy ,scriptures1 and therefore cannot be held or defended4 ,wherefore1 since no mention is there made of two articles of the order1 to wit1 the order 'not to teach1' and 'in any manner1' you argued that we ought to believe that1 in the lapse of fourteen or sixteen years1 they had escaped your memory1 and that this was also the reason why you were silent as to the order1 when you sought permission to publish your book1 and that this is said by you1 not to excuse your error1 but that it may be attributed to vain-glorious ambition rather than to malice4 ,but this very certificate1 produced on your behalf1 has greatly aggravated your offence1 since it is therein declared1 that the said opinion is contrary to the ,holy ,scriptures1 and yet you have dared to treat of it1 and to argue that it is probable2 nor is there any extenuation in the license artfully and cunningly extorted by you1 since you did not intimate the command imposed upon you4 ,but whereas1 it appeared to ,us that you had not disclosed the whole truth with regard to your intentions1 ,we thought it necessary to proceed to the rigorous examination of you1 in which 7without any prejudice to what you had confessed1 and which is above detailed against you1 with regard to your said intention7 you answered like a good ,catholic4 ,therefore1 having seen and maturely considered the merits of your cause1 with your said confessions and excuses1 and every thing else which ought to be seen and considered1 ,we have come to the underwritten final sentence against you3 ,invoking1 therefore1 the most holy name of our ,lord ,jesus ,christ1 and of his ,most ,glorious ,virgin ,mother1 ,mary1 by this ,our final sentence1 which1 sitting in council and judgement for the tribunal of the ,reverend ,masters of ,sacred ,theology1 and ,doctors of both ,laws1 ,our ,assessors1 ,we put forth in this writing touching the matters and controversies before ,us1 between the ,magnificent ,charles ,sincerus1 ,doctor of both ,laws1 ,fiscal ,proctor of this ,holy ,office1 of the one part1 and you1 ,galileo ,galilei1 an examined and confessed criminal from this present writing now in progress1 as above1 of the other part1 ,we pronounce1 judge1 and declare1 that you1 the said ,galileo1 by reason of these things which have been detailed in the course of this writing1 and which1 as above1 you have confessed1 have rendered yourself vehemently suspected1 by this ,holy ,office1 of heresy2 that is to say1 that you believe and hold the false doctrine1 and contrary to the ,holy and ,divine ,scriptures1 namely1 that the sun is the centre of the world1 and that it does not move from east to west1 and that the earth does move1 and is not the centre of the world2 also1 that an opinion can be held and supported1 as probable1 after it has been declared and finally decreed contrary to the ,holy ,scripture1 and consequently1 that you have incurred all the censures and penalties enjoined and promulgated in the sacred canons1 and other general and particular constitutions against delinquents of this description4 ,from which it is ,our pleasure that you be absolved1 provided that1 with a sincere heart and unfeigned faith1 in ,our presence1 you abjure1 curse1 and detest1 the said errors and heresies1 and every other error and heresy1 contrary to the ,catholic and ,apostolic ,church of ,rome1 in the form now shown to you4 ,but that your grievous and pernicious error and transgression may not go altogether unpunished1 and that you may be made more cautious in future1 and may be a warning to others to abstain from delinquencies of this sort1 ,we decree1 that the book of the ,dialogues of ,galileo ,galilei be prohibited by a public edict1 and ,we condemn you to the formal prison of this ,holy ,office for a period determinable at ,our pleasure2 and1 by way of salutary penance1 ,we order you1 during the next three years1 to recite1 once a week1 the seven penitential psalms1 reserving to ,ourselves the power of moderating1 commuting1 or taking off the whole or part of the said punishment1 or penance4 ,and so ,we say1 pronounce1 and by ,our sentence declare1 decree1 and reserve1 in this and in every other better form and manner1 which lawfully ,we may and can use4 ,so ,we1 the subscribing ,cardinals1 pronounce4 ,subscribed by seven ,cardinals4 ,in conformity with the foregoing sentence1 ,galileo was made to kneel before the ,inquisition1 and make the following ,abjuration3 ,i1 ,galileo ,galilei1 son of the late ,vincenzo ,galilei1 of ,florence1 aged seventy years1 being brought personally to judgement1 and kneeling before you1 ,most ,eminent and ,most ,reverend ,lords ,cardinals1 ,general ,inquisitors of the ,universal ,christian ,republic against heretical depravity1 having before my eyes the ,holy ,gospels1 which ,i touch with my own hands1 swear1 that ,i have always believed1 and with the help of ,god will in future believe1 every article which the ,holy ,catholic and ,apostolic ,church of ,rome holds1 teaches1 and preaches4 ,but because ,i had been enjoined1 by this ,holy ,office1 altogether to abandon the false opinion which maintains that the sun is the centre and immovable1 and forbidden to hold1 defend1 or teach1 the said false doctrine1 in any manner3 and after it had been signified to me that the said doctrine is repugnant to the ,holy ,scripture1 ,i have written and printed a book1 in which ,i treat of the same doctrine now condemned1 and adduce reasons with great force in support of the same1 without giving any solution1 and therefore have been judged grievously suspected of heresy2 that is to say1 that ,i held and believed that the sun is the centre of the world and immovable1 and that the earth is not the centre and movable2 willing1 therefore1 to remove from the minds of ,your ,eminences1 and of every ,catholic ,christian1 this vehement suspicion rightfully entertained towards me1 with a sincere heart and unfeigned faith1 ,i abjure1 curse1 and defeat1 the said errors and heresies1 and generally every other error and sect contrary to the said ,holy ,church2 and ,i swear1 that ,i will never more in future say or assert any thing1 verbally or in writing1 which may give rise to a similar suspicion of me3 but if ,i shall know any heretic1 or any one suspected of heresy1 that ,i will denounce him to this ,holy ,office1 or to the ,inquisitor and ,ordinary of the place in which ,i may be4 ,i swear1 moreover1 and promise1 that ,i will fulfil and observe fully1 all the penances which have been or shall be laid on me by this ,holy ,office4 ,but if it shall happen that ,i violate any of my said promises1 oaths1 and protestations1 7which ,god avert67 ,i subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons1 and other general and particular constitutions1 against delinquents of this description4 ,so may ,god help me1 and his ,holy ,gospels1 which ,i touch with my own hands4 ,i1 the above-named ,galileo ,galilei1 have abjured1 sworn1 promised1 and bound myself1 as above2 and in witness thereof1 with my own hand have subscribed this present writing of my abjuration1 which ,i have recited1 word for word4 ,at ,rome1 in the ,convent of ,minerva1 twenty-second ,june1 #afcc1 ,i1 ,galileo ,galilei1 have abjured as above1 with my own hand4 ,from the court ,galileo was conducted to prison1 to be immured for life in one of the dungeons of the ,inquisition4 ,his sentence was afterwards mitigated1 and he was permitted to return to ,florence2 but the humiliation to which he had been subjected pressed heavily on his spirits1 beset as he was with infirmities1 and totally blind1 and he never more talked or wrote on the subject of astronomy4 ,there was enough in the character of ,galileo to command a high admiration4 ,there was much1 also1 in his sufferings in the cause of science1 to excite the deepest sympathy1 and even compassion4 ,he is moreover universally represented to have been a man of great equanimity1 and of a noble and generous disposition4 ,no scientific character of the age1 or perhaps of any age1 forms a structure of finer proportions1 or wears in a higher degree the grace of symmetry4 ,still1 we cannot approve of his employing artifice in the promulgation of truth2 and we are compelled to lament that his lofty spirit bowed in the final conflict4 ,how far1 therefore1 he sinks below the dignity of the ,christian martyr6 ,at the age of seventy1 says ,dr4 ,brewster1 in his life of ,sir ,isaac ,newton1 on his bended knees1 and with his right hand resting on the ,holy ,evangelists1 did this patriarch of science avow his present and past belief in the dogmas of the ,romish ,church1 abandon as false and heretical the doctrine of the earth's motion and of the sun's immobility1 and pledge himself to denounce to the ,inquisition any other person who was even suspected of heresy4 ,he abjured1 cursed1 and detested1 those eternal and immutable truths which the ,almighty had permitted him to be the first to establish4 ,had ,galileo but added the courage of the martyr to the wisdom of the sage2 had he carried the glance of his indignant eye round the circle of his judges2 had he lifted his hands to heaven1 and called the living ,god to witness the truth and immutability of his opinions2 the bigotry of his enemies would have been disarmed1 and science would have enjoyed a memorable triumph4 ,,letter ,,xxiii4 ,,saturn4--,,uranus4--,,asteroids4 ,into the ,heaven of ,heavens ,i have presumed1 ,an earthly guest1 and drawn empyreal air4--,milton4 ,,the consideration of the system of ,jupiter and his satellites led us to review the interesting history of ,galileo1 who first1 by means of the telescope1 disclosed the knowledge of that system to the world4 ,i will now proceed with the other superior planets4 ,saturn1 as well as ,jupiter1 has within itself a system on a scale of great magnificence4 ,in size it is next to ,jupiter the largest of the planets1 being seventy-nine thousand miles in diameter1 or about one thousand times as large as the earth4 ,it has likewise belts on its surface1 and is attended by seven satellites4 ,but a still more wonderful appendage is its ,ring1 a broad wheel1 encompassing the planet at a great distance from it4 ,as ,saturn is nine hundred millions of miles from us1 we require a more powerful telescope to see his glories1 in all their magnificence1 than we do to enjoy a full view of the system of ,jupiter4 ,when we are privileged with a view of ,saturn1 in his most favorable positions1 through a telescope of the larger class1 the mechanism appears more wonderful than even that of ,jupiter4 ,saturn's ring1 when viewed with telescopes of a high power1 is found to consist of two concentred rings1 separated from each other by a dark space4 ,although this division of the rings appears to us1 on account of our immense distance1 as only a fine line1 yet it is1 in reality1 an interval of not less than eighteen hundred miles4 ,the dimensions of the whole system are1 in round numbers1 as follows3 ,miles4 ,diameter of the planet1 #gi1jjj ,from the surface of the planet to the inner ring1 #bj1jjj ,breadth of the inner ring1 #ag1jjj ,interval between the rings1 #a1hjj ,breadth of the outer ring1 #aj1ejj ,extreme dimensions from outside to outside1 #agf1jjj ,figure #fj1 facing page #bdg1 represents ,saturn1 as it appears to a powerful telescope1 surrounded by its rings1 and having its body striped with dark belts1 somewhat similar1 but broader and less strongly marked than those of ,jupiter4 ,in telescopes of inferior power1 but still sufficient to see the ring distinctly1 we should scarcely discern the belts at all4 ,we might1 however1 observe the shadow cast upon the ring by the planet1 7as seen in the figure on the right1 on the upper side27 and1 in favorable situations of the planet1 we might discern glimpses of the shadow of the ring on the body of the planet1 on the lower side beneath the ring4 ,to see the division of the ring and the satellites requires a better telescope than is in possession of most observers4 ,with smaller telescopes1 we may discover an oval figure of peculiar appearance1 which it would be difficult to interpret4 ,galileo1 who first saw it in the year #afaj1 recognised this peculiarity1 but did not know what it meant4 ,seeing something in the centre with two projecting arms1 one on each side1 he concluded that the planet was triple-shaped4 ,this was1 at the time1 all he could learn respecting it1 as the telescopes he possessed were very humble1 compared with those now used by astronomers4 ,the first constructed by him magnified but three times2 his second1 eight times2 and his best1 only thirty times1 which is no better than a common ship-glass4 ,it was the practice of the astronomers of those days to give the first intimation of a new discovery in a ,latin verse1 the letters of which were transposed4 ,this would enable them to claim priority1 in case any other person should contest the honor of the discovery1 and at the same time would afford opportunity to complete their observations1 before they published a full account of them4 ,accordingly1 ,galileo announced the discovery of the singular appearance of ,saturn under this disguise1 in a line which1 when the transposed letters were restored to their proper places1 signified that he had observed1 that the most distant planet is triple-formed4#ac ,he shortly afterwards1 at the request of his patron1 the ,emperor ,rodolph1 gave the solution1 and added1 ,i have1 with great admiration1 observed that ,saturn is not a single star1 but three together1 which1 as it were1 touch each other2 they have no relative motion1 and are constituted of this form1 o,oo1 the middle one being somewhat larger than the two lateral ones4 ,if we examine them with an eyeglass which magnifies the surface less than one thousand times1 the three stars do not appear very distinctly1 but ,saturn has an oblong appearance1 like that of an olive1 thus1 oblong symbol4 ,now1 ,i have discovered a court for ,jupiter1 7alluding to his satellites17 and two servants for this old man1 7,saturn17 who aid his steps1 and never quit his side4 ,it was by this mystic light that ,galileo groped his way through an organization which1 under the more powerful glasses of his successors1 was to expand into a mighty orb1 encompassed by splendid rings of vast dimensions1 the whole attended by seven bright satellites4 ,this system was first fully developed by ,huyghens1 a ,dutch astronomer1 about forty years afterwards4#ad ,it requires a superior telescope to see it to advantage2 but1 when seen through such a telescope1 it is one of the most charming spectacles afforded to that instrument4 ,to give some idea of the properties of a telescope suited to such observations1 ,i annex an extract from an account1 that was published a few years since1 of a telescope constructed by ,mr4 ,tully1 a distinguished ,english artist4 ,the length of the instrument was twelve feet1 but was easily adjusted1 and was perfectly steady4 ,the magnifying powers ranged from two hundred to seven hundred and eighty times2 but the great excellence of the telescope consisted more in the superior distinctness and brilliancy with which objects were seen through it1 than in its magnifying powers4 ,with a power of two hundred and forty1 the light of ,jupiter was almost more than the eye could bear1 and his satellites appeared as bright as ,sirius1 but with a clear and steady light2 and the belts and spots on the face of the planet were most distinctly defined4 ,with a power of nearly four hundred1 ,saturn appeared large and well defined1 and was one of the most beautiful objects that can well be conceived4 ,that the ring is a solid opaque substance1 is shown by its throwing its shadow on the body of the planet on the side nearest the sun1 and on the other side receiving that of the body4 ,the ring encompasses the equatorial regions of the planet1 and the planet revolves on an axis which is perpendicular to the plane of the ring in about ten and a half hours4 ,this is known by observing the rotation of certain dusky spots1 which sometimes appear on its surface4 ,this motion is nearly the same with the diurnal motion of ,jupiter1 subjecting places on the equator of the planet to a very swift revolution1 and occasioning a high degree of compression at the poles1 the equatorial being to the polar diameter in the high ratio of eleven to ten4 ,saturn's ring1 in its revolution around the sun1 always remains parallel to itself4 ,if we hold opposite to the eye a circular ring or disk1 like a piece of coin1 it will appear as a complete circle only when it is at right angles to the axis of vision4 ,when it is oblique to that axis1 it will be projected into an ellipse more and more flattened1 as its obliquity is increased1 until1 when its plane coincides with the axis of vision1 it is projected into a straight line4 ,please to take some circle1 as a flat plate1 7whose rim may well represent the ring of ,saturn17 and hold it in these different positions before the eye4 ,now1 place on the table a lamp to represent the sun1 and holding the ring at a certain distance1 inclined a little towards the lamp1 carry it round the lamp1 always keeping it parallel to itself4 ,during its revolution1 it will twice present its edge to the lamp at opposite points2 and twice1 at places ninety degrees distant from those points1 it will present its broadest face towards the lamp4 ,at intermediate points1 it will exhibit an ellipse more or less open1 according as it is nearer one or the other of the preceding positions4 ,it will be seen1 also1 that in one half of the revolution1 the lamp shines on one side of the ring1 and in the other half of the revolution1 on the other side4 ,such would be the successive appearances of ,saturn's ring to a spectator on the sun2 and since the earth is1 in respect to so distant a body as ,saturn1 very near the sun1 these appearances are presented to us nearly in the same manner as though we viewed them from the sun4 ,accordingly1 we sometimes see ,saturn's ring under the form of a broad ellipse1 which grows continually more and more acute1 until it passes into a line1 and we either lose sight of it1 altogether1 or1 by the aid of the most powerful telescopes1 we see it as a fine thread of light drawn across the disk1 and projecting out from it on each side4 ,as the whole revolution occupies thirty years1 and the edge is presented to the sun twice in the revolution1 this last phenomenon1 namely1 the disappearance of the ring1 takes place every fifteen years4 ,illustration ,fig4 #fa4 ,you may perhaps gain a still clearer idea of the foregoing appearances from the following diagram1 ,fig4 #fa4 ,let ,a1 ,b1 ,c1 c41 represent successive positions of ,saturn and his ring1 in different parts of his orbit1 while a b represents the orbit of the earth4 ,please to remark1 that these orbits are drawn so elliptical1 not to represent the eccentricity of either the earth's or ,saturn's orbit1 but merely as the projection of circles seen very obliquely4 ,also1 imagine one half of the body of the planet and of the ring to be above the plane of the paper1 and the other half below it4 ,were the ring1 when at ,c and ,g1 perpendicular to ,c ,g1 it would be seen by a spectator situated at a or b as a perfect circle2 but being inclined to the line of vision twenty-eight degrees four minutes1 it is projected into an ellipse4 ,this ellipse contracts in breadth as the ring passes towards its nodes at ,a and ,e1 where it dwindles into a straight line4 ,from ,e to ,g the ring opens again1 becomes broadest at ,g1 and again contracts1 till it becomes a straight line at ,a1 and from this point expands1 till it recovers its original breadth at ,c4 ,these successive appearances are all exhibited to a telescope of moderate powers4 ,the ring is extremely thin1 since the smallest satellite1 when projected on it1 more than covers it4 ,the thickness is estimated at only one hundred miles4 ,saturn's ring shines wholly by reflected light derived from the sun4 ,this is evident from the fact that that side only which is turned towards the sun is enlightened2 and it is remarkable1 that the illumination of the ring is greater than that of the planet itself1 but the outer ring is less bright than the inner4 ,although we view ,saturn's ring nearly as though we saw it from the sun1 yet the plane of the ring produced may pass between the earth and the sun1 in which case1 also1 the ring becomes invisible1 the illuminated side being wholly turned from us4 ,thus1 when the ring is approaching its node at ,e1 a spectator at a would have the dark side of the ring presented to him4 ,the ring was invisible in #ahcc1 and will be invisible again in #ahdg4 ,the northern side of the ring will be in sight until #ahee1 when the southern side will come into view4 ,it appears1 therefore1 that there are three causes for the disappearance of ,saturn's ring3 first1 when the edge of the ring is presented to the sun2 secondly1 when the edge is presented to the earth2 and thirdly1 when the unilluminated side is towards the earth4 ,saturn's ring revolves in its own plane in about ten and a half hours4 ,la ,place inferred this from the doctrine of universal gravitation4 ,he proved that such a rotation was necessary2 otherwise1 the matter of which the ring is composed would be precipitated upon its primary4 ,he showed that1 in order to sustain itself1 its period of rotation must be equal to the time of revolution of a satellite1 circulating around ,saturn at a distance from it equal to that of the middle of the ring1 which period would be about ten and a half hours4 ,by means of spots in the ring1 ,dr4 ,herschel followed the ring in its rotation1 and actually found its period to be the same as assigned by ,la ,place1--a coincidence which beautifully exemplifies the harmony of truth4 ,although the rings have very nearly the same centre with the planet itself1 yet1 recent measurements of extreme delicacy have demonstrated1 that the coincidence is not mathematically exact1 but that the centre of gravity of the rings describes around that of the body a very minute orbit4 ,this fact1 says ,sir ,j4 ,herschel1 unimportant as it may seem1 is of the utmost consequence to the stability of the system of rings4 ,supposing them mathematically perfect in their circular form1 and exactly concentric with the planet1 it is demonstrable that they would form 7in spite of their centrifugal force7 a system in a state of unstable equilibrium1 which the slightest external power would subvert1 not by causing a rupture in the substance of the rings1 but by precipitating them unbroken upon the surface of the planet4 ,the ring may be supposed of an unequal breadth in its different parts1 and as consisting of irregular solids1 whose common centre of gravity does not coincide with the centre of the figure4 ,were it not for this distribution of matter1 its equilibrium would be destroyed by the slightest force1 such as the attraction of a satellite1 and the ring would finally precipitate itself upon the planet4 ,sir ,j4 ,herschel further observes1 that1 as the smallest difference of velocity between the planet and its rings must infallibly precipitate the rings upon the planet1 never more to separate1 it follows1 either that their motions in their common orbit round the sun must have been adjusted to each other by an external power1 with the minutest precision1 or that the rings must have been formed about the planet while subject to their common orbitual motion1 and under the full and free influence of all the acting forces4 ,the rings of ,saturn must present a magnificent spectacle from those regions of the planet which lie on their enlightened sides1 appearing as vast arches spanning the sky from horizon to horizon1 and holding an invariable situation among the stars4 ,on the other hand1 in the region beneath the dark side1 a solar eclipse of fifteen years in duration1 under their shadow1 must afford 7to our ideas7 an inhospitable abode to animated beings1 but ill compensated by the full light of its satellites4 ,but we shall do wrong to judge of the fitness or unfitness of their condition1 from what we see around us1 when1 perhaps1 the very combinations which convey to our minds only images of horror1 may be in reality theatres of the most striking and glorious displays of beneficent contrivance4 ,saturn is attended by seven satellites4 ,although they are bodies of considerable size1 their great distance prevents their being visible to any telescope but such as afford a strong light and high magnifying powers4 ,the outermost satellite is distant from the planet more than thirty times the planet's diameter1 and is by far the largest of the whole4 ,it exhibits1 like the satellites of ,jupiter1 periodic variations of light1 which prove its revolution on its axis in the time of a sidereal revolution about ,saturn1 as is the case with our moon1 while performing its circuit about the earth4 ,the next satellite in order1 proceeding inwards1 is tolerably conspicuous2 the three next are very minute1 and require powerful telescopes to see them2 while the two interior satellites1 which just skirt the edge of the ring1 and move exactly in its plane1 have never been discovered but with the most powerful telescopes which human art has yet constructed1 and then only under peculiar circumstances4 ,at the time of the disappearance of the rings1 7to ordinary telescopes17 they were seen by ,sir ,william ,herschel1 with his great telescope1 projected along the edge of the ring1 and threading1 like beads1 the thin fibre of light to which the ring is then reduced4 ,owing to the obliquity of the ring1 and of the orbits of the satellites1 to that of their primary1 there are no eclipses of the satellites1 the two interior ones excepted1 until near the time when the ring is seen edgewise4 ,the firmament of ,saturn will unquestionably present to view a more magnificent and diversified scene of celestial phenomena than that of any other planet in our system4 ,it is placed nearly in the middle of that space which intervenes between the sun and the orbit of the remotest planet4 ,including its rings and satellites1 it may be considered as the largest body or system of bodies within the limits of the solar system2 and it excels them all in the sublime and diversified apparatus with which it is accompanied4 ,in these respects1 ,saturn may justly be considered as the sovereign among the planetary hosts4 ,the prominent parts of its celestial scenery may be considered as belonging to its own system of rings and satellites1 and the views which will occasionally be opened of the firmament of the fixed stars2 for few of the other planets will make their appearance in its sky4 ,jupiter will appear alternately as a morning and an evening star1 with about the same degree of brilliancy it exhibits to us2 but it will seldom be conspicuous1 except near the period of its greatest elongation2 and it will never appear to remove from the sun further than thirty-seven degrees1 and consequently will not appear so conspicuous1 nor for such a length of time1 as ,venus does to us4 ,uranus is the only other planet which will be seen from ,saturn1 and it will there be distinctly perceptible1 like a star of the third magnitude1 when near the time of its opposition to the sun4 ,but near the time of its conjunction it will be completely invisible1 being then eighteen hundred millions of miles more distant than at the opposition1 and eight hundred millions of miles more distant from ,saturn than it ever is from the earth at any period4#ae ,,uranus4--,uranus is the remotest planet belonging to our system1 and is rarely visible1 except to the telescope4 ,although his diameter is more than four times that of the earth1 being thirty-five thousand one hundred and twelve miles1 yet his distance from the sun is likewise nineteen times as great as the earth's distance1 or about eighteen hundred millions of miles4 ,his revolution around the sun occupies nearly eighty-four years1 so that his position in the heavens1 for several years in succession1 is nearly stationary4 ,his path lies very nearly in the ecliptic1 being inclined to it less than one degree4 ,the sun himself1 when seen from ,uranus dwindles almost to a star1 subtending1 as it does1 an angle of only one minute and forty seconds2 so that the surface of the sun would appear there four hundred times less than it does to us4 ,this planet was discovered by ,sir ,william ,herschel on the thirteenth of ,march1 #agha4 ,his attention was attracted to it by the largeness of its disk in the telescope2 and finding that it shifted its place among the stars1 he at first took it for a comet1 but soon perceived that its orbit was not eccentric1 like the orbits of comets1 but nearly circular1 like those of the planets4 ,it was then recognised as a new member of the planetary system1 a conclusion which has been justified by all succeeding observations4 ,it was named by the discoverer the ,george ,star1 7,georgium ,sidus17 after his munificent patron1 ,george the ,third2 in the ,united ,states1 and in some other countries1 it was called ,herschel2 but the name ,uranus1 from a ,greek word1 7 ,ouranos1 ,ouranos17 signifying the oldest of the gods1 has finally prevailed4 ,so distant is ,uranus from the sun1 that light itself1 which moves nearly twelve millions of miles every minute1 would require more than two hours and a half to pass to it from the sun4 ,and now1 having contemplated all the planets separately1 just cast your eyes on the diagram facing page #bcf1 ,fig4 #ec1 and you will see a comparative view of the various magnitudes of the sun1 as seen from each of the planets4 ,uranus is attended by six satellites4 ,so minute objects are they1 that they can be seen only by powerful telescopes4 ,indeed1 the existence of more than two is still considered as somewhat doubtful4 ,these two1 however1 offer remarkable and indeed quite unexpected and unexampled peculiarities4 ,contrary to the unbroken analogy of the whole planetary system1 the planes of their orbits are nearly perpendicular to the ecliptic1 and in these orbits their motions are retrograde2 that is1 instead of advancing from west to east around their primary1 as is the case with all the other planets and satellites1 they move in the opposite direction4 ,with this exception1 all the motions of the planets1 whether around their own axes1 or around the sun1 are from west to east4 ,the sun himself turns on his axis from west to east2 all the primary planets revolve around the sun from west to east2 their revolutions on their own axes are also in the same direction2 all the secondaries1 with the single exception above mentioned1 move about their primaries from west to east2 and1 finally1 such of the secondaries as have been discovered to have a diurnal revolution1 follow the same course4 ,such uniformity among so many motions could have resulted only from forces impressed upon them by the same ,omnipotent hand2 and few things in the creation more distinctly proclaim that ,god made the world4 ,retiring now to this furthest verge of the solar system1 let us for a moment glance at the aspect of the firmament by night4 ,notwithstanding we have taken a flight of eighteen hundred millions of miles1 the same starry canopy bends over our heads2 ,sirius still shines with exactly the same splendor as here2 ,orion1 the ,scorpion1 the ,great and the ,little ,bear1 all occupy the same stations2 and the ,galaxy spans the sky with the same soft and mysterious light4 ,the planets1 however1 with the exception of ,saturn1 are all lost to the view1 being too near the sun ever to be seen2 and ,saturn himself is visible only at distant intervals1 at periods of fifteen years1 when at its greatest elongations from the sun1 and is then too near the sun to permit a clear view of his rings1 much less of the satellites that unite with the rings to compose his gorgeous retinue4 ,comets1 moving slowly as they do when so distant from the sun1 will linger much longer in the firmament of ,uranus than in ours4 ,although the sun sheds by day a dim and cheerless light1 yet the six satellites that enlighten and diversify the nocturnal sky present interesting aspects4 ,let us suppose one satellite presenting a surface in the sky eight or ten times larger than our moon2 a second1 five or six times larger2 a third1 three times larger2 a fourth1 twice as large2 a fifth1 about the same size as the moon2 a sixth1 somewhat smaller2 and1 perhaps1 three or four others of different apparent dimensions3 let us suppose two or three of those1 of different phases1 moving along the concave of the sky1 at one period four or five of them dispersed through the heavens1 one rising above the horizon1 one setting1 one on the meridian1 one towards the north1 and another towards the south2 at another period1 five or six of them displaying their lustre in the form of a half moon1 or a crescent1 in one quarter of the heavens2 and1 at another time1 the whole of these moons shining1 with full enlightened hemispheres1 in one glorious assemblage1 and we shall have a faint idea of the beauty1 variety1 and sublimity of the firmament of ,uranus4#af ,the ,new ,planets1--,ceres1 ,pallas1 ,juno1 and ,vesta4--,the commencement of the present century was rendered memorable in the annals of astronomy1 by the discovery of four new planets1 occupying the long vacant tract between ,mars and ,jupiter4 ,kepler1 from some analogy which he found to subsist among the distances of the planets from the sun1 had long before suspected the existence of one at this distance2 and his conjecture was rendered more probable by the discovery of ,uranus1 which follows the analogy of the other planets4 ,so strongly1 indeed1 were astronomers impressed with the idea that a planet would be found between ,mars and ,jupiter1 that1 in the hope of discovering it1 an association was formed on the continent of ,europe1 of twenty-four observers1 who divided the sky into as many zones1 one of which was allotted to each member of the association4 ,the discovery of the first of these bodies was1 however1 made accidentally by ,piazzi1 an astronomer of ,palermo1 on the first of ,january1 #ahja4 ,it was shortly afterwards lost sight of on account of its proximity to the sun1 and was not seen again until the close of the year1 when it was re-discovered in ,germany4 ,piazzi called it ,ceres1 in honor of the tutelary goddess of ,sicily1 and her emblem1 the sickle1 7,planet3 ,ceres7 has been adopted as its appropriate symbol4 ,the difficulty of finding ,ceres induced ,dr4 ,olbers1 of ,bremen1 to examine with particular care all the small stars that lie near her path1 as seen from the earth2 and1 while prosecuting these observations1 in ,march1 #ahjb1 he discovered another similar body1 very nearly at the same distance from the sun1 and resembling the former in many other particulars4 ,the discoverer gave to this second planet the name of ,pallas1 choosing for its symbol the lance1 7,planet3 ,pallas7 the characteristic of ,minerva4 ,the most surprising circumstance connected with the discovery of ,pallas was the existence of two planets at nearly the same distance from the sun1 and apparently crossing the ecliptic in the same part of the heavens1 or having the same node4 ,on account of this singularity1 ,dr4 ,olbers was led to conjecture that ,ceres and ,pallas are only fragments of a larger planet1 which had formerly circulated at the same distance1 and been shattered by some internal convulsion4 ,the hypothesis suggested the probability that there might be other fragments1 whose orbits might be expected to cross the ecliptic at a common point1 or to have the same node4 ,dr4 ,olbers1 therefore1 proposed to examine carefully1 every month1 the two opposite parts of the heavens in which the orbits of ,ceres and ,pallas intersect one another1 with a view to the discovery of other planets1 which might be sought for in those parts with a greater chance of success1 than in a wider zone1 embracing the entire limits of these orbits4 ,accordingly1 in #ahjd1 near one of the nodes of ,ceres and ,pallas1 a third planet was discovered4 ,this was called ,juno1 and the character 7,planet3 ,juno7 was adopted for its symbol1 representing the starry sceptre of the ,queen of ,olympus4 ,pursuing the same researches1 in #ahjg a fourth planet was discovered1 to which was given the name of ,vesta1 and for its symbol the character 7,planet3 ,vesta7 was chosen1--an altar surmounted with a censer holding the sacred fire4 ,the average distance of these bodies from the sun is two hundred and sixty-one millions of miles2 and it is remarkable that their orbits are very near together4 ,taking the distance of the earth from the sun for unity1 their respective distances are #b4gg1 #b4gg1 #b4fg1 #b4cg4 ,their times of revolution around the sun are nearly equal1 averaging about four and a half years4 ,in respect to the inclination of their orbits to the ecliptic1 there is also considerable diversity4 ,the orbit of ,vesta is inclined only about seven degrees1 while that of ,pallas is more than thirty-four degrees4 ,they all1 therefore1 have a higher inclination than the orbits of the old planets1 and of course make excursions from the ecliptic beyond the limits of the zodiac4 ,hence they have been called the ultra-zodiacal planets4 ,when first discovered1 before their place in the system was fully ascertained it was also proposed to call them asteroids1 a name implying that they were planets under the form of stars4 ,their title1 however1 to take their rank among the primary planets1 is now generally conceded4 ,the eccentricity of their orbits is also1 in general1 greater than that of the old planets4 ,you will recollect that this language denotes that their orbits are more elliptical1 or depart further from the circular form4 ,the eccentricities of the orbits of ,pallas and ,juno exceed that of the orbit of ,mercury4 ,the asteroids differ so much1 however1 in eccentricity1 that their orbits may cross each other4 ,the orbits of the old planets are so nearly circular1 and at such a great distance apart1 that there is no danger of their interfering with each other4 ,the earth1 for example1 when at its nearest distance from the sun1 will never come so near it as ,venus is when at its greatest distance1 and therefore can never cross the orbit of ,venus4 ,but since the average distance of ,ceres and ,pallas from the sun is about the same1 while the eccentricity of the orbit of ,pallas is much greater than that of ,ceres1 consequently1 ,pallas may come so near to the sun at its perihelion1 as to cross the orbit of ,ceres4 ,the small size of the asteroids constitutes one of their most remarkable peculiarities4 ,the difficulty of estimating the apparent diameter of bodies at once so very small and so far off1 would lead us to expect different results in the actual estimates4 ,accordingly1 while ,dr4 ,herschel estimates the diameter of ,pallas at only eighty miles1 ,schroeter places it as high as two thousand miles1 or about the diameter of the moon4 ,the volume of ,vesta is estimated at only one fifteen thousandth part of the earth's1 and her surface is only about equal to that of the kingdom of ,spain4 ,these little bodies are surrounded by atmospheres of great extent1 some of which are uncommonly luminous1 and others appear to consist of nebulous matter1 like that of comets4 ,these planets shine with a more vivid light than might be expected1 from their great distance and diminutive size2 but a good telescope is essential for obtaining a distinct view of their phenomena4 ,although the great chasm which occurs between ,mars and ,jupiter1--a chasm of more than three hundred millions of miles1--suggested long ago the idea of other planetary bodies occupying that part of the solar system1 yet the discovery of the asteroids does not entirely satisfy expectation since they are bodies so dissimilar to the other members of the series in size1 in appearance1 and in the form and inclinations of their orbits4 ,hence1 ,dr4 ,olbers1 the discoverer of three of these bodies1 held that they were fragments of a single large planet1 which once occupied that place in the system1 and which exploded in different directions by some internal violence4 ,of the fragments thus projected into space1 some would be propelled in such directions and with such velocities1 as1 under the force of projection and that of the solar attraction would make them revolve in regular orbits around the sun4 ,others would be so projected among the other bodies in the system1 as to be thrown in very irregular orbits1 apparently wandering lawless through the skies4 ,the larger fragments would receive the least impetus from the explosive force1 and would therefore circulate in an orbit deviating less than any other of the fragments from the original path of the large planet2 while the lesser fragments1 being thrown off with greater velocity1 would revolve in orbits more eccentric1 and more inclined to the ecliptic4 ,dr4 ,brewster1 editor of the ',edinburgh ,encyclopedia1' and the well-known author of various philosophical works1 espoused this hypothesis with much zeal2 and1 after summing up the evidence in favor of it1 he remarks as follows3 ,these singular resemblances in the motions of the greater fragments1 and in those of the lesser fragments1 and the striking coincidences between theory and observation in the eccentricity of their orbits1 in their inclination to the ecliptic1 in the position of their nodes1 and in the places of their perihelia1 are phenomena which could not possibly result from chance1 and which concur to prove1 with an evidence amounting almost to demonstration1 that the four new planets have diverged from one common node1 and have therefore composed a single planet4 ,the same distinguished writer supposes that some of the smallest fragments might even have come within reach of the earth's attraction1 and by the combined effects of their projectile forces and the attraction of the earth1 be made to revolve around this body as the larger fragments are carried around the sun2 and that these are in fact the bodies which afford those meteoric stones which are occasionally precipitated to the earth4 ,it is now a well-ascertained fact1 a fact which has been many times verified in our own country1 that large meteors1 in the shape of fire-balls1 traversing the atmosphere1 sometimes project to the earth masses of stony or ferruginous matter4 ,such were the meteoric stones which fell at ,weston1 in ,connecticut1 in #ahjg1 of which a full and interesting account was published1 after a minute examination of the facts1 by ,professors ,silliman and ,kingsley1 of ,yale ,college4 ,various accounts of similar occurrences may be found in different volumes of the ,american ,journal of ,science4 ,it is for the production of these wonderful phenomena that ,dr4 ,brewster supposes the explosion of the planet1 which1 according to ,dr4 ,olbers1 produced the asteroids1 accounts4 ,others1 however1 as ,sir ,john ,herschel1 have been disposed to ascribe very little weight to the doctrine of ,olbers4 ,,footnotes3 #ac ,altissimum planetam tergeminum observavi4 ,or1 as transposed1 ,smaismrmilme poeta leumi bvne nugttaviras4 #ad ,in imitation of ,galileo1 ,huyghens announced his discovery in this form3 a a a a a a a c c c c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o p p q r r s t t t t t u u u u u2 which he afterwards recomposed into this sentence3 ,annulo cingitur1 tenui1 plano1 nusquam cohrente1 ad eclipticam inclinato4 #ae ,dick's ',celestial ,scenery4' #af ,dick's ',celestial ,scenery4' ,,letter ,,xxiv4 ,,the ,,planetary ,,motions4----,,kepler',s ,,laws4----,,kepler4 ,god of the rolling orbs above6 ,thy name is written clearly bright ,in the warm day's unvarying blaze1 ,or evening's golden shower of light2 ,for every fire that fronts the sun1 ,and every spark that walks alone ,around the utmost verge of heaven1 ,was kindled at thy burning throne4--,peabody4 ,,if we could stand upon the sun and view the planetary motions1 they would appear to us as simple as the motions of equestrians riding with different degrees of speed around a large ring1 of which we occupied the centre4 ,we should see all the planets coursing each other from west to east1 through the same great highway1 7the ,zodiac17 no one of them1 with the exception of the asteroids1 deviating more than seven degrees from the path pursued by the earth4 ,most of them1 indeed1 would always be seen moving much nearer than that to the ecliptic4 ,we should see the planets moving on their way with various degrees of speed4 ,mercury would make the entire circuit in about three months1 hurrying on his course with a speed about one third as great as that by which the moon revolves around the earth4 ,the most distant planets1 on the other hand1 move at so slow a pace1 that we should see ,mercury1 ,venus1 the ,earth1 and ,mars1 severally overtaking them a great many times1 before they had completed their revolutions4 ,but though the movements of some were comparatively rapid1 and of others extremely slow1 yet they would not seem to differ materially1 in other respects3 each would be making a steady and nearly uniform march along the celestial vault4 ,such would be the simple and harmonious motions of the planets1 as they would be seen from the sun1 the centre of their motions2 and such they are1 in fact4 ,but two circumstances conspire to make them appear exceedingly different from these1 and vastly more complicated2 one is1 that we view them out of the centre of their motions2 the other1 that we are ourselves in motion4 ,i have already explained to you the effect which these two causes produce on the apparent motions of the inferior planets1 ,mercury and ,venus4 ,let us now see how they effect those of the superior planets1 ,mars1 ,jupiter1 ,saturn1 and ,uranus4 ,orreries1 or machines intended to exhibit a model of the solar system1 are sometimes employed to give a popular view of the planetary motions2 but they oftener mislead than give correct ideas4 ,they may assist reflection1 but they can never supply its place4 ,the impossibility of representing things in their just proportions will be evident1 when we reflect that1 to do this1 if in an orrery we make ,mercury as large as a cherry1 we should have to represent the sun six feet in diameter4 ,if we preserve the same proportions1 in regard to distance1 we must place ,mercury two hundred and fifty feet1 and ,uranus twelve thousand five hundred feet1 or more than two miles from the sun4 ,the mind of the student of astronomy must1 therefore1 raise itself from such imperfect representations of celestial phenomena1 as are afforded by artificial mechanism1 and1 transferring his contemplations to the celestial regions themselves1 he must conceive of the sun and planets as bodies that bear an insignificant ratio to the immense spaces in which they circulate1 resembling more a few little birds flying in the open sky1 than they do the crowded machinery of an orrery4 ,the real motions of the planets1 indeed1 or such as orreries usually exhibit1 are very easily conceived of1 as before explained2 but the apparent motions are1 for the most part1 entirely different from these4 ,the apparent motions of the inferior planets have been already explained4 ,you will recollect that ,mercury and ,venus move backwards and forwards across the sun1 the former never being seen further than twenty-nine degrees1 and the latter never more than about forty-seven degrees1 from that luminary2 that1 while passing from the greatest elongation on one side1 to the greatest elongation on the other side1 through the superior conjunction1 the apparent motions of these planets are accelerated by the motion of the earth2 but that1 while moving through the inferior conjunction1 at which time their motions are retrograde1 they are apparently retarded by the earth's motion4 ,let us now see what are the apparent motions of the superior planets4 ,let ,a1 ,b1 ,c1 ,fig4 #fb1 page #bid1 represent the earth in different positions in its orbit1 ,m1 a superior planet1 as ,mars1 and ,n ,r1 an arc of the concave sphere of the heavens4 ,first1 suppose the planet to remain at rest in ,m1 and let us see what apparent motions it will receive from the real motions of the earth4 ,when the earth is at ,b1 it will see the planet in the heavens at ,n2 and as the earth moves successively through ,c1 ,d1 ,e1 ,f1 the planet will appear to move through ,o1 ,p1 ,q1 ,r4 ,b and ,f are the two points of greatest elongation of the earth from the sun1 as seen from the planet2 hence1 between these two points1 while passing through its orbit most remote from the planet1 7when the planet is seen in superior conjunction17 the earth1 by its own motion1 gives an apparent motion to the planet in the order of the signs2 that is1 the apparent motion given by the real motion of the earth is direct4 ,but in passing from ,f to ,b through ,a1 when the planet is seen in opposition1 the apparent motion given to the planet by the earth's motion is from ,r to ,n1 and is therefore retrograde4 ,as the arc described by the earth1 when the motion is direct1 is much greater than when the motion is retrograde1 while the apparent arc of the heavens described by the planet from ,n to ,r1 in the one case1 and from ,r to ,n1 in the other1 is the same in both cases1 the retrograde motion is much swifter than the direct1 being performed in much less time4 ,illustration ,fig4 #fb4 ,but the superior planets are not in fact at rest1 as we have supposed1 but are all the while moving eastward1 though with a slower motion than the earth4 ,indeed1 with respect to the remotest planets1 as ,saturn and ,uranus1 the forward motion is so exceedingly slow1 that the above representation is nearly true for a single year4 ,still1 the effect of the real motions of all the superior planets1 eastward1 is to increase the direct apparent motion communicated by the earth1 and to diminish the retrograde motion4 ,this will be evident from inspecting the figure2 for if the planet actually moves eastward while it is apparently carried eastward by the earth's motion1 the whole motion eastward will be equal to the sum of the two2 and if1 while it is really moving eastward1 it is apparently carried westward still more by the earth's motion1 the retrograde movement will equal the difference of the two4 ,if ,mars stood still while the earth went round the sun1 then a second opposition1 as at ,a1 would occur at the end of one year from the first2 but1 while the earth is performing this circuit1 ,mars is also moving the same way1 more than half as fast2 so that1 when the earth returns to ,a1 the planet has already performed more than half the same circuit1 and will have completed its whole revolution before the earth comes up with it4 ,indeed ,mars1 after having been seen once in opposition1 does not come into opposition again until after two years and fifty days4 ,and since the planet is then comparatively near to us1 as at ,m1 while the earth is at ,a1 and appears very large and bright1 rising unexpectedly about the time the sun sets1 he surprises the world as though it were some new celestial body4 ,but on account of the slow progress of ,saturn and ,uranus1 we find1 after having performed one circuit around the sun1 that they are but little advanced beyond where we left them at the last opposition4 ,the time between one opposition of ,saturn and another is only a year and thirteen days4 ,it appears1 therefore1 that the superior planets steadily pursue their course around the sun1 but that their apparent retrograde motion1 when in opposition1 is occasioned by our passing by them with a swifter motion1 of which we are unconscious1 like the apparent backward motion of a vessel1 when we overtake it and pass by it rapidly in a steam-boat4 ,such are the real and the apparent motions of the planets4 ,let us now turn our attention to the laws of the planetary orbits4 ,there are three great principles1 according to which the motions of the earth and all the planets around the sun are regulated1 called ,,kepler',s ,,laws1 having been first discovered by the astronomer whose name they bear4 ,they may appear to you1 at first1 dry and obscure2 yet they will be easily understood from the explanations which follow2 and so important have they proved in astronomical inquiries1 that they have acquired for their renowned discoverer the appellation of the ',legislator of the ,skies4' ,we will consider each of these laws separately2 and1 for the sake of rendering the explanation clear and intelligible1 ,i shall perhaps repeat some things that have been briefly mentioned before4 ,illustration ,fig4 #fc4 ,,first ,,law4--,the orbits of the earth and all the planets are ellipses1 having the sun in the common focus4 ,in a circle1 all the diameters are equal to one another2 but if we take a metallic wire or hoop1 and draw it out on opposite sides1 we elongate it into an ellipse1 of which the different diameters are very unequal4 ,that which connects the points most distant from each other is called the transverse1 and that which is at right angles to this is called the conjugate1 axis4 ,thus1 ,a ,b1 ,fig4 #fc1 is the transverse axis1 and ,c ,d1 the conjugate of the ellipse ,a ,b ,c4 ,by such a process of elongating the circle into an ellipse1 the centre of the circle may be conceived of as drawn opposite ways to ,e and ,f1 each of which becomes a focus1 and both together are called the foci of the ellipse4 ,the distance ,g ,e1 or ,g ,f1 of the focus from the centre is called the eccentricity of the ellipse2 and the ellipse is said to be more or less eccentric1 as the distance of the focus from the centre is greater or less4 ,figure #fd represents such a collection of ellipses around the common focus ,f1 the innermost1 ,a ,g ,d1 having a small eccentricity1 or varying little from a circle1 while the outermost1 ,a ,c ,b1 is an eccentric ellipse4 ,the orbits of all the bodies that revolve about the sun1 both planets and comets1 have1 in like manner1 a common focus1 in which the sun is situated1 but they differ in eccentricity4 ,most of the planets have orbits of very little eccentricity1 differing little from circles1 but comets move in very eccentric ellipses4 ,the earth's path around the sun varies so little from a circle1 that a diagram representing it truly would scarcely be distinguished from a perfect circle2 yet1 when the comparative distances of the sun from the earth are taken at different seasons of the year1 we find that the difference between their greatest and least distances is no less than three millions of miles4 ,illustration ,fig4 #fd4 ,,second ,,law4--,the radius vector of the earth1 or of any planet1 describes equal areas in equal times4 ,you will recollect that the radius vector is a line drawn from the centre of the sun to a planet revolving about the sun4 ,this definition ,i have somewhere given you before1 and perhaps it may appear to you like needless repetition to state it again4 ,in a book designed for systematic instruction1 where all the articles are distinctly numbered1 it is commonly sufficient to make a reference back to the article where the point in question is explained2 but ,i think1 in ,letters like these1 you will bear with a little repetition1 rather than be at the trouble of turning to the ,index and hunting up a definition long since given4 ,illustration ,fig4 #fe4 ,in ,figure #fe1 ,e a1 ,e b1 ,e c1 c41 are successive representations of the radius vector4 ,now1 if a planet sets out from a1 and travels round the sun in the direction of a b c1 it will move faster when nearer the sun1 as at a1 than when more remote from it1 as at m2 yet1 if a b and m n be arcs described in equal times1 then1 according to the foregoing law1 the space ,e a b will be equal to the space ,e m n2 and the same is true of all the other spaces described in equal times4 ,although the figure ,e a b is much shorter than ,e m n1 yet its greater breadth exactly counterbalances the greater length of those figures which are described by the radius vector where it is longer4 ,,third ,,law4--,the squares of the periodical times are as the cubes of the mean distances from the sun4 ,the periodical time of a body is the time it takes to complete its orbit1 in its revolution about the sun4 ,thus the earth's periodic time is one year1 and that of the planet ,jupiter about twelve years4 ,as ,jupiter takes so much longer time to travel round the sun than the earth does1 we might suspect that his orbit is larger than that of the earth1 and of course1 that he is at a greater distance from the sun2 and our first thought might be1 that he is probably twelve times as far off2 but ,kepler discovered that the distance does not increase as fast as the times increase1 but that the planets which are more distant from the sun actually move slower than those which are nearer4 ,after trying a great many proportions1 he at length found that1 if we take the squares of the periodic times of two planets1 the greater square contains the less1 just as often as the cube of the distance of the greater contains that of the less4 ,this fact is expressed by saying1 that the squares of the periodic times are to one another as the cubes of the distances4 ,this law is of great use in determining the distance of the planets from the sun4 ,suppose1 for example1 that we wish to find the distance of ,jupiter4 ,we can easily determine1 from observation1 what is ,jupiter's periodical time1 for we can actually see how long it takes for ,jupiter1 after leaving a certain part of the heavens to come round to the same part again4 ,let this period be twelve years4 ,the earth's period is of course one year2 and the distance of the earth1 as determined from the sun's horizontal parallax1 as already explained1 is about ninety-five millions of miles4 ,now1 we have here three terms of a proportion to find the fourth1 and therefore the solution is merely a simple case of the rule of three4 ,thus3--the square of #a year 3 square of #ab years 33 cube of #ie1jjj1jjj 3 cube of ,jupiter's distance4 ,the three first terms being known1 we have only to multiply together the second and third and divide by the first1 to obtain the fourth term1 which will give us the cube of ,jupiter's distance from the sun2 and by extracting the cube root of this sum1 we obtain the distance itself4 ,in the same manner we may obtain the respective distances of all the other planets4 ,so truly is this a law of the solar system1 that it holds good in respect to the new planets1 which have been discovered since ,kepler's time1 as well as in the case of the old planets4 ,it also holds good in respect to comets1 and to all bodies belonging to the solar system1 which revolve around the sun as their centre of motion4 ,hence1 it is justly regarded as one of the most interesting and important principles yet developed in astronomy4 ,but who was this ,kepler1 that gained such an extraordinary insight into the laws of the planetary system1 as to be called the ',legislator of the ,skies8' ,john ,kepler was one of the most remarkable of the human race1 and ,i think ,i cannot gratify or instruct you more1 than by occupying the remainder of this ,letter with some particulars of his history4 ,kepler was a native of ,germany4 ,he was born in the ,duchy of ,wurtemberg1 in #aega4 ,as ,copernicus1 ,tycho ,brahe1 ,galileo1 ,kepler1 and ,newton1 are names that are much associated in the history of astronomy1 let us see how they stood related to each other in point of time4 ,copernicus was born in #adgc2 ,tycho1 in #aedf2 ,galileo1 in #aefd2 ,kepler1 in #aega2 and ,newton1 in #afdb4 ,hence1 ,copernicus was seventy-three years before ,tycho1 and ,tycho ninety-six years before ,newton4 ,they all lived to an advanced age1 so that ,tycho1 ,galileo1 and ,kepler1 were contemporary for many years2 and ,newton1 as ,i mentioned in the sketch ,i gave you of his life1 was born the year that ,galileo died4 ,kepler was born of parents who were then in humble circumstances1 although of noble descent4 ,their misfortunes1 which had reduced them to poverty1 seem to have been aggravated by their own unhappy dispositions2 for his biographer informs us1 that his mother was treated with a degree of barbarity by her husband and brother-in-law1 that was hardly exceeded by her own perverseness4 ,it is fortunate1 therefore1 that ,kepler1 in his childhood1 was removed from the immediate society and example of his parents1 and educated at a public school at the expense of the ,duke of ,wurtemberg4 ,he early imbibed a taste for natural philosophy1 but had conceived a strong prejudice against astronomy1 and even a contempt for it1 inspired1 probably1 by the arrogant and ridiculous pretensions of the astrologers1 who constituted the principal astronomers of his country4 ,a vacant post1 however1 of teacher of astronomy1 occurred when he was of a suitable age to fill it1 and he was compelled to take it by the authority of his tutors1 though with many protestations1 on his part1 wishing to be provided for in some other more brilliant profession4 ,happy is genius1 when it lights on a profession entirely consonant to its powers1 where the objects successively presented to it are so exactly suited to its nature1 that it clings to them as the loadstone to its kindred metal among piles of foreign ores4 ,nothing could have been more congenial to the very mental constitution of ,kepler1 than the study of astronomy1--a science where the most capacious understanding may find scope in unison with the most fervid imagination4 ,much as has been said against hypotheses in philosophy1 it is nevertheless a fact1 that some of the greatest truths have been discovered in the pursuit of hypotheses1 in themselves entirely false2 truths1 moreover1 far more important than those assumed by the hypotheses2 as ,columbus1 in searching for a northwest passage to ,india1 discovered a new world4 ,thus ,kepler groped his way through many false and absurd suppositions1 to some of the most sublime discoveries ever made by man4 ,the fundamental principle which guided him was not1 however1 either false or absurd4 ,it was1 that ,god1 who made the world1 had established1 throughout all his works1 fixed laws1--laws that are often so definite as to be capable of expression in exact numerical terms4 ,in accordance with these views1 he sought for numerical relations in the disposition and arrangement of the planets1 in respect to their number1 the times of their revolution1 and their distances from one another4 ,many1 indeed1 of the subordinate suppositions which he made1 were extremely fanciful2 but he tried his own hypotheses by a rigorous mathematical test1 wherever he could apply it2 and as soon as he discovered that a supposition would not abide this test1 he abandoned it without the least hesitation1 and adopted others1 which he submitted to the same severe trial1 to share1 perhaps1 the same fate4 ,after many failures1 he says1 ,i was comforted by observing that the motions1 in every case1 seemed to be connected with the distances2 and that1 when there was a great gap between the orbits1 there was the same between the motions4 ,and ,i reasoned that1 if ,god had adapted motions to the orbits in some relation to the distances1 he had also arranged the distances themselves in relation to something else4 ,in two years after he commenced the study of astronomy1 he published a book1 called the ',mysterium ,cosmographicum1' a name which implies an explanation of the mysteries involved in the construction of the universe4 ,this work was full of the wildest speculations and most extravagant hypotheses1 the most remarkable of which was1 that the distances of the planets from the sun are regulated by the relations which subsist between the five regular solids4 ,it is well known to geometers1 that there are and can be only five regular solids4 ,these are1 first1 the tetraedron1 a four-sided figure1 all whose sides are equal and similar triangles2 secondly1 the cube1 contained by six equal squares2 thirdly1 an octaedron1 an eight-sided figure1 consisting of two four-sided pyramids joined at their bases2 fourthly1 a dodecaedron1 having twelve five-sided or pentagonal faces2 and1 fifthly1 an icosaedron1 contained by twenty equal and similar triangles4 ,you will be much at a loss1 ,i think1 to imagine what relation ,kepler could trace between these strange figures and the distances of the several planets from the sun4 ,he thought he discovered a connexion between those distances and the spaces which figures of this kind would occupy1 if interposed in certain ways between them4 ,thus1 he says the ,earth is a circle1 the measure of all2 round it describe a dodecaedron1 and the circle including this will be the orbit of ,mars4 ,round this circle describe a tetraedron1 and the circle including this will be the orbit of ,jupiter4 ,describe a cube round this1 and the circle including it will be the orbit of ,saturn4 ,now1 inscribe in the earth an icosaedron1 and the circle included in this will give the orbit of ,venus4 ,in this inscribe an octaedron1 and the circle included in this will be the orbit of ,mercury4 ,on this supposed discovery ,kepler exults in the most enthusiastic expressions4 ,the intense pleasure ,i have received from this discovery never can be told in words4 ,i regretted no more time wasted2 ,i tired of no labor2 ,i shunned no toil of reckoning2 days and nights ,i spent in calculations1 until ,i could see whether this opinion would agree with the orbits of ,copernicus1 or whether my joy was to vanish into air4 ,i willingly subjoin that sentiment of ,archytas1 as given by ,cicero2 ',if ,i could mount up into heaven1 and thoroughly perceive the nature of the world and the beauty of the stars1 that admiration would be without a charm for me1 unless ,i had some one like you1 reader1 candid1 attentive1 and eager for knowledge1 to whom to describe it4' ,if you acknowledge this feeling1 and are candid1 you will refrain from blame1 such as1 not without cause1 ,i anticipate2 but if1 leaving that to itself1 you fear1 lest these things be not ascertained1 and that ,i have shouted triumph before victory1 at least approach these pages1 and learn the matter in consideration3 you will not find1 as just now1 new and unknown planets interposed2 that boldness of mine is not approved2 but those old ones very little loosened1 and so furnished by the interposition 7however absurd you may think it7 of rectilinear figures1 that in future you may give a reason to the rustics1 when they ask for the hooks which keep the skies from falling4 ,when ,tycho ,brahe1 who had then retired from his famous ,uraniburg1 and was settled in ,prague1 met with this work of ,kepler's1 he immediately recognised under this fantastic garb the lineaments of a great astronomer4 ,he needed such an unwearied and patient calculator as he perceived ,kepler to be1 to aid him in his labors1 in order that he might devote himself more unreservedly to the taking of observations1--an employment in which he delighted1 and in which1 as ,i mentioned1 in giving you a sketch of his history1 he excelled all men of that and preceding ages4 ,kepler1 therefore1 at the express invitation of ,tycho1 went to ,prague1 and joined him in the capacity of assistant4 ,had ,tycho been of a nature less truly noble1 he might have looked with contempt on one who had made so few observations1 and indulged so much in wild speculation2 or he might have been jealous of a rising genius1 in which he descried so many signs of future eminence as an astronomer2 but1 superior to all the baser motives1 he extends to the young aspirant the hand of encouragement1 in the following kind invitation3 ,come not as a stranger1 but as a very welcome friend2 come1 and share in my observations1 with such instruments as ,i have with me4 ,several years previous to this1 ,kepler1 after one or two unsuccessful trials1 had found him a wife1 from whom he expected a considerable fortune2 but in this he was disappointed2 and so poor was he1 that1 when on his journey to ,prague1 in company with his wife1 being taken sick1 he was unable to defray the expenses of the journey1 and was forced to cast himself on the bounty of ,tycho4 ,in the course of the following year1 while absent from ,prague1 he fancied that ,tycho had injured him1 and accordingly addressed to the noble ,dane a letter full of insults and reproaches4 ,a mild reply from ,tycho opened the eyes of ,kepler to his own ingratitude4 ,his better feelings soon returned1 and he sent to his great patron this humble apology3 ,most noble ,tycho6 ,how shall ,i enumerate1 or rightly estimate1 your benefits conferred on me6 ,for two months you have liberally and gratuitously maintained me1 and my whole family2 you have provided for all my wishes2 you have done me every possible kindness2 you have communicated to me every thing you hold most dear2 no one1 by word or deed1 has intentionally injured me in any thing2 in short1 not to your own children1 your wife1 or yourself1 have you shown more indulgence than to me4 ,this being so1 as ,i am anxious to put upon record1 ,i cannot reflect1 without consternation1 that ,i should have been so given up by ,god to my own intemperance1 as to shut my eyes on all these benefits2 that1 instead of modest and respectful gratitude1 ,i should indulge for three weeks in continual moroseness towards all your family1 and in headlong passion and the utmost insolence towards yourself1 who possess so many claims on my veneration1 from your noble family1 your extraordinary learning1 and distinguished reputation4 ,whatever ,i have said or written against the person1 the fame1 the honor1 and the learning1 of your ,excellency2 or whatever1 in any other way1 ,i have injuriously spoken or written1 7if they admit no other more favorable interpretation17 as to my grief ,i have spoken and written many things1 and more than ,i can remember2 all and every thing ,i recant1 and freely and honestly declare and profess to be groundless1 false1 and incapable of proof4 ,this was ample satisfaction to the generous ,tycho4 ,to err is human3 to forgive1 divine4 ,on ,kepler's return to ,prague1 he was presented to the ,emperor by ,tycho1 and honored with the title of ,imperial ,mathematician4 ,this was in #afja1 when he was thirty years of age4 ,tycho died shortly after1 and ,kepler succeeded him as principal mathematician to the ,emperor2 but his salary was badly paid1 and he suffered much from pecuniary embarrassments4 ,although he held the astrologers1 or those who told fortunes by the stars1 in great contempt1 yet he entertained notions of his own1 on the same subject1 quite as extravagant1 and practised the art of casting nativities1 to eke out a support for his family4 ,when ,galileo began to observe with his telescope1 and announced1 in rapid succession1 his wonderful discoveries1 ,kepler entered into them with his characteristic enthusiasm1 although they subverted many of his favorite hypotheses4 ,but such was his love of truth1 that he was among the first to congratulate ,galileo1 and a most engaging correspondence was carried on between these master-spirits4 ,the first planet1 which occupied the particular attention of ,kepler1 was ,mars1 the long and assiduous study of whose motions conducted him at length to the discovery of those great principles called ',kepler's ,laws4' ,rarely do we meet with so remarkable a union of a vivid fancy with a profound intellect4 ,the hasty and extravagant suggestions of the former were submitted to the most laborious calculations1 some of which1 that were of great length1 he repeated seventy times4 ,this exuberance of fancy frequently appears in his style of writing1 which occasionally assumes a tone ludicrously figurative4 ,he seems constantly to contemplate ,mars as a valiant hero1 who had hitherto proved invincible1 and who would often elude his own efforts to conquer him1 ,while thus triumphing over ,mars1 and preparing for him1 as for one altogether vanquished1 tabular prisons1 and equated1 eccentric fetters1 it is buzzed here and there1 that the victory is vain1 and that the war is raging anew as violently as before4 ,for the enemy1 left at home a despised captive1 has burst all the chains of the equation1 and broken forth of the prisons of the tables4 ,skirmishes routed my forces of physical causes1 and1 shaking off the yoke1 regained their liberty4 ,and now1 there was little to prevent the fugitive enemy from effecting a junction with his own rebellious supporters1 and reducing me to despair1 had ,i not suddenly sent into the field a reserve of new physical reasonings1 on the rout and dispersion of the veterans1 and diligently followed1 without allowing the slightest respite1 in the direction in which he had broken out4 ,but he pursued this warfare with the planet until he gained a full conquest1 by the discovery of the first two of his laws1 namely1 that he revolves in an elliptical orbit1 and that his radius vector passes over equal spaces in equal times4 ,domestic troubles1 however1 involved him in the deepest affliction4 ,poverty1 the loss of a promising and favorite son1 the death of his wife1 after a long illness2--these were some of the misfortunes that clustered around him4 ,although his first marriage had been an unhappy one1 it was not consonant to his genius to surrender any thing with only a single trial4 ,accordingly1 it was not long before he endeavored to repair his loss by a second alliance4 ,he commissioned a number of his friends to look out for him1 and he soon obtained a tabular list of eleven ladies1 among whom his affections wavered4 ,the progress of his courtship is thus narrated in the interesting ',life' contained in the ',library of ,useful ,knowledge4' ,it furnishes so fine a specimen of his eccentricities1 that ,i cannot deny myself the pleasure of transcribing the passage for your perusal4 ,it is taken from an account which ,kepler himself gave in a letter to a friend4 ,the first on the list was a widow1 an intimate friend of his first wife and who1 on many accounts1 appeared a most eligible match4 ,at first1 she seemed favorably inclined to the proposal3 it is certain that she took time to consider it1 but at last she very quietly excused herself4 ,finding her afterwards less agreeable in person than he had anticipated1 he considered it a fortunate escape1 mentioning1 among other objections1 that she had two marriageable daughters1 whom1 by the way1 he had got on his list for examination4 ,he was much troubled to reconcile his astrology with the fact of his having taken so much pains about a negotiation not destined to succeed4 ,he examined the case professionally4 ',have the stars1' says he1 'exercised any influence here8 ,for1 just about this time1 the direction of the mid-heaven is in hot opposition to ,mars1 and the passage of ,saturn through the ascending point of the zodiac1 in the scheme of my nativity1 will happen again next ,november and ,december4 ,but1 if these are the causes1 how do they act8 ,is that explanation the true one1 which ,i have elsewhere given8 ,for ,i can never think of handing over to the stars the office of deities1 to produce effects4 ,let us1 therefore1 suppose it accounted for by the stars1 that at this season ,i am violent in my temper and affections1 in rashness of belief1 in a show of pitiful tender-heartedness1 in catching at reputation by new and paradoxical notions1 and the singularity of my actions2 in busily inquiring into1 and weighing1 and discussing1 various reasons2 in the uneasiness of my mind1 with respect to my choice4 ,i thank ,god1 that that did not happen which might have happened2 that this marriage did not take place4 ,now for the others4' ,of these1 one was too old2 another1 in bad health2 another1 too proud of her birth and quarterings2 a fourth had learned nothing but showy accomplishments1 not at all suitable to the kind of life she would have to lead with him4 ,another grew impatient1 and married a more decided admirer while he was hesitating4 ',the mischief1' says he1 'in all these attachments was1 that1 whilst ,i was delaying1 comparing1 and balancing1 conflicting reasons1 every day saw me inflamed with a new passion4' ,by the time he reached ,no4 #h1 of his list1 he found his match in this respect4 ',fortune has avenged herself at length on my doubtful inclinations4 ,at first1 she was quite complying1 and her friends also4 ,presently1 whether she did or did not consent1 not only ,i1 but she herself1 did not know4 ,after the lapse of a few days1 came a renewed promise1 which1 however1 had to be confirmed a third time3 and1 four days after that1 she again repented her conformation1 and begged to be excused from it4 ,upon this1 ,i gave her up1 and this time all my counsellors were of one opinion4' ,this was the longest courtship in the list1 having lasted three whole months2 and1 quite disheartened by its bad success1 ,kepler's next attempt was of a more timid complexion4 ,his advances to ,no4 #i were made by confiding to her the whole story of his recent disappointment1 prudently determining to be guided in his behavior1 by observing whether the treatment he experienced met with a proper degree of sympathy4 ,apparently1 the experiment did not succeed2 and1 when almost reduced to despair1 ,kepler betook himself to the advice of a friend1 who had for some time past complained that she was not consulted in this difficult negotiation4 ,when she produced ,no4 #aj1 and the first visit was paid1 the report upon her was as follows3 ',she has1 undoubtedly1 a good fortune1 is of good family1 and of economical habits3 but her physiognomy is most horribly ugly2 she would be stared at in the streets1 not to mention the striking disproportion in our figures4 ,i am lank1 lean1 and spare2 she is short and thick4 ,in a family notorious for fatness1 she is considered superfluously fat4' ,the only objection to ,no4 #aa seems to have been1 her excessive youth2 and when this treaty was broken off1 on that account1 ,kepler turned his back upon all his advisers1 and chose for himself one who had figured as ,no4 #e1 in his list1 to whom he professes to have felt attached throughout1 but from whom the representations of his friends had hitherto detained him1 probably on account of her humble station4 ,having thus settled his domestic affairs1 ,kepler now betook himself1 with his usual industry1 to his astronomical studies1 and brought before the world the most celebrated of his publications1 entitled ',harmonics4' ,in the fifth book of this work he announced his ,third ,law1--that the squares of the periodical times of the planets are as the cubes of the distances4 ,kepler's rapture on detecting it was unbounded4 ,what1 says he1 ,i prophesied two-and-twenty years ago1 as soon as ,i discovered the five solids among the heavenly orbits2 what ,i firmly believed long before ,i had seen ,ptolemy's ,harmonics2 what ,i had promised my friends in the title of this book1 which ,i named before ,i was sure of my discovery2 what1 sixteen years ago1 ,i urged as a thing to be sought2 that for which ,i joined ,tycho ,brahe1 for which ,i settled in ,prague1 for which ,i have devoted the best part of my life to astronomical contemplations2--at length ,i have brought to light1 and have recognised its truth beyond my most sanguine expectations4 ,it is now eighteen months since ,i got the first glimpse of light1 three months since the dawn1 very few days since the unveiled sun1 most admirable to gaze on1 burst out upon me4 ,nothing holds me3 ,i will indulge in my sacred fury2 ,i will triumph over mankind by the honest confession1 that ,i have stolen the golden vases of the ,egyptians to build up a tabernacle for my ,god1 far from the confines of ,egypt4 ,if you forgive me1 ,i rejoice3 if you are angry1 ,i can bear it2 the die is cast1 the book is written1 to be read either now or by posterity1--,i care not which4 ,i may well wait a century for a reader1 as ,god has waited six thousand years for an observer4 ,in accordance with the notion he entertained respecting the music of the spheres1 he made ,saturn and ,jupiter take the bass1 ,mars the tenor1 the ,earth and ,venus the counter1 and ,mercury the treble4 ,the misery in which ,kepler lived1 says ,sir ,david ,brewster1 in his ',life of ,newton1' forms a painful contrast with the services which he performed for science4 ,the pension on which he subsisted was always in arrears2 and though the three emperors1 whose reigns he adorned1 directed their ministers to be more punctual in its payment1 the disobedience of their commands was a source of continual vexation to ,kepler4 ,when he retired to ,silesia1 to spend the remainder of his days1 his pecuniary difficulties became still more harassing4 ,necessity at length compelled him to apply personally for the arrears which were due2 and he accordingly set out1 in #afcj1 when nearly sixty years of age1 for ,ratisbon2 but1 in consequence of the great fatigue which so long a journey on horseback produced1 he was seized with a fever1 which put an end to his life4 ,professor ,whewell 7in his interesting work on ,astronomy and ,general ,physics considered with reference to ,natural ,theology7 expresses the opinion that ,kepler1 notwithstanding his constitutional oddities1 was a man of strong and lively piety4 ,his ',commentaries on the ,motions of ,mars' he opens with the following passage3 ,i beseech my reader1 that1 not unmindful of the ,divine goodness bestowed on man1 he do with me praise and celebrate the wisdom and greatness of the ,creator1 which ,i open to him from a more inward explication of the form of the world1 from a searching of causes1 from a detection of the errors of vision2 and that thus1 not only in the firmness and stability of the earth1 he perceive with gratitude the preservation of all living things in ,nature as the gift of ,god1 but also that in its motion1 so recondite1 so admirable1 he acknowledge the wisdom of the ,creator4 ,but him who is too dull to receive this science1 or too weak to believe the ,copernican system without harm to his piety1--him1 ,i say1 ,i advise that1 leaving the school of astronomy1 and condemning1 if he please1 any doctrines of the philosophers1 he follow his own path1 and desist from this wandering through the universe2 and1 lifting up his natural eyes1 with which he alone can see1 pour himself out in his own heart1 in praise of ,god the ,creator2 being certain that he gives no less worship to ,god than the astronomer1 to whom ,god has given to see more clearly with his inward eye1 and who1 for what he has himself discovered1 both can and will glorify ,god4 ,in a ,life of ,kepler1 very recently published in his native country1 founded on manuscripts of his which have lately been brought to light1 there are given numerous other examples of a similar devotional spirit4 ,kepler thus concludes his ,harmonics3 ,i give ,thee thanks1 ,lord and ,creator1 that ,thou has given me joy through ,thy creation2 for ,i have been ravished with the work of ,thy hands4 ,i have revealed unto mankind the glory of ,thy works1 as far as my limited spirit could conceive their infinitude4 ,should ,i have brought forward any thing that is unworthy of ,thee1 or should ,i have sought my own fame1 be graciously pleased to forgive me4 ,as ,galileo experienced the most bitter persecutions from the ,church of ,rome1 so ,kepler met with much violent opposition and calumny from the ,protestant clergy of his own country1 particularly for adopting1 in an almanac which1 as astronomer royal1 he annually published1 the reformed calendar1 as given by the ,pope of ,rome4 ,his opinions respecting religious liberty1 also1 appear to have been greatly in advance of the times in which he lived4 ,in answer to certain calumnies with which he was assailed1 for his boldness in reasoning from the light of ,nature1 he uttered these memorable words3 ,the day will soon break1 when pious simplicity will be ashamed of its blind superstition2 when men will recognise truth in the book of ,nature as well as in the ,holy ,scriptures1 and rejoice in the two revelations4 ,,letter ,,xxv4 ,,comets4 ----,fancy now no more ,wantons on fickle pinions through the skies1 ,but1 fixed in aim1 and conscious of her power1 ,sublime from cause to cause exults to rise1 ,creation's blended stores arranging as she flies4--,beattie4 ,,nothing in astronomy is more truly admirable1 than the knowledge which astronomers have acquired of the motions of comets1 and the power they have gained of predicting their return4 ,indeed1 every thing appertaining to this class of bodies is so wonderful1 as to seem rather a tale of romance than a simple recital of facts4 ,comets are truly the knights-errant of astronomy4 ,appearing suddenly in the nocturnal sky1 and often dragging after them a train of terrific aspect1 they were1 in the earlier ages of the world1 and indeed until a recent period1 considered as peculiarly ominous of the wrath of ,heaven1 and as harbingers of wars and famines1 of the dethronement of monarchs1 and the dissolution of empires4 ,science has1 it is true1 disarmed them of their terrors1 and demonstrated that they are under the guidance of the same ,hand1 that directs in their courses the other members of the solar system2 but she has1 at the same time1 arrayed them in a garb of majesty peculiarly her own4 ,although the ancients paid little attention to the ordinary phenomena of ,nature1 hardly deeming them worthy of a reason1 yet1 when a comet blazed forth1 fear and astonishment conspired to make it an object of the most attentive observation4 ,hence the aspects of remarkable comets1 that have appeared at various times1 have been handed down to us1 often with circumstantial minuteness1 by the historians of different ages4 ,the comet which appeared in the year #acj1 before the ,christian era1 at the birth of ,mithridates1 is said to have had a disk equal in magnitude to that of the sun4 ,ten years before this1 one was seen1 which1 according to ,justin1 occupied a fourth part of the sky1 that is1 extended over forty-five degrees1 and surpassed the sun in splendor4 ,in the year #djj1 one was seen which resembled a sword in shape1 and extended from the zenith to the horizon4 ,such are some of the accounts of comets of past ages2 but it is probable we must allow much for the exaggerations naturally accompanying the descriptions of objects in themselves so truly wonderful4 ,a comet1 when perfectly formed1 consists of three parts1 the nucleus1 the envelope1 and the tail4 ,the nucleus1 or body of the comet1 is generally distinguished by its forming a bright point in the centre of the head1 conveying the idea of a solid1 or at least of a very dense1 portion of matter4 ,though it is usually exceedingly small1 when compared with the other parts of the comet1 and is sometimes wanting altogether1 yet it occasionally subtends an angle capable of being measured by the telescope4 ,the envelope 7sometimes called the coma1 from a ,latin word signifying hair1 in allusion to its hairy appearance7 is a dense nebulous covering1 which frequently renders the edge of the nucleus so indistinct1 that it is extremely difficult to ascertain its diameter with any degree of precision4 ,many comets have no nucleus1 but present only a nebulous mass1 exceedingly attenuated on the confines1 but gradually increasing in density towards the centre4 ,indeed1 there is a regular gradation of comets1 from such as are composed merely of a gaseous or vapory medium1 to those which have a well-defined nucleus4 ,in some instances on record1 astronomers have detected with their telescopes small stars through the densest part of a comet4 ,the tail is regarded as an expansion or prolongation of the coma2 and presenting1 as it sometimes does1 a train of appalling magnitude1 and of a pale1 portentous light1 it confers on this class of bodies their peculiar celebrity4 ,these several parts are exhibited in ,fig4 #fg1 which ,illustration ,figures #fg1 #fh4 ,,comets ,,of #afhj ,,and #ahaa4 represents the appearance of the comet of #afhj4 ,fig4 #fh also exhibits that of the comet of #ahaa4 ,the number of comets belonging to the solar system1 is probably very great4 ,many no doubt escape observation1 by being above the horizon in the day-time4 ,seneca mentions1 that during a total eclipse of the sun1 which happened sixty years before the ,christian era1 a large and splendid comet suddenly made its appearance1 being very near the sun4 ,the leading particulars of at least one hundred and thirty have been computed1 and arranged in a table1 for future comparison4 ,of these1 six are particularly remarkable2 namely1 the comets of #afhj1 #aggj1 and #ahaa2 and those which bear the names of ,halley1 ,biela1 and ,encke4 ,the comet of #afhj was remarkable1 not only for its astonishing size and splendor1 and its near approach to the sun1 but is celebrated for having submitted itself to the observations of ,sir ,isaac ,newton1 and for having enjoyed the signal honor of being the first comet whose elements were determined on the sure basis of mathematics4 ,the comet of #aggj is memorable for the changes its orbit has undergone by the action of ,jupiter1 as ,i shall explain to you more particularly hereafter4 ,the comet of #ahaa was the most remarkable in its appearance of all that have been seen in the present century4 ,it had scarcely any perceptible nucleus1 but its train was very long and broad1 as is represented in ,fig4 #fh4 ,halley's comet 7the same which reappeared in #ahce7 is distinguished as that whose return was first successfully predicted1 and whose orbit is best determined2 and ,biela's and ,encke's comets are well known for their short periods of revolution1 which subject them frequently to the view of astronomers4 ,in magnitude and brightness1 comets exhibit great diversity4 ,history informs us of comets so bright1 as to be distinctly visible in the day-time1 even at noon1 and in the brightest sunshine4 ,such was the comet seen at ,rome a little before the assassination of ,julius ,csar4 ,the comet of #afhj covered an arc of the heavens of ninety-seven degrees1 and its length was estimated at one hundred and twenty-three millions of miles4 ,that of #ahaa had a nucleus of only four hundred and twenty-eight miles in diameter1 but a tail one hundred and thirty-two millions of miles long4 ,had it been coiled around the earth like a serpent1 it would have reached round more than five thousand times4 ,other comets are exceedingly small1 the nucleus being in one case estimated at only twenty-five miles2 and some1 which are destitute of any perceptible nucleus1 appear to the largest telescopes1 even when nearest to us1 only as a small speck of fog1 or as a tuft of down4 ,the majority of comets can be seen only by the aid of the telescope4 ,indeed1 the same comet has very different aspects1 at its different returns4 ,halley's comet1 in #acje1 was described by the historians of that age as the comet of terrific magnitude2 7cometa horrend magnitudinis27 in #adef its tail reached from the horizon to the zenith1 and inspired such terror1 that1 by a decree of the ,pope of ,rome1 public prayers were offered up at noonday in all the ,catholic churches1 to deprecate the wrath of heaven2 while in #afhb its tail was only thirty degrees in length2 and in #agei it was visible only to the telescope until after it had passed its perihelion4 ,at its recent return1 in #ahce1 the greatest length of the tail was about twelve degrees4 ,these changes in the appearance of the same comet are partly owing to the different positions of the earth with respect to them1 being sometimes much nearer to them when they cross its track than at others2 also1 one spectator1 so situated as to see the comet at a higher angle of elevation1 or in a purer sky1 than another1 will see the train longer than it appears to another less favorably situated2 but the extent of the changes are such as indicate also a real change in magnitude and brightness4 ,the periods of comets in their revolutions around the sun are equally various4 ,encke's comet1 which has the shortest known period1 completes its revolution in three and one third years2 or1 more accurately1 in twelve hundred and eight days2 while that of #ahaa is estimated to have a period of thirty-three hundred and eighty three years4 ,the distances to which different comets recede from the sun are equally various4 ,while ,encke's comet performs its entire revolution within the orbit of ,jupiter1 ,halley's comet recedes from the sun to twice the distance of ,uranus2 or nearly thirty-six hundred millions of miles4 ,some comets1 indeed1 are thought to go a much greater distance from the sun than this1 while some are supposed to pass into curves which do not1 like the ellipse1 return into themselves2 and in this case they never come back to the sun4 7,see ,fig4 #cd1 page #aec47 ,comets shine by reflecting the light of the sun4 ,in one or two instances1 they have been thought to exhibit distinct phases1 like the moon1 although the nebulous matter with which the nucleus is surrounded would commonly prevent such phases from being distinctly visible1 even when they would otherwise be apparent4 ,moreover1 certain qualities of polarized light1--an affection by which a ray of light seems to have different properties on different sides1--enable opticians to decide whether the light of a given body is direct or reflected2 and ,m4 ,arago1 of ,paris1 by experiments of this kind on the light of the comet of #ahai1 ascertained it to be reflected light4 ,the tail of a comet usually increases very much as it approaches the sun2 and it frequently does not reach its maximum until after the perihelion passage4 ,in receding from the sun1 the tail again contracts1 and nearly or quite disappears before the body of the comet is entirely out of sight4 ,the tail is frequently divided into two portions1 the central parts1 in the direction of the axis1 being less bright than the marginal parts4 ,in #agdd a comet appeared which had six tails spread out like a fan4 ,the tails of comets extend in a direct line from the sun1 although more or less curved1 like a long quill or feather1 being convex on the side next to the direction in which they are moving1--a figure which may result from the less velocity of the portion most remote from the sun4 ,expansions of the envelope have also been at times observed on the side next the sun2 but these seldom attain any considerable length4 ,the quantity of matter in comets is exceedingly small4 ,their tails consist of matter of such tenuity1 that the smallest stars are visible through them4 ,they can only be regarded as masses of thin vapor1 susceptible of being penetrated through their whole substance by the sunbeams1 and reflecting them alike from their interior parts and from their surfaces4 ,it appears perhaps incredible1 that so thin a substance should be visible by reflected light1 and some astronomers have held that the matter of comets is self-luminous2 but it requires but very little light to render an object visible in the night1 and a light vapor may be visible when illuminated throughout an immense stratum1 which could not be seen if spread over the face of the sky like a thin cloud4 ,the highest clouds that float in our atmosphere1 says ,sir ,john ,herschel1 must be looked upon as dense and massive bodies1 compared with the filmy and all but spiritual texture of a comet4 ,the small quantity of matter in comets is proved by the fact1 that they have at times passed very near to some of the planets1 without disturbing their motions in any appreciable degree4 ,thus the comet of #aggj1 in its way to the sun1 got entangled among the satellites of ,jupiter1 and remained near them four months2 yet it did not perceptibly change their motions4 ,the same comet1 also1 came very near the earth2 so that1 had its quantity of matter been equal to that of the earth1 it would1 by its attraction1 have caused the earth to revolve in an orbit so much larger than at present1 as to have increased the length of the year two hours and forty-seven minutes4 ,yet it produced no sensible effect on the length of the year1 and therefore its mass1 as is shown by ,la ,place1 could not have exceeded #a_/ejjj of that of the earth1 and might have been less than this to any extent4 ,it may indeed be asked1 what proof we have that comets have any matter1 and are not mere reflections of light4 ,the answer is1 that1 although they are not able by their own force of attraction to disturb the motions of the planets1 yet they are themselves exceedingly disturbed by the action of the planets1 and in exact conformity with the laws of universal gravitation4 ,a delicate compass may be greatly agitated by the vicinity of a mass of iron1 while the iron is not sensibly affected by the attraction of the needle4 ,by approaching very near to a large planet1 a comet may have its orbit entirely changed4 ,this fact is strikingly exemplified in the history of the comet of #aggj4 ,at its appearance in #aggj1 its orbit was found to be an ellipse1 requiring for a complete revolution only five and a half years2 and the wonder was1 that it had not been seen before1 since it was a very large and bright comet4 ,astronomers suspected that its path had been changed1 and that it had been recently compelled to move in this short ellipse1 by the disturbing force of ,jupiter and his satellites4 ,the ,french ,institute1 therefore1 offered a high prize for the most complete investigation of the elements of this comet1 taking into account any circumstances which could possibly have produced an alteration in its course4 ,by tracing back the movements of this comet1 for some years previous to #aggj1 it was found that1 at the beginning of #agfg1 it had entered considerably within the sphere of ,jupiter's attraction4 ,calculating the amount of this attraction from the known proximity of the two bodies1 it was found what must have been its orbit previous to the time when it became subject to the disturbing action of ,jupiter4 ,it was therefore evident why1 as long as it continued to circulate in an orbit so far from the centre of the system1 it was never visible from the earth4 ,in ,january1 #agfg1 ,jupiter and the comet happened to be very near to one another1 and as both were moving in the same direction1 and nearly in the same plane1 they remained in the neighborhood of each other for several months1 the planet being between the comet and the sun4 ,the consequence was1 that the comet's orbit was changed into a smaller ellipse1 in which its revolution was accomplished in five and a half years4 ,but as it approached the sun1 in #aggi1 it happened again to fall in with ,jupiter4 ,it was in the month of ,june that the attraction of the planet began to have a sensible effect2 and it was not until the month of ,october following1 that they were finally separated4 ,at the time of their nearest approach1 in ,august1 ,jupiter was distant from the comet only #a_/dia of its distance from the sun1 and exerted an attraction upon it two hundred and twenty-five times greater than that of the sun4 ,by reason of this powerful attraction1 ,jupiter being further from the sun than the comet1 the latter was drawn out into a new orbit1 which even at its perihelion came no nearer to the sun than the planet ,ceres4 ,in this third orbit1 the comet requires about twenty years to accomplish its revolution2 and being at so great a distance from the earth1 it is invisible1 and will for ever remain so unless1 in the course of ages1 it may undergo new perturbations1 and move again in some smaller orbit1 as before4 ,with the foregoing leading facts respecting comets in view1 ,i will now explain to you a few things equally remarkable respecting their motions4 ,the paths of the planets around the sun being nearly circular1 we are able to see a planet in every part of its orbit4 ,but the case is very different with comets4 ,for the greater part of their course1 they are wholly out of sight1 and come into view only while just in the neighborhood of the sun4 ,this you will readily see must be the case1 by inspecting the frontispiece1 which represents the orbit of ,biela's comet1 in #ahcb4 ,sometimes1 the orbit is so eccentric1 that the place of the focus occupied by the sun appears almost at the extremity of the orbit4 ,this was the case with the orbit of the comet of #afhj4 ,indeed1 this comet1 at its perihelion1 came in fact nearer to the sun than the sixth part of the sun's diameter1 being only one hundred and forty-six thousand miles from the surface of the sun1 which1 you will remark1 is only a little more than half the distance of the moon from the earth2 while1 at its aphelion1 it was estimated to be thirteen thousand millions of miles from the sun1--more than eleven thousand millions of miles beyond the planet ,uranus4 ,its velocity1 when nearest the sun1 exceeded a million of miles an hour4 ,to describe such an orbit as was assigned to it by ,sir ,isaac ,newton1 would require five hundred and seventy-five years4 ,during all this period1 it was entirely out of view to the inhabitants of the earth1 except the few months1 while it was running down to the sun from such a distance as the orbit of ,jupiter and back4 ,the velocity of bodies moving in such eccentric orbits differs widely in different parts of their orbits4 ,in the remotest parts it is so slow1 that years would be required to pass over a space equal to that which it would run over in a single day1 when near the sun4 ,the appearances of the same comet at different periods of its return are so various1 that we can never pronounce a given comet to be the same with one that has appeared before1 from any peculiarities in its physical aspect1 as from its color1 magnitude1 or shape2 since1 in all these respects1 it is very different at different returns2 but it is judged to be the same if its path through the heavens1 as traced among the stars1 is the same4 ,the comet whose history is the most interesting1 and which both of us have been privileged to see1 is ,halley's4 ,just before its latest visit1 in #ahce1 its return was anticipated with so much expectation1 not only by astronomers1 but by all classes of the community1 that a great and laudable eagerness universally prevailed1 to learn the particulars of its history4 ,the best summary of these1 which ,i met with1 was given in the ,edinburgh ,review for ,april1 #ahce4 ,i might content myself with barely referring you to that well-written article2 but1 as you may not have the work at hand1 and would1 moreover1 probably not desire to read the whole article1 ,i will abridge it for your perusal1 interspersing some remarks of my own4 ,i have desired to give you1 in the course of these ,letters1 some specimen of the labors of astronomers1 and shall probably never be able to find a better one4 ,it is believed that the first recorded appearance of ,halley's comet was that which was supposed to signalize the birth of ,mithridates1 one hundred and thirty years before the birth of ,christ4 ,it is said to have appeared for twenty-four days2 its light is said to have surpassed that of the sun2 its magnitude to have extended over a fourth part of the firmament2 and it is stated to have occupied1 consequently1 about four hours in rising and setting4 ,in the year #cbc1 a comet appeared in the sign ,virgo4 ,another1 according to the historians of the ,lower ,empire1 appeared in the year #cii1 seventy-six years after the last1 at an interval corresponding to that of ,halley's comet4 ,the interval between the birth of ,mithridates and the year #cbc was four hundred and fifty-three years1 which would be equivalent to six periods of seventy-five and a half years4 ,thus it would seem1 that in the interim there were five returns of this comet unobserved1 or at least unrecorded4 ,the appearance in the year #cii was attended with extraordinary circumstances4 ,it was described in the old writers as a comet of monstrous size and appalling aspect1 its tail seeming to reach down to the ground4 ,the next recorded appearance of a comet agreeing with the ascertained period marks the taking of ,rome1 in the year #eej1--;an interval of one hundred and fifty-one years1 or two periods of seventy-five and a half years having elapsed4 ,one unrecorded return must1 therefore1 have taken place in the interim4 ,the next appearance of a comet1 coinciding with the assigned period1 is three hundred and eighty years afterwards2 namely1 in the year #icj1--;five revolutions having been completed in the interval4 ,the next appearance is recorded in the year #ajje1 after an interval of a single period of seventy-five years4 ,three revolutions would now seem to have passed unrecorded1 when the comet again makes its appearance in #abcj4 ,in this1 as well as in former appearances1 it is proper to state1 that the sole test of identity of these cornets with that of ,halley is the coincidence of the times1 as near as historical records enable us to ascertain1 with the epochs at which the comet of ,halley might be expected to appear4 ,that such evidence1 however1 is very imperfect1 must be evident1 if the frequency of cometary appearances be considered1 and if it be remembered1 that hitherto we find no recorded observations1 which could enable us to trace1 even with the rudest degree of approximation1 the paths of those comets1 the times of whose appearances raise a presumption of their identity with that of ,halley4 ,we now1 however1 descend to times in which more satisfactory evidence may be expected4 ,in the year #acje1 a year in which the return of ,halley's comet might have been expected1 there is recorded a comet of remarkable character3 ,a comet of terrific dimensions made its appearance about the time of the feast of the ,passover1 which was followed by a ,great ,plague4 ,had the terrific appearance of this body alone been recorded1 this description might have passed without the charge of great exaggeration2 but when we find the ,great ,plague connected with it as a consequence1 it is impossible not to conclude1 that the comet was seen by its historians through the magnifying medium of the calamity which followed it4 ,another appearance is recorded in the year #achj1 unaccompanied by any other circumstance than its mere date4 ,this1 however1 is in strict accordance with the ascertained period of ,halley's comet4 ,we now arrive at the first appearance at which observations were taken1 possessing sufficient accuracy to enable subsequent investigators to determine the path of the comet2 and this is accordingly the first comet the identity of which with the comet of ,halley can be said to be conclusively established4 ,in the year #adef1 a comet is stated to have appeared of unheard of magnitude2 it was accompanied by a tail of extraordinary length1 which extended over sixty degrees1 7a third part of the heavens17 and continued to be seen during the whole month of ,june4 ,the influence which was attributed to this appearance renders it probable1 that in the record there is more or less of exaggeration4 ,it was considered as the celestial indication of the rapid success of ,mohammed the ,second1 who had taken ,constantinople1 and struck terror into the whole ,christian world4 ,pope ,calixtus the ,second levelled the thunders of the ,church against the enemies of his faith1 terrestrial and celestial2 and in the same ,bull excommunicated the ,turks and the comet2 and1 in order that the memory of this manifestation of his power should be for ever preserved1 he ordained that the bells of all the churches should be rung at mid-day1--a custom which is preserved in those countries to our times4 ,the extraordinary length and brilliancy which was ascribed to the tail1 upon this occasion1 have led astronomers to investigate the circumstances under which its brightness and magnitude would be the greatest possible2 and upon tracing back the motion of the comet to the year #adef1 it has been found that it was then actually in the position1 with respect to the earth and sun1 most favorable to magnitude and splendor4 ,so far1 therefore1 the result of astronomical calculation corroborates the records of history4 ,the next return took place in #aeca4 ,pierre ,appian1 who first ascertained the fact that the tails of comets are usually turned from the sun1 examined this comet with a view to verify his statement1 and to ascertain the true direction of its tail4 ,he made1 accordingly1 numerous observations upon its position1 which1 although rude1 compared with the present standard of accuracy1 were still sufficiently exact to enable ,halley to identify this comet with that observed by himself4 ,the next return took place in #afjg1 when the comet was observed by ,kepler4 ,this astronomer first saw it on the evening of the twenty-sixth of ,september1 when it had the appearance of a star of the first magnitude1 and1 to his vision1 was without a tail2 but the friends who accompanied him had better sight1 and distinguished the tail4 ,before three o'clock the following morning the tail had become clearly visible1 and had acquired great magnitude4 ,two days afterwards1 the comet was observed by ,longomontanus1 a distinguished philosopher of the time4 ,he describes its appearance1 to the naked eye1 to be like ,jupiter1 but of a paler and more obscured light2 that its tail was of considerable length1 of a paler light than that of the head1 and more dense than the tails of ordinary comets4 ,the next appearance1 and that which was observed by ,halley himself1 took place in #afhb1 a little before the publication of the ',principia4' ,in the interval between #afjg and #afhb1 practical astronomy had made great advances2 instruments of observation had been brought to a state of comparative perfection2 numerous observatories had been established1 and the management of them had been confided to the most eminent men in ,europe4 ,in #afhb1 the scientific world was therefore prepared to examine the visitor of our system with a degree of care and accuracy before unknown4 ,in the year #afhf1 about four years afterwards1 ,newton published his ',principia1' in which he applied to the comet of #afhj the general principles of physical investigation first promulgated in that work4 ,he explained the method of determining1 by geometrical construction1 the visible portion of the path of a body of this kind1 and invited astronomers to apply these principles to the various recorded comets1--to discover whether some among them might not have appeared at different epochs1 the future returns of which might consequently be predicted4 ,such was the effect of the force of analogy upon the mind of ,newton1 that1 without awaiting the discovery of a periodic comet1 he boldly assumed these bodies to be analogous to planets in their revolution round the sun4 ,extraordinary as these conjectures must have appeared at the time1 they were soon strictly realized4 ,halley1 who was then a young man1 but possessed one of the best minds in ,england1 undertook the labor of examining the circumstances attending all the comets previously recorded1 with a view to discover whether any1 and which of them1 appeared to follow the same path4 ,antecedently to the year #agjj1 four hundred and twenty-five of these bodies had been recorded in history2 but those which had appeared before the fourteenth century had not been submitted to any observations by which their paths could be ascertained1--at least1 not with a sufficient degree of precision1 to afford any hope of identifying them with those of other comets4 ,subsequently to the year #acjj1 however1 ,halley found twenty-four comets on which observations had been made and recorded1 with a degree of precision sufficient to enable him to calculate the actual paths which these bodies followed while they were visible4 ,he examined1 with the most elaborate care1 the courses of each of these twenty-four bodies2 he found the exact points at which each one of them crossed the ecliptic1 or their nodes2 also the angle which the direction of their motion made with that plane1--that is1 the inclination of their orbits2 he also calculated the nearest distance at which each of them approached the sun1 or their perihelion distance2 and the exact place of the body when at that nearest point1--that is1 the longitude of the perihelion4 ,these particulars are called the elements of a comet1 because1 when ascertained1 they afford sufficient data for determining a comet's path4 ,on comparing these paths1 ,halley found that one1 which had appeared in #affa1 followed nearly the same path as one which had appeared in #aecb4 ,supposing1 then1 these to be two successive appearances of the same comet1 it would follow1 that its period would be one hundred and twenty-nine years1 reckoning from #affa4 ,had this conjecture been well founded1 the comet must have appeared about the year #agij4 ,no comet1 however1 appeared at or near that time1 following a similar path4 ,in his second conjecture1 ,halley was more fortunate1 as indeed might be expected1 since it was formed upon more conclusive grounds4 ,he found that the paths of comets which had appeared in #aeca and #afjg were nearly identical1 and that they were in fact the same as the path followed by the comet observed by himself in #afhb4 ,he suspected1 therefore1 that the appearances at these three epochs were produced by three successive returns of the same comet1 and that1 consequently1 its period in its orbit must be about seventy-five and a half years4 ,the probability of this conclusion is strikingly exhibited to the eye1 by presenting the elements in a tabular form1 from which it will at once be seen how nearly they correspond at these regular intervals4 ,time4,inclination of,long4 of the ,long4 ,per4,per4 ,dist4 ,course4 the orbit4 node4 #adef #agef #dhcj #cjajj #jeh ,retrograde4 #aeca #ag #ef #di #be #cja #ci #j #eg #afjg #ag #jb #ej #ba #cjb #af #j #eh #afhb #ag #db #ej #dh #cja #cf #j #eh ,so little was the scientific world1 at this time1 prepared for such an announcement1 that ,halley himself only ventured at first to express his opinion in the form of conjecture2 but1 after some further investigation of the circumstances of the recorded comets1 he found three which1 at least in point of time1 agreed with the period assigned to the comet of #afhb4 ,collecting confidence from these circumstances1 he announced his discovery as the result of observation and calculation combined1 and entitled to as much confidence as any other consequence of an established physical law4 ,there were1 nevertheless1 two circumstances which might be supposed to offer some difficulty4 ,first1 the intervals between the supposed successive returns were not precisely equal2 and1 secondly1 the inclination of the comet's path to the plane of the earth's orbit was not exactly the same in each case4 ,halley1 however1 with a degree of sagacity which1 considering the state of knowledge at the time1 cannot fail to excite unqualified admiration1 observed1 that it was natural to suppose that the same causes which disturbed the planetary motions must likewise act upon comets2 and that their influence would be so much the more sensible upon these bodies1 because of their great distances from the sun4 ,thus1 as the attraction of ,jupiter for ,saturn was known to affect the velocity of the latter planet1 sometimes retarding and sometimes accelerating it1 according to their relative position1 so as to affect its period to the extent of thirteen days1 it might well be supposed1 that the comet might suffer by a similar attraction an effect sufficiently great1 to account for the inequality observed in the interval between its successive returns3 and also for the variation to which the direction of its path upon the plane of the ecliptic was found to be subject4 ,he observed1 in fine1 that1 as in the interval between #afjg and #afhb1 the comet passed so near ,jupiter that its velocity must have been augmented1 and consequently its period shortened1 by the action of that planet1 this period1 therefore1 having been only seventy-five years1 he inferred that the following period would probably be seventy-six years1 or upwards2 and consequently1 that the comet ought not to be expected to appear until the end of #ageh1 or the beginning of #agei4 ,it is impossible to imagine any quality of mind more enviable than that which1 in the existing state of mathematical physics1 could have led to such a prediction4 ,the imperfect state of mathematical science rendered it impossible for ,halley to offer to the world a demonstration of the event which he foretold4 ,the theory of gravitation1 which was in its infancy in the time of ,halley's investigations1 had grown to comparative maturity before the period at which his prediction could be fulfilled4 ,the exigencies of that theory gave birth to new and more powerful instruments of mathematical inquiry3 the differential and integral calculus1 or the science of fluxions1 as it is sometimes called1--a branch of the mathematics1 expressed by algebraic symbols1 but capable of a much higher reach1 as an instrument of investigation1 than either algebra or geometry1--was its first and greatest offspring4 ,this branch of science was cultivated with an ardor and success by which it was enabled to answer all the demands of physics1 and it contributed largely to the advancement of mechanical science itself1 building upon the laws of motion a structure which has since been denominated ',celestial ,mechanics4' ,newton's discoveries having obtained reception throughout the scientific world1 his inquiries and his theories were followed up2 and the consequences of the great principle of universal gravitation were rapidly developed4 ,since1 according to this doctrine1 every body in nature attracts and is attracted by every other body1 it follows1 that the comet was liable to be acted on by each of the planets1 as well as by the sun1--a circumstance which rendered its movements much more difficult to follow1 than would be the case were it subject merely to the projectile force and to the solar attraction4 ,to estimate the time it would take for a ship to cross the ,atlantic would be an easy task1 were she subject to only one constant wind2 but to estimate1 beforehand1 the exact influence which all other winds and the tides might have upon her passage1 some accelerating and some retarding her course1 would present a problem of the greatest difficulty4 ,clairaut1 however1 a celebrated ,french mathematician1 undertook to estimate the effects that would be produced on ,halley's comet by the attractions of all the planets4 ,his aim was to investigate general rules1 by which the computation could be made arithmetically1 and hand them over to the practical calculator1 to make the actual computations4 ,lalande1 a practical astronomer1 no less eminent in his own department1 and who indeed first urged ,clairaut to this inquiry1 undertook the management of the astronomical and arithmetical part of the calculation4 ,in this prodigious labor 7for it was one of most appalling magnitude7 he was assisted by the wife of an eminent watchmaker in ,paris1 named ,lepaute1 whose exertions on this occasion have deservedly registered her name in astronomical history4 ,it is difficult to convey to one who is not conversant with such investigations1 an adequate notion of the labor which such an inquiry involved4 ,the calculation of the influence of any one planet of the system upon any other is itself a problem of some complexity and difficulty2 but still1 one general computation1 depending upon the calculation of the terms of a certain series1 is sufficient for its solution4 ,this comparative simplicity arises entirely from two circumstances which characterize the planetary orbits4 ,these are1 that1 though they are ellipses1 they differ very slightly from circles2 and though the planets do not move in the plane of the ecliptic1 yet none of them deviate considerably from that plane4 ,but these characters do not belong to the orbits of comets1 which1 on the contrary1 are highly eccentric1 and make all possible angles with the ecliptic4 ,the consequence of this is1 that the calculation of the disturbances produced in the cometary orbits by the action of the planets must be conducted not like the planets1 in one general calculation applicable to the whole orbits1 but in a vast number of separate calculations2 in which the orbit is considered1 as it were1 bit by bit1 each bit requiring a calculation similar to the whole orbit of the planet4 ,now1 when it is considered that the period of ,halley's comet is about seventy-five years1 and that every portion of its course1 for two successive periods1 was necessary to be calculated separately in this way1 some notion may be formed of the labor encountered by ,lalande and ,madame ,lepaute4 ,during six months1 says ,lalande1 we calculated from morning till night1 sometimes even at meals2 the consequence of which was1 that ,i contracted an illness which changed my constitution for the remainder of my life4 ,the assistance rendered by ,madame ,lepaute was such1 that1 without her1 we never could have dared to undertake this enormous labor1 in which it was necessary to calculate the distance of each of the two planets1 ,jupiter and ,saturn1 from the comet1 and their attraction upon that body1 separately1 for every successive degree1 and for one hundred and fifty years4 ,the attraction of a body is proportioned to its quantity of matter4 ,therefore1 before the attraction exerted upon the comet by the several planets within whose influence it might fall1 could be correctly estimated1 it was necessary to know the mass of each planet2 and though the planets had severally been weighed by methods supplied by ,newton's ',principia1' yet the estimate had not then attained the same measure of accuracy as it has now reached2 nor was it certain that there was not 7as it has since appeared that there actually was7 one or more planets beyond ,saturn1 whose attractions might likewise influence the motions of the comet4 ,clairaut1 making the best estimate he was able1 under all these disadvantages1 of the disturbing influence of the planets1 fixed the return of the comet to the place of its nearest distance from the sun on the fourth of ,april1 #agei4 ,in the successive appearances of the comet1 subsequently to #adef1 it was found to have gradually decreased in magnitude and splendor4 ,while in #adef it reached across one third part of the firmament1 and spread terror over ,europe1 in #afjg1 its appearance1 when observed by ,kepler and ,longomontanus1 was that of a star of the first magnitude2 and so trifling was its tail that1 ,kepler himself1 when he first saw it1 doubted whether it had any4 ,in #afhb1 it excited little attention1 except among astronomers4 ,supposing this decrease of magnitude and brilliancy to be progressive1 ,lalande entertained serious apprehensions that on its expected return it might be so inconsiderable1 as to escape the observation even of astronomers2 and thus1 that this splendid example of the power of science1 and unanswerable proof of the principle of gravitation1 would be lost to the world4 ,it is not uninteresting to observe the misgivings of this distinguished astronomer with respect to the appearance of the body1 mixed up with his unshaken faith in the result of the astronomical inquiry4 ,we cannot doubt1 says he1 that it will return2 and even if astronomers cannot see it1 they will not therefore be the less convinced of its presence4 ,they know that the faintness of its light1 its great distance1 and perhaps even bad weather1 may keep it from our view4 ,but the world will find it difficult to believe us2 they will place this discovery1 which has done so much honor to modern philosophy1 among the number of chance predictions4 ,we shall see discussions spring up again in colleges1 contempt among the ignorant1 terror among the people2 and seventy-six years will roll away1 before there will be another opportunity of removing all doubt4 ,fortunately for science1 the arrival of the expected visitor did not take place under such untoward circumstances4 ,as the commencement of the year #agei approached1 astronomers1 says ,voltaire1 hardly went to bed at all4 ,the honor1 however1 of the first glimpse of the stranger was not reserved for the possessors of scientific rank1 nor for the members of academies or universities4 ,on the night of ,christmas-day1 #ageh1 ,george ,palitzch1 of ,politz1 near ,dresden1--a peasant1 says ,sir ,john ,herchel1 by station1 an astronomer by nature1 first saw the comet4 ,an astronomer of ,leipzic found it soon after2 but1 with the mean jealousy of a miser1 he concealed his treasure1 while his contemporaries throughout ,europe were vainly directing their anxious search after it to other quarters of the heavens4 ,at this time1 ,delisle1 a ,french astronomer1 and his assistant1 ,messier1 who1 from his unweared assiduity in the pursuit of comets1 was called the ,comet-,hunter1 had been constantly engaged1 for eighteen months1 in watching for the return of ,halley's comet4 ,messier passed his life in search of comets4 ,it is related of him1 that when he was in expectation of discovering a comet1 his wife was taken ill and died4 ,while attending on her1 being withdrawn from his observatory1 another astronomer anticipated him in the discovery4 ,messier was in despair4 ,a friend1 visiting him1 began to offer some consolation for the recent affliction he had suffered4 ,messier1 thinking only of the comet1 exclaimed1 ,i had discovered twelve3 alas1 that ,i should be robbed of the thirteenth by ,montague6--and his eyes filled with tears4 ,then1 remembering that it was necessary to mourn for his wife1 whose remains were still in the house1 he exclaimed1 ,ah6 this poor woman6 7ah6 cette pauvre femme17 and again wept for his comet4 ,we can easily imagine how eagerly such an enthusiast would watch for ,halley's comet2 and we could almost wish that it had been his good fortune to be the first to announce its arrival3 but1 being misled by a chart which directed his attention to the wrong part of the firmament1 a whole month elapsed after its discovery by ,palitzch1 before he enjoyed the delightful spectacle4 ,the comet arrived at its perihelion on the thirteenth of ,march1 only twenty-three days from the time assigned by ,clairaut4 ,it appeared very round1 with a brilliant nucleus1 well distinguished from the surrounding nebulosity4 ,it had1 however1 no appearance of a tail4 ,it became lost in the sun1 as it approached its perihelion1 and emerged again1 on the other side of the sun1 on the first of ,april4 ,its exhibiting an appearance1 so inferior to what it presented on some of its previous returns1 is partly accounted for by its being seen by the ,european astronomers under peculiarly disadvantageous circumstances1 being almost always within the twilight1 and in the most unfavorable situations4 ,in the southern hemisphere1 however1 the circumstances for observing it were more favorable1 and there it exhibited a tail varying from ten to forty-seven degrees in length4 ,in my next ,letter ,i will give you some particulars respecting the late return of ,halley's comet4 ,,letter ,,xxvi4 ,,comets1 ,,continued4 ,incensed with indignation1 ,satan stood ,unterrified1 and like a comet burned1 ,that fires the length of ,ophiucus huge ,in the ,arctic sky1 and from his horrid train ,shakes pestilence and war4--,milton4 ,,among other great results which have marked the history of ,halley's comet1 it has itself been a criterion of the existing state of the mathematical and astronomical sciences4 ,we have just seen how far the knowledge of the great laws of physical astronomy1 and of the higher mathematics1 enabled the astronomers of #afhb and #agei1 respectively1 to deal with this wonderful body2 and let us now see what higher advantages were possessed by the astronomers of #ahce4 ,during this last interval of seventy-six years1 the science of mathematics1 in its most profound and refined branches1 has made prodigious advances1 more especially in its application to the laws of the celestial motions1 as exemplified in the ',mecanique ,celeste' of ,la ,place4 ,the methods of investigation have acquired greater simplicity1 and have likewise become more general and comprehensive2 and mechanical science1 in the largest sense of that term1 now embraces in its formularies the most complicated motions1 and the most minute effects of the mutual influences of the various members of our system4 ,you will probably find it difficult to comprehend1 how such hidden facts can be disclosed by formularies1 consisting of a's and b's1 and x's and y's1 and other algebraic symbols2 nor will it be easy to give you a clear idea of this subject1 without a more extensive acquaintance than you have formed with algebraic investigations2 but you can easily understand that even an equation expressed in numbers may be so changed in its form1 by adding1 subtracting1 multiplying and dividing1 as to express some new truth at every transformation4 ,some idea of this may be formed by the simplest example4 ,take the following3 #cdg4 ,this equation expresses the fact1 that three added to four is equal to seven4 ,by multiplying all the terms by #b1 we obtain a new equation1 in which #fhad4 ,this expresses a new truth2 and by varying the form1 by similar operations1 an indefinite number of separate truths may be elicited from the simple fundamental expression4 ,i will add another illustration1 which involves a little more algebra1 but not1 ,i think1 more than you can understand2 or1 if it does1 you will please pass over it to the next paragraph4 ,according to a rule of arithmetical progression1 the sum of all the terms is equal to half the sum of the extremes multiplied into the number of terms4 ,calling the sum of the terms s1 the first term a1 the last h1 and the number of terms n1 and we have 7#a_/b7n7ah7s2 or n7ah7#bs2 or ah#bs_/n2 or a7#bs_/n7-h2 or h7#bs_/n7-a4 ,these are only a few of the changes which may be made in the original expression1 still preserving the equality between the quantities on the left hand and those on the right2 yet each of these transformations expresses a new truth1 indicating distinct and 7as might be the case7 before unknown relations between the several quantities of which the whole expression is composed4 ,the last1 for example1 shows us that the last term in an arithmetical series is always equal to twice the sum of the whole series divided by the number of terms and diminished by the first term4 ,in analytical formularies1 as expressions of this kind are called1 the value of a single unknown quantity is sometimes given in a very complicated expression1 consisting of known quantities2 but before we can ascertain their united value1 we must reduce them1 by actually performing all the additions1 subtractions1 multiplications1 divisions1 raising to powers1 and extracting roots1 which are denoted by the symbols4 ,this makes the actual calculations derived from such formularies immensely laborious4 ,we have already had an instance of this in the calculations made by ,lalande and ,madame ,lepaute1 from formularies furnished by ,clairaut4 ,the analytical formularies1 contained in such works as ,la ,place's ',mecanique ,celeste1' exhibit to the eye of the mathematician a record of all the evolutions of the bodies of the solar system in ages past1 and of all the changes they must undergo in ages to come4 ,such has been the result of the combination of transcendent mathematical genius and unexampled labor and perseverance1 for the last century4 ,the learned societies established in various centres of civilization have more especially directed their attention to the advancement of physical astronomy1 and have stimulated the spirit of inquiry by a succession of prizes1 offered for the solutions of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge4 ,among these questions1 the determination of the return of comets1 and the disturbances which they experience in their course1 by the action of the planets near which they happen to pass1 hold a prominent place4 ,in #ahbf1 the ,french ,institute offered a prize for the determination of the exact time of the return of ,halley's comet to its perihelion in #ahce4 ,m4 ,pontecoulant aspired to the honor4 ,after calculations1 says he1 of which those alone who have engaged in such researches can estimate the extent and appreciate the fastidious monotony1 ,i arrived at a result which satisfied all the conditions proposed by the ,institute4 ,i determined the perturbations of ,halley's comet1 by taking into account the simultaneous actions of ,jupiter1 ,saturn1 ,uranus1 and the ,earth1 and ,i then fixed its return to its perihelion for the seventh of ,november4 ,subsequently to this1 however1 ,m4 ,pontecoulant made some further researches1 which led him to correct the former result2 and he afterwards altered the time to ,november fourteenth4 ,it actually came to its perihelion on the sixteenth1 within two days of the time assigned4 ,nothing can convince us more fully of the complete mastery which astronomers have at last acquired over these erratic bodies1 than to read in the ,edinburgh ,review for ,april1 #ahce1 the paragraph containing the final results of all the labors and anticipations of astronomers1 matured as they were1 in readiness for the approaching visitant1 and then to compare the prediction with the event1 as we saw it fulfilled a few months afterwards4 ,the paragraph was as follows3 ,on the whole1 it may be considered as tolerably certain1 that the comet will become visible in every part of ,europe about the latter end of ,august1 or beginning of ,september1 next4 ,it will most probably be distinguishable by the naked eye1 like a star of the first magnitude1 but with a duller light than that of a planet1 and surrounded with a pale nebulosity1 which will slightly impair its splendor4 ,on the night of the seventh of ,october1 the comet will approach the well-known constellation of the ,great ,bear2 and between that and the eleventh1 it will pass directly through the seven conspicuous stars of that constellation1 7the ,dipper47 ,towards the end of ,november1 the comet will plunge among the rays of the sun1 and disappear1 and will not issue from them1 on the other side1 until the end of ,december4 ,let us now see how far the actual appearances corresponded to these predictions4 ,the comet was first discovered from the observatory at ,rome1 on the morning of the fifth of ,august2 by ,professor ,struve1 at ,dorpat1 on the twentieth2 in ,england and ,france1 on the twenty-third2 and at ,yale ,college1 by ,professor ,loomis and myself1 on the thirty-first4 ,on the morning of that day1 between two and three o'clock1 in obedience to the directions which the great minds that had marked out its path among the stars had prescribed1 we directed ,clarke's telescope 7a noble instrument1 belonging to ,yale ,college7 towards the northeastern quarter of the heavens1 and lo6 there was the wanderer so long foretold1--a dim speck of fog on the confines of creation4 ,it came on slowly1 from night to night1 increasing constantly in magnitude and brightness1 but did not become distinctly visible to the naked eye until the twenty-second of ,september4 ,for a month1 therefore1 astronomers enjoyed this interesting spectacle before it exhibited itself to the world at large4 ,from this time it moved rapidly along the northern sky1 until1 about the tenth of ,october1 it traversed the constellation of the ,great ,bear1 passing a little above1 instead of through the seven conspicuous stars constituting the ,dipper4 ,at this time it had a lengthened train1 and became1 as you doubtless remember1 an object of universal interest4 ,early in ,november1 the comet ran down to the sun1 and was lost in his beams2 but on the morning of ,december thirty-first1 ,i again obtained1 through ,clarke's telescope1 a distinct view of it on the other side of the sun1 a moment before the morning dawn4 ,this return of ,halley's comet was an astronomical event of transcendent importance4 ,it was the chronicler of ages1 and carried us1 by a few steps1 up to the origin of time4 ,if a gallant ship1 which has sailed round the globe1 and commanded successively the admiration of many great cities1 diverse in language and customs1 is invested with a peculiar interest1 what interest must attach to one that has made the circuit of the solar system1 and fixed the gaze of successive worlds6 ,so intimate1 moreover1 is the bond which binds together all truths in one indissoluble chain1 that the establishment of one great truth often confirms a multitude of others1 equally important4 ,thus the return of ,halley's comet1 in exact conformity with the predictions of astronomers1 established the truth of all those principles by which those predictions were made4 ,it afforded most triumphant proof of the doctrine of universal gravitation1 and of course of the received laws of physical astronomy2 it inspired new confidence in the power and accuracy of that instrument 7the calculus7 by means of which its elements had been investigated2 and it proved that the different planets1 which exerted upon it severally a disturbing force proportioned to their quantity of matter1 had been correctly weighed1 as in a balance4 ,i must now leave this wonderful body to pursue its sublime march far beyond the confines of ,uranus1 7a distance it has long since reached17 and take a hasty notice of two other comets1 whose periodic returns have also been ascertained2 namely1 those of ,biela and ,encke4 ,biela's comet has a period of six years and three quarters4 ,it has its perihelion near the orbit of the earth1 and its aphelion a little beyond that of ,jupiter4 ,its orbit1 therefore1 is far less eccentric than that of ,halley's comet2 7see ,frontispiece27 it neither approaches so near the sun1 nor departs so far from it1 as most other known comets3 some1 indeed1 never come nearer to the sun than the orbit of ,jupiter1 while they recede to an incomprehensible distance beyond the remotest planet4 ,we might even imagine that they would get beyond the limits of the sun's attraction2 nor is this impossible1 although1 according to ,la ,place1 the solar attraction is sensible throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun1 or nearly ten thousand billions of miles4 ,some months before the expected return of ,biela's comet1 in #ahcb1 it was announced by astronomers1 who had calculated its path1 that it would cross the plane of the earth's orbit very near to the earth's path1 so that1 should the earth happen at the time to be at that point of her revolution1 a collision might take place4 ,this announcement excited so much alarm among the ignorant classes in ,france1 that it was deemed expedient by the ,french academy1 that one of their number should prepare and publish an article on the subject1 with the express view of allaying popular apprehension4 ,this task was executed by ,m4 ,arago4 ,he admitted that the earth would in fact pass so near the point where the comet crossed the plane of its orbit1 that1 should they chance to meet there1 the earth would be enveloped in the nebulous atmosphere of the comet4 ,he1 however1 showed that the earth would not be near that point at the same time with the comet1 but fifty millions of miles from it4 ,the comet came at the appointed time1 but was so exceedingly faint and small1 that it was visible only to the largest telescopes4 ,in one respect1 its diminutive size and feeble light enhanced the interest with which it was contemplated2 for it was a sublime spectacle to see a body1 which1 as projected on the celestial vault1 even when magnified a thousand times1 seemed but a dim speck of fog1 still pursuing its way1 in obedience to the laws of universal gravitation1 with the same regularity as ,jupiter and ,saturn4 ,we are apt to imagine that a body1 consisting of such light materials that it can be compared only to the thinnest fog1 would be dissipated and lost in the boundless regions of space2 but so far is this from the truth1 that1 when subjected to the action of the same forces of projection and solar attraction1 it will move through the void regions of space1 and will describe its own orbit about the sun with the same unerring certainty1 as the densest bodies of the system4 ,encke's comet1 by its frequent returns1 7once in three and a third years17 affords peculiar facilities for ascertaining the laws of its revolution2 and it has kept the appointments made for it with great exactness4 ,on its return in #ahci1 it exhibited to the telescope a globular mass of nebulous matter1 resembling fog1 and moved towards its perihelion with great rapidity4 ,it makes its entire excursions within the orbit of ,jupiter4 ,but what has made ,encke's comet particularly famous1 is its having first revealed to us the existence of a resisting medium in the planetary spaces4 ,it has long been a question1 whether the earth and planets revolve in a perfect void1 or whether a fluid of extreme rarity may not be diffused through space4 ,a perfect vacuum was deemed most probable1 because no such effects on the motions of the planets could be detected as indicated that they encountered a resisting medium4 ,but a feather1 or a lock of cotton1 propelled with great velocity1 might render obvious the resistance of a medium which would not be perceptible in the motions of a cannon ball4 ,accordingly1 ,encke's comet is thought to have plainly suffered a retardation from encountering a resisting medium in the planetary regions4 ,the effect of this resistance1 from the first discovery of the comet to the present time1 has been to diminish the time of its revolution about two days4 ,such a resistance1 by destroying a part of the projectile force1 would cause the comet to approach nearer to the sun1 and thus to have its periodic time shortened4 ,the ultimate effect of this cause will be to bring the comet nearer to the sun1 at every revolution1 until it finally falls into that luminary1 although many thousand years will be required to produce this catastrophe4 ,it is conceivable1 indeed1 that the effects of such a resistance may be counteracted by the attraction of one or more of the planets1 near which it may pass in its successive returns to the sun4 ,still1 it is not probable that this cause will exactly counterbalance the other2 so that1 if there is such an elastic medium diffused through the planetary regions1 it must follow that1 in the lapse of ages1 every comet will fall into the sun4 ,newton conjectured that this would be the case1 although he did not found his opinion upon the existence of such a resisting medium as is now detected4 ,to such an opinion he adhered to the end of life4 ,at the age of eighty-three1 in a conversation with his nephew1 he expressed himself thus3 ,i cannot say when the comet of #afhj will fall into the sun2 possibly after five or six revolutions2 but whenever that time shall arrive1 the heat of the sun will be raised by it to such a point1 that our globe will be burned1 and all the animals upon it will perish4 ,of the physical nature of comets little is understood4 ,the greater part of them are evidently mere masses of vapor1 since they permit very small stars to be seen through them4 ,in ,september1 #ahcb1 ,sir ,john ,herschel1 when observing ,biela's comet1 saw that body pass directly between his eye and a small cluster of minute telescopic stars of the sixteenth or seventeenth magnitude4 ,this little constellation occupied a space in the heavens1 the breadth of which was not the twentieth part of that of the moon2 yet the whole of the cluster was distinctly visible through the comet4 ,a more striking proof1 says ,sir ,john ,herschel1 could not have been afforded1 of the extreme transparency of the matter of which this comet consists4 ,the most trifling fog would have entirely effaced this group of stars1 yet they continued visible through a thickness of the comet which1 calculating on its distance and apparent diameter1 must have exceeded fifty thousand miles1 at least towards its central parts4 ,from this and similar observations1 it is inferred1 that the nebulous matter of comets is vastly more rare than that of the air we breathe1 and hence1 that1 were more or less of it to be mingled with the earth's atmosphere1 it would not be perceived1 although it might possibly render the air unwholesome for respiration4 ,m4 ,arago1 however1 is of the opinion1 that some comets1 at least1 have a solid nucleus4 ,it is difficult1 on any other supposition1 to account for the strong light which some of them have exhibited1--a light sufficiently intense to render them visible in the day-time1 during the presence of the sun4 ,the intense heat to which comets are subject1 in approaching so near the sun as some of them do1 is alleged as a sufficient reason for the great expansion of the thin vapory atmospheres which form their tails2 and the inconceivable cold to which they are subject1 in receding to such a distance from the sun1 is supposed to account for the condensation of the same matter until it returns to its original dimensions4 ,thus the great comet of #afhj1 at its perihelion1 approached within one hundred and forty-six thousand miles of the surface of the sun1 a distance of only one sixth part of the sun's diameter4 ,the heat which it must have received was estimated to be equal to twenty-eight thousand times that which the earth receives in the same time1 and two thousand times hotter than red-hot iron4 ,this temperature would be sufficient to volatilize the most obdurate substances1 and to expand the vapor to vast dimensions2 and the opposite effects of the extreme cold to which it would be subject in the regions remote from the sun would be adequate to condense it into its former volume4 ,this explanation1 however1 does not account for the direction of the tail1 extending1 as it usually does1 only in a line opposite to the sun4 ,some writers1 therefore1 suppose that the nebulous matter of the comet1 after being expanded to such a volume that the particles are no longer attracted to the nucleus1 unless by the slightest conceivable force1 are carried off in a direction from the sun1 by the impulse of the solar rays themselves4 ,but to assign such a power to the sun's rays1 while they have never been proved to have any momentum1 is unphilosophical2 and we are compelled to place the phenomena of comets' tails among the points of astronomy yet to be explained4 ,since comets which approach very near the sun1 like the comet of #afhj1 cross the orbits of all the planets1 the possibility that one of them may strike the earth has frequently been suggested4 ,still it may quiet our apprehensions on this subject1 to reflect on the vast amplitude of the planetary spaces1 in which these bodies are not crowded together1 as we see them erroneously represented in orreries and diagrams1 but are sparsely scattered at immense distances from each other4 ,they are like insects flying1 singly1 in the expanse of heaven4 ,if a comet's tail lay with its axis in the plane of the ecliptic when it was near the sun1 we can imagine that the tail might sweep over the earth2 but the tail may be situated at any angle with the ecliptic1 as well as in the same plane with it1 and the chances that it will not be in the same plane are almost infinite4 ,it is also extremely improbable that a comet will cross the plane of the ecliptic precisely at the earth's path in that plane1 since it may as probably cross it at any other point nearer or more remote from the sun4 ,a ,french writer of some eminence 7,du ,sejour7 has discussed this subject with ability1 and arrived at the following conclusions3 ,that of all the comets whose paths had been ascertained1 none could pass nearer to the earth than about twice the moon's distance2 and that none ever did pass nearer to the earth than nine times the moon's distance4 ,the comet of #aggj1 already mentioned1 which became entangled among the satellites of ,jupiter1 came within this limit4 ,some have taken alarm at the idea that a comet1 by approaching very near to the earth1 might raise so high a tide1 as to endanger the safety of maritime countries especially3 but this writer shows1 that the comet could not possibly remain more than two hours so near the earth as a fourth part of the moon's distance2 and it could not remain even so long1 unless it passed the earth under very peculiar circumstances4 ,for example1 if its orbit were nearly perpendicular to that of the earth1 it could not remain more than half an hour in such a position4 ,under such circumstances1 the production of a tide would be impossible4 ,eleven hours1 at least1 would be necessary to enable a comet to produce an effect on the waters of the earth1 from which the injurious effects so much dreaded would follow4 ,the final conclusion at which he arrives is1 that although1 in strict geometrical rigor1 it is not physically impossible that a comet should encounter the earth1 yet the probability of such an event is absolutely nothing4 ,m4 ,arago1 also1 has investigated the probability of such a collision on the mathematical doctrine of chances1 and remarks as follows3 ,suppose1 now1 a comet1 of which we know nothing but that1 at its perihelion1 it will be nearer the sun than we are1 and that its diameter is equal to one fourth that of the earth2 the doctrine of chances shows that1 out of two hundred and eighty-one millions of cases1 there is but one against us2 but one1 in which the two bodies could meet4 ,la ,place has assigned the consequences that would result from a direct collision between the earth and a comet4 ,it is easy1 says he1 to represent the effects of the shock produced by the earth's encountering a comet4 ,the axis and the motion of rotation changed2 the waters abandoning their former position to precipitate themselves towards the new equator2 a great part of men and animals whelmed in a universal deluge1 or destroyed by the violent shock imparted to the terrestrial globe2 entire species annihilated2 all the monuments of human industry overthrown2--such are the disasters which the shock of a comet would necessarily produce4 ,la ,place1 nevertheless1 expresses a decided opinion that the orbits of the planets have never yet been disturbed by the influence of comets4 ,comets1 moreover1 have been1 and are still to some degree1 supposed to exercise much influence in the affairs of this world1 affecting the weather1 the crops1 the public health1 and a great variety of atmospheric commotions4 ,even ,halley1 finding that his comet must have been near the earth at the time of the ,deluge1 suggested the possibility that the comet caused that event1--an idea which was taken up by ,whiston1 and formed into a regular theory4 ,in ,gregory's ,astronomy1 an able work1 published at ,oxford in #agjb1 the author remarks1 that among all nations and in all ages1 it has been observed1 that the appearance of a comet has always been followed by great calamities2 and he adds1 it does not become philosophers lightly to set down these things as fables4 ,among the various things ascribed to comets by a late ,english writer1 are hot and cold seasons1 tempests1 hurricanes1 violent hail-storms1 great falls of snow1 heavy rains1 inundations1 droughts1 famines1 thick fogs1 flies1 grasshoppers1 plague1 dysentery1 contagious diseases among animals1 sickness among cats1 volcanic eruptions1 and meteors1 or shooting stars4 ,these notions are too ridiculous to require a distinct refutation2 and ,i will only add1 that we have no evidence that comets have hitherto ever exercised the least influence upon the affairs of this world2 and we still remain in darkness1 with respect to their physical nature1 and the purposes for which they were created4 ,,letter ,,xxvii4 ,,meteoric ,,showers4 ,oft shalt thou see1 ere brooding storms arise1 ,star after star glide headlong down the skies1 ,and1 where they shot1 long trails of lingering light ,sweep far behind1 and gild the shades of night4--,virgil4 ,,few subjects of astronomy have excited a more general interest1 for several years past1 than those extraordinary exhibitions of shooting stars1 which have acquired the name of meteoric showers4 ,my reason for introducing the subject to your notice1 in this place1 is1 that these small bodies are1 as ,i believe1 derived from nebulous or cometary bodies1 which belong to the solar system1 and which1 therefore1 ought to be considered1 before we take our leave of this department of creation1 and naturally come next in order to comets4 ,the attention of astronomers was particularly directed to this subject by the extraordinary shower of meteors which occurred on the morning of the thirteenth of ,november1 #ahcc4 ,i had the good fortune to witness these grand celestial fire-works1 and felt a strong desire that a phenomenon1 which1 as it afterwards appeared1 was confined chiefly to ,north ,america1 should here command that diligent inquiry into its causes1 which so sublime a spectacle might justly claim4 ,as ,i think you were not so happy as to witness this magnificent display1 ,i will endeavor to give you some faint idea of it1 as it appeared to me a little before daybreak4 ,imagine a constant succession of fire-balls1 resembling sky-rockets1 radiating in all directions from a point in the heavens a few degrees southeast of the zenith1 and following the arch of the sky towards the horizon4 ,they commenced their progress at different distances from the radiating point2 but their directions were uniformly such1 that the lines they described1 if produced upwards1 would all have met in the same part of the heavens4 ,around this point1 or imaginary radiant1 was a circular space of several degrees1 within which no meteors were observed4 ,the balls1 as they travelled down the vault1 usually left after them a vivid streak of light2 and1 just before they disappeared1 exploded1 or suddenly resolved themselves into smoke4 ,no report of any kind was observed1 although we listened attentively4 ,beside the foregoing distinct concretions1 or individual bodies1 the atmosphere exhibited phosphoric lines1 following in the train of minute points1 that shot off in the greatest abundance in a northwesterly direction4 ,these did not so fully copy the figure of the sky1 but moved in paths more nearly rectilinear1 and appeared to be much nearer the spectator than the fire-balls4 ,the light of their trains was also of a paler hue1 not unlike that produced by writing with a stick of phosphorus on the walls of a dark room4 ,the number of these luminous trains increased and diminished alternately1 now and then crossing the field of view1 like snow drifted before the wind1 although1 in fact1 their course was towards the wind4 ,from these two varieties1 we were presented with meteors of various sizes and degrees of splendor3 some were mere points1 while others were larger and brighter than ,jupiter or ,venus2 and one1 seen by a credible witness1 at an earlier hour1 was judged to be nearly as large as the moon4 ,the flashes of light1 although less intense than lightning1 were so bright1 as to awaken people in their beds4 ,one ball that shot off in the northwest direction1 and exploded a little northward of the star ,capella1 left1 just behind the place of explosion1 a phosphorescent train of peculiar beauty4 ,this train was at first nearly straight1 but it shortly began to contract in length1 to dilate in breadth1 and to assume the figure of a serpent drawing itself up1 until it appeared like a small luminous cloud of vapor4 ,this cloud was borne eastward1 7by the wind1 as was supposed1 which was blowing gently in that direction17 opposite to the direction in which the meteor itself had moved1 remaining in sight several minutes4 ,the point from which the meteors seemed to radiate kept a fixed position among the stars1 being constantly near a star in ,leo1 called ,gamma ,leonis4 ,such is a brief description of this grand and beautiful display1 as ,i saw it at ,new ,haven4 ,the newspapers shortly brought us intelligence of similar appearances in all parts of the ,united ,states1 and many minute descriptions were published by various observers2 from which it appeared1 that the exhibition had been marked by very nearly the same characteristics wherever it had been seen4 ,probably no celestial phenomenon has ever occurred in this country1 since its first settlement1 which was viewed with so much admiration and delight by one class of spectators1 or with so much astonishment and fear by another class4 ,it strikingly evinced the progress of knowledge and civilization1 that the latter class was comparatively so small1 although it afforded some few examples of the dismay with which1 in barbarous ages of the world1 such spectacles as this were wont to be regarded4 ,one or two instances were reported1 of persons who died with terror2 many others thought the last great day had come2 and the untutored black population of the ,south gave expression to their fears in cries and shrieks4 ,after collecting and collating the accounts given in all the periodicals of the country1 and also in numerous letters addressed either to my scientific friends or to myself1 the following appeared to be the leading facts attending the phenomenon4 ,the shower pervaded nearly the whole of ,north ,america1 having appeared in nearly equal splendor from the ,british possessions on the north to the ,west-,india ,islands and ,mexico on the south1 and from sixty-one degrees of longitude east of the ,american coast1 quite to the ,pacific ,ocean on the west4 ,throughout this immense region1 the duration was nearly the same4 ,the meteors began to attract attention by their unusual frequency and brilliancy1 from nine to twelve o'clock in the evening2 were most striking in their appearance from two to five2 arrived at their maximum1 in many places1 about four o'clock2 and continued until rendered invisible by the light of day4 ,the meteors moved either in right lines1 or in such apparent curves1 as1 upon optical principles1 can be resolved into right lines4 ,their general tendency was towards the northwest1 although1 by the effect of perspective1 they appeared to move in various directions4 ,such were the leading phenomena of the great meteoric shower of ,november #ac1 #ahcc4 ,for a fuller detail of the facts1 as well as of the reasonings that were built on them1 ,i must beg leave to refer you to some papers of mine in the twenty-fifth and twenty-sixth volumes of the ,american ,journal of ,science4 ,soon after this wonderful occurrence1 it was ascertained that a similar meteoric shower had appeared in #agii1 and1 what was remarkable1 almost at exactly the same time of year1 namely1 on the morning of the twelfth of ,november2 and we were again surprised as well as delighted1 at receiving successive accounts from different parts of the world of the phenomenon1 as having occurred on the morning of the same thirteenth of ,november1 in #ahcj1 #ahca1 and #ahcb4 ,hence this was evidently an event independent of the casual changes of the atmosphere2 for1 having a periodical return1 it was undoubtedly to be referred to astronomical causes1 and its recurrence1 at a certain definite period of the year1 plainly indicated some relation to the revolution of the earth around the sun4 ,it remained1 however1 to develope the nature of this relation1 by investigating1 if possible1 the origin of the meteors4 ,the views to which ,i was led on this subject suggested the probability that the same phenomenon would recur on the corresponding seasons of the year1 for at least several years afterwards2 and such proved to be the fact1 although the appearances1 at every succeeding return1 were less and less striking1 until #ahci1 when1 so far as ,i have heard1 they ceased altogether4 ,mean-while1 two other distinct periods of meteoric showers have1 as already intimated1 been determined2 namely1 about the ninth of ,august1 and seventh of ,december4 ,the facts relative to the history of these periods have been collected with great industry by ,mr4 ,edward ,c4 ,herrick2 and several of the most ingenious and most useful conclusions1 respecting the laws that regulate these singular exhibitions1 have been deduced by ,professor ,twining4 ,several of the most distinguished astronomers of the ,old ,world1 also1 have engaged in these investigations with great zeal1 as ,messrs4 ,arago and ,biot1 of ,paris2 ,doctor ,olbers1 of ,bremen2 ,m4 ,wartmann1 of ,geneva2 and ,m4 ,quetelet1 of ,brussels4 ,but you will be desirous to learn what are the conclusions which have been drawn respecting these new and extraordinary phenomena of the heavens4 ,as the inferences to which ,i was led1 as explained in the twenty-sixth volume of the ',american ,journal of ,science1' have1 at least in their most important points1 been sanctioned by astronomers of the highest respectability1 ,i will venture to give you a brief abstract of them1 with such modifications as the progress of investigation since that period has rendered necessary4 ,the principal questions involved in the inquiry were the following3--,was the origin of the meteors within the atmosphere1 or beyond it8 ,what was the height of the place above the surface of the earth8 ,by what force were the meteors drawn or impelled towards the earth8 ,in what directions did they move8 ,with what velocity8 ,what was the cause of their light and heat8 ,of what size were the larger varieties8 ,at what height above the earth did they disappear8 ,what was the nature of the luminous trains which sometimes remained behind8 ,what sort of bodies were the meteors themselves2 of what kind of matter constituted2 and in what manner did they exist before they fell to the earth8 ,finally1 what relations did the source from which they emanated sustain to our earth8 ,in the first place1 the meteors had their origin beyond the limits of our atmosphere4 ,we know whether a given appearance in the sky is within the atmosphere or beyond it1 by this circumstance3 all bodies near the earth1 including the atmosphere itself1 have a common motion with the earth around its axis from west to east4 ,when we see a celestial object moving regularly from west to east1 at the same rate as the earth moves1 leaving the stars behind1 we know it is near the earth1 and partakes1 in common with the atmosphere1 of its diurnal rotation3 but when the earth leaves the object behind2 or1 in other words1 when the object moves westward along with the stars1 then we know that it is so distant as not to participate in the diurnal revolution of the earth1 and of course to be beyond the atmosphere4 ,the source from which the meteors emanated thus kept pace with the stars1 and hence was beyond the atmosphere4 ,in the second place1 the height of the place whence the meteors proceeded was very great1 but it has not yet been accurately determined4 ,regarding the body whence the meteors emanated after the similitude of a cloud1 it seemed possible to obtain its height in the same manner as we measure the height of a cloud1 or indeed the height of the moon4 ,although we could not see the body itself1 yet the part of the heavens whence the meteors came would indicate its position4 ,this point we called the radiant2 and the question was1 whether the radiant was projected by distant observers on different parts of the sky2 that is1 whether it had any parallax4 ,i took much pains to ascertain the truth of this matter1 by corresponding with various observers in different parts of the ,united ,states1 who had accurately noted the position of the radiant among the fixed stars1 and supposed ,i had obtained such materials as would enable us to determine the parallax1 at least approximately2 although such discordances existed in the evidence as reasonably to create some distrust of its validity4 ,putting together1 however1 the best materials ,i could obtain1 ,i made the height of the radiant above the surface of the earth twenty-two hundred and thirty-eight miles4 ,when1 however1 ,i afterwards obtained1 as ,i supposed1 some insight into the celestial origin of the meteors1 ,i at once saw that the meteoric body must be much further off than this distance2 and my present impression is1 that we have not the means of determining what its height really is4 ,we may safely place it at many thousand miles4 ,in the third place1 with respect to the force by which the meteors were drawn or impelled towards the earth1 my first impression was1 that they fell merely by the force of gravity2 but the velocity which1 on careful investigation by ,professor ,twining and others1 has been ascribed to them1 is greater than can possibly result from gravity1 since a body can never acquire1 by gravity alone1 a velocity greater than about seven miles per second4 ,some other cause1 beside gravity1 must therefore act1 in order to give the meteors so great an apparent velocity4 ,in the fourth place1 the meteors fell towards the earth in straight lines1 and in directions which1 within considerable distances1 were nearly parallel with each other4 ,the courses are inferred to have been in straight lines1 because no others could have appeared to spectators in different situations to have described arcs of great circles4 ,in order to be projected into the arc of a great circle1 the line of descent must be in a plane passing through the eye of the spectator2 and the intersection of such planes1 passing through the eyes of different spectators1 must be straight lines4 ,the lines of direction are inferred to have been parallel1 on account of their apparent radiation from one point1 that being the vanishing point of parallel lines4 ,this may appear to you a little paradoxical1 to infer that lines are parallel1 because they diverge from one and the same point2 but it is a well-known principle of perspective1 that parallel lines1 when continued to a great distance from the eye1 appear to converge towards the remoter end4 ,you may observe this in two long rows of trees1 or of street lamps4 ,illustration ,fig4 #fi4 ,some idea of the manner in which the meteors fell1 and of the reason of their apparent radiation from a common point1 may be gathered from the annexed diagram4 ,let ,a ,b ,c1 ,fig4 #fi1 represent the vault of the sky1 the centre of which1 ,d1 being the place of the spectator4 ,let #a1 #b1 #c1 c41 represent parallel lines directed towards the earth4 ,a luminous body descending through #a' #a1 coinciding with the line ,d ,e1 coincident with the axis of vision1 7or the line drawn from the meteoric body to the eye17 would appear stationary all the while at #a1 because distant bodies always appear stationary when they are moving either directly towards us or directly from us4 ,a body descending through #b #b1 would seem to describe the short arc #b' #b'1 appearing to move on the concave of the sky between the lines drawn from the eye to the two extremities of its line of motion2 and1 for a similar reason1 a body descending through #c #c1 would appear to describe the larger arc #c' #c'4 ,hence1 those meteors which fell nearer to the axis of vision1 would describe shorter arcs1 and move slower1 while those which were further from the axis and nearer the horizon would appear to describe longer arcs1 and to move with greater velocity2 the meteors would all seem to radiate from a common centre1 namely1 the point where the axis of vision met the celestial vault2 and if any meteor chanced to move directly in the line of vision1 it would be seen as a luminous body1 stationary1 for a few seconds1 at the centre of radiation4 ,to see how exactly the facts1 as observed1 corresponded to these inferences1 derived from the supposition that the meteors moved in parallel lines1 take the following description1 as given immediately after the occurrence1 by ,professor ,twining4 ,in the vicinity of the radiant point1 a few star-like bodies were observed1 possessing very little motion1 and leaving very little length of trace4 ,further off1 the motions were more rapid and the traces longer2 and most rapid of all1 and longest in their traces1 were those which originated but a few degrees above the horizon1 and descended down to it4 ,in the fifth place1 had the meteors come from a point twenty-two hundred and thirty-eight miles from the earth1 and derived their apparent velocity from gravity alone1 then it would be found1 by a very easy calculation1 that their actual velocity was about four miles per second2 but1 as already intimated1 the velocity observed was estimated much greater than could be accounted for on these principles2 not less1 indeed1 than fourteen miles per second1 and1 in some instances1 much greater even than this4 ,the motion of the earth in its orbit is about nineteen miles per second2 and the most reasonable supposition we can make1 at present1 to account for the great velocity of the meteors1 is1 that they derived a relative motion from the earth's passing rapidly by them1--a supposition which is countenanced by the fact that they generally tended westward contrary to the earth's motion in its orbit4 ,in the sixth place1 the meteors consisted of combustible matter1 and took fire1 and were consumed1 in traversing the atmosphere4 ,that these bodies underwent combustion1 we had the direct evidence of the senses1 inasmuch as we saw them burn4 ,that they took fire in the atmosphere1 was inferred from the fact that they were not luminous in their original situations in space1 otherwise1 we should have seen the body from which they emanated2 and had they been luminous before reaching the atmosphere1 we should have seen them for a much longer period than they were in sight1 as they must have occupied a considerable time in descending towards the earth from so great a distance1 even at the rapid rate at which they travelled4 ,the immediate consequence of the prodigious velocity with which the meteors fell into the atmosphere must be a powerful condensation of the air before them1 retarding their progress1 and producing1 by a sudden compression of the air1 a great evolution of heat4 ,there is a little instrument called the air-match1 consisting of a piston and cylinder1 like a syringe1 in which we strike a light by suddenly forcing down the piston upon the air below4 ,as the air cannot escape1 it is suddenly compressed1 and gives a spark sufficient to light a piece of tinder at the bottom of the cylinder4 ,indeed1 it is a well-known fact1 that1 whenever air is suddenly and forcibly compressed1 heat is elicited2 and1 if by such a compression as may be given by the hand in the air-match1 heat is evolved sufficient to fire tinder1 what must be the heat evolved by the motion of a large body in the atmosphere1 with a velocity so immense4 ,it is common to resort to electricity as the agent which produces the heat and light of shooting stars2 but even were electricity competent to produce this effect1 its presence1 in the case before us1 is not proved2 and its agency is unnecessary1 since so swift a motion of the meteors themselves1 suddenly condensing the air before them1 is both a known and adequate cause of an intense light and heat4 ,a combustible body falling into the atmosphere1 under such circumstances1 would become speedily ignited1 but could not burn freely1 until it became enveloped in air of greater density2 but1 on reaching the lower portions of the atmosphere1 it would burn with great rapidity4 ,in the seventh place1 some of the larger meteors must have been bodies of great size4 ,according to the testimony of various individuals1 in different parts of the ,united ,states1 a few fire-balls appeared as large as the full moon4 ,dr4 ,smith1 7then of ,north ,carolina1 but since surgeon-general of the ,texian army17 who was travelling all night on professional business1 describes one which he saw in the following terms3 ,in size it appeared somewhat larger than the full moon rising4 ,i was startled by the splendid light in which the surrounding scene was exhibited1 rendering even small objects quite visible2 but ,i heard no noise1 although every sense seemed to be suddenly aroused1 in sympathy with the violent impression on the sight4 ,this description implies not only that the body was very large1 but that it was at a considerable distance from the spectator4 ,its actual size will depend upon the distance2 for1 as it appeared under the same angle as the moon1 its diameter will bear the same ratio to the moon's1 as its distance bears to the moon's distance4 ,we could1 therefore1 easily ascertain how large it was1 provided we could find how far it was from the observer4 ,if it was one hundred and ten miles distant1 its diameter was one mile1 and in the same proportion for a greater or less distance2 and1 if only at the distance of one mile1 its diameter was forty-eight feet4 ,for a moderate estimate1 we will suppose it to have been twenty-two miles off2 then its diameter was eleven hundred and fifty-six feet4 ,upon every view of the case1 therefore1 it must be admitted1 that these were bodies of great size1 compared with other objects which traverse the atmosphere4 ,we may further infer the great magnitude of some of the meteors1 from the dimensions of the trains1 or clouds1 which resulted from their destruction4 ,these often extended over several degrees1 and at length were borne along in the direction of the wind1 exactly in the manner of a small cloud4 ,it was an interesting problem to ascertain1 if possible1 the height above the earth at which these fire-balls exploded1 or resolved themselves into a cloud of smoke4 ,this would be an easy task1 provided we could be certain that two or more distant observers could be sure that both saw the same meteor2 for as each would refer the place of explosion1 or the position of the cloud that resulted from it1 to a different point of the sky1 a parallax would thus be obtained1 from which the height might be determined4 ,the large meteor which is mentioned in my account of the shower1 7see page #cdh17 as having exploded near the star ,capella1 was so peculiar in its appearance1 and in the form and motions of the small cloud which resulted from its combustion1 that it was noticed and distinguished by a number of observers in distant parts of the country4 ,all described the meteor as exhibiting1 substantially1 the same peculiarities of appearance2 all agreed very nearly in the time of its occurrence2 and1 on drawing lines1 to represent the course and direction of the place where it exploded to the view of each of the observers respectively1 these lines met in nearly one and the same point1 and that was over the place where it was seen in the zenith4 ,little doubt1 therefore1 could remain1 that all saw the same body2 and on ascertaining1 from a comparison of their observations1 the amount of parallax1 and thence deducing its height1--a task which was ably executed by ,professor ,twining1--the following results were obtained3 that this meteor1 and probably all the meteors1 entered the atmosphere with a velocity not less1 but perhaps greater1 than fourteen miles in a second2 that they became luminous many miles from the earth1--in this case1 over eighty miles2 and became extinct high above the surface1--in this case1 nearly thirty miles4 ,in the eighth place1 the meteors were combustible bodies1 and were constituted of light and transparent materials4 ,the fact that they burned is sufficient proof that they belonged to the class of combustible bodies2 and they must have been composed of very light materials1 otherwise their momentum would have been sufficient to enable them to make their way through the atmosphere to the surface of the earth4 ,to compare great things with small1 we may liken them to a wad discharged from a piece of artillery1 its velocity being supposed to be increased 7as it may be7 to such a degree1 that it shall take fire as it moves through the air4 ,although it would force its way to a great distance from the gun1 yet1 if not consumed too soon1 it would at length be stopped by the resistance of the air4 ,although it is supposed that the meteors did in fact slightly disturb the atmospheric equilibrium1 yet1 had they been constituted of dense matter1 like meteoric stones1 they would doubtless have disturbed it vastly more4 ,their own momentum would be lost only as it was imparted to the air2 and had such a number of bodies1--some of them quite large1 perhaps a mile in diameter1 and entering the atmosphere with a velocity more than forty times the greatest velocity of a cannon ball1--had they been composed of dense1 ponderous matter1 we should have had appalling evidence of this fact1 not only in the violent winds which they would have produced in the atmosphere1 but in the calamities they would have occasioned on the surface of the earth4 ,the meteors were transparent bodies2 otherwise1 we cannot conceive why the body from which they emanated was not distinctly visible1 at least by reflecting the light of the sun4 ,if only the meteors which were known to fall towards the earth had been collected and restored to their original connexion in space1 they would have composed a body of great extent2 and we cannot imagine a body of such dimensions1 under such circumstances1 which would not be visible1 unless formed of highly transparent materials4 ,by these unavoidable inferences respecting the kind of matter of which the meteors were composed1 we are unexpectedly led to recognise a body bearing1 in its constitution1 a strong analogy to comets1 which are also composed of exceedingly light and transparent1 and1 as there is much reason to believe1 of combustible matter4 ,we now arrive at the final inquiry1 what relations did the body which afforded the meteoric shower sustain to the earth8 ,was it of the nature of a satellite1 or terrestrial comet1 that revolves around the earth as its centre of motion8 ,was it a collection of nebulous1 or cometary matter1 which the earth encountered in its annual progress8 or was it a comet1 which chanced at this time to be pursuing its path along with the earth1 around their common centre of motion8 ,it could not have been of the nature of a satellite to the earth1 7or one of those bodies which are held by some to afford the meteoric stones1 which sometimes fall to the earth from huge meteors that traverse the atmosphere17 because it remained so long stationary with respect to the earth4 ,a body so near the earth as meteors of this class are known to be1 could not remain apparently stationary among the stars for a moment2 whereas the body in question occupied the same position1 with hardly any perceptible variation1 for at least two hours4 ,nor can we suppose that the earth1 in its annual progress1 came into the vicinity of a nebula1 which was either stationary1 or wandering lawless through space4 ,such a collection of matter could not remain stationary within the solar system1 in an insulated state1 for1 if not prevented by a motion of its own1 or by the attraction of some nearer body1 it would have proceeded directly towards the sun2 and had it been in motion in any other direction than that in which the earth was moving1 it would soon have been separated from the earth2 since1 during the eight hours1 while the meteoric shower was visible1 the earth moved in its orbit through the space of nearly five hundred and fifty thousand miles4 ,the foregoing considerations conduct us to the following train of reasoning4 ,first1 if all the meteors which fell on the morning of ,november #ac1 #ahcc1 had been collected and restored to their original connexion in space1 they would of themselves have constituted a nebulous body of great extent2 but we have reason to suppose that they1 in fact1 composed but a small part of the mass from which they emanated1 since1 after the loss of so much matter as proceeded from it in the great meteoric shower of #agii1 and in the several repetitions of it that preceded the year #ahcc1 it was still capable of affording so copious a shower on that year2 and similar showers1 more limited in extent1 were repeated for at least five years afterwards4 ,we are therefore to regard the part that descended only as the extreme portions of a body or collection of meteors1 of unknown extent1 existing in the planetary spaces4 ,secondly1 since the earth fell in with this body in the same part of its orbit1 for several years in succession1 it must either have remained there while the earth was performing its whole revolution around the sun1 or it must itself have had a revolution1 as well as the earth4 ,but ,i have already shown that it could not have remained stationary in that part of space2 therefore1 it must have had a revolution around the sun4 ,thirdly1 its period of revolution must have either been greater than the earth's1 equal to it1 or less4 ,it could not have been greater1 for then the two bodies could not have been together again at the end of the year1 since the meteoric body would not have completed its revolution in a year4 ,its period might obviously be the same as the earth's1 for then they might easily come together again after one revolution of each2 although their orbits might differ so much in shape as to prevent their being together at any intermediate point4 ,but the period of the body might also be less than that of the earth1 provided it were some aliquot part of a year1 so as to revolve just twice1 or three times1 for example1 while the earth revolves once4 ,let us suppose that the period is one third of a year4 ,then1 since we have given the periodic times of the two bodies1 and the major axis of the orbit of one of them1 namely1 of the earth1 we can1 by ,kepler's law1 find the major axis of the other orbit2 for the square of the earth's periodic time #ab is to the square of the body's time 7#a_/c7b as the cube of the major axis of the earth's orbit is to the cube of the major axis of the orbit in question4 ,now1 the three first terms of this proportion are known1 and consequently1 it is only to solve a case in the simple rule of three1 to find the term required4 ,on making the calculation1 it is found1 that the supposition of a periodic time of only one third of a year gives an orbit of insufficient length2 the whole major axis would not reach from the sun to the earth2 and consequently1 a body revolving in it could never come near to the earth4 ,on making trial of six months1 we obtain an orbit which satisfies the conditions1 being such as is represented by the diagram on page #cfb1 ,fig4 #fi'1 where the outer circle denotes the earth's orbit1 the sun being in the centre1 and the inner ellipse denotes the path of the meteoric body4 ,the two bodies are together at the top of the figure1 being the place of the meteoric body's aphelion on the thirteenth of ,november1 and the figures #aj1 #bj1 c41 denote the relative positions of the earth and the body for every ten days1 for a period of six months1 in which time the body would have returned to its aphelion4 ,illustration ,fig4 #fi'4 ,such would be the relation of the body that affords the meteoric shower of ,november1 provided its revolution is accomplished in six months2 but it is still somewhat uncertain whether the period be half a year or a year2 it must be one or the other4 ,if we inquire1 now1 why the meteors always appear to radiate from a point in the constellation ,leo1 recollecting that this is the point to which the body is projected among the stars1 the answer is1 that this is the very point towards which the earth is moving in her orbit at that time2 so that if1 as we have proved1 the earth passed through or near a nebulous body on the thirteenth of ,november1 that body must necessarily have been projected into the constellation ,leo1 else it could not have lain directly in her path4 ,i consider it therefore as established by satisfactory proof1 that the meteors of ,november thirteenth emanate from a nebulous or cometary body1 revolving around the sun1 and coming so near the earth at that time that the earth passes through its skirts1 or extreme portions1 and thus attracts to itself some portions of its matter1 giving to the meteors a greater velocity than could be imparted by gravity alone1 in consequence of passing rapidly by them4 ,all these conclusions were made out by a process of reasoning strictly inductive1 without supposing that the meteoric body itself had ever been seen4 ,but there are some reasons for believing that we do actually see it1 and that it is no other than that mysterious appearance long known under the name of the zodiacal light4 ,this is a faint light1 which at certain seasons of the year appears in the west after evening twilight1 and at certain other seasons appears in the east before the dawn1 following or preceding the track of the sun in a triangular figure1 with its broad base next to the sun1 and its vertex reaching to a greater or less distance1 sometimes more than ninety degrees from that luminary4 ,you may obtain a good view of it in ,february or ,march1 in the west1 or in ,october1 in the morning sky4 ,the various changes which this light undergoes at different seasons of the year are such as to render it probable1 to my mind1 that this is the very body which affords the meteoric showers2 its extremity coming1 in ,november1 within the sphere of the earth's attraction4 ,but1 as the arguments for the existence of a body in the planetary regions1 which affords these showers1 were drawn without the least reference to the zodiacal light1 and are good1 should it finally be proved that this light has no connexion with them1 ,i will not occupy your attention with the discussion of this point1 to the exclusion of topics which will probably interest you more4 ,it is perhaps most probable1 that the meteoric showers of ,august and ,december emanate from the same body4 ,i know of nothing repugnant to this conclusion1 although it has not yet been distinctly made out4 ,had the periods of the earth and of the meteoric body been so adjusted to each other that the latter was contained an exact even number of times in the former2 that is1 had it been exactly either a year or half a year2 then we might expect a similar recurrence of the meteoric shower every year2 but only a slight variation in such a proportion between the two periods would occasion the repetition of the shower for a few years in succession1 and then an intermission of them1 for an unknown length of time1 until the two bodies were brought into the same relative situation as before4 ,disturbances1 also1 occasioned by the action of ,venus and ,mercury1 might wholly subvert this numerical relation1 and increase or diminish the probability of a repetition of the phenomenon4 ,accordingly1 from the year #ahcj1 when the meteoric shower of ,november was first observed1 until #ahcc1 there was a regular increase of the exhibition2 in #ahcc1 it came to its maximum2 and after that time it was repeated upon a constantly diminishing scale1 until #ahch1 since which time it has not been observed4 ,perhaps ages may roll away before the world will be again surprised and delighted with a display of celestial fire-works equal to that of the morning of ,november #ac1 #ahcc4 ,,letter ,,xxviii4 ,,fixed ,,stars4 ----,o1 majestic ,night6 ,nature's great ancestor6 ,day's elder born1 ,and fated to survive the transient sun6 ,by mortals and immortals seen with awe6 ,a starry crown thy raven brow adorns1 ,an azure zone thy waist2 clouds1 in heaven's loom ,wrought1 through varieties of shape and shade1 ,in ample folds of drapery divine1 ,thy flowing mantle form2 and heaven throughout ,voluminously pour thy pompous train4--,young4 ,,since the solar system is but one among a myriad of worlds which astronomy unfolds1 it may appear to you that ,i have dwelt too long on so diminutive a part of creation1 and reserved too little space for the other systems of the universe4 ,but however humble a province our sun and planets compose1 in the vast empire of ,jehovah1 yet it is that which most concerns us2 and it is by the study of the laws by which this part of creation is governed1 that we learn the secrets of the skies4 ,until recently1 the observation and study of the phenomena of the solar system almost exclusively occupied the labors of astronomers4 ,but ,sir ,william ,herschel gave his chief attention to the sidereal heavens1 and opened new and wonderful fields of discovery1 as well as of speculation4 ,the same subject1 has been prosecuted with similar zeal and success by his son1 ,sir ,john ,herschel1 and ,sir ,james ,south1 in ,england1 and by ,professor ,struve1 of ,dorpat1 until more has been actually achieved than preceding astronomers had ventured to conjecture4 ,a limited sketch of these wonderful discoveries is all that ,i propose to offer you4 ,the fixed stars are so called1 because1 to common observation1 they always maintain the same situations with respect to one another4 ,the stars are classed by their apparent magnitudes4 ,the whole number of magnitudes recorded are sixteen1 of which the first six only are visible to the naked eye2 the rest are telescopic stars4 ,these magnitudes are not determined by any very definite scale1 but are merely ranked according to their relative degrees of brightness1 and this is left in a great measure to the decision of the eye alone4 ,the brightest stars1 to the number of fifteen or twenty1 are considered as stars of the first magnitude2 the fifty or sixty next brightest1 of the second magnitude2 the next two hundred1 of the third magnitude2 and thus the number of each class increases rapidly1 as we descend the scale1 so that no less than fifteen or twenty thousand are included within the first seven magnitudes4 ,the stars have been grouped in constellations from the most remote antiquity2 a few1 as ,orion1 ,bootes1 and ,ursa ,major1 are mentioned in the most ancient writings1 under the same names as they bear at present4 ,the names of the constellations are sometimes founded on a supposed resemblance to the objects to which they belong2 as the ,swan and the ,scorpion were evidently so denominated from their likeness to those animals2 but in most cases1 it is impossible for us to find any reason for designating a constellation by the figure of the animal or hero which is employed to represent it4 ,these representations were probably once blended with the fables of pagan mythology4 ,the same figures1 absurd as they appear1 are still retained for the convenience of reference2 since it is easy to find any particular star1 by specifying the part of the figure to which it belongs2 as when we say1 a star is in the neck of ,taurus1 in the knee of ,hercules1 or in the tail of the ,great ,bear4 ,this method furnishes a general clue to its position2 but the stars belonging to any constellation are distinguished according to their apparent magnitudes1 as follows3 ,first1 by the ,greek letters1 ,alpha1 ,beta1 ,gamma1 c4 ,thus1 ,alpha ,orionis denotes the largest star in ,orion2 ,beta ,andromed the second star in ,andromeda2 and ,gamma ,leonis1 the third brightest star in the ,lion4 ,when the number of the ,greek letters is insufficient to include all the stars in a constellation1 recourse is had to the letters of the ,roman alphabet1 a1 b1 c1 c42 and in all cases where these are exhausted the final resort is to numbers4 ,this is evidently necessary1 since the largest constellations contain many hundreds or even thousands of stars4 ,catalogues of particular stars have also been published1 by different astronomers1 each author numbering the individual stars embraced in his list according to the places they respectively occupy in the catalogue4 ,these references to particular catalogues are sometimes entered on large celestial globes4 ,thus we meet with a star marked #hd ,h41 meaning that this is its number in ,herschel's catalogue2 or #adj ,m41 denoting the place the star occupies in the catalogue of ,mayer4 ,the earliest catalogue of the stars was made by ,hipparchus1 of the ,alexandrian school1 about one hundred and forty years before the ,christian era4 ,a new star appearing in the firmament1 he was induced to count the stars1 and to record their positions1 in order that posterity might be able to judge of the permanency of the constellations4 ,his catalogue contains all that were conspicuous to the naked eye in the latitude of ,alexandria1 being one thousand and twenty-two4 ,most persons1 unacquainted with the actual number of the stars which compose the visible firmament1 would suppose it to be much greater than this2 but it is found that the catalogue of ,hipparchus embraces nearly all that can now be seen in the same latitude2 and that on the equator1 where the spectator has both the northern and southern hemispheres in view1 the number of stars that can be counted does not exceed three thousand4 ,a careless view of the firmament in a clear night gives us the impression of an infinite number of stars2 but when we begin to count them1 they appear much more sparsely distributed than we supposed1 and large portions of the sky appear almost destitute of stars4 ,by the aid of the telescope1 new fields of stars present themselves1 of boundless extent2 the number continually augmenting1 as the powers of the telescope are increased4 ,lalande1 in his ',histoire ,celeste1' has registered the positions of no less than fifty thousand2 and the whole number visible in the largest telescopes amounts to many millions4 ,when you look at the firmament on a clear ,autumnal or ,winter evening1 it appears so thickly studded with stars1 that you would perhaps imagine that the task of learning even the brightest of them would be almost hopeless4 ,let me assure you1 this is all a mistake4 ,on the contrary1 it is a very easy task to become acquainted with the names and positions of the stars of the first magnitude1 and of the leading constellations4 ,if you will give a few evenings to the study1 you will be surprised to find1 both how rapidly you can form these new acquaintances1 and how deeply you will become interested in them4 ,i would advise you1 at first1 to obtain1 for an evening or two1 the assistance of some friend who is familiar with the stars1 just to point out a few of the most conspicuous constellations4 ,this will put you on the track1 and you will afterwards experience no difficulty in finding all the constellations and stars that are particularly worth knowing2 especially if you have before you a map of the stars1 or1 what is much better1 a celestial globe4 ,it is a pleasant evening recreation for a small company of young astronomers to go out together1 and learn one or two constellations every favorable evening1 until the whole are mastered4 ,if you have a celestial globe1 rectify it for the evening2 that is1 place it in such a position1 that the constellations shall be seen on it in the same position with respect to the horizon1 that they have at that moment in the sky itself4 ,to do this1 ,i first elevate the north pole until the number of degrees on the brass meridian from the pole to the horizon corresponds to my latitude1 7forty-one degrees and eighteen minutes47 ,i then find the sun's place in the ecliptic1 by looking for the day of the month on the broad horizon1 and against it noting the corresponding sign and degree4 ,i now find the same sign and degree on the ecliptic itself1 and bring that point to the brass meridian4 ,as that will be the position of the sun at noon1 ,i set the hour-index at twelve1 and then turn the globe westward1 until the index points to the given hour of the evening4 ,if ,i now inspect the figures of the constellations1 and then look upward at the firmament1 ,i shall see that the latter are spread over the sky in the same manner as the pictures of them are painted on the globe4 ,i will point out a few marks by which the leading constellations may be recognised2 this will aid you in finding them1 and you can afterwards learn the individual stars of a constellation1 to any extent you please1 by means of the globes or maps4 ,let us begin with the ,constellations of the ,zodiac1 which1 succeeding each other1 as they do1 in a known order1 are most easily found4 ,aries 7the ,ram7 is a small constellation1 known by two bright stars which form his head1 ,alpha and ,beta ,arietis4 ,these two stars are about four degrees apart2 and directly south of ,beta1 at the distance of one degree1 is a smaller star1 ,gamma ,arietis4 ,it has been already intimated that the ,vernal equinox probably was near the head of ,aries1 when the signs of the zodiac received their present names4 ,taurus 7the ,bull7 will be readily found by the seven stars1 or ,pleiades1 which lie in his neck4 ,the largest star in ,taurus is ,aldebaran1 in the ,bull's eye1 a star of the first magnitude1 of a reddish color1 somewhat resembling the planet ,mars4 ,aldebaran and four other stars1 close together in the face of ,taurus1 compose the ,hyades4 ,gemini 7the ,twins7 is known by two very bright stars1 ,castor and ,pollux1 five degrees asunder4 ,castor 7the northern7 is of the first1 and ,pollux of the second1 magnitude4 ,cancer 7the ,crab47 ,there are no large stars in this constellation1 and it is regarded as less remarkable than any other in the zodiac4 ,it contains1 however1 an interesting group of small stars1 called ,prsepe1 or the nebula of ,cancer1 which resembles a comet1 and is often mistaken for one1 by persons unacquainted with the stars4 ,with a telescope of very moderate powers this nebula is converted into a beautiful assemblage of exceedingly bright stars4 ,leo 7the ,lion7 is a very large constellation1 and has many interesting members4 ,regulus 7,alpha ,leonis7 is a star of the first magnitude1 which lies directly in the ecliptic1 and is much used in astronomical observations4 ,north of ,regulus1 lies a semicircle of bright stars1 forming a sickle1 of which ,regulus is the handle4 ,denebola1 a star of the second magnitude1 is in the ,lion's tail1 twenty-five degrees northeast of ,regulus4 ,virgo 7the ,virgin7 extends a considerable way from west to east1 but contains only a few bright stars4 ,spica1 however1 is a star of the first magnitude1 and lies a little east of the place of the ,autumnal equinox4 ,eighteen degrees eastward of ,denebola1 and twenty degrees north of ,spica1 is ,vindemiatrix1 in the arm of ,virgo1 a star of the third magnitude4 ,libra 7the ,balance7 is distinguished by three large stars1 of which the two brightest constitute the beam of the balance1 and the smallest forms the top or handle4 ,scorpio 7the ,scorpion7 is one of the finest of the constellations4 ,his head is formed of five bright stars1 arranged in the arc of a circle1 which is crossed in the centre by the ecliptic nearly at right angles1 near the brightest of the five1 ,beta ,scorpionis4 ,nine degrees southeast of this is a remarkable star of the first magnitude1 of a reddish color1 called ,cor ,scorpionis1 or ,antares4 ,south of this1 a succession of bright stars sweep round towards the east1 terminating in several small stars1 forming the tail of the ,scorpion4 ,sagittarius 7the ,archer47 ,northeast of the tail of the ,scorpion are three stars in the arc of a circle1 which constitute the bow of the ,archer1 the central star being the brightest1 directly west of which is a bright star which forms the arrow4 ,capricornus 7the ,goat7 lies northeast of ,sagittarius1 and is known by two bright stars1 three degrees apart1 which form the head4 ,aquarius 7the ,water-,bearer7 is recognised by two stars in a line with ,alpha ,capricorni1 forming the shoulders of the figure4 ,these two stars are ten degrees apart2 and three degrees southeast is a third star1 which1 together with the other two1 make an acute triangle1 of which the westernmost is the vertex4 ,pisces 7the ,fishes7 lie between ,aquarius and ,aries4 ,they are not distinguished by any large stars1 but are connected by a series of small stars1 that form a crooked line between them4 ,piscis ,australia1 the ,southern ,fish1 lies directly below ,aquarius1 and is known by a single bright star far in the south1 having a declination of thirty degrees4 ,the name of this star is ,fomalhaut1 and it is much used in astronomical measurements4 ,the constellations of the zodiac1 being first well learned1 so as to be readily recognised1 will facilitate the learning of others that lie north and south of them4 ,let us1 therefore1 next review the principal ,northern ,constellations1 beginning north of ,aries1 and proceeding from west to east4 ,andromeda is characterized by three stars of the second magnitude1 situated in a straight line1 extending from west to east4 ,the middle star is about seventeen degrees north of ,beta ,arietis4 ,it is in the girdle of ,andromeda1 and is named ,mirach4 ,the other two lie at about equal distances1 fourteen degrees west and east of ,mirach4 ,the western star1 in the head of ,andromeda1 lies in the equinoctial colure4 ,the eastern star1 ,alamak1 is situated in the foot4 ,perseus lies directly north of the ,pleiades1 and contains several bright stars4 ,about eighteen degrees from the ,pleiades is ,algol1 a star of the second magnitude1 in the head of ,medusa1 which forms a part of the figure2 and nine degrees northeast of ,algol is ,algenib1 of the same magnitude1 in the back of ,perseus4 ,between ,algenib and the ,pleiades are three bright stars1 at nearly equal intervals1 which compose the right leg of ,perseus4 ,auriga 7the ,wagoner7 lies directly east of ,perseus1 and extends nearly parallel to that constellation1 from north to south4 ,capella1 a very white and beautiful star of the first magnitude1 distinguishes this constellation4 ,the feet of ,auriga are near the ,bull's horns4 ,the ,lynx comes next1 but presents nothing particularly interesting1 containing no stars above the fourth magnitude4 ,leo ,minor consists of a collection of small stars north of the sickle in ,leo1 and south of the ,great ,bear4 ,its largest star is only of the third magnitude4 ,coma ,berenices is a cluster of small stars1 north of ,denebola1 in the tail of the ,lion1 and of the head of ,virgo4 ,about twelve degrees directly north of ,berenice's hair1 is a single bright star1 called ,cor ,caroli1 or ,charles's ,heart4 ,bootes1 which comes next1 is easily found by means of ,arcturus1 a star of the first magnitude1 of a reddish color1 which is situated near the knee of the figure4 ,arcturus is accompanied by three small stars1 forming a triangle a little to the southwest4 ,two bright stars1 ,gamma and ,delta ,bootis1 form the shoulders1 and ,beta1 of the third magnitude1 is in the head1 of the figure4 ,corona ,borealis1 7the ,crown17 which is situated east of ,bootes1 is very easily recognised1 composed as it is of a semicircle of bright stars4 ,in the centre of the bright crown is a star of the second magnitude1 called ,gemma3 the remaining stars are all much smaller4 ,hercules1 lying between the ,crown on the west and the ,lyre on the east1 is very thickly set with stars1 most of which are quite small4 ,this constellation covers a great extent of the sky1 especially from north to south1 the head terminating within fifteen degrees of the equator1 and marked by a star of the third magnitude1 called ,ras ,algethi1 which is the largest in the constellation4 ,ophiucus is situated directly south of ,hercules1 extending some distance on both sides of the equator1 the feet resting on the ,scorpion4 ,the head terminates near the head of ,hercules1 and1 like that1 is marked by a bright star within five degrees of ,alpha ,herculis ,ophiucus is represented as holding in his hands the ,serpent1 the head of which1 consisting of three bright stars1 is situated a little south of the ,crown4 ,the folds of the serpent will be easily followed by a succession of bright stars1 which extend a great way to the east4 ,aquila 7the ,eagle7 is conspicuous for three bright stars in its neck1 of which the central one1 ,altair1 is a very brilliant white star of the first magnitude4 ,antinous lies directly south of the ,eagle1 and north of the head of ,capricornus4 ,delphinus 7the ,dolphin7 is a small but beautiful constellation1 a few degrees east of the ,eagle1 and is characterized by four bright stars near to one another1 forming a small rhombic square4 ,another star of the same magnitude1 five degrees south1 makes the tail4 ,pegasus lies between ,aquarius on the southwest and ,andromeda on the northeast4 ,it contains but few large stars4 ,a very regular square of bright stars is composed of ,alpha ,andromed and the three largest stars in ,pegasus2 namely1 ,scheat1 ,markab1 and ,algenib4 ,the sides composing this square are each about fifteen degrees4 ,algenib is situated in the equinoctial colure4 ,we may now review the ,constellations which surround the north pole1 within the circle of perpetual apparition4 ,ursa ,minor 7the ,little ,bear7 lies nearest the pole4 ,the pole-star1 ,polaris1 is in the extremity of the tail1 and is of the third magnitude4 ,three stars in a straight line1 four degrees or five degrees apart1 commencing with the pole-star1 lead to a trapezium of four stars1 and the whole seven form together a dipper1--the trapezium being the body and the three stars the handle4 ,ursa ,major 7the ,great ,bear7 is situated between the pole and the ,lesser ,lion1 and is usually recognised by the figure of a larger and more perfect dipper which constitutes the hinder part of the animal4 ,this has also seven stars1 four in the body of the ,dipper and three in the handle4 ,all these are stars of much celebrity4 ,the two in the western side of the ,dipper1 ,alpha and ,beta1 are called ,pointers1 on account of their always being in a right line with the pole-star1 and therefore affording an easy mode of finding that4 ,the first star in the tail1 next the body1 is named ,alioth1 and the second1 ,mizar4 ,the head of the ,great ,bear lies far to the westward of the ,pointers1 and is composed of numerous small stars2 and the feet are severally composed of two small stars very near to each other4 ,draco 7the ,dragon7 winds round between the ,great and the ,little ,bear2 and1 commencing with the tail1 between the ,pointers and the pole-star1 it is easily traced by a succession of bright stars extending from west to east4 ,passing under ,ursa ,minor1 it returns westward1 and terminates in a triangle which forms the head of ,draco1 near the feet of ,hercules1 northwest of ,lyra4 ,cepheus lies eastward of the breast of the ,dragon1 but has no stars above the third magnitude4 ,cassiopeia is known by the figure of a chair1 composed of four stars which form the legs1 and two which form the back4 ,this constellation lies between ,perseus and ,cepheus1 in the ,milky ,way4 ,cygnus 7the ,swan7 is situated also in the ,milky ,way1 some distance southwest of ,cassiopeia1 towards the ,eagle4 ,three bright stars1 which lie along the ,milky ,way1 form the body and neck of the ,swan1 and two others1 in a line with the middle one of the three1 one above and one below1 constitute the wings4 ,this constellation is among the few that exhibit some resemblance to the animals whose names they bear4 ,lyra 7the ,lyre7 is directly west of the ,swan1 and is easily distinguished by a beautiful white star of the first magnitude1 ,alpha ,lyr4 ,the ,southern ,constellations are comparatively few in number4 ,i shall notice only the ,whale1 ,orion1 the ,greater and ,lesser ,dog1 ,hydra1 and the ,crow4 ,cetus 7the ,whale7 is distinguished rather for its extent than its brilliancy1 reaching as it does through forty degrees of longitude1 while none of its stars1 except one1 are above the third magnitude4 ,menkar 7,alpha ,ceti7 in the mouth1 is a star of the second magnitude2 and several other bright stars1 directly south of ,aries1 make the head and neck of the ,whale4 ,mira1 7,omicron ,ceti17 in the neck of the ,whale1 is a variable star4 ,orion is one of the largest and most beautiful of the constellations1 lying southeast of ,taurus4 ,a cluster of small stars forms the head2 two large stars1 ,betalgeus of the first and ,bellatrix of the second magnitude1 make the shoulders2 three more bright stars compose the buckler1 and three the sword2 and ,rigel1 another star of the first magnitude1 makes one of the feet4 ,in this constellation there are seventy stars plainly visible to the naked eye1 including two of the first magnitude1 four of the second1 and three of the third4 ,canis ,major lies southeast of ,orion1 and is distinguished chiefly by its containing the largest of the fixed stars1 ,sirius4 ,canis ,minor1 a little north of the equator1 between ,canis ,major and ,gemini1 is a small constellation1 consisting chiefly of two stars1 of which1 ,procyon is of the first magnitude4 ,hydra has its head near ,procyon1 consisting of a number of stars of ordinary brightness4 ,about fifteen degrees southeast of the head is a star of the second magnitude1 forming the heart1 7,cor ,hydr27 and eastward of this is a long succession of stars of the fourth and fifth magnitudes1 composing the body and tail1 and reaching a few degrees south of ,spica ,virginis4 ,corvus 7the ,crow7 is represented as standing on the tail of ,hydra4 ,it consists of small stars1 only three of which are as large as the third magnitude4 ,in assigning the places of individual stars1 ,i have not aimed at great precision2 but such a knowledge as you will acquire of the constellations and larger stars1 by nothing more even than you can obtain from the foregoing sketch1 will not only add greatly to the interest with which you will ever afterwards look at the starry heavens1 but it will enable you to locate any phenomenon that may present itself in the nocturnal sky1 and to understand the position of any object that may be described1 by assigning its true place among the stars2 although ,i hope you will go much further than this mere outline1 in cultivating an actual acquaintance with the stars4 ,leaving1 now1 these great divisions of the bodies of the firmament1 let us ascend to the next order of stars1 composing ,,clusters4 ,in various parts of the nocturnal heavens are seen large groups which1 either by the naked eye1 or by the aid of the smallest telescope1 are perceived to consist of a great number of small stars4 ,such are the ,pleiades1 ,coma ,berenices1 and ,prsepe1 or the ,bee-hive1 in ,cancer4 ,the ,pleiades1 or ,seven ,stars1 as they are called1 in the neck of ,taurus1 is the most conspicuous cluster4 ,when we look directly at this group1 we cannot distinguish more than six stars2 but by turning the eye sideways upon it1 we discover that there are many more2 for it is a remarkable fact that indirect vision is far more delicate than direct4 ,thus we can see the zodiacal light or a comet's tail much more distinctly and better defined1 if we fix one eye on a part of the heavens at some distance and turn the other eye obliquely upon the object1 than we can by looking directly towards it4 ,telescopes show the ,pleiades to contain fifty or sixty stars1 crowded together1 and apparently insulated from the other parts of the heavens4 ,coma ,berenices has fewer stars1 but they are of a larger class than those which compose the ,pleiades4 ,the ,bee-hive1 or ,nebula of ,cancer1 as it is called1 is one of the finest objects of this kind for a small telescope1 being by its aid converted into a rich congeries of shining points4 ,the head of ,orion affords an example of another cluster1 though less remarkable than those already mentioned4 ,these clusters are pleasing objects to the telescope2 and since a common spyglass will serve to give a distinct view of most of them1 every one may have the power of taking the view4 ,but we pass1 now1 to the third order of stars1 which present themselves much more obscurely to the gaze of the astronomer1 and require large instruments for the full developement of their wonderful organization4 ,these are the ,,nebul4 ,illustration ,figures #gj1 #ga1 #gb1 #gc4 ,,clusters ,,of ,,stars ,,and ,,nebul4 ,nebul are faint misty appearances which are dimly seen among the stars1 resembling comets1 or a speck of fog4 ,they are usually resolved by the telescope into myriads of small stars2 though in some instances1 no powers of the telescope have been found sufficient thus to resolve them4 ,the ,galaxy or ,milky ,way1 presents a continued succession of large nebulas4 ,the telescope reveals to us innumerable objects of this kind4 ,sir ,william ,herschel has given catalogues of two thousand nebul1 and has shown that the nebulous matter is distributed through the immensity of space in quantities inconceivably great1 and in separate parcels1 of all shapes and sizes1 and of all degrees of brightness between a mere milky appearance and the condensed light of a fixed star4 ,in fact1 more distinct nebul have been hunted out by the aid of telescopes than the whole number of stars visible to the naked eye in a clear ,winter's night4 ,their appearances are extremely diversified4 ,in many of them we can easily distinguish the individual stars2 in those apparently more remote1 the interval between the stars diminishes1 until it becomes quite imperceptible2 and in their faintest aspect they dwindle to points so minute1 as to be appropriately denominated star-dust4 ,beyond this1 no stars are distinctly visible1 but only streaks or patches of milky light4 ,the diagram facing page #cgi represents a magnificent nebula in the ,galaxy4 ,in objects so distant as the fixed stars1 any apparent interval must denote an immense space2 and just imagine yourself situated any where within the grand assemblage of stars1 and a firmament would expand itself over your head like that of our evening sky1 only a thousand times more rich and splendid4 ,many of the nebul exhibit a tendency towards a globular form1 and indicate a rapid condensation towards the centre4 ,this characteristic is exhibited in the forms represented in ,figs4 #gj and #ga4 ,we have here two specimens of nebul of the nearer class1 where the stars are easily discriminated4 ,in ,figs4 #gb and #gc we have examples of two others of the remoter kind1 one of which is of the variety called star-dust4 ,these wonderful objects1 however1 are not confined to the spherical form1 but exhibit great varieties of figure4 ,sometimes they appear as ovals2 sometimes they are shaped like a fan2 and the unresolvable kind often affect the most fantastic forms4 ,the opposite diagram1 ,fig4 #gd1 as well as the preceding1 affords a specimen of these varieties1 as given in ,professor ,nichols's ',architecture of the ,heavens1' where they are faithfully copied from the papers of ,herschel1 in the ',philosophical ,transactions4' ,illustration ,figure #gd4 ,,various ,,forms ,,of ,,nebul4 ,sir ,john ,herschel has recently returned from a residence of five years at the ,cape of ,good ,hope1 with the express view of exploring the hidden treasures of the southern hemisphere4 ,the kinds of nebul are in general similar to those of the northern hemisphere1 and the forms are equally various and singular4 ,the ,magellan ,clouds1 two remarkable objects seen among the stars of that hemisphere1 and celebrated among navigators1 appeared to the great telescope of ,herschel 7as we are informed by ,professor ,nichols7 no longer as simple milky spots1 or permanent light flocculi of cloud1 as they appear to the unassisted eye1 but shone with inconceivable splendor4 ,the ,nubecula ,major1 as the larger object is called1 is a congeries of clusters of stars1 of irregular form1 globular clusters and nebul of various magnitudes and degrees of condensation1 among which is interspersed a large portion of irresolvable nebulous matter1 which may be1 and probably is1 star-dust1 but which the power of the twenty-feet telescope shows only as a general illumination of the field of view1 forming a bright ground on which the other objects are scattered4 ,the ,nubecula ,minor 7the lesser cloud7 exhibited appearances similar1 though inferior in degree4 ,illustration ,figure #ge4 ,a ,,nebula ,,in ,,the ,,milky ,,way4 ,it is a grand idea1 first conceived by ,sir ,william ,herschel1 and generally adopted by astronomers1 that the whole ,galaxy1 or ,milky ,way1 is nothing else than a nebula1 and appears so extended1 merely because it happens to be that particular nebula to which we belong4 ,according to this view1 our sun1 with his attendant planets and comets1 constitutes but a single star of the ,galaxy1 and our firmament of stars1 or visible heavens1 is composed of the stars of our nebula alone4 ,an inhabitant of any of the other nebul would see spreading over him a firmament equally spacious1 and in some cases inconceivably more brilliant4 ,it is an exalted spectacle to travel over the ,galaxy in a clear night1 with a powerful telescope1 with the heart full of the idea that every star is a world4 ,sir ,william ,herschel1 by counting the stars in a single field of his telescope1 estimated that fifty thousand had passed under his review in a zone two degrees in breadth1 during a single hour's observation4 ,notwithstanding the apparent contiguity of the stars which crowd the ,galaxy1 it is certain that their mutual distances must be inconceivably great4 ,it is with some reluctance that ,i leave1 for the present1 this fairy land of astronomy2 but ,i must not omit1 before bringing these ,letters to a conclusion1 to tell you something respecting other curious and interesting objects to be found among the stars4 ,,variable ,,stars are those which undergo a periodical change of brightness4 ,one of the most remarkable is the star ,mira1 in the ,whale1 7,omicron ,ceti47 ,it appears once in eleven months1 remains at its greatest brightness about a fortnight1 being then1 on some occasions1 equal to a star of the second magnitude4 ,it then decreases about three months1 until it becomes completely invisible1 and remains so about five months1 when it again becomes visible1 and continues increasing during the remaining three months of its period4 ,another very remarkable variable star is ,algol1 7,beta ,persei47 ,it is usually visible as a star of the second magnitude1 and continues such for two days and fourteen hours1 when it suddenly begins to diminish in splendor1 and in about three and a half hours is reduced to the fourth magnitude4 ,it then begins again to increase1 and in three and a half hours more is restored to its usual brightness1 going through all its changes in less than three days4 ,this remarkable law of variation appears strongly to suggest the revolution round it of some opaque body1 which1 when interposed between us and ,algol1 cuts off a large portion of its light4 ,it is1 says ,sir ,j4 ,herschel1 an indication of a high degree of activity in regions where1 but for such evidences1 we might conclude all lifeless4 ,our sun requires almost nine times this period to perform a revolution on its axis4 ,on the other hand1 the periodic time of an opaque revolving body1 sufficiently large1 which would produce a similar temporary obscuration of the sun1 seen from a fixed star1 would be less than fourteen hours4 ,the duration of these periods is extremely various4 ,while that of ,beta ,persei1 above mentioned1 is less than three days1 others are more than a year2 and others1 many years4 ,,temporary ,,stars are new stars1 which have appeared suddenly in the firmament1 and1 after a certain interval1 as suddenly disappeared1 and returned no more4 ,it was the appearance of a new star of this kind1 one hundred and twenty-five years before the ,christian era1 that prompted ,hipparchus to draw up a catalogue of the stars1 the first on record4 ,such1 also1 was the star which suddenly shone out1 ,a4,d4 #chi1 in the ,eagle1 as bright as ,venus1 and1 after remaining three weeks1 disappeared entirely4 ,at other periods1 at distant intervals1 similar phenomena have presented themselves4 ,thus the appearance of a star in #aegb was so sudden1 that ,tycho ,brahe1 returning home one day1 was surprised to find a collection of country people gazing at a star which he was sure did not exist half an hour before4 ,it was then as bright as ,sirius1 and continued to increase until it surpassed ,jupiter when brightest1 and was visible at mid-day4 ,in a month it began to diminish2 and1 in three months afterwards1 it had entirely disappeared4 ,it has been supposed by some that1 in a few instances1 the same star has returned1 constituting one of the periodical or variable stars of a long period4 ,moreover1 on a careful reexamination of the heavens1 and a comparison of catalogues1 many stars are now discovered to be missing4 ,,double ,,stars are those which appear single to the naked eye1 but are resolved into two by the telescope2 or1 if not visible to the naked eye1 are seen in the telescope so close together as to be recognised as objects of this class4 ,sometimes1 three or more stars are found in this near connexion1 constituting triple1 or multiple stars4 ,castor1 for example1 when seen by the naked eye1 appears as a single star1 but in a telescope even of moderate powers1 it is resolved into two stars1 of between the third and fourth magnitudes1 within five seconds of each other4 ,these two stars are nearly of equal size2 but more commonly1 one is exceedingly small in comparison with the other1 resembling a satellite near its primary1 although in distance1 in light1 and in other characteristics1 each has all the attributes of a star1 and the combination1 therefore1 cannot be that of a planet with a satellite4 ,in most instances1 also1 the distance between these objects is much less than five seconds2 and1 in many cases1 it is less than one second4 ,the extreme closeness1 together with the exceeding minuteness1 of most of the double stars1 requires the best telescopes united with the most acute powers of observation4 ,indeed1 certain of these objects are regarded as the severest tests both of the excellence of the instruments and of the skill of the observer4 ,the diagram on page #chb1 ,fig4 #gf1 represents four double stars1 as seen with appropriate magnifiers4 ,no4 #a1 exhibits ,epsilon ,bootis with a power of three hundred and fifty2 ,no4 #b1 ,rigel1 with a power of one hundred and thirty2 ,no4 #c1 the ,pole-star1 with a power of one hundred2 and ,no4 #d1 ,castor1 with a power of three hundred4 ,our knowledge of the double stars almost commenced with ,sir ,william ,herschel1 about the year #aghj4 ,at the time he began his search for them1 he was acquainted with only four4 ,within five years he discovered nearly seven hundred double stars1 and during his life1 he observed no less than twenty-four hundred4 ,in his ,memoirs1 published in the ,philosophical ,transactions1 he gave most accurate measurements of the distances between the two stars1 and of the angle which a line joining the two formed with a circle parallel to the equator4 ,these data would enable him1 or at least posterity1 to judge whether these minute bodies ever change their position with respect to each other4 ,since #ahba1 these researches have been prosecuted1 with great zeal and industry1 by ,sir ,james ,south and ,sir ,john ,herschel1 in ,england2 while ,professor ,struve1 of ,dorpat1 with the celebrated telescope of ,fraunhofer1 has published1 from his own observations1 a catalogue of three thousand double stars1 the determination of which involved the distinct and most minute inspection of at least one hundred and twenty thousand stars4 ,sir ,john ,herschel1 in his recent survey of the southern hemisphere1 is said to have added to the catalogue of double stars nearly three thousand more4 ,illustration ,fig4 #gf4 ,two circumstances add a high degree of interest to the phenomena of double stars3 the first is1 that a few of them1 at least1 are found to have a revolution around each other2 the second1 that they are supposed to afford the means of ascertaining the parallax of the fixed stars4 ,but ,i must defer these topics till my next ,letter4 ,,letter ,,xxix4 ,,fixed ,,stars ,,continued4 ,o how canst thou renounce the boundless store ,of charms that ,nature to her votary yields8 ,the warbling woodland1 the resounding shore1 ,the pomp of groves1 and garniture of fields2 ,all that the genial ray of morning yields1 ,and all that echoes to the song of even1 ,all that the mountain's sheltering bosom shields1 ,and all the dread magnificence of heaven1-- ,o how canst thou renounce1 and hope to be forgiven6--,beattie4 ,in #ahjc1 ,sir ,william ,herschel first determined and announced to the world1 that there exist among the stars separate systems1 composed of two stars revolving about each other in regular orbits4 ,these he denominated binary stars1 to distinguish them from other double stars where no such motion is detected1 and whose proximity to each other may possibly arise from casual juxtaposition1 or from one being in the range of the other4 ,between fifty and sixty instances of changes1 to a greater or less amount1 of the relative positions of double stars1 are mentioned by ,sir ,william ,herschel2 and a few of them had changed their places so much1 within twenty-five years1 and in such order1 as to lead him to the conclusion that they performed revolutions1 one around the other1 in regular orbits4 ,these conclusions have been fully confirmed by later observers2 so that it is now considered as fully established1 that there exist among the fixed stars binary systems1 in which two stars perform to each other the office of sun and planet1 and that the periods of revolution of more than one such pair have been ascertained with some degree of exactness4 ,immersions and emersions of stars behind each other have been observed1 and real motions among them detected1 rapid enough to become sensible and measurable in very short intervals of time4 ,the periods of the double stars are very various1 ranging1 in the case of those already ascertained1 from forty-three years to one thousand4 ,their orbits are very small ellipses1 only a few seconds in the longest direction1 and more eccentric than those of the planets4 ,a double star in the ,northern ,crown 7,eta ,coron7 has made a complete revolution since its first discovery1 and is now far advanced in its second period2 while a star in the ,lion 7,gamma ,leonis7 requires twelve hundred years to complete its circuit4 ,you may not at once see the reason why these revolutions of one member of a double star around the other1 should be deemed facts of such extraordinary interest2 to you they may appear rather in the light of astronomical curiosities4 ,but remark1 that the revolutions of the binary stars have assured us of this most interesting fact1 that the law of gravitation extends to the fixed stars4 ,before these discoveries1 we could not decide1 except by a feeble analogy1 that this law transcended the bounds of the solar system4 ,indeed1 our belief of the fact rested more upon our idea of unity of design in the works of the ,creator1 than upon any certain proof2 but the revolution of one star around another1 in obedience to forces which are proved to be similar to those which govern the solar system1 establishes the grand conclusion1 that the law of gravitation is truly the law of the material universe4 ,we have the same evidence1 says ,sir ,john ,herschel1 of the revolutions of the binary stars about each other1 that we have of those of ,saturn and ,uranus about the sun2 and the correspondence between their calculated and observed places1 in such elongated ellipses1 must be admitted to carry with it a proof of the prevalence of the ,newtonian law of gravity in their systems1 of the very same nature and cogency as that of the calculated and observed places of comets round the centre of our own system4 ,but it is not with the revolution of bodies of a cometary or planetary nature round a solar centre1 that we are now concerned2 it is with that of sun around sun1 each1 perhaps1 accompanied with its train of planets and their satellites1 closely shrouded from our view by the splendor of their respective suns1 and crowded into a space1 bearing hardly a greater proportion to the enormous interval which separates them1 than the distances of the satellites of our planets from their primaries bear to their distances from the sun itself4 ,many of the double stars are of different colors2 and ,sir ,john ,herschel is of the opinion that there exist in nature suns of different colors4 ,it may1 says he1 be easier suggested in words than conceived in imagination1 what variety of illumination two suns1 a red and a green1 or a yellow and a blue one1 must afford to a planet circulating about either2 and what charming contrasts and 'grateful vicissitudes' a red and a green day1 for instance1 alternating with a white one and with darkness1 might arise from the presence or absence of one or other or both above the horizon4 ,insulated stars of a red color1 almost as deep as that of blood1 occur in many parts of the heavens2 but no green or blue star1 of any decided hue1 has ever been noticed unassociated with a companion brighter than itself4 ,beside these revolutions of the binary stars1 some of the fixed stars appear to have a real motion in space4 ,there are several apparent changes of place among the stars1 arising from real changes in the earth1 which1 as we are not conscious of them1 we refer to the stars2 but there are other motions among the stars which cannot result from any changes in the earth1 but must arise from changes in the stars themselves4 ,such motions are called the proper motions of the stars4 ,nearly two thousand years ago1 ,hipparchus and ,ptolemy made the most accurate determinations in their power of the relative situations of the stars1 and their observations have been transmitted to us in ,ptolemy's ',almagest2' from which it appears that the stars retain at least very nearly the same places now as they did at that period4 ,still1 the more accurate methods of modern astronomers have brought to light minute changes in the places of certain stars1 which force upon us the conclusion1 either that our solar system causes an apparent displacement of certain stars1 by a motion of its own in space1 or that they have themselves a proper motion4 ,possibly1 indeed1 both these causes may operate4 ,if the sun1 and of course the earth which accompanies him1 is actually in motion1 the fact may become manifest from the apparent approach of the stars in the region which he is leaving1 and the recession of those which lie in the part of the heavens towards which he is travelling4 ,were two groves of trees situated on a plain at some distance apart1 and we should go from one to the other1 the trees before us would gradually appear further and further asunder1 while those we left behind would appear to approach each other4 ,some years since1 ,sir ,william ,herschel supposed he had detected changes of this kind among two sets of stars in opposite points of the heavens1 and announced that the solar system was in motion towards a point in the constellation ,hercules2 but other astronomers have not found the changes in question such as would correspond to this motion1 or to any motion of the sun2 and1 while it is a matter of general belief that the sun has a motion in space1 the fact is not considered as yet entirely proved4 ,in most cases1 where a proper motion in certain stars has been suspected1 its annual amount has been so small1 that many years are required to assure us1 that the effect is not owing to some other cause than a real progressive motion in the stars themselves2 but in a few instances the fact is too obvious to admit of any doubt4 ,thus1 the two stars1 #fa ,cygni1 which are nearly equal1 have remained constantly at the same or nearly at the same distance of fifteen seconds1 for at least fifty years past4 ,mean-while1 they have shifted their local situation in the heavens four minutes twenty-three seconds1 the annual proper motion of each star being five seconds and three tenths1 by which quantity this system is every year carried along in some unknown path1 by a motion which for many centuries must be regarded as uniform and rectilinear4 ,a greater proportion of the double stars than of any other indicate proper motions1 especially the binary stars1 or those which have a revolution around each other4 ,among stars not double1 and no way differing from the rest in any other obvious particular1 a star in the constellation ,cassiopeia1 7,mu ,cassiopei7 has the greatest proper motion of any yet ascertained1 amounting to nearly four seconds annually4 ,you have doubtless heard much respecting the immeasurable distances of the fixed stars1 and will desire to learn what is known to astronomers respecting this interesting subject4 ,we cannot ascertain the actual distance of any of the fixed stars1 but we can certainly determine that the nearest star is more than twenty millions of millions of miles from the earth1 7#bj1jjj1jjj1jjj1jjj47 ,for all measurements relating to the distances of the sun and planets1 the radius of the earth furnishes the base line4 ,the length of this line being known1 and the horizontal parallax of the sun or any planet1 we have the means of calculating the distance of the body from us1 by methods explained in a previous ,letter4 ,but any star1 viewed from the opposite sides of the earth1 would appear from both stations to occupy precisely the same situation in the celestial sphere1 and of course it would exhibit no horizontal parallax4 ,but astronomers have endeavored to find a parallax in some of the fixed stars1 by taking the diameter of the earth's orbit as a base line4 ,yet even a change of position amounting to one hundred and ninety millions of miles proved1 until very recently1 insufficient to alter the place of a single star1 so far as to be capable of detection by very refined observations2 from which it was concluded that the stars have not even any annual parallax2 that is1 the angle subtended by the semidiameter of the earth's orbit1 at the nearest fixed star1 is insensible4 ,the errors to which instrumental measurements are subject1 arising from the defects of instruments themselves1 from refraction1 and from various other sources of inaccuracy1 are such1 that the angular determinations of arcs of the heavens cannot be relied on to less than one second1 and therefore cannot be appreciated by direct measurement4 ,it follows1 that1 when viewed from the nearest star1 the diameter of the earth's orbit would be insensible2 the spider-line of the telescope would more than cover it4 ,taking1 however1 the annual parallax of a fixed star at one second1 it can be demonstrated1 that the distance of the nearest fixed star must exceed #iejjjjjj #bjjjjj #aijjjjjjj #ajjjjj1 or one hundred thousand times one hundred and ninety millions of miles4 ,of a distance so vast we can form no adequate conceptions1 and even seek to measure it only by the time that light 7which moves more than one hundred and ninety-two thousand miles per second1 and passes from the sun to the earth in eight minutes and seven seconds7 would take to traverse it1 which is found to be more than three and a half years4 ,if these conclusions are drawn with respect to the largest of the fixed stars1 which we suppose to be vastly nearer to us than those of the smallest magnitude1 the idea of distance swells upon us when we attempt to estimate the remoteness of the latter4 ,as it is uncertain1 however1 whether the difference in the apparent magnitudes of the stars is owing to a real difference1 or merely to their being at various distances from the eye1 more or less uncertainty must attend all efforts to determine the relative distances of the stars2 but astronomers generally believe1 that the lower orders of stars are vastly more distant from us than the higher4 ,of some stars it is said1 that thousands of years would be required for their light to travel down to us4 ,i have said that the stars have always been held1 until recently1 to have no annual parallax2 yet it may be observed that astronomers were not exactly agreed on this point4 ,dr4 ,brinkley1 a late eminent ,irish astronomer1 supposed that he had detected an annual parallax in ,alpha ,lyr1 amounting to one second and thirteen hundreths1 and in ,alpha ,aquil1 of one second and forty-two hundreths4 ,these results were controverted by ,mr4 ,pond1 of the ,royal ,observatory of ,greenwich2 and ,mr4 ,struve1 of ,dorpat1 has shown that1 in a number of cases1 the supposed parallax is in a direction opposite to that which would arise from the motion of the earth4 ,hence it is considered doubtful whether1 in all cases of an apparent parallax1 the effect is not wholly due to errors of observation4 ,but as if nothing was to be hidden from our times1 the long sought for parallax among the fixed stars has at length been found1 and consequently the distance of some of these bodies1 at least1 is no longer veiled in mystery4 ,in the year #ahch1 ,professor ,bessel1 of ,kningsberg1 announced the discovery of a parallax in one of the stars of the ,swan1 7#fa ,cygni17 amounting to about one third of a second4 ,this seems1 indeed1 so small an angle1 that we might have reason to suspect the reality of the determination2 but the most competent judges who have thoroughly examined the process by which the discovery was made1 assent to its validity4 ,what1 then1 do astronomers understand1 when they say that a parallax has been discovered in one of the fixed stars1 amounting to one third of a second8 ,they mean that the star in question apparently shifts its place in the heavens1 to that amount1 when viewed at opposite extremities of the earth's orbit1 namely1 at points in space distant from each other one hundred and ninety millions of miles4 ,on calculating the distance of the star from us from these data1 it is found to be six hundred and fifty-seven thousand seven hundred times ninety-five millions of miles1--a distance which it would take light more than ten years to traverse4 ,indirect methods have been proposed1 for ascertaining the parallax of the fixed stars1 by means of observations on the double stars4 ,if the two stars composing a double star are at different distances from us1 parallax would affect them unequally1 and change their relative positions with respect to each other2 and since the ordinary sources of error arising from the imperfection of instruments1 from precession1 and from refraction1 would be avoided1 7as they would affect both objects alike1 and therefore would not disturb their relative positions17 measurements taken with the micrometer of changes much less than one second may be relied on4 ,sir ,john ,herschel proposed a method1 by which changes may be determined that amount to only one fortieth of a second4 ,the immense distance of the fixed stars is inferred also from the fact1 that the largest telescopes do not increase their apparent magnitude4 ,they are still points1 when viewed with glasses that magnify five thousand times4 ,with respect to the ,,nature ,,of ,,the ,,stars1 it would seem fruitless to inquire into the nature of bodies so distant1 and which reveal themselves to us only as shining points in space4 ,still1 there are a few very satisfactory inferences that can be made out respecting them4 ,first1 the fixed stars are bodies greater than our earth4 ,if this were not the case1 they would not be visible at such an immense distance4 ,dr4 ,wollaston1 a distinguished ,english philosopher1 attempted to estimate the magnitudes of certain of the fixed stars from the light which they afford4 ,by means of an accurate photometer1 7an instrument for measuring the relative intensities of light17 he compared the light of ,sirius with that of the sun4 ,he next inquired how far the sun must be removed from us1 in order to appear no brighter than ,sirius4 ,he found the distance to be one hundred and forty-one thousand times its present distance4 ,but ,sirius is more than two hundred thousand times as far off as the sun2 hence he inferred that1 upon the lowest computation1 it must actually give out twice as much light as the sun2 or that1 in point of splendor1 ,sirius must be at least equal to two suns4 ,indeed1 he has rendered it probable1 that its light is equal to that of fourteen suns4 ,there is reason1 however1 to believe that the stars are actually of various magnitudes1 and that their apparent difference is not owing merely to their different distances4 ,bessel estimates the quantity of matter in the two members of a double star in the ,swan1 as less than half that of the sun4 ,secondly1 the fixed stars are suns4 ,we have already seen that they are large bodies2 that they are immensely further off than the furthest planet2 that they shine by their own light2 in short1 that their appearance is1 in all respects1 the same as the sun would exhibit if removed to the region of the stars4 ,hence we infer that they are bodies of the same kind with the sun4 ,we are justified1 therefore1 by a sound analogy1 in concluding that the stars were made for the same end as the sun1 namely1 as the centres of attraction to other planetary worlds1 to which they severally dispense light and heat4 ,although the starry heavens present1 in a clear night1 a spectacle of unrivalled grandeur and beauty1 yet it must be admitted that the chief purpose of the stars could not have been to adorn the night1 since by far the greater part of them are invisible to the naked eye2 nor as landmarks to the navigator1 for only a very small proportion of them are adapted to this purpose2 nor1 finally1 to influence the earth by their attractions1 since their distance renders such an effect entirely insensible4 ,if they are suns1 and if they exert no important agencies upon our world1 but are bodies evidently adapted to the same purpose as our sun1 then it is as rational to suppose that they were made to give light and heat1 as that the eye was made for seeing and the ear for hearing4 ,it is obvious to inquire1 next1 to what they dispense these gifts1 if not to planetary worlds2 and why to planetary worlds1 if not for the use of percipient beings8 ,we are thus led1 almost inevitably1 to the idea of a plurality of worlds2 and the conclusion is forced upon us1 that the spot which the ,creator has assigned to us is but a humble province in his boundless empire4 ,,letter ,,xxx4 ,,system ,,of ,,the ,,world ,o how unlike the complex works of man1 ,heaven's easy1 artless1 unincumbered1 plan4--,cowper4 ,,having now explained to you1 as far as ,i am able to do it in so short a space1 the leading phenomena of the heavenly bodies1 it only remains to inform you of the different systems of the world which have prevailed in different ages1--a subject which will necessarily involve a sketch of the history of astronomy4 ,by a system of the world1 ,i understand an explanation of the arrangement of all the bodies that compose the material universe1 and of their relations to each other4 ,it is otherwise called the ',mechanism of the ,heavens2' and indeed1 in the system of the world1 we figure to ourselves a machine1 all parts of which have a mutual dependence1 and conspire to one great end4 ,the machines that were first invented1 says ,adam ,smith1 to perform any particular movement1 are always the most complex2 and succeeding artists generally discover that1 with fewer wheels1 and with fewer principles of motion1 than had originally been employed1 the same effects may be more easily produced4 ,the first systems1 in the same manner1 are always the most complex2 and a particular connecting chain or principle is generally thought necessary1 to unite every two seemingly disjointed appearances2 but it often happens1 that one great connecting principle is afterwards found to be sufficient to bind together all the discordant phenomena that occur in a whole species of things6 ,this remark is strikingly applicable to the origin and progress of systems of astronomy4 ,it is a remarkable fact in the history of the human mind1 that astronomy is the oldest of the sciences1 having been cultivated1 with no small success1 long before any attention was paid to the causes of the common terrestrial phenomena4 ,the opinion has always prevailed among those who were unenlightened by science1 that very extraordinary appearances in the sky1 as comets1 fiery meteors1 and eclipses1 are omens of the wrath of heaven4 ,they have1 therefore1 in all ages1 been watched with the greatest attention3 and their appearances have been minutely recorded by the historians of the times4 ,the idea1 moreover1 that the aspects of the stars are connected with the destinies of individuals and of empires1 has been remarkably prevalent from the earliest records of history down to a very late period1 and1 indeed1 still lingers among the uneducated and credulous4 ,this notion gave rise to ,,astrology1--an art which professed to be able1 by a knowledge of the varying aspects of the planets and stars1 to penetrate the veil of futurity1 and to foretel approaching irregularities of ,nature herself1 and the fortunes of kingdoms and of individuals4 ,that department of astrology which took cognizance of extraordinary occurrences in the natural world1 as tempests1 earthquakes1 eclipses1 and volcanoes1 both to predict their approach and to interpret their meaning1 was called natural astrology3 that which related to the fortunes of men and of empires1 judicial astrology4 ,among many ancient nations1 astrologers were held in the highest estimation1 and were kept near the persons of monarchs2 and the practice of the art constituted a lucrative profession throughout the middle ages4 ,nor were the ignorant and uneducated portions of society alone the dupes of its pretensions4 ,hippocrates1 the ',father of ,medicine1' ranks astrology among the most important branches of knowledge to the physician2 and ,tycho ,brahe1 and ,lord ,bacon1 were firm believers in its mysteries4 ,astrology1 fallacious as it was1 must be acknowledged to have rendered the greatest services to astronomy1 by leading to the accurate observation and diligent study of the stars4 ,at a period of very remote antiquity1 astronomy was cultivated in ,china1 ,india1 ,chaldea1 and ,egypt4 ,the ,chaldeans were particularly distinguished for the accuracy and extent of their astronomical observations4 ,calisthenes1 the ,greek philosopher who accompanied ,alexander the ,great in his ,eastern conquests1 transmitted to ,aristotle a series of observations made at ,babylon nineteen centuries before the capture of that city by ,alexander2 and the wise men of ,babylon and the ,chaldean astrologers are referred to in the ,sacred ,writings4 ,they enjoyed a clear sky and a mild climate1 and their pursuits as shepherds favored long-continued observations2 while the admiration and respect accorded to the profession1 rendered it an object of still higher ambition4 ,in the seventh century before the ,christian era1 astronomy began to be cultivated in ,greece2 and there arose successively three celebrated astronomical schools1--the school of ,miletus1 the school of ,crotona1 and the school of ,alexandria4 ,the first was established by ,thales1 six hundred and forty years before ,christ2 the second1 by ,pythagoras1 one hundred and forty years afterwards2 and the third1 by the ,ptolemies of ,egypt1 about three hundred years before the ,christian era4 ,as ,egypt and ,babylon were renowned among the most ancient nations1 for their knowledge of the sciences1 long before they were cultivated in ,greece1 it was the practice of the ,greeks1 when they aspired to the character of philosophers and sages1 to resort to these countries to imbibe wisdom at its fountains4 ,thales1 after extensive travels in ,crete and ,egypt1 returned to his native place1 ,miletus1 a town on the coast of ,asia ,minor1 where he established the first school of astronomy in ,greece4 ,although the minds of these ancient astronomers were beclouded with much error1 yet ,thales taught a few truths which do honor to his sagacity4 ,he held that the stars are formed of fire2 that the moon receives her light from the sun1 and is invisible at her conjunctions because she is hid in the sun's rays4 ,he taught the sphericity of the earth1 but adopted the common error of placing it in the centre of the world4 ,he introduced the division of the sphere into five zones1 and taught the obliquity of the ecliptic4 ,he was acquainted with the ,saros1 or sacred period of the ,chaldeans1 7see page #aib17 and employed it in calculating eclipses4 ,it was ,thales that predicted the famous eclipse of the sun which terminated the war between the ,lydians and the ,medes1 as mentioned in a former ,letter4 ,indeed1 ,thales is universally regarded as a bright but solitary star1 glimmering through mists on the distant horizon4 ,to ,thales succeeded1 in the school of ,miletus1 two other astronomers of much celebrity1 ,anaximander and ,anaxagoras4 ,among many absurd things held by ,anaximander1 he first taught the sublime doctrine that the planets are inhabited1 and that the stars are suns of other systems4 ,anaxagoras attempted to explain all the secrets of the skies by natural causes4 ,his reasonings1 indeed1 were alloyed with many absurd notions2 but still he alone1 among the astronomers1 maintained the existence of one ,god4 ,his doctrines alarmed his countrymen1 by their audacity and impiety to their gods1 whose prerogatives he was thought to invade2 and1 to deprecate their wrath1 sentence of death was pronounced on the philosopher and all his family1--a sentence which was commuted only for the sad alternative of perpetual banishment4 ,the very genius of the heathen mythology was at war with the truth4 ,false in itself1 it trained the mind to the love of what was false in the interpretation of nature2 it arrayed itself against the simplicity of truth1 and persecuted and put to death its most ardent votaries4 ,the religion of the ,bible1 on the other hand1 lends all its aid to truth in nature as well as in morals and religion4 ,in its very genius it inculcates and inspires the love of truth2 it suggests1 by its analogies1 the existence of established laws in the system of the world2 and holds out the moon and the stars1 which the ,creator has ordained1 as fit objects to give us exalted views of his glory and wisdom4 ,pythagoras was the founder of the celebrated school of ,crotona4 ,he was a native of ,samos1 an island in the gean sea1 and flourished about five hundred years before the ,christian era4 ,after travelling more than thirty years in ,egypt and ,chaldea1 and spending several years more at ,sparta1 to learn the laws and institutions of ,lycurgus1 he returned to his native island to dispense the riches he had acquired to his countrymen4 ,but they1 probably fearful of incurring the displeasure of the gods by the freedom with which he inquired into the secrets of the skies1 gave him so unwelcome a reception1 that he retired from them1 in disgust1 and established his school at ,crotona1 on the southeastern coast of ,italy4 ,hither1 as to an oracle1 the fame of his wisdom attracted hundreds of admiring pupils1 whom he instructed in every species of knowledge4 ,from the visionary notions which are generally understood to have been entertained on the subject of astronomy1 by the ancients1 we are apt to imagine that they knew less than they actually did of the truths of this science4 ,but ,pythagoras was acquainted with many important facts in astronomy1 and entertained many opinions respecting the system of the world1 which are now held to be true4 ,among other things well known to ,pythagoras1 either derived from his own investigations1 or received from his predecessors1 were the following2 and we may note them as a synopsis of the state of astronomical knowledge at that age of the world4 ,first1 the principal constellations4 ,these had begun to be formed in the earliest ages of the world4 ,several of them1 bearing the same name as at present1 are mentioned in the writings of ,hesiod and ,homer2 and the sweet influences of the ,pleiades1 and the bands of ,orion1 are beautifully alluded to in the book of ,job4 ,secondly1 eclipses4 ,pythagoras knew both the causes of eclipses and how to predict them2 not1 indeed1 in the accurate manner now practised1 but by means of the ,saros4 ,thirdly1 ,pythagoras had divined the true system of the world1 holding that the sun1 and not the earth1 7as was generally held by the ancients1 even for many ages after ,pythagoras17 is the centre around which all the planets revolve2 and that the stars are so many suns1 each the centre of a system like our own4 ,among lesser things1 he knew that the earth is round2 that its surface is naturally divided into five zones2 and that the ecliptic is inclined to the equator4 ,he also held that the earth revolves daily on its axis1 and yearly around the sun2 that the galaxy is an assemblage of small stars2 and that it is the same luminary1 namely1 ,venus1 that constitutes both the morning and evening star2 whereas all the ancients before him had supposed that each was a separate planet1 and accordingly the morning star was called ,lucifer1 and the evening star1 ,hesperus4 ,he held1 also1 that the planets were inhabited1 and even went so far as to calculate the size of some of the animals in the moon4 ,pythagoras was also so great an enthusiast in music1 that he not only assigned to it a conspicuous place in his system of education1 but even supposed that the heavenly bodies themselves were arranged at distances corresponding to the intervals of the diatonic scale1 and imagined them to pursue their sublime march to notes created by their own harmonious movements1 called the 'music of the spheres2' but he maintained that this celestial concert1 though loud and grand1 is not audible to the feeble organs of man1 but only to the gods4 ,with few exceptions1 however1 the opinions of ,pythagoras on the system of the world were founded in truth4 ,yet they were rejected by ,aristotle1 and by most succeeding astronomers1 down to the time of ,copernicus2 and in their place was substituted the doctrine of crystalline spheres1 first taught by ,eudoxus1 who lived about three hundred and seventy years before ,christ4 ,according to this system1 the heavenly bodies are set like gems in hollow solid orbs1 composed of crystal so transparent1 that no anterior orb obstructs in the least the view of any of the orbs that lie behind it4 ,the sun and the planets have each its separate orb2 but the fixed stars are all set in the same grand orb2 and beyond this is another still1 the primum mobile1 which revolves daily1 from east to west1 and carries along with it all the other orbs4 ,above the whole spreads the grand empyrean1 or third heavens1 the abode of perpetual serenity4 ,to account for the planetary motions1 it was supposed that each of the planetary orbs1 as well as that of the sun1 has a motion of its own1 eastward1 while it partakes of the common diurnal motion of the starry sphere4 ,aristotle taught that these motions are effected by a tutelary genius of each planet1 residing in it1 and directing its motions1 as the mind of man directs his movements4 ,two hundred years after ,pythagoras1 arose the famous school of ,alexandria1 under the ,ptolemies4 ,these were a succession of ,egyptian kings1 and are not to be confounded with ,ptolemy1 the astronomer4 ,by the munificent patronage of this enlightened family1 for the space of three hundred years1 beginning at the death of ,alexander the ,great1 from whom the eldest of the ,ptolemies had received his kingdom1 the school of ,alexandria concentrated in its vast library and princely halls1 erected for the accommodation of the philosophers1 nearly all the science and learning of the world4 ,in wandering over the immense territories of ignorance and barbarism which covered1 at that time1 almost the entire face of the earth1 the eye reposes upon this little spot1 as upon a verdant island in the midst of the desert4 ,among the choice fruits that grew in this garden of astronomy were several of the most distinguished ornaments of ancient science1 of whom the most eminent were ,hipparchus and ,ptolemy4 ,hipparchus is justly considered as the ,newton of antiquity4 ,he sought his knowledge of the heavenly bodies not in the illusory suggestions of a fervid imagination1 but in the vigorous application of an intellect of the first order4 ,previous to this period1 celestial observations were made chiefly with the naked eye3 but ,hipparchus was in possession of instruments for measuring angles1 and knew how to resolve spherical triangles4 ,these were great steps beyond all his predecessors4 ,he ascertained the length of the year within six minutes of the truth4 ,he discovered the eccentricity1 or elliptical figure1 of the solar orbit1 although he supposed the sun actually to move uniformly in a circle1 but the earth to be placed out of the centre4 ,he also determined the positions of the points among the stars where the earth is nearest to the sun1 and where it is most remote from it4 ,he formed very accurate estimates of the obliquity of the ecliptic and of the precession of the equinoxes4 ,he computed the exact period of the synodic revolution of the moon1 and the inclination of the lunar orbit2 discovered the backward motion of her node and of her line of apsides2 and made the first attempts to ascertain the horizontal parallaxes of the sun and moon4 ,upon the appearance of a new star in the firmament1 he undertook1 as already mentioned1 to number the stars1 and to assign to each its true place in the heavens1 in order that posterity might have the means of judging what changes1 if any1 were going forward among these apparently unalterable bodies4 ,although ,hipparchus is generally considered as belonging to the ,alexandrian school1 yet he lived at ,rhodes1 and there made his astronomical observations1 about one hundred and forty years before the ,christian era4 ,one of his treatises has come down to us2 but his principal discoveries have been transmitted through the ',almagest' of ,ptolemy4 ,ptolemy flourished at ,alexandria nearly three centuries after ,hipparchus1 in the second century after ,christ4 ,his great work1 the ',almagest1' which has conveyed to us most that we know respecting the astronomical knowledge of the ancients1 was the universal text-book of astronomers for fourteen centuries4 ,illustration ,fig4 #gg4 ,the name of this celebrated astronomer has also descended to us1 associated with the system of the world which prevailed from ,ptolemy to ,copernicus1 called the ,ptolemaic ,system4 ,the doctrines of the ,ptolemaic system did not originate with ,ptolemy1 but1 being digested by him out of materials furnished by various hands1 it has come down to us under the sanction of his name4 ,according to this system1 the earth is the centre of the universe1 and all the heavenly bodies daily revolve around it1 from east to west4 ,but although this hypothesis would account for the apparent diurnal motion of the firmament1 yet it would not account for the apparent annual motion of the sun1 nor for the slow motions of the planets from west to east4 ,in order to explain these phenomena1 recourse was had to deferents and epicycles1--an explanation devised by ,apollonius1 one of the greatest geometers of antiquity4 ,he conceived that1 in the circumference of a circle1 having the earth for its centre1 there moves the centre of a smaller circle in the circumference of which the planet revolves4 ,the circle surrounding the earth was called the deferent1 while the smaller circle1 whose centre was always in the circumference of the deferent1 was called the epicycle4 ,thus1 if ,e1 ,fig4 #gg1 represents the earth1 ,,abc will be the deferent1 and ,,dfg1 the epicycle2 and it is obvious that the motion of a body from west to east1 in this small circle1 would be alternately direct1 stationary1 and retrograde1 as was explained1 in a previous ,letter1 to be actually the case with the apparent motions of the planets4 ,the hypothesis1 however1 is inconsistent with the phases of ,mercury and ,venus1 which1 being between us and the sun1 on both sides of the epicycle1 would present their dark sides towards us at both conjunctions with the sun1 whereas1 at one of the conjunctions1 it is known that they exhibit their disks illuminated4 ,it is1 moreover1 absurd to speak of a geometrical centre1 which has no bodily existence1 moving round the earth on the circumference of another circle4 ,in addition to these absurdities1 the whole ,ptolemaic system is encumbered with the following difficulties3 ,first1 it is a mere hypothesis1 having no evidence in its favor except that it explains the phenomena4 ,this evidence is insufficient of itself1 since it frequently happens that each of two hypotheses1 which are directly opposite to each other1 will explain all the known phenomena4 ,but the ,ptolemaic system does not even do this1 as it is inconsistent with the phases of ,mercury and ,venus1 as already observed4 ,secondly1 now that we are acquainted with the distances of the remoter planets1 and especially the fixed stars1 the swiftness of motion1 implied in a daily revolution of the starry firmament around the earth1 renders such a motion wholly incredible4 ,thirdly1 the centrifugal force which would be generated in these bodies1 especially in the sun1 renders it impossible that they can continue to revolve around the earth as a centre4 ,absurd1 however1 as the system of ,ptolemy was1 for many centuries no great philosophic genius appeared to expose its fallacies1 and it therefore guided the faith of astronomers of all countries down to the time of ,copernicus4 ,after the age of ,ptolemy1 the science made little progress4 ,with the decline of ,grecian liberty1 the arts and sciences declined also2 and the ,romans1 then masters of the world1 were ever more ambitious to gain conquests over man than over matter2 and they accordingly never produced a single great astronomer4 ,during the middle ages1 the ,arabians were almost the only astronomers1 and they cultivated this noble study chiefly as subsidiary to astrology4 ,at length1 in the fifteenth century1 ,copernicus arose1 and after forty years of intense study and meditation1 divined the true system of the world4 ,you will recollect that the ,copernican system maintains1 #a4 ,that the apparent diurnal motions of the heavenly bodies1 from east to west1 is owing to the real revolution of the earth on its own axis from west to east2 and1 #b4 ,that the sun is the centre around which the earth and planets all revolve from west to east4 ,it rests on the following arguments3 ,in the first place1 the earth revolves on its own axis4 ,first1 because this supposition is vastly more simple4 ,secondly1 it is agreeable to analogy1 since all the other planets that afford any means of determining the question1 are seen to revolve on their axes4 ,thirdly1 the spheroidal figure of the earth is the figure of equilibrium1 that results from a revolution on its axis4 ,fourthly1 the diminished weight of bodies at the equator indicates a centrifugal force arising from such a revolution4 ,fifthly1 bodies let fall from a high eminence1 fall eastward of their base1 indicating that when further from the centre of the earth they were subject to a greater velocity1 which1 in consequence of their inertia1 they do not entirely lose in descending to the lower level4 ,in the second place1 the planets1 including the earth1 revolve about the sun4 ,first1 the phases of ,mercury and ,venus are precisely such1 as would result from their circulating around the sun in orbits within that of the earth2 but they are never seen in opposition1 as they would be1 if they circulate around the earth4 ,secondly1 the superior planets do indeed revolve around the earth2 but they also revolve around the sun1 as is evident from their phases1 and from the known dimensions of their orbits2 and that the sun1 and not the earth1 is the centre of their motions1 is inferred from the greater symmetry of their motions1 as referred to the sun1 than as referred to the earth2 and especially from the laws of gravitation1 which forbid our supposing that bodies so much larger than the earth1 as some of these bodies are1 can circulate permanently around the earth1 the latter remaining all the while at rest4 ,in the third place1 the annual motion of the earth itself is indicated also by the most conclusive arguments4 ,for1 first1 since all the planets1 with their satellites and the comets1 revolve about the sun1 analogy leads us to infer the same respecting the earth and its satellite1 as those of ,jupiter and ,saturn1 and indicates that it is a law of the solar system that the smaller bodies revolve about the larger4 ,secondly1 on the supposition that the earth performs an annual revolution around the sun1 it is embraced along with the planets1 in ,kepler's law1 that the squares of the times are as the cubes of the distances2 otherwise1 it forms an exception1 and the only known exception1 to this law4 ,such are the leading arguments upon which rests the ,copernican system of astronomy4 ,they were1 however1 only very partially known to ,copernicus himself1 as the state both of mechanical science1 and of astronomical observation1 was not then sufficiently matured to show him the strength of his own doctrine1 since he knew nothing of the telescope1 and nothing of the principle of universal gravitation4 ,the evidence of this beautiful system being left by ,copernicus in so imperfect a state1 and indeed his own reasonings in support of it being tinctured with some errors1 we need not so much wonder that ,tycho ,brahe1 who immediately followed ,copernicus1 did not give it his assent1 but1 influenced by certain passages of ,scripture1 he still maintained1 with ,ptolemy1 that the earth is in the centre of the universe2 and he accounted for the diurnal motions in the same manner as ,ptolemy had done1 namely1 by an actual revolution of the whole host of heaven around the earth every twenty-four hours4 ,but he rejected the scheme of deferents and epicycles1 and held that the moon revolves about the earth as the centre of her motions2 but that the sun and not the earth is the centre of the planetary motions2 and that the sun1 accompanied by the planets1 moves around the earth once a year1 somewhat in the manner in which we now conceive of ,jupiter and his satellites as revolving around the sun4 ,this system is liable to most of the objections that lie against the ,ptolemaic system1 with the disadvantage of being more complex4 ,kepler and ,galileo1 however1 as appeared in the sketch of their lives1 embraced the theory of ,copernicus with great avidity1 and all their labors contributed to swell the evidence of its truth4 ,when we see with what immense labor and difficulty the disciples of ,ptolemy sought to reconcile every new phenomenon of the heavens with their system1 and then see how easily and naturally all the successive discoveries of ,galileo and ,kepler fall in with the theory of ,copernicus1 we feel the full force of those beautiful lines of ,cowper which ,i have chosen for the motto of this ,letter4 ,newton received the torch of truth from ,galileo1 and transmitted it to his successors1 with its light enlarged and purified2 and since that period1 every new discovery1 whether the fruit of refined instrumental observation or of profound mathematical analysis1 has only added lustre to the glory of ,copernicus4 ,with ,newton commenced a new and wonderful era in astronomy1 distinguished above all others1 not merely for the production of the greatest of men1 but also for the establishment of those most important auxiliaries to our science1 the ,royal ,society of ,london1 the ,academy of ,sciences at ,paris1 and the ,observatory of ,greenwich4 ,i may add the commencement of the ,transactions of the ,royal ,society1 and the ,memoirs of the ,academy of ,sciences1 which have been continued to the present time1--both precious storehouses of astronomical riches4 ,the ,observatory of ,greenwich1 moreover1 has been under the direction of an extraordinary succession of great astronomers4 ,their names are ,flamstead1 ,halley1 ,bradley1 ,maskeleyne1 ,pond1 and ,airy1--the last being still at his post1 and worthy of continuing a line so truly illustrious4 ,the observations accumulated at this celebrated ,observatory are so numerous1 and so much superior to those of any other institution in the world1 that it has been said that astronomy would suffer little1 if all other contemporary observations of the same kind were annihilated4 ,sir ,william ,herschel1 however1 labored chiefly in a different sphere4 ,the ,astronomers ,royal devoted themselves not so much to the discovery of new objects among the heavenly bodies1 as to the exact determination of the places of the bodies already known1 and to the developement of new laws or facts among the celestial motions4 ,but ,herschel1 having constructed telescopes of far greater reach than any ever used before1 employed them to sound new and untried depths in the profundities of space4 ,we have already seen what interesting and amazing discoveries he made of double stars1 clusters1 and nebul4 ,the ,english have done most for astronomy in observation and discovery2 but the ,french and ,germans1 in developing1 by the most profound mathematical investigation1 the great laws of physical astronomy4 ,it only remains to inquire1 whether the ,copernican system is now to be regarded as a full exposition of the ',mechanism of the ,heavens1' or whether there subsist higher orders of relations between the fixed stars themselves4 ,the revolutions of the binary stars afford conclusive evidence of at least subordinate systems of suns1 governed by the same laws as those which regulate the motions of the solar system4 ,the nebul also compose peculiar systems1 in which the members are evidently bound together by some common relation4 ,in these marks of organization1--of stars associated together in clusters2 of sun revolving around sun2 and of nebul disposed in regular figures1--we recognise different members of some grand system1 links in one great chain that binds together all parts of the universe2 as we see ,jupiter and his satellites combined in one subordinate system1 and ,saturn and his satellites in another1--each a vast kingdom1 and both uniting with a number of other individual parts1 to compose an empire still more vast4 ,this fact being now established1 that the stars are immense bodies1 like the sun1 and that they are subject to the laws of gravitation1 we cannot conceive how they can be preserved from falling into final disorder and ruin1 unless they move in harmonious concert1 like the members of the solar system4 ,otherwise1 those that are situated on the confines of creation1 being retained by no forces from without1 while they are subject to the attraction of all the bodies within1 must leave their stations1 and move inward with accelerated velocity2 and thus all the bodies in the universe would at length fall together in the common centre of gravity4 ,the immense distance at which the stars are placed from each other would indeed delay such a catastrophe2 but this must be the ultimate tendency of the material world1 unless sustained in one harmonious system by nicely-adjusted motions4 ,to leave entirely out of view our confidence in the wisdom and preserving goodness of the ,creator1 and reasoning merely from what we know of the stability of the solar system1 we should be justified in inferring1 that other worlds are not subject to forces which operate only to hasten their decay1 and to involve them in final ruin4 ,we conclude1 therefore1 that the material universe is one great system2 that the combination of planets with their satellites constitutes the first or lowest order of worlds2 that next to these1 planets are linked to suns2 that these are bound to other suns1 composing a still higher order in the scale of being2 and finally1 that all the different systems of worlds move around their common centre of gravity4 ,,letter ,,xxxi4 ,,natural ,,theology4 ----,philosophy1 baptized ,in the pure fountain of ,eternal ,love1 ,has eyes indeed2 and1 viewing all she sees ,as meant to indicate a ,god to man1 ,gives ,him the praise1 and forfeits not her own4--,cowper4 ,i ,,intended1 my dear ,friend1 to comply with your request that ,i would discuss the arguments which astronomy affords to natural theology2 but these ,letters have been already extended so much further than ,i anticipated1 that ,i shall conclude with suggesting a few of those moral and religious reflections1 which ought always to follow in the train of such a survey of the heavenly bodies as we have now taken4 ,although there is evidence enough in the structure1 arrangement1 and laws1 which prevail among the heavenly bodies1 to prove the existence of ,god1 yet ,i think there are many subordinate parts of ,his works far better adapted to this purpose than these1 being more fully within our comprehension4 ,it was intended1 no doubt1 that the evidence of ,his being should be accessible to all ,his creatures1 and should not depend on a kind of knowledge possessed by comparatively few4 ,the mechanism of the eye is probably not more perfect than that of the universe2 but we can analyze it better1 and more fully understand the design of each part4 ,but the existence of ,god being once proved1 and it being admitted that ,he is the ,creator and ,governor of the world1 then the discoveries of astronomy are admirably adapted to perform just that office in relation to the ,great ,first ,cause1 which is assigned to them in the ,bible1 namely1 to declare the glory of ,god1 and to show ,his handiwork4 ,in other words1 the discoveries of astronomy are peculiarly fitted1--more so1 perhaps1 than any other department of creation1--to exhibit the unity1 power1 and wisdom1 of the ,creator4 ,the most modern discoveries have multiplied the proofs of the unity of ,god4 ,it has usually been offered as sufficient evidence of the truth of this doctrine1 that the laws of ,nature are found to be uniform when applied to the utmost bounds of the solar system2 that the law of gravitation controls alike the motions of ,mercury1 and those of ,uranus2 and that its operation is one and the same upon the moon and upon the satellites of ,saturn4 ,it was1 however1 impossible1 until recently1 to predicate the same uniformity in the great laws of the universe respecting the starry worlds1 except by a feeble analogy4 ,however improbable1 it was still possible1 that in these distant worlds other laws might prevail1 and other ,lords exercise dominion4 ,but the discovery of the revolutions of the binary stars1 in exact accordance with the law of gravitation1 not merely in a single instance1 but in many instances1 in all cases1 indeed1 wherever those revolutions have advanced so far as to determine their law of action1 gives us demonstration1 instead of analogy1 of the prevalence of the same law among the other systems as that which rules in ours4 ,the marks of a still higher organization in the structure of clusters and nebul1 all bearing that same characteristic union of resemblance and variety which belongs to all the other works of creation that fall under our notice1 speak loudly of one1 and only one1 grand design4 ,every new discovery of the telescope1 therefore1 has added new proofs to the great truth that ,god is one3 nor1 so far as ,i know1 has a single fact appeared1 that is not entirely consonant with it4 ,light1 moreover1 which brings us intelligence1 and1 in most cases1 the only intelligence we have1 of these remote orbs1 testifies to the same truth1 being similar in its properties and uniform in its motions1 from whatever star it emanates4 ,in displays of the power of ,jehovah1 nothing can compare with the starry heavens4 ,the magnitudes1 distances1 and velocities1 of the heavenly bodies are so much beyond every thing of this kind which belongs to things around us1 from which we borrowed our first ideas of these qualities1 that we can scarcely avoid looking with incredulity at the numerical results to which the unerring principles of mathematics have conducted us4 ,and when we attempt to apply our measures to the fixed stars1 and especially to the nebul1 the result is absolutely overwhelming3 the mind refuses its aid in our attempts to grasp the great ideas4 ,nor less conspicuous1 among the phenomena of the heavenly bodies1 is the wisdom of the ,creator4 ,in the first place1 this attribute is every where exhibited in the happy adaptation of means to their ends4 ,no principle can be imagined more simple1 and at the same time more effectual to answer the purposes which it serves1 than gravitation4 ,no position can be given to the sun and planets so fitted1 as far as we can judge1 to fulfil their mutual relations1 as that which the ,creator has given them4 ,i say1 as far as we can judge2 for we find this to be the case in respect to our own planet and its attendant satellite1 and hence have reason to infer that the same is the case in the other planets1 evidently holding1 as they do1 a similar relation to the sun4 ,thus the position of the earth at just such a distance from the sun as suits the nature of its animal and vegetable kingdoms1 and confining the range of solar heat1 vast as it might easily become1 within such narrow bounds2 the inclination of the earth's axis to the plane of its orbit1 so as to produce the agreeable vicissitudes of the seasons1 and increase the varieties of animal and vegetable life1 still confining the degree of inclination so exactly within the bounds of safety1 that1 were it much to transcend its present limits1 the changes of temperature of the different seasons would be too sudden and violent for the existence of either animals or vegetables2 the revolution of the earth on its axis1 so happily dividing time into hours of business and of repose2 the adaptation of the moon to the earth1 so as to afford to us her greatest amount of light just at the times when it is needed most1 and giving to the moon just such a quantity of matter1 and placing her at just such a distance from the earth1 as serves to raise a tide productive of every conceivable advantage1 without the evils which would result from a stagnation of the waters on the one hand1 or from their overflow on the other2--these are a few examples of the wisdom displayed in the mutual relations instituted between the sun1 the earth1 and the moon4 ,in the second place1 similar marks of wisdom are exhibited in the many useful and important purposes which the same thing is made to serve4 ,thus the sun is at once the great regulator of the planetary motions1 and the fountain of light and heat4 ,the moon both gives light by night and raises the tides4 ,or1 if we would follow out this principle where its operations are more within our comprehension1 we may instance the atmosphere4 ,when man constructs an instrument1 he deems it sufficient if it fulfils one single purpose as the watch1 to tell the hour of the day1 or the telescope1 to enable him to see distant objects2 and had a being like ourselves made the atmosphere1 he would have thought it enough to have created a medium so essential to animal life1 that to live is to breathe1 and to cease to breathe is to die4 ,but beside this1 the atmosphere has manifold uses1 each entirely distinct from all the others4 ,it conveys to plants1 as well as animals1 their nourishment and life2 it tempers the heat of ,summer with its breezes2 it binds down all fluids1 and prevents their passing into the state of vapor2 it supports the clouds1 distils the dew1 and waters the earth with showers2 it multiplies the light of the sun1 and diffuses it over earth and sky2 it feeds our fires1 turns our machines1 wafts our ships1 and conveys to the ear all the sentiments of language1 and all the melodies of music4 ,in the third place1 the wisdom of the ,creator is strikingly manifested in the provision he has made for the stability of the universe4 ,the perturbations occasioned by the motions of the planets1 from their action on each other1 are very numerous1 since every body in the system exerts an attraction on every other1 in conformity with the law of universal gravitation4 ,venus and ,mercury1 approaching1 as they do at times1 comparatively near to the earth1 sensibly disturb its motions2 and the satellites of the remoter planets greatly disturb each other's movements4 ,nor was it possible to endow this principle with the properties it has1 and make it operate as it does in regulating the motions of the world1 without involving such an incident4 ,on this subject1 ,professor ,whewell1 in his excellent work composing one of the ,bridgewater ,treatises1 remarks3 ,the derangement which the planets produce in the motion of one of their number will be very small1 in the course of one revolution2 but this gives us no security that the derangement may not become very large1 in the course of many revolutions4 ,the cause acts perpetually1 and it has the whole extent of time to work in4 ,is it not easily conceivable1 then1 that1 in the lapse of ages1 the derangements of the motions of the planets may accumulate1 the orbits may change their form1 and their mutual distances may be much increased or diminished8 ,is it not possible that these changes may go on without limit1 and end in the complete subversion and ruin of the system8 ,if1 for instance1 the result of this mutual gravitation should be to increase considerably the eccentricity of the earth's orbit1 or to make the moon approach continually nearer and nearer to the earth1 at every revolution1 it is easy to see that1 in the one case1 our year would change its character1 producing a far greater irregularity in the distribution of the solar heat2 in the other1 our satellite must fall to the earth1 occasioning a dreadful catastrophe4 ,if the positions of the planetary orbits1 with respect to that of the earth1 were to change much1 the planets might sometimes come very near us1 and thus increase the effect of their attraction beyond calculable limits4 ,under such circumstances1 'we might have years of unequal length1 and seasons of capricious temperature2 planets and moons1 of portentous size and aspect1 glaring and disappearing at uncertain intervals2 tides1 like deluges1 sweeping over whole continents2 and perhaps the collision of two of the planets1 and the consequent destruction of all organization on both of them4' ,the fact really is1 that changes are taking place in the motions of the heavenly bodies1 which have gone on progressively1 from the first dawn of science4 ,the eccentricity of the earth's orbit has been diminishing from the earliest observations to our times4 ,the moon has been moving quicker from the time of the first recorded eclipses1 and is now in advance1 by about four times her own breadth1 of what her own place would have been1 if it had not been affected by this acceleration4 ,the obliquity of the ecliptic1 also1 is in a state of diminution1 and is now about two fifths of a degree less than it was in the time of ,aristotle4 ,but amid so many seeming causes of irregularity and ruin1 it is worthy of a grateful notice1 that effectual provision is made for the stability of the solar system4 ,the full confirmation of this fact is among the grand results of physical astronomy4 ,newton did not undertake to demonstrate either the stability or instability of the system4 ,the decision of this point required a great number of preparatory steps and simplifications1 and such progress in the invention and improvement of mathematical methods1 as occupied the best mathematicians of ,europe for the greater part of the last century4 ,towards the end of that time1 it was shown by ,la ,grange and ,la ,place1 that the arrangements of the solar system are stable2 that1 in the long run1 the orbits and motions remain unchanged2 and that the changes in the orbits1 which take place in shorter periods1 never transgress certain very moderate limits4 ,each orbit undergoes deviations on this side and on that side of its average state2 but these deviations are never very great1 and it finally recovers from them1 so that the average is preserved4 ,the planets produce perpetual perturbations in each other's motions2 but these perturbations are not indefinitely progressive1 but periodical1 reaching a maximum value1 and then diminishing4 ,the periods which this restoration requires are1 for the most part1 enormous1--not less than thousands1 and in some instances1 millions1 of years4 ,indeed1 some of these apparent derangements have been going on in the same direction from the creation of the world4 ,but the restoration is in the sequel as complete as the derangement2 and in the mean time the disturbance never attains a sufficient amount seriously to affect the stability of the system4 ',i have succeeded in demonstrating1' says ,la ,place1 'that1 whatever be the masses of the planets1 in consequence of the fact that they all move in the same direction1 in orbits of small eccentricity1 and but slightly inclined to each other1 their secular irregularities are periodical1 and included within narrow limits2 so that the planetary system will only oscillate about a mean state1 and will never deviate from it1 except by a very small quantity4 ,the ellipses of the planets have been and always will be nearly circular4 ,the ecliptic will never coincide with the equator2 and the entire extent of the variation1 in its inclination1 cannot exceed three degrees4' ,to these observations of ,la ,place1 ,professor ,whewell adds the following1 on the importance1 to the stability of the solar system1 of the fact that those planets which have great masses have orbits of small eccentricity4 ,the planets ,mercury and ,mars1 which have much the largest eccentricity among the old planets1 are those of which the masses are much the smallest4 ,the mass of ,jupiter is more than two thousand times that of either of these planets4 ,if the orbit of ,jupiter were as eccentric as that of ,mercury1 all the security for the stability of the system1 which analysis has yet pointed out1 would disappear4 ,the earth and the smaller planets might1 by the near approach of ,jupiter at his perihelion1 change their nearly circular orbits into very long ellipses1 and thus might fall into the sun1 or fly off into remoter space4 ,it is further remarkable1 that in the newly-discovered planets1 of which the orbits are still more eccentric than that of ,mercury1 the masses are still smaller1 so that the same provision is established in this case1 also4 ,with this hasty glance at the unity1 power1 and wisdom1 of the ,creator1 as manifested in the greatest of ,his works1 ,i close4 ,i hope enough has been said to vindicate the sentiment that called ',devotion1 daughter of ,astronomy6' ,i do not pretend that this1 or any other science1 is adequate of itself to purify the heart1 or to raise it to its ,maker2 but ,i fully believe that1 when the heart is already under the power of religion1 there is something in the frequent and habitual contemplation of the heavenly bodies under all the lights of modern astronomy1 very favorable to devotional feelings1 inspiring1 as it does1 humility1 in unison with an exalted sentiment of grateful adoration4 ,,letter ,,xxxii4 ,,recent ,,discoveries4 ,all are but parts of one stupendous whole4--,pope4 ,,within a few years1 astronomy has been enriched with a number of valuable discoveries1 of which ,i will endeavor to give you a summary account in this letter4 ,the heavens have been explored with far more powerful telescopes than before2 instrumental measurements have been carried to an astonishing degree of accuracy2 numerous additions have been made to the list of small planets or asteroids2 a comet has appeared of extraordinary splendor1 remarkable1 above all others1 for its near approach to the sun2 the distances of several of the fixed stars1 an element long sought for in vain1 have been determined2 a large planet1 composing in itself a magnificent world1 has been added to the solar system1 at such a distance from the central luminary as nearly to double the supposed dimensions of that system2 various nebul1 before held to be irresolvable1 have been resolved into stars2 and a new satellite has been added to ,saturn4 ,,improvements ,,in ,,the ,,telescope4--,herschel's forty-feet telescope1 of which ,i gave an account in my fourth letter 7see page #cf71 remained for half a century unequalled in magnitude and power2 but in #ahdb1 ,lord ,rosse1 an ,irish nobleman1 commenced a telescope on a scale still more gigantic4 ,like ,herschel's1 it was a reflector1 the image being formed by a concave mirror4 ,this was six feet in diameter1 and weighed three tons2 and the tube was fifty feet in length4 ,the entire cost of the instrument was sixty thousand dollars4 ,its reflecting surface is nearly twice as great as the great ,herschelian1 and consequently it greatly exceeds all instruments hitherto constructed in the amount of light which it collects and transmits to the eye2 and this adapts it peculiarly to viewing those objects1 as nebul1 whose light is exceedingly faint4 ,accordingly1 it has revealed to us new wonders in this curious department of astronomy4 ,some idea of the great dimensions of the ,leviathan telescope 7as this instrument has been called7 may be formed when it is said that the ,dean of ,ely1 a full-sized man1 walked through the tube from one end to the other1 with an umbrella over his head4 ,but still greater advances have been made in refracting than in reflecting telescopes4 ,such was the difficulty of obtaining large pieces of glass which are free from impurities1 and such the liability of large lenses to form obscure and colored images1 that it was formerly supposed impossible to make a refracting telescope larger in diameter than five or six inches2 but their size has been increased from one step to another1 until they are now made more than fifteen inches in diameter2 and so completely have all the difficulties arising from the imperfections of glass1 and from optical defects inherent in lenses1 been surmounted1 that the great telescopes of ,pulkova1 at ,st4 ,petersburgh1 and of ,harvard ,university 7the two finest refractors in the world7 are considered among the most perfect productions of the arts4 ,a lens of only #ae inches in diameter seems1 indeed1 diminutive when compared with a concave reflector of six feet2 but for most purposes of the astronomer1 the ,pulkova and ,cambridge instruments are more useful than such great reflectors as those of ,herschel and ,rosse4 ,if there is any particular in which these are more effective1 it is in observations on the faintest nebul1 where it is necessary to collect and convey to the eye the greatest possible beam of light4 ,,instrumental ,,measurements4--,when astronomical instruments were first employed to measure the angular distance between two points on the celestial sphere1 it was not attempted to measure spaces smaller than ten minutes--a space equal to the third part of the breadth of the full moon4 ,tycho ,brahe1 however1 carried his measures to sixty times that degree of minuteness1 having devised means of determining angles no larger than ten seconds1 or the one hundred and eightieth part of the breadth of the lunar disk4 ,for many years past1 astronomers have carried these measures to single seconds1 or have determined spaces no greater than the eighteen hundredth part of the diameter of the moon4 ,this is considered the smallest arc which can be accurately measured directly on the limb of an instrument2 but differences between spaces may be estimated to a far greater degree of accuracy than this1 even to the hundredth part of a second--a space less than that intercepted by a spider's web held before the eye4 ,,discovery ,,of ,,new ,,planets4--,in my twenty-third letter 7see page #bhf71 ,i gave an account of the small planets called asteroids1 which lie between the orbits of ,mars and ,jupiter4 ,when that letter was written1 no longer ago than #ahdj1 only four of those bodies had been discovered1 namely1 ,ceres1 ,pallas1 ,juno1 and ,vesta4 ,within a few years past1 nineteen more have been added1 making the number of the asteroids known at present twenty-three1 and every year adds one or more to the list4#ag ,the idea first suggested by ,olbers1 one of the earliest discoverers of asteroids1 that they are fragments of a large single planet once revolving between ,mars and ,jupiter1 has gained credit since the discovery of so many additional bodies of the same class1 all1 like the former1 exceedingly small and irregular in their motions1 although there are still great difficulties in tracing them to a common origin4 ,,great ,,comet ,,of #ahdc4--,this is the most wonderful body that has appeared in the heavens in modern times2 first1 on account of its appearing1 when first seen1 in the broad light of noonday2 and1 secondly1 on account of its approaching so near the sun as almost to graze his surface4 ,it was first discovered1 in ,new ,england1 on the #bhth of ,february1 a little eastward of the sun1 shining like a white cloud illuminated by the solar rays4 ,it arrested the attention of many individuals from half past seven in the morning until three o'clock in the afternoon1 when the sky became obscured by clouds4 ,in ,mexico1 it was observed from nine in the morning until sunset4 ,at a single station in ,south ,america1 it was said to have been seen on the #bgth of ,february1 almost in contact with the sun4 ,early in ,march1 it had receded so far to the eastward of that body as to be visible in the southwest after sunset1 throwing upward a long train1 which increased in length from night to night until it covered a space of #dj degrees4 ,its position may be seen on a celestial globe adjusted to the latitude of ,new ,haven 7#da #ah7 for the #bjth of ,march1 by tracing a line1 or1 rather1 a broad band proceeding from the place of the sun towards the bright star ,sirius1 in the south1 between the ears of the ,hare and the feet of ,orion4 ,the comet passed its perihelion on the #bgth of ,february1 at which time it almost came in contact with the sun4 ,to prevent its falling into the sun it was endued with a prodigious velocity2 a velocity so great that1 had it continued at the same rate as at the instant of perihelion passage1 it would have whirled round the sun in two hours and a half4 ,it did1 in fact1 complete more than half its revolution around the sun in that short period1 and it made more than three quarters of its circuit around the sun in one day4 ,its velocity1 when nearest the sun1 exceeded a million of miles per hour1 and its tail1 at its greatest elongation1 was one hundred and eight millions of miles2 a length more than sufficient to have reached from the sun to the earth4 ,its heat was estimated to be #dg1jjj times greater than that received by the earth from a vertical sun1 and consequently it was more intense than that produced by the most powerful blowpipes1 and sufficient to melt like wax the most infusible bodies4 ,no doubt1 when in the vicinity of the sun1 the solid matter of the comet was first melted and then converted into vapor1 which itself became red hot1 or1 more properly speaking1 white hot4 ,much discussion has arisen among astronomers respecting the periodic time of this comet4 ,its most probable period is about #age years4 ,,distances ,,of ,,the ,,stars4--,i have already mentioned 7page #chi7 that the distance of at least one of the fixed stars has at length been determined1 although at so great a distance that its annual parallax is only about one third of a second1 implying a distance from the sun of nearly sixty millions of millions of miles4 ,of a distance so immense the mind can form no adequate conception4 ,the most successful effort towards it is made by gradual and successive approximations4 ,let us1 therefore1 take the motion of a rail-way car as the most rapid with which we are familiar1 and apply it first to the planetary spaces1 and then to the vast interval that separates these nether worlds from the fixed stars4 ,a rail-way car1 travelling constantly night and day at the rate of twenty miles per hour1 would make #dhj miles per day4 ,at this rate1 to travel around the earth on a great circle would require about #ej days1 and #ejj days to reach the moon4 ,if we took our departure from the sun1 and journeyed night and day1 we should reach ,mercury in a little more than #bjj years1 ,venus in nearly #djj1 and the ,earth in #edg years2 but to reach ,neptune1 the outermost planet1 would require #af1jjj years4 ,great as appear the dimensions of the solar system1 when we imagine ourselves thus borne along from world to world1 yet this space is small compared with that which separates us from the fixed stars2 for to reach #fa ,cygni it would take #cbd1jjj1jjj years4 ,but this is believed1 for certain satisfactory reasons1 to be one of the nearest of the stars4 ,several other stars whose parallax has been determined are at a much greater distance than #fa ,cygni4 ,the pole star is five times as far off2 and the greater part of the stars are at distances inconceivably more remote4 ,such1 especially1 are those which compose the faintest nebul4 ,,discovery ,,of ,,the ,,planet ,,neptune4--,from the earliest ages down to the year #agha1 the solar system was supposed to terminate with the planet ,saturn1 at the distance of nine hundred millions of miles from the sun2 but the discovery of ,uranus added another world1 and doubled the dimensions of the solar system4 ,it seemed improbable that any more planets should exist at a distance still more remote1 since such a body could hardly receive any of the vivifying influences of the central luminary4 ,still1 certain irregularities to which the ,uranus was subject1 led to the suspicion that there exists a planet beyond it1 which1 by its attractions1 caused these irregularities4 ,impressed with this belief1 two young astronomers of great genius1 ,le ,verrier1 of ,france1 and ,adams1 of ,england1 applied themselves to the task of finding the hidden planet4 ,the direction in which the disturbed body was moved afforded some clue to the part of the heavens where the disturbing body lay concealed2 the kind of action it excited at different times indicated that it was beyond ,uranus1 and not this side of that planet2 and the magnitude of the forces it exerted gave some intimation of its size and mass4 ,the law of distances from the sun which the superior planets observe 7,saturn being nearly twice the distance of ,jupiter1 and ,uranus twice that of ,saturn71 led both these astronomers to assume that the body sought was nearly double the distance of ,uranus from the sun4 ,with these few and imperfect data1 as so many leading-strings proceeding from the planet ,uranus1 they felt their way into the abysses of space by the aid of two sure guides--the law of gravitation and the higher geometry4 ,both astronomers arrived at nearly the same results1 although they wrought independently of each other1 and each1 indeed1 without the knowledge of the other4 ,le ,verrier was the first to make public his conclusions1 which he communicated to the ,french ,academy at their sitting1 ,august #ca1 #ahdf4 ,they saw that there existed1 at nearly double the distance of ,uranus from the sun1 a planet larger than that body2 that it lay near a certain star seen at that season in the southwest1 in the evening sky2 that1 on account of its immense distance1 it was invisible to the naked eye1 and could be distinctly seen with a perceptible disk only by the most powerful telescopes2 being no brighter than a star of the ninth magnitude1 and subtending an angle of only three seconds4 ,le ,verrier communicated these results to ,dr4 ,galle1 of ,berlin1 with the request that he would search for the stranger with his powerful telescope1 pointing out the exact spot in the heavens where it would be found4 ,on the same evening1 ,dr4 ,galle directed his instrument to that part of the heavens1 and immediately the planet presented itself to view1 within one degree of the very spot assigned to it by ,le ,verrier4 ,subsequent investigations have shown that its apparent size is within half a second of that which the same sagacious mind foresaw1 and that its diameter is nearly equal to that of ,uranus1 being #ca1jjj1 while ,uranus is #ce1jjj miles4#ah ,the distance from the sun is less than was predicted1 being only about #cjjj1 instead of #cfjj millions of miles2 and its periodic time is #afd-a_/b1 instead of #bag years1 as was supposed by ,le ,verrier4 ,one satellite only has yet been discovered1 and this was first seen by ,professor ,bond with the great telescope of ,harvard ,university4 ,,recent ,,telescopic ,,discoveries4--,the great reflecting telescope of ,lord ,rosse1 and the powerful refracting telescopes of ,pulkova and ,cambridge1 have opened new fields of discovery to the delighted astronomer4 ,a new satellite has been added to ,saturn1 first revealed to the ,cambridge instrument1 making the entire number of moons that adorn the nocturnal sky of that remarkable planet no less than eight4 ,still more wonderful things have been disclosed among the remotest ,nebul4 ,a number of these objects before placed among the irresolvable nebul1 and supposed to consist not of stars1 but of mere nebulous matter1 have been resolved into stars2 others1 of which we before saw only a part1 have revealed themselves under new and strange forms1 one resembling an animal with huge branching arms1 and hence called the crab nebula2 another imitating a scroll or vortex1 and called the whirlpool nebula2 and other figures1 which to ordinary telescopes appear only as dim specks on the confines of creation1 are presented to these wonderful instruments as glorious firmaments of stars4 ,in the year #ahcc1 ,sir ,john ,herschel left ,england for the ,cape of ,good ,hope1 furnished with powerful instruments for observing the stars and nebul of the southern hemisphere1 which had never been examined in a manner suited to disclose their full glories4 ,this great astronomer and benefactor to science devoted five years of the most assiduous toil in observing and delineating the astronomical objects of that portion of the heavens4 ,he had before extended the catalogue of nebul begun by his illustrious father1 ,sir ,william ,herschel1 to the number of #bcjg2 and beginning at that point1 he swelled the number1 by his labors at the ,cape of ,good ,hope1 to #djae4 ,he extended also the list of double stars from #ccdf to #eddi1 and showed that the luminous spots near the ,south ,pole1 known to sailors by the name of the ,magellan ,clouds1 consist of an assemblage of several hundred brilliant nebul4 ,the ,united ,states have contributed their full share to the recent progress of astronomy4 ,powerful telescopes have been imported1 made by the first ,european artists1 and numerous others1 of scarcely inferior workmanship and power1 have been produced by artists of our own4 ,the ,american astronomers have also been the first to bring the electric telegraph into use in astronomical observations2 electric clocks have been so constructed as to beat simultaneously at places distant many hundred miles from each other1 and thus to furnish means of determining the difference of longitude between places with an astonishing degree of accuracy2 and facilities for recording observations on the stars have been devised which render the work vastly more rapid as well as more accurate than before4 ,indeed1 the inventive genius for which ,americans have been distinguished in all the useful arts seems now destined to be equally conspicuous in promoting the researches of science4 ,,footnotes3 #ag ,the names of all the asteroids known at present are as follows3 #a4 ,ceres4 #i4 ,metis4 #ag4 ,psyche4 #b4 ,pallas4 #aj4 ,hygeia4 #ah4 ,melpomene4 #c4 ,juno4 #aa4 ,parthenope4 #ai4 ,fortuna4 #d4 ,vesta4 #ab4 ,victoria4 #bj4 ,massalia4 #e4 ,astra4 #ac4 ,egeria4 #ba4 ,lutetia4 #f4 ,hebe4 #ad4 ,irene4 #bb4 ,calliope4 #g4 ,iris4 #ae4 ,eunomia4 #bc4 ,un-named4 #h4 ,flora4 #af4 ,thetis4 #ah ,sir ,john ,herschel1 however1 states its diameter at #da1ejj miles ,,index4 ,a4 ,alamak1 #cga ,aldebaran1 #cfi ,alexandrian school1 #cid ,algenib1 #cga ,algol1 #cga ,alioth1 #cgd ,almagest1 #ad ,altair1 #cgc ,altitude1 #bj ,amplitude1 #bj ,anaxagoras1 #cie ,anaximander1 #cie ,andromeda1 #cga ,antares1 #cgj ,antinous1 #cgc ,apogee1 #ahg ,apsides1 #ahh ,aquarius1 #cga ,aquila1 #cgc ,archimedes1 #acf ,arcturus1 #cgb ,aries1 #cfi ,aristotle1 #acf ,astrology1 #cic ,astronomers royal1 #dh1 #djd ,astronomical clock1 #ea ,astronomical tables1 #aij ,astronomy1 #ag history of1 #ad1 #cib ,atmosphere1 #ajj1 #daj ,attraction1 #ace ,auriga1 #cga ,axis of the ,earth1 #ba ,azimuth1 #bj ,b4 ,bacon1 #af1 #acf ,base line1 #gf ,base of verification1 #gi ,bellatrix1 #cge ,betalgeus1 #cge ,bissextile1 #fd ,bootes1 #cgb ,bouguer1 #gd ,bowditch1 #adh ,brahean system1 #djc ,c4 ,csar1 ,julius1 #fd ,calendar1 ,grecian1 #fg ,gregorian1 #fe ,cancer1 #cfi ,canis ,major1 #cge ,canis ,minor1 #cge ,capella1 #cgb ,capricorn1 #cgj ,cassiopeia1 #cgd ,catalogues of the stars1 #cfg ,central forces1 #acj ,cepheus1 #cgd ,ceres1 #bhg ,cetus1 #cgd ,chronology1 #aeg ,chronometers1 #baj ,circles1 great and small1 #ai of diurnal revolution1 #ha of perpetual apparition1 #he of perpetual occultation1 #he vertical1 #bj ,clusters1 #cgf ,colures1 #bc ,coma ,berenices1 #cgb ,comet1 ,biela's1 #cci ,encke's1 #cdj ,halley's1 #cbc ,comets1 #cac brightness of1 #cae ,comets1 distances of1 #cag light of1 #cag magnitude of1 #cae mass of1 #cah motions of1 #cbj number of1 #cae periods of1 #caf perturbations of1 #cai structure of1 #cad tails of1 #cag ,complement1 #ah ,conjunction1 #bjj ,constellations1 #cff ,copernican system1 #bef1 #dja ,copernicus1 #ad1 #bee ,cor ,caroli1 #cgb ,cor ,hydr1 #cge ,corona ,borealis1 #cgb ,corvus1 #cge ,crotona1 #cid ,crystalline spheres1 #cig ,cygnus1 #cgd ,d4 ,day1 astronomical1 #fa sidereal1 #fj solar1 #fj ,days of the week1 #fh ,declination1 #bd ,deferents1 #djj ,denebola1 #cgj ,distances of the heavenly bodies1 how measured1 #id ,distances of the stars1 #chg ,dolphin1 #cgc ,double stars1 #cha ,draco1 #cgd ,e4 ,earth1 diameter of the1 #gh ellipticity of the1 #gh figure of the1 #fi motion of the1 #abf orbit of the1 #adi ,eclipses1 annular1 #bjd calculation of1 #bja of the moon1 #aie of the sun1 #bjc ,ecliptic1 #bb ,epicycles1 #djj ,equation of time1 #fa ,equations1 periodical1 #aic secular1 #aic tabular1 #aij ,equator1 #ba ,equinoxes1 #bb precession of the1 #aed ,eudoxus1 #cig ,f4 ,fomalhaut1 #cga ,fraunhofer1 #cg ,g4 ,galaxy1 #cgi ,galileo1 #ae abjuration of1 #bgb condemnation of1 #bff life of1 #beh persecutions of1 #bfe ,gemini1 #cfi ,gemma1 #cgb ,globes1 artificial1 #be ,gravitation1 universal1 #ade ,gravity1 terrestrial1 #acd ,h4 ,hercules1 #cgb ,herschel1 ,sir ,wm41 #cf1 #aje1 #chc ,hesperus1 #cig ,hipparchus1 #cih ,horizon1 rational1 #bj sensible1 #bj ,hour-circles1 #ba ,huyghens1 #gb ,i4 ,inductive system1 #acg ,inquisition1 #ach ,instruments1 astronomical1 #bi ,j4 ,juno1 #bhh ,jupiter1 #bdg belts of1 #bdh diameter of1 #bdg distance of1 #bdg eclipses of1 #bej magnitude of1 #bdg satellites of1 #bej scenery of1 #bdg telescopic view of1 #bdg ,k4 ,kepler1 #cjj ,kepler's laws1 #bif ,l4 ,latitude1 #bb how found1 #baj ,laws of motion1 #abf terrestrial gravity1 #aci ,leap year1 #fd ,leo1 #cgj ,leo ,minor1 #cgb ,libra1 #cgj ,librations of the moon1 #agi ,light1 velocity of1 how measured1 #beb ,longitude1 celestial1 #bd terrestrial1 #bb its importance1 #bjh how found1 #baj by chronometers1 #baj by eclipses1 #bab by ,jupiter's satellites1 #bea by lunar method1 #bac ,lucifer1 #cig ,lynx1 #cgb ,m4 ,magnitudes1 how measured1 #id ,magellan clouds1 #cgh ,mars1 #bde changes of1 #bde distance of1 #bde revolutions of1 #bdf ,mecanique ,celeste1 #adh ,mercury1 #bcj conjunctions of1 #bca diurnal revolution of1 #bce phases of1 #bcd sidereal revolut'n of1 #bca synodical revolut'n of1 #bca transits of1 #bcg ,meridian1 #bj ,meteoric showers1 #cdf origin of1 #cej ,meteoric stones1 #bij ,metonic cycle1 #aib ,miletus1 school of1 #cid ,milky ,way1 #cgi ,mira1 #cge ,mirach1 #cga ,mizar1 #cgd ,month1 sidereal1 #agc synodical1 #agc ,moon1 #aeg atmosphere of the1 #afg cusps of the1 #agd diameter of the1 #aeh distance of the1 #aeh eclipses of the1 #aie harvest1 #agg irregularities of the1 #ahf librations of the1 #agi light of the1 #aeh mountains in the1 #aei nodes of the1 #agc phases of the1 #agd revolutions of the1 #agh-ahb scenery of the1 #afc telescopic appearance of the1 #aeh volcanoes in the1 #aff volume of the1 #aeh ,motion1 laws of1 #abf ,motions of the planets1 #bia ,mural circle1 #ed ,n4 ,nadir1 #bj ,nature of the stars1 #cij ,nebul1 #cgg ,new planets1 #bhf distances of1 #bhh origin of1 #bhi periods of1 #bhh size of1 #bhi ,new style1 #ff ,newton1 #af1 #adc ,o4 ,oblique sphere1 #hd ,obliquity of the ecliptic1 #aae effect of1 on the ,seasons1 #abc how found1 #aag ,observatory1 #db ,greenwich1 #db-dh ,tycho's1 #db ,old style1 #ff ,ophiucus1 #cgb ,opposition1 #bjj ,orion1 #cge ,orreries1 #aab1 #bib ,p4 ,pallas1 #bhg ,parallactic arc1 #ia ,parallax1 #ij1 #chi annual1 #chg horizontal1 #ic how found1 #id ,parallel sphere1 #hd ,parallels of latitude1 #bd ,pegasus1 #cgc ,pendulum1 #gi ,perigee1 #ahg ,periodical inequalities1 #aic ,perseus1 #cga ,pisces1 #cga ,piscis ,australis1 #cga ,planets1 #bbe distances of1 #bbh inferior1 #bbg magnitudes of1 #bbi periods1 #bbi superior1 #bdc ,pleiades1 #cfi ,pointers1 #cgd ,polar distance1 #bb ,polaris1 #cgc ,pole1 #ai of the earth1 #ba ,pollux1 #cfi ,power of the ,deity1 #djh ,prsepe1 #cfi ,precession1 #aee ,prime vertical1 #bj ,primum mobile1 #cih ,principia1 #adg ,procyon1 #cge ,projection of the sphere1 #bg ,proper motions of the stars1 #chd ,ptolemaic system1 #cii ,ptolemy1 #cih ,pythagoras1 #cid ,q4 ,quadrant1 #ah ,r4 ,radius1 #ag ,refraction1 #ie ,regulus1 #cgj ,resolution of motion1 #acb ,resultant1 #acb ,revolution1 annual1 #aaa diurnal1 #aaa ,rigel1 #cge ,right ascension1 #bc ,right sphere1 #hc ,s4 ,sagittarius1 #cgj ,saros1 #aib ,saturn1 #bgd diameter of1 #bgd ring of1 #bge satellites of1 #bhb scenery of1 #bhc ,scorpio1 #cgj ,seasons1 #aai ,secondary1 #ai ,secular inequalities1 #aic ,serpent1 #cgc ,sextant1 #eg ,sidereal day1 #ha month1 #agc ,signs1 #bc ,sirius1 #cge ,solstices1 #bc ,sphere1 celestial1 #ai doctrine of the1 #af oblique1 #hd parallel1 #hd right1 #hc terrestrial1 #ai ,spica1 #cgj ,spots on the sun1 #ajd cause of1 #ajf dimensions of1 #aje number of1 #ajd ,stability of the universe1 #daj ,stars1 fixed1 #cfe ,stylus1 #fc ,sun1 #aja attraction of the1 #aaj density of the1 #ajc diameter of the1 #ajb distance of the1 #aja mass of the1 #ajc nature and constitution of the1 #ajg revolutions of the1 #ajd ,sun1 spots on the1 #ajd volume of the1 #ajc ,supplement1 #ah ,system of the world1 #cib-djf ,brahean1 #djc ,copernican1 #dja ,ptolemaic1 #cii ,t4 ,tangent1 #abi ,taurus1 #cfi ,telescope1 the1 #ca achromatic1 #cd directions for using1 #ci ,dorpat1 #cg ,herschelian1 #cf history of1 #cc reflecting1 #cd ,temperature1 changes of1 #abd ,temporary stars1 #chj ,terminator1 #aai1 #aei ,thales1 #cid ,tides1 #baf cause of1 #baf spring and neap1 #bai ,time1 #ei apparent1 #fa equation of1 #fa mean1 #fa sidereal1 #fj ,transits1 #bcg ,triangulation1 #ge ,tropic1 #aag ,twilight1 #ih ,u4 ,unity of the ,deity1 #djg ,uranus1 #bhc diameter of1 #bhc distance of1 #bhd history of1 #bhd period of1 #bhd satellites of1 #bhd scenery of1 #bhe ,ursa ,major1 #cgc ,ursa ,minor1 #cgc ,v4 ,variable stars1 #cgi ,venus1 #bcj conjunctions of1 #bca mountains of1 #bcg phases of1 #bcd revolutions of1 #bcb transits of1 #bci ,vesta1 #bhh ,vindemiatrix1 #cgj ,virgo1 #cgj ,y4 ,year1 astronomical1 #fc tropical1 #aef ,z4 ,zenith1 #bj ,zenith distance1 #ba ,zodiac1 #be ,zodiacal light1 #cfc ,zones1 #be ,,recent ,,discoveries4 ,improvements in the ,telescope1 #dad ,rosse's ,leviathan ,telescope1 #dae ,pulkova and ,cambridge ,telescopes1 #dae ,improvements in instrumental ,measurements1 #daf ,new ,planets and ,asteroids1 #daf ,great ,comet of #ahdc1 #dag ,distances of the ,stars1 #dah ,discovery of ,neptune1 #dai ,recent telescopic discoveries1 #dbj ,longitude by the ,electric ,telegraph1 #dbb 99 99 99 99 99 ,transcriber's ,notes ,obvious punctuation and spelling errors repaired4 ,greek transliterations are inclosed by equals signs4 ,inconsistent hyphenation has been repaired4 ,characters that could not be fully expressed are unpacked and shown within braces1 e4g4 oblong symbol4 ,in ambiguous cases1 the text has been left as it appears in the original book4 ,in particular many mismatched quotation marks1 have not been changed4 ,page #bf1 knittingneedle changed to knitting needle4 ,page #bda1 trignometry changed to trigonometry4 ,page #cjc1 dedecaedron changed to dodecaedron4 ,page #cib1 generrally changed to generally4