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dicted. If some obscurity still rests over the nature of | brook, are only familiar and particular instances of a comets and their trains, yet we know that they consti- great law extending throughout the universe, and contute one family with the planets. They all move in trolling alike the mote which glitters in the sun-beam elliptic orbits ; for as to parabolic orbits, we may al- and the planet which sweeps iis ample rounds through ways substitute elliptic ones more or less elongated, the regions of space. which will satisfy observations equally as well. Much In the second place, astronomy furnishes us with our less has any orbit been proved to be hyberbolic. This measure of time. We have no adequate means of meabinds all of them to our system as component parts, suring time but by motion; and motion for this purand subjects them to the same dynamical laws which pose must be perfectly uniform. If the force of gragovern all the rest. On account indeed, of the great vitation is always the same at the same place—which is eccentricity of their orbits, and the smallness of that not only very probable but susceptible of experimental portion of each which is visible to us, we cannot calcu- proof-it can be mathematically demonstrated, that the late their periodical times with the same precision as in oscillations of a cycloidal pendulum, as well as those of the case of the planets ; still the returns of several have a pendulum vibrating in extremely small circular arcs, been determined with sufficient accuracy to warrant the are isocronous. Such a pendulum therefore might furassertion, that if our data could be obtained more pre nish us a unit of time : yet it would be an objectionable cisely, their periods might in all cases be truly estima- one in several respects. In the first place, there is nothled. In regard to a collision between one of these ing requiring us to adopt a pendulum of one length rathbodies and the earth, it may be shown to be impossible, er than another ; the unit of time then would be different so far as the 117 comets whose orbits have been calcu- at different places, unless mankind agreed universally to ted, are concerned. If the perihelian distance exceeds adopt one of the same length. In the second place, should the distance of the earth from the sun, the orbit of the they thus agree, to say nothing of the practical difficulty comel, though in the place of the ecliptic, must include of making two pendulums of precisely the same length, that of the earth : so that in this case there canno: pos- these pendulunis will not vibrate equally when suspendsibly be a collision. If the perihelian distance be less ed at different points upon the earth's surface. In the than the distance of the earth from the sun, and the or- third place, the oscillation of a pendulum, is a portion bit still in the plane of the ecliptic, there will be two of time too small to serve as a unit. While then the intersections, and consequently iwo chances of encoun- pendulum in the present improved state of its applicater, but this case is not to be found in nature. All of tion to clocks, is of very essential service in dividing the known orbits are inclined to the ecliptic, and gene- time into minute portions, for the reasons just stated rally at a very considerable angle; in such a manner, it cannot afford a convenient standard of time. that when the radius vector is equal to that of the earth, Writers on physical astronomy have proved that its latitude is so great, that the comet will pass at a con- among the ever varying elements of the solar system, siderable distance either above or below the earth. But the period of the earth's rotation on its axis is immutaare we not in danger of being enveloped by one of those ble. Many causes indeed might be conceived to affect vast luminous appendages extending so many millions the truth of this statement: such as the descent of riof miles? Not at all. The tail is always upon the pro- vers–the ascent of vapors—the projected matter of longation of the radius vector, so that to envelop the volcanoes-the constani friction of the trade windsearib, it is necessary for the comet to be at the same time and the action of the sun, moon and planets, which is in its inferior conjunction and at one of its nodes ; condi. known to be quite considerable in modifying its motion tions difficult to be united, if not wholly incompatible. in its orbit. But not one of these singly, nor all comNeilber have we any thing to fear from the periurbing bined, can produce any perceptible effect upon either force of such comets as approach the nearest to us. The the period or the axis of rotation. By this uniform nearest of all was that of 1770, which approached within rotation then, we are furnished with as perfect a stand800,000 leagues; but Dusejour has shown that the ef- ard of time as we could wish. Yet its practical applifects would be inconsiderable at the distance of 13,000 cation is encumbered with some difficulties. If the leagues. And we do certainly know that our astronomi- stars were absolutely fixed, the successive returns of cal tables have needed no corrections on account of the any one of them to the meridian of a place, would mark attraction of comets; a sufficient proof of the smallness the period of that rotation, and the siderial days would of their nucleus and the extreme tenuity of the matter all be equal among themselves. But there are derangcomposing their trains. If additional evidence of this ing causes, variable in their effects, both as to degree fact were required, it is furnished by the comet of 1770; and direction, which render the transits of all the stars which actually became entangled among the satellites unequal, when compared, the one with another. These of Jupiter, and yet produced no perceptible derange- inequalites are indeed extremely small, and altogether ment in their motions. (Se Astronomie par Delambre, imperceptible in the course of a few days. But still T. III. Ch. 20.)
they exist, and become perceptible in their accumulaFurthermore, chymistry and its kindred sciences tions. If, however, we define a siderial day to be the have been very justly considered important, by reason time of the earth’s rotation, although it is not equal of the erroneous impressions they have served to re- precisely to the interval between the transists of a star, move relative to the constitution of the material world; yet it is a quantity which may be calculated from that nor has astronomy been less serviceable in this respect. interval, and therefore available as a unit of time. But
The stars are no longer believed to preside over the our daily occupations and our seasons of labor and of destinies of men. We consider it of no great conse- rest being regulated by the motion of the sun, it is very quence now-a-days under what aspect of the planets a desirable to adopt its transits as our measure of time, man be born; and the points of the horoscope are instead of those of a fixed star. For if we were to mere objects of curiosity. The sun, planets, and as reckon the day as commencing at the arrival of any serablage of fixed stars are no longer linked severally star on the meridian, in the course of a year this arrival to transparent shells, by the revolution of which they would happen when the sun would be at all possible are carried about us in twenty-four hours. The earth angular disiances from the same meridian, and conseis no longer the centre of the universe, essentially en- quently our days so reckoned would be commencing at dowed with immobility and extending indefinitely be different parts of the working day, which is naturally neath and around us : but takes its place as an incon- determined by the sun. Hence mankind have univer. siderable satellite to the sun, and by a double motion, sally agreed to make use of the motion of the sun as a the one on its axis, and the other in its orbit, gives rise standard of time; the returns of which to the same meri. to the succession of day and night, and the recurrence dian and equinox, constitute the day and the year. But of the seasons. We no longer stand in need of vorti- the solar days are not equal among themselves, for two ces to explain the celestial motions, but are perfectly reasons: the first is, because the proper motion of the assured that the falling of a leaf, and the running of a sun is unequal, owing to the eccentricity of its orbit;
the second is, because its proper motion is not in the fective. The zenith distance of the sun at Alexandria, plane of the apparent revolution of the heavens, owing was observed with a very imperfect instrument; no to the obliquity of the ecliptic.
allowance was made for atmospheric refraction-for the To make the inequality of the proper motion arising parallax and semi-diameter of the sun-and the dis. from the eccentricity of the orbit disappear, we ima- tance between Alexandria and Syene was rudely meagine a second sun to move uniformly in the ecliptic, sured along the surface of the earth. But modern and to arrive at the extremity of the major axis, at the science has brought this method to a great degree of same instant with the true sun. To make the inequality perfection, and as conducted in England by Colonel arising from the obliquity of the ecliptic disappear, we Mudge, in France by Delambre and Mechain, in Peru imagine a third sun to move uniformly in the equator, by Bouguer and La Condamine, and in Lapland by so as to pass the equinoxes at the same moment with Clairaut and Maupertuis, is one of the proudest monuthe second sun. The interval between the transits of ments of the scientific character of the age. The the third sun constitutes the mean solar day; that be- lengths of a degree of the meridian, when ihus meatween any two consecutive transits of the true sun, the sured under different latitudes are found to be unequal. true solar day; and the difference between these days is They increase from the equator to the pole, and very the equation of time. It is to the motion of this third nearly in the ratio of the squares of the sines of latisun, or to mean time, we adjust our clocks and watches; tude. These data being ascertained, it is a simple and we obtain it always from the true time by apply. mathematical problem to determine the solid of revoluing the equation of time, which is beforehand accu- tion which is best adapted to them. We thus find the rately calculated for every day and hour of the year. earth to be an elliptic spheriod, whose equatorial radius In these remarks, we have supposed the position of the is equal to 3962.6 miles, and polar radius to 3949.7 equinoxes and the obliquity of the ecliptic to be con- miles; its compression being represented by the fracstant. They both however are variable; and it is im- tion 1-309 nearly. portant to ascertain the effect which their variations The second method is, by observing the intensity of will have on the length of the mean day. This has gravitation at different points on the earth's surface ; been done by Laplace, who has proved that its length which is done very accurately by means of the seconds will be altered only a few seconds in the course of many pendulum. The length of a pendulum vibrating semillions of years. (Méchanique Celeste. B. V. Ch. 1.) conds is found to increase from the equator to the poles
The return of the second sun to the vernal equinox in the ratio of the squares of the sines of latitude. determines the tropical year. I ought properly to say Instead then of the measured length of a degree on difsomething here relative to the determination of the ferent parts of a meridian, as in the former case, we length of the year, and to the several revisions which may employ the lengths of a pendulum which vibrates have been had of the calendar. I have already, how seconds at these same points; since they increase acever, unduly extended my remarks upon this branch of cording to the same law. And this method indeed is to our subject, and must pass on to others.
be preferred somewhat to the former one, because it is In the third place : although the appearances both easier of application, and the irregularities of the earth, on land and sea, and particularly the changes in the affect the observations in a much less sensible manner. zenith distances of the stars, which are so very ob The third method is, by observing the inequalities in servable in travelling towards either pole, did at an the motion of the moon, which result from the want of early period suggest the idea of the earth's surface perfect sphericity in the earth, and comparing the being in some manner curved; yet the notions enter-values derived from observation, with those which retained were generally fanciful and incorrect; as that of sult from theory, on the supposition that the earth is an Aristotle's, for instance, who supposed the curvature to elliptic spheriod, which exerts upon the moon an action extend but in one direction, or in other words, that the modified by its figure. Pontécoulant considers this as earth was shaped like a drum. Further observation the most wonderful result of the application of analysis soon, indeed, corrected this, and other equally absurd to the law of universal attraction, and as meriting a notions, and induced the scientific of those early ages very important place in the history of the progress of to settle down in the opinion that its shape was a per- the human mind. Laplace first conceived the idea, and fect sphere. Under this supposition, we find Anaxi- in his immortal work, the Mechan que Celeste, has de mander, Eratosthenes and Posidonius, making rude at- veloped it in all its details. Employing the observa. tempts at ils measurement and the location of places tions of Burg, he finds the compression of the earth upon its surface. It was not, however, until astronomy equal to 1-304; which, considering the difficulties en had attained a greater degree of perfection, that the cumbering every other method, is to be relied on as the true figure and size of the earth beceme known. Mo- most correct determination. dern astronomy furnishes four methods by which this Tlie fourth and last method is, by the nutation of the important problem may be solved.
earth's axis, and the precession of the equinoxes. This The first is, by the actual measurement of arcs of me. does not determine the ellipticity of the earth precisely, ridians and of parallels on different parts of its surface. but defines limits within which its value must of necessiThe principle on which this method is founded, is ex- ty lie. These limits are 1-279 and 1-578. (See Theorie tremely simple. The difference between the zenith Analytique du Systeme du Monde, par Pontécoulant. T. II, distances of the same star observed at any two places p. 475.) on the same meridian, is the celestial arc which mea In the fourth place : how may we ascertain our true sures the distance between the zeniths of these places ; position on this globe of ours? In principle just as we and the distance between the places themselves is the should ascertain the position of any point upon that length of the corresponding terrestrial arc; and as this foor. By measurement we should obtain its perpendi. celestial arc is to 360 degrees, so is the length of the cular distance from two adjacent walls. This would terrestrial arc to the whole circumference of the earth. perfectly define the point, so that we could locate it acThus, on the day of the summer solstice, Eratosthenes curately upon a plot of the floor, were it required. So observed at Syene, that the sun shone perpendicular it is with regard to places upon the surface of the earth. into a well, and that the tallest objects had no shadow. We refer them to two fixed circles at right angles to The sun, therefore, was in the zenith of that place. each other; the one, any assumed meridian, and the On the same day the sun was observed at Alexandria other, the equinoctial line. The only difference is, that to be 7° 12' to the south of the zenith, and consequently instead of measuring, as in the instance of a point on this was the difference between the zeniths of the two the floor, in a straight line, and reckoning in feet and places. Then as 70 124: 360° : : 5000 stadia (the inches; we measure along circles, and reckon in degrees, measured distance between Alexandria and Syene) : minutes and seconds. The distance of a place from the 250,000 stadia nearly,—the circumference of the earth. equinoctial line we call latitude, and its distance from the This method as applied by Eratosthenes was very de.assumed meridian we call longitude. . I can here but
breifly allude to some of the simplest methods of find the night of the 28th it is agreed to explode a sky-rocket ing these two elements; and shall confine myself entire- in the neighborhood of Cumberland Court House, and ly to the principles upon which they are based. During that it may be seen from both this place and Richmond. the apparent revolution of the heavens, there are two on the appointed night, two observers, the one in points which have no motion. These are called poles of Lynchburg and the other in Richmond, take their stathe heavens, and the one which is visible to us is the lions at clocks nicely adjusted to the local times of the north pole. Upon any clear night the stars near this two places, and keep a look out for the expected explopole may be seen to describe circles whose circumferen- sion. On account of the great velocity of light, they ces are greater in proportion to their distances from it; will both see it at the same instant of absolute time; and all, whose disiances are less than the altitude of the and each notes down the moment of its occurrence as pole above the horizon, will never set. Such are called indicated by his clock. By comparing these moments circumpolar stars. It may be readily proved that the with each other, the difference of longitude in time is at latitude of any place is equal to the altitude of the pole once determined. Now in place of the sky-rocket, above the horizon of that place. If then the pole were substitute an eclipse of one of Jupiter's satellites, or an a point visibly marked out in the heavens, we should immersion of one of them into the shadow of its prionly have to take its altitude with a suitable instrument mary, or the beginning or ending of an eclipse of the and apply the correction for refraction, nutation, &c. to moon, or the true conjunction of the sun and moon in obtain the latitude of a place. But the pole is not thus an eclipse of the sun, and you will have the principle visibly marked, though there is a star of the second of several valuable and practical methods of finding ihe magnitude very near to it. It however will add but longitude. little to the difficulty of the problem, to observe the But the phenomena just spoken of, occur but occagreatest and least altitudes of a circumpolar star: the sionally, and require a telescope of moderate power. mean between which will be evidently the altitude of And considering how frequently the longitude is rethe pole, or which is the same thing, the latitude of the quired at sea, it is highly desirable to devise a method place. Again, the distance from the zenith to the equa- which may be employed daily if circumstances demand. ior (which is the latitude,) is equal to 900 minus the Such a method we have in lunar distances, first hinted altitude of the plane of the equator above the horizon. at by Werner, and applied by Frisius; and afterwards But the meridian altitude of the sun, plus or minus its perfected by Halley, La Caille and Maskalyne. The declination, according as it is south or north, is equal to principle of this method is simple, though its applicathe altitude of the equator. This then is another very tion is laborious. If the face of a clock were visibly ready method of observing the latitude of a place; and traced out in the heavens in characters so legible that is by no means confined to the sun. Any planet or all the world could read them, (See Herschel,) and fixed star will serve our purpose as well. Other methods, were nicely adjusted to Greenwich mean time; from as by the altitudes of any iwo fixed stars-by two alti- the remarks which I have made it is obvious, that by tudes of the same star-by the hour angle and azimuth the comparison of the local time of any place with that of the sun, while they are simple enough in practice, indicated by this celestial clock, we should at once obare too complicated to explain in a popular way. tain the difference of longitude between Greenwich and
The problem of finding the longitude of a place is not that place. Such a clock we have, unlike indeed our quite so easily resolved, although several methods have artificial ones in its construction, yet free from their been devised for this purpose. They all, however, are errors and derangements, and therefore greatly to be based upon a common principle, to explain which, we preferred, although a little more difficult to be interpreted. must first draw a distinction between absolute and local The apparent concave sphere is the dial-plate-the time. Absolute time is reckoned from some epoch com- fixed stars are the figures engraven upon its face and mon to the whole earth, as for instance, the arrival of the moon is the moveable index, which points out by the sun at the equinox'; while local time is reckoned its position among the stars the local time of that place from some epoch peculiar to a place, such for example, to which this celestial clock is set. It is adjusted to as the arrival of the sun to the meridian of a place, and Greenwich time in the following manner. The lunar is different for different places. Every well adjusted tables have been brought to such a degree of perfection clock shows local mean time, and without alteration, by the analytical researches of Laplace and the nuwould not answer for any other place under a different merical calculations of Delambre, that we may ascermeridian. A watch, for example, adjusted to the mean tain years before hand and for any given moment the time of Lynchburg, would not answer for Richmond or precise angular distance of the moon from any fixed Nashville. Now, in what does this difference between star. These calculations are made for very short interthe local times of any two places, consist? In nothing vals of time and for the meridian of Greenwich and more than the lapse of time which the sun requires to inserted in the nautical almanac. Then if at any place, pass from the meridian of the one place to that of the as at this for instance, by means of a suitable instruOther; and since it passes over 360° in 24 hours, it will ment, we observe the distance of the moon from any pass over 15° in one hour, and so on proportionally for noted fixed star near to and in the direction of its path, shorter intervals of time. So that if we knew the dif- together with the altitudes of the moon and star, we ference of the local times of any two places, we should have the data necessary for calculating the precise hour know their difference of longitude, by simply converting of the observation and the true distance corresponding the difference of their times into degrees, minutes and to that hour. Opposite this true distance in the nautiseconds, on the principle above explained. If a watch cal almanac, the corresponding Greenwich time is tabuthen, perfectly regular in its motion, were adjusted to lated. The difference of these times, is the difference Lynchburg tíme, and being transported to Richmond, of longitude, as in the former methods. It may be well were placed by the side of one equally regular and ad- to remark here, that though the details of this method justed to the time of that place, a simple comparison of are numerous and tedious, its accuracy in the hands of their faces would give us the difference of the longitudes skilful observers, has been abundantly tested-especiof the two places. But watches and clocks cannot be ally in the voyages of Maskelyne and Rossel. These made to run with perfect regularity. Much indeed has are the most important methods of calculating the pobeen done to bring them to a considerable degree of sition of places on the earth. And of what immense perfection, and for the space of a few hours their irregu- advantage are they to the interests of mankind ! Withlarity may be rendered quite imperceptible. To have out them, each one's knowledge of the earth would the full advantage, however, of a time-piece, it must be have been limited to his own narrow observations and ftationary and its rate of going tested frequently by the vague and uncertain information of itinerants. delicate observations. This is incompatible with its Maps and charts, and a science of geography, would removal from place to place, as above spoken of;—but have been unknown. No whitening sail would have this difficulty may be thus obviated. Suppose, that on I been seen upon that vast expanse of waters which
separates our continents: and no country could have cation of the pendulum, depends upon two principles had any other commerce than such as might be carried immediately deduced from the law of gravitation. The on along its winding shores and its inland streams. first is, that the vibrations of a pendulum are isochronal,
In the fifth place: the interests of every commercial provided the arcs of vibration be extremely small. The people, require that all measures of length, weight and second is, that the same pendulum will perform an capacity in use among them be uniform. They cannot equal number of vibrations in equal portions of time, be so rendered unless proper units be assumed, by com- provided its length remains unaltered. The immediate parison with which all others may from time to time be deduction from the last mentioned property is, that the iested, and if erroneous, corrected. New measures are length of a pendulum made to virbrate seconds at any not generally taken immediately from these assumed place is an invariable quantity: Now by an act of unils, but from others which have been so iaken; and Parliament, the yard is declared to be made up of 36 as it is extremely difficult, if not impossible to cui iwo equal parts, the length of each of these being such, rods of precisely the same length, after a while, errors that 39 of them and 131–1000 of a part shall constitute of a considerable magnitude arise: as one may convince the length of a seconds pendulum vibrating under the himself by referring to a Report made to ihe U. S. circumstances above mentioned. Should every measuSenate in 1821, on" Weights and Measures,” by J. ring rod in the kingdom, together with all measures of Q. Adams; or to one more recently made in accordance weight and capacity, be destroyed, how easy would be with a resolution of Congress by F. S. Hassler. For the task to restore them. For this purpose, we have example, the Winchester bushel was made, by an act only on the prescribed latitude, in the vacuum of an of Congress, the standard dry measure of capacity, and air pump and at 600 F., to so adjust the length of a ordered to be used in all the custom houses ihroughout pendulum, that it shall perform 86,164 oscillations duthe Union. But in Hassler's “Report,” we find the ring the revolution of a fixed star. Then if the length bushel measure at Newburn, N. C., containing 87lbs. of this pendulum be divided into 39.134 equal parts, 8oz. of distilled water at 400 of Fahrenheit, while that thirty six of these will be the yard. Having thus restoat Washington, N.C. contained only 721bs. 12oz. Here red the unit of linear measures, those of weight and cawe have a difference of 14lbs. 12oz. between these pacity follow of course, since by the act of Parliament two measures purporting to be the same. Again, the above referred to, they are made to depend upon linear capacity of the bushel at Bath, Me., is recorded as measurement. It may be well just here to remark, that being 1925 cubic inches—that at Norfolk, Va., 22254 the mutual convertibility of the points of suspension cubic inches-and that at Plymouth, Mass., 2359 cubic and oscillation in the compound pendulum, as practicalinches. Between the two former, there is a difference !y applied by Capt. Kater, enables us to measure the of 300} cubic inches ; and between the first and third, lengih of the seconds pendulum with extreme accuracy. a difference of no less than 434 cubic inches. These The standard above explained is not without its objec. reports show similar diversities among the measures tions. One far more elegant and scientific, though not of length and weight. With a view to correct these so readily applied, is that employed by the French. errors, proceedings were instituted by Congress in The 1-10,000,000th part of the quadrant of a meridian 1831, under the personal supervision of Mr. Hassler, they assumed to be the metre-their unit of linear meaby whom the necessary units were procured and laid sure. In order to recover it at any time, it is only neup in the Department of State, and correct copies cessary to measure the quadrant of the meridian with a distributed to the various custom houses. The units rod of any arbitrary and unknown length. Suppose the of measure to be employed in this adjustment, were length of the meridian proves to be 8,000,000 of this declared by an act of Congress to be as follows; viz: arbitrary rod. This rod then is to the metre as 10,000,000 the troy pound, made by Capt. Kater, in 1824, for the to 8,000,000, or as 10 to 3. In other words, if this rod U. S. Mint, and at the special request of Mr. Gallatin, be divided into 10 equal parts, 8 of them will be the was adopted as the unit of weights. This pound is length of the metre. "Doubtless an error will occur in subdivided into 5760 grains, and the pound avoirdupois measuring the quadrant of the meridian : but only the made to consist of 7000 such grains.' The bushel was 1-10,000,000th part of this can effect the metre. (For made the unit of dry measure, and contains 77.6274 Ibs. fuller details see Base du Systeme Metrique.) avoir, of distilled water at 400 Fahrenheit. The gallon In the sixth place : the application of astronomical was made the unit of liquid measure, and contains science to the determination of chronological dates, is 8.33888lbs. avoirdupois of distilled water at the same one in which the learned have always been deeply temperature. A copy of the yard laid up in the interested. To such a degree of perfection have the Exchequer of England, and made by Thomas Jones of solar and lunar tables been brought, that the state of London at the request of our State Department, was the heavens at any former period may be ascertained made the unit of lengibi.
with great precision. Any well attested observation, It is evident that all our measures of length, weight therefore, made by ancient astronomers, enables us to and capacity are referred to these particular units, and ascertain the time at which the observation was made. by comparison with them, are to be corrected. But I must limit myself to two or three illustrations these units are liable to be lost by fire, by foreign inva. In an ancient volume, which escaped the general con. sion, or by some other accident. And if not so; yet by Nagration of the Chinese books by order of the emperor use and by corrosion, the metals of which they are Tsin-chi-hoang, 246 years before the christian era, there composed may perceptibly wear away. How important is recorded an observation of Tcheou-Koung: by which then is it to fix some standard of measures, which will be ascertained that at the city of Loyang, å gnomon of be independent of moral revolutions, so that it may be 8 Chinese feet cast, on the day of summer solstice, a consulted centuries hence with the same results we ob- shadow of 1.5 feet: and on the day of winter solstice a tain now; and to which the units above spoken of may shadow of 13 feet. These measured lengths of the themselves be referred for correction if erroneous, or for shadows at the two solstices, enable us to deduce the restoration if lost. In not containing a provision of extreme distances of the sun from the zenith of Loyang. this sort, the act of Congress on "Weights and Mea. Indeed, in each case the zenith distance is nothing more sures” is manifes:ly defective. The governments of than the angle which the solar rays made with the England and France have paid very special attention to axis of the gnomon, the tangent of which in the first, is this point. The former has adopted as a standard, the expressed by 1.5-8, and in the second by 13-8. After length of a pendulum vibrating seconds on the parallel of making the necessary corrections for the semi-diameter London in the vacuum of an air-pump and at 60° of F. of the sun, parallax and refraction, we find the zenith The latter the one-10,000,000th part of the quadrant of distance at the summer solstice to be 109 534 74.5); a meridian. These are the only standards as yet and the zenith distance at the winter solstice to be known; and their accuracy depends upon the improved 580 41 131.81. The half sum of thes distances, riz: state of astronomy and the arts. This beautiful appli-| 34° 47' 104.66, is the latitude of Loyang ;-the half dif
ference, viz: 230 54 31.15, is the obliquity of the ecliptic the magnitudes and distances of the heavenly bodies, al the time of observation. But this obliquity is a va are fanciful and false. This, however, is a mistake. riable quantity, whose law of variation is well known, By measuring the height of the building we now occupy, and by which we can determine what the obliquity was and by taking the angles at its summit and base beat any given time past, or at what time the obliquity tween a vertical line, and an imaginary one drawn to was of a given value. The time corresponding to its any distant point, as for example to the top of the value as deduced from the above observation, is 1100 Peaks of Otter, every schoolboy knows that the distance years B.C. This determination is altogether accurate, of that point from us becomes known. Such precisely provided the observation of the Chinese philosopher be is the solution of the problem for finding the distance of $0. This, however, can be tested ; and as follows. the earth from the sun. And I venture to assert, that Geographers agree that the place formerly called Loy- a mechanic could not by means of a foot rule, ascertain ang, is now called Hou-an-fou. Three observations on the length of this floor, without making a proportionathe latitude of this place, performed by Father Gaubie, ble error greater than that which enters into our estia learned missionary to China, give for its value 340 mated distance from the sun. For, if in applying the 47' 13#; which differs but 21 from the result of Tcheouo rule successively along the floor about 50 times, he Koung. (See Biot or Freret.)
should make an error of only the one fiftieth of an inch, The next example I will introduce in the words of this will allow an error of 3,200 miles in an equally Bailey as quoted by Brayley. “There is probably no accurate measurement of the distance of the earth from fact in ancient history, that has given rise to so much the sun-an error so great, that it is excluded by the interest as the solar eclipse, mentioned by Herodotus, perfection of modern astronomical instruments. This and which, owing to a singular coincidence, put an end distance is thus found to be about 96,000,000 of miles : to a furious war that raged between Cyaxares, king of and its diameter, which is readily deduced from its disMcdia, and Alyattes, king of Lydia. According to the tance, such that if its centre coincided with that of the account given by that historian, the contest had con earth, ils radius would extend to nearly double the distinued five years: in the sixth, there was a sort of noctur- tance of the moon from us, although the distance of this nal combat. For, after an equal fortune on both sides, satellite is not less than 237,000 miles. Far as the and whilst the two armies were engaging, the day sud- earth seems to be from the sun, yet it is near compared denly became night. The Lydians and the Medes, see- with the distance of the planet Uranus. At this point ing that the night had thus taken the place of the day, our progress is stayed—a point, seen from which, our own desisted from the combat, and both parties became sun is reduced to a mere speck. Beyond this ulmost desirous of making peace. The fact is here very clearly verge of our own system, and between it and the nearrelated; but, unfortunately, there is nothing, either in est star, “there is a great gulf fixed,” which it is imposthe statement itself, or in the contiguous passages to sible for calculation to pass. Forsakir the infinitesidetermine, with any degree of accuracy, the time mal dimensions of our own globe, we eagerly seize wherein this singular phenomenon took place. And upon the diameter of our orbit as the base of a triangle this is the more to be regretted, because the dates of whose apex shall extend to the stars. But sublime as several other events, might be determined if the era of the assumption is, it proves ineffectual: for our orbit this eclipse were correctly known.”
itself, whose diameter is 192,000,000 of miles, dwindles From other sources we know that this eclipse must to a mere point compared with the distance of the have occurred between the years 580 and 650 B.C. It nearest fixed star. But there is abundant reason to beis only necessary then to calculate all the solar eclipses lieve that the fixed stars are of the same nature with visible in Asia Minor during this interval of 70 years: our sun, and made to fulfil similar offices of shedding a labor which has been performed with ability by light and heat to attendant planets; and from what we Bailey. And in all this time, he found only one eclipse know of our own system, we cannot put from us the which fulfilled the conditions required. This happened conclusion that all of the others are contrived for the on Sept. 30th, 610 B. C. It was total, to part of Asia abode of animated and rational creatures. How magMinor, Armenia and Media ; "and the path of the nificent is the scale of creation here presented to us! moon's umbra lay in the very track in which the two Where shall we find a parallel ? Whether we consider hostile armies probably met. For it passed over the the number--the magnitude-the distances of the heamouth of the Halys, just at the point at which Crasus, venly bodies-or the ends they probably subserve, we the immediate successor of Alyattes, crossed that river are at once elevated to conceptions by far too vast for in order to attack the Median empire."
the grasp of a finite mind. Here is an exhibition which The last illustration I shall give, under this head of overwhelms us with the omnipotence of Him who spake, our subject, is the detection of an error of upwards of and it was done! I cannot forbear to add, that the use four years in the vulgar era of our Saviour's birth-an made of such contemplations by the eloquent Psalmist, era which owes its origin to Dionysius Exiguus, a Ro- was no less philosophical than devout. Feeling the full man abbot.
force of the argument of the existence and the power of Josephus records an eclipse of the moon as happening God drawn from the grandeur of the universe, he exduring the last illness of Herod. This eclipse by com- claims--"The Heavens declare the glory of God, and pulation, must have occurred on March 13th, 4710 of the the firmament sheweth his handy work. Day unto day Julian period. Our Saviour was born at that time ; for uttereth speech, and night unto night sheweth knowHerod sought the life of the young child. The latestledge. There is no speech nor language where their time, therefore, at which we can fix the era of his birth, voice is not heard.” That many very eminent cultiva. is about the end of the year 4709 of the Julian period; cors of this science have been infidels, and some of them whereas our vulgar era places it in the year 4713—at atheists, I am ready to admit. But this is only another least four years too late.
confirmation of the well established truth : that without These instances will serve to show, in what manner the light of Revelation and those corresponding affechistory owes its best established dates to astronomy. tions of heart which it is intended to produce, man sees
In the sixth and last place : passing by many very not God in the works of his power. The whole history interesting relations which astronomy bears to other of our species abundantly confirms this remark. To sciences, I will conclude this lecture with a few remarks take but one instance, and that a very familiar one : in upon the vast conceptions of the power of God, which what age or portion of the world, was there ever exthis science above all others impresses upon the mind libited a development of mental energy, surpassing to say nothing of his wisdom and goodness which we that which adorned the republic of Greece? It was the find everywhere displayed in the laws which he has country of a line of heroes from Codrus to Philopemen. chosen for the government of all those various motions There, the sculptured marble and the painted canvass which we observe in the universe. It is too frequently were well nigh made to breathe. There flowed the supposed that the estimates of astronomers relative to I majestic numbers of a Homer, and the exquisitely po,