brook, are only familiar and particular instances of a great law extending throughout the universe, and controlling alike the mote which glitters in the sun-beam and the planet which sweeps its ample rounds through the regions of space.

dicted. If some obscurity still rests over the nature of | comets and their trains, yet we know that they constitute one family with the planets. They all move in elliptic orbits; for as to parabolic orbits, we may always substitute elliptic ones more or less elongated, 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 severa! 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 nothted. 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 comet, though in the plane of the ecliptic, must include of making two pendulums of precisely the same length, that of the earth; so that in this case there cannot pos- these pendulumis 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 two 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 vast luminous appendages extending so many millions of miles? Not at all. The tail is always upon the prolongation of the radius vector, so that to envelop the earth, it is necessary for the comet to be at the same time in its inferior conjunction and at one of its nodes; conditions difficult to be united, if not wholly incompatible. Neither have we any thing to fear from the perturbing force of such comets as approach the nearest to us. The nearest of all was that of 1770, which approached within 800,000 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 leagues. And we do certainly know that our astronomical tables have needed no corrections on account of the attraction of comets; a sufficient proof of the smallness of their nucleus and the extreme tenuity of the matter composing their trains. If additional evidence of this fact were required, it is furnished by the comet of 1770; which actually became entangled among the satellites of Jupiter, and yet produced no perceptible derangement in their motions. (Se Astronomie par Delambre, T. III. Ch.20.)

ble. Many causes indeed might be conceived to affect the truth of this statement: such as the descent of rivers-the ascent of vapors-the projected matter of volcanoes--the constant friction of the trade windsand the action of the sun, moon and planets, which is known to be quite considerable in modifying its motion in its orbit. But not one of these singly, nor all combined, can produce any perceptible effect upon either the period or the axis of rotation. By this uniform rotation then, we are furnished with as perfect a stand

cation is encumbered with some difficulties. If the stars were absolutely fixed, the successive returns of any one of them to the meridian of a place, would mark the period of that rotation, and the siderial days would all be equal among themselves. But there are deranging causes, variable in their effects, both as to degree and direction, which render the transits of all the stars unequal, when compared, the one with another. These inequalites are indeed extremely small, and altogether imperceptible in the course of a few days. But still 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 semblage 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 distances 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 universiderable 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 merito 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 to the obliquity of the ecliptic.

was observed with a very imperfect instrument; no allowance was made for atmospheric refraction-for the parallax and semi-diameter of the sun-and the distance between Alexandria and Syene was rudely measured along the surface of the earth. But modern science has brought this method to a great degree of perfection, and as conducted in England by Colonel Mudge, in France by Delambre and Mechain, in Peru by Bouguer and La Condamine, and in Lapland by Clairaut and Maupertuis, is one of the proudest monuments of the scientific character of the age. The lengths of a degree of the meridian, when thus measured under different latitudes are found to be unequal. They increase from the equator to the pole, and very nearly in the ratio of the squares of the sines of latitude. These data being ascertained, it is a simple tion which is best adapted to them. We thus find the earth to be an elliptic spheriod, whose equatorial radius is equal to 3962.6 miles, and polar radius to 3949.7 miles; its compression being represented by the frac tion 1-309 nearly.

To make the inequality of the proper motion arising from the eccentricity of the orbit disappear, we imagine a second sun to move uniformly in the ecliptic, and to arrive at the extremity of the major axis, at the same instant with the true sun. To make the inequality arising from the obliquity of the ecliptic disappear, we imagine a third sun to move uniformly in the equator, so as to pass the equinoxes at the same moment with the second sun. The interval between the transits of the third sun constitutes the mean solar day; that between any two consecutive transits of the true sun, the true solar day; and the difference between these days is the equation of time. It is to the motion of this third sun, or to mean time, we adjust our clocks and watches; and we obtain it always from the true time by apply-mathematical problem to determine the solid of revolu ing the equation of time, which is beforehand accurately calculated for every day and hour of the year. In these remarks, we have supposed the position of the equinoxes and the obliquity of the ecliptic to be constant. They both however are variable; and it is important 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 dif something 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 easier of application, and the irregularities of the earth, affect the observations in a much less sensible manner.

In the third place: although the appearances both on land and sea, and particularly the changes in the 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 demander, Eratosthenes and Posidonius, making rude at-veloped it in all its details. Employing the observatempts at its measurement and the location of places upon its surface. It was not, however, until astronomy had attained a greater degree of perfection, that the true figure and size of the earth beceme known. Modern astronomy furnishes four methods by which this important problem may be solved.

The first is, by the actual measurement of arcs of meridians and of parallels on different parts of its surface. The principle on which this method is founded, is extremely simple. The difference between the zenith distances of the same star observed at any two places on the same meridian, is the celestial arc which measures the distance between the zeniths of these places; and the distance between the places themselves is the length of the corresponding terrestrial arc; and as this celestial arc is to 360 degrees, so is the length of the terrestrial arc to the whole circumference of the earth. Thus, on the day of the summer solstice, Eratosthenes observed at Syene, that the sun shone perpendicular into a well, and that the tallest objects had no shadow. The sun, therefore, was in the zenith of that place. On the same day the sun was observed at Alexandria to be 7° 12' to the south of the zenith, and consequently this was the difference between the zeniths of the two places. Then as 7° 12′: 360° : 5000 stadia (the measured distance between Alexandria and Syene) 250,000 stadia nearly, the circumference of the earth. This method as applied by Eratosthenes was very de

tions of Burg, he finds the compression of the earth equal to 1-304; which, considering the difficulties encumbering every other method, is to be relied on as the most correct determination.

The fourth and last method is, by the nutation of the earth's axis, and the precession of the equinoxes. This does not determine the ellipticity of the earth precisely, but defines limits within which its value must of necessity lie. These limits are 1-279 and 1-578. (See Theorie Analytique du Systeme du Monde, par Pontécoulant. T. II, p. 475.)

In the fourth place: how may we ascertain our true position on this globe of ours? In principle just as we should ascertain the position of any point upon that floor. By measurement we should obtain its perpendi cular distance from two adjacent walls. This would perfectly define the point, so that we could locate it accurately upon a plot of the floor, were it required. So it is with regard to places upon the surface of the earth. We refer them to two fixed circles at right angles to each other; the one, any assumed meridian, and the other, the equinoctial line. The only difference is, that instead of measuring, as in the instance of a point on the floor, in a straight line, and reckoning in feet and inches; we measure along circles, and reckon in degrees, minutes and seconds. The distance of a place from the equinoctial line we call latitude, and its distance from the 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 tions 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 distances 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 the magnitude very near to it. It however will add but longitude. little to the difficulty of the problem, to observe the greatest and least altitudes of a circumpolar star: the mean between which will be evidently the altitude of the pole, or which is the same thing, the latitude of the place. Again, the distance from the zenith to the equator (which is the latitude,) is equal to 90° minus the altitude of the plane of the equator above the horizon. But the meridian altitude of the sun, plus or minus its declination, according as it is south or north, is equal to the altitude of the equator. This then is another very ready method of observing the latitude of a place; and is by no means confined to the sun. Any planet or fixed star will serve our purpose as well. Other methods, as by the altitudes of any two fixed stars-by two altitudes of the same star-by the hour angle and azimuth of the sun, while they are simple enough in practice, are too complicated to explain in a popular way.

The problem of finding the longitude of a place is not quite so easily resolved, although several methods have been devised for this purpose. They all, however, are based upon a common principle, to explain which, we must first draw a distinction between absolute and local time. Absolute time is reckoned from some epoch common to the whole earth, as for instance, the arrival of the sun at the equinox; while local time is reckoned from some epoch peculiar to a place, such for example, as the arrival of the sun to the meridian of a place, and is different for different places. Every well adjusted clock shows local mean time, and without alteration, would not answer for any other place under a different meridian. A watch, for example, adjusted to the mean time of Lynchburg, would not answer for Richmond or Nashville. Now, in what does this difference between the local times of any two places, consist? In nothing more than the lapse of time which the sun requires to pass from the meridian of the one place to that of the other; and since it passes over 360° in 24 hours, it will pass over 15° in one hour, and so on proportionally for shorter intervals of time. So that if we knew the difference of the local times of any two places, we should know their difference of longitude, by simply converting the difference of their times into degrees, minutes and seconds, on the principle above explained. If a watch then, perfectly regular in its motion, were adjusted to Lynchburg time, and being transported to Richmond, were placed by the side of one equally regular and adjusted to the time of that place, a simple comparison of their faces would give us the difference of the longitudes of the two places. But watches and clocks cannot be made to run with perfect regularity. Much indeed has been done to bring them to a considerable degree of perfection, and for the space of a few hours their irregularity may be rendered quite imperceptible. To have the full advantage, however, of a time-piece, it must be stationary and its rate of going tested frequently by delicate observations. This is incompatible with its removal from place to place, as above spoken of;—but this difficulty may be thus obviated. Suppose, that on

But the phenomena just spoken of, occur but occasionally, and require a telescope of moderate power. And considering how frequently the longitude is required at sea, it is highly desirable to devise a method which may be employed daily if circumstances demand. Such a method we have in lunar distances, first hinted at by Werner, and applied by Frisius; and afterwards perfected by Halley, La Caille and Maskalyne. The principle of this method is simple, though its application is laborious. If the face of a clock were visibly traced out in the heavens in characters so legible that all the world could read them, (See Herschel,) and were nicely adjusted to Greenwich mean time; from the remarks which I have made it is obvious, that by the comparison of the local time of any place with that indicated by this celestial clock, we should at once obtain the difference of longitude between Greenwich and that place. Such a clock we have, unlike indeed our artificial ones in its construction, yet free from their errors and derangements, and therefore greatly to be preferred, although a little more difficult to be interpreted. The apparent concave sphere is the dial-plate-the fixed stars are the figures engraven upon its face-and the moon is the moveable index, which points out by its position among the stars the local time of that place to which this celestial clock is set. It is adjusted to Greenwich time in the following manner. The lunar tables have been brought to such a degree of perfection by the analytical researches of Laplace and the numerical calculations of Delambre, that we may ascertain years before hand and for any given moment the precise angular distance of the moon from any fixed star. These calculations are made for very short intervals of time and for the meridian of Greenwich and inserted in the nautical almanac. Then if at any place, as at this for instance, by means of a suitable instrument, we observe the distance of the moon from any noted fixed star near to and in the direction of its path, together with the altitudes of the moon and star, we have the data necessary for calculating the precise hour of the observation and the true distance corresponding to that hour. Opposite this true distance in the nautical almanac, the corresponding Greenwich time is tabulated. The difference of these times, is the difference of longitude, as in the former methods. It may be well to remark here, that though the details of this method are numerous and tedious, its accuracy in the hands of skilful observers, has been abundantly tested-especially in the voyages of Maskelyne and Rossel. These are the most important methods of calculating the position of places on the earth. And of what immense advantage are they to the interests of mankind! Without them, each one's knowledge of the earth would have been limited to his own narrow observations and the vague and uncertain information of itinerants. Maps and charts, and a science of geography, would have been unknown. No whitening sail would have been seen upon that vast expanse of waters which

ference, viz: 23° 54′ 3.15, is the obliquity of the ecliptic at the time of observation. But this obliquity is a variable quantity, whose law of variation is well known, and by which we can determine what the obliquity was at any given time past, or at what time the obliquity was of a given value. The time corresponding to its value as deduced from the above observation, is 1100 years B. C. This determination is altogether accurate, provided the observation of the Chinese philosopher be so. This, however, can be tested; and as follows. Geographers agree that the place formerly called Loyang, is now called Hou-an-fou. Three observations on the latitude of this place, performed by Father Gaubie, a learned missionary to China, give for its value 34° 47/ 13; which differs but 2" from the result of TcheouKoung. (See Biot or Freret.)

the magnitudes and distances of the heavenly bodies, are fanciful and false. This, however, is a mistake. By measuring the height of the building we now occupy, and by taking the angles at its summit and base between a vertical line, and an imaginary one drawn to any distant point, as for example to the top of the Peaks of Otter, every schoolboy knows that the distance of that point from us becomes known. Such precisely is the solution of the problem for finding the distance of the earth from the sun. And I venture to assert, that a mechanic could not by means of a foot rule, ascertain the length of this floor, without making a proportionable error greater than that which enters into our estimated distance from the sun. For, if in applying the rule successively along the floor about 50 times, he 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 disMedia, 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, its 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, seeing that the night had thus taken the place of the day, desisted from the combat, and both parties became desirous of making peace. The fact is here very clearly related; but, unfortunately, there is nothing, either in the statement itself, or in the contiguous passages to determine, with any degree of accuracy, the time wherein this singular phenomenon took place. And this is the more to be regretted, because the dates of several other events, might be determined if the era of this eclipse were correctly known."

From other sources we know that this eclipse must have occurred between the years 580 and 650 B. C. It is only necessary then to calculate all the solar eclipses visible in Asia Minor during this interval of 70 years: a labor which has been performed with ability by Bailey. And in all this time, he found only one eclipse which fulfilled the conditions required. This happened on Sept. 30th, 610 B. C. It was total, to part of Asia Minor, Armenia and Media; "and the path of the moon's umbra lay in the very track in which the two hostile armies probably met. For it passed over the mouth of the Halys, just at the point at which Croesus, the immediate successor of Alyattes, crossed that river in order to attack the Median empire."

with the distance of the planet Uranus. At this point our progress is stayed-a point, seen from which, our own sun is reduced to a mere speck. Beyond this utmost verge of our own system, and between it and the nearest star, "there is a great gulf fixed," which it is impossible for calculation to pass. Forsaking the infinitesimal dimensions of our own globe, we eagerly seize upon the diameter of our orbit as the base of a triangle whose apex shall extend to the stars. But sublime as the assumption is, it proves ineffectual: for our orbit itself, whose diameter is 192,000,000 of miles, dwindles to a mere point compared with the distance of the nearest fixed star. But there is abundant reason to believe that the fixed stars are of the same nature with our sun, and made to fulfil similar offices of shedding light and heat to attendant planets; and from what we know of our own system, we cannot put from us the' conclusion that all of the others are contrived for the abode of animated and rational creatures. How magnificent is the scale of creation here presented to us! Where shall we find a parallel? Whether we consider the number--the magnitude-the distances of the heavenly bodies-or the ends they probably subserve, we are at once elevated to conceptions by far too vast for the grasp of a finite mind. Here is an exhibition which overwhelms us with the omnipotence of Him who spake, and it was done! I cannot forbear to add, that the use made of such contemplations by the eloquent Psalmist, was no less philosophical than devout. Feeling the full 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 putation, must have occurred on March 13th, 4710 of the Julian period. Our Saviour was born at that time; for Herod sought the life of the young child. The latest time, therefore, at which we can fix the era of his birth, is about the end of the year 4709 of the Julian period; whereas our vulgar era places it in the year 4713-at least four years too late.

The last illustration I shall give, under this head of our subject, is the detection of an error of upwards of four years in the vulgar era of our Saviour's birth-an era which owes its origin to Dionysius Exiguus, a Roman abbot.

the firmament sheweth his handy work. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language where their voice is not heard." That many very eminent cultiva tors of this science have been infidels, and some of them atheists, I am ready to admit. But this is only another 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-hibited a development of mental energy, surpassing to say nothing of his wisdom and goodness which we find everywhere displayed in the laws which he has chosen for the government of all those various motions which we observe in the universe. It is too frequently supposed that the estimates of astronomers relative to

that which adorned the republic of Greece? It was the country of a line of heroes from Codrus to Philopemen. There, the sculptured marble and the painted canvass were well nigh made to breathe. There flowed the majestic numbers of a Homer, and the exquisitely po VOL. IV.-17