For if that of Mars had amounted to much above a quarter of a minute, it would have been perceptible; estimating it, then, at 25, it followed that the solar parallax could not exceed 10". This was a great step made in the knowledge of our system, and showed that the sun was at the distance of at least 22326 semidiameters of the earth removed from our planet. It is curious to trace the progress of our knowledge on this interesting point. Aristarchus began by proving that the sun was nineteen times more distant from us than the moon this determination seems to have been admitted by Ptolemy and Tycho Brahé, who made the sun's parallax three minutes: Kepler reduced it to one minute, and Cassini to 10": astronomers of the present day only admit between 8" and 9", corresponding to a distance of about ninety-five millions of miles. The comparison of the apparent semidiameter shows the radius of the sun to be more than a hundred times that of the earth, Were the centre of the former supposed to coincide with the centre of the latter, the sun's external circumference would reach half as far again as the orbit of the moon. We shall perhaps form the best idea of the relative magnitudes and distance of these two bodies, by considering that if the former be represented by a globe of nine inches diameter, the latter must be a globule of one-twelfth of an inch in diameter, revolving round the former at the distance of seventy-five feet. There is a curious phenomenon connected with the sun, first noticed by Cassini in the year 1683*. It consists in a pale light, very much resembling in appearance the tail of a comet, which is occasionally visible towards the time of the equinox, extending a considerable way along the zodiac, whence it has received the name of zodiacal light. The smallest stars are visible through it; its form may be compared to that of a cone whose base is the diameter of the sun. It does not always appear with equal brightness; in many years it is altogether invisible; and it would seem that it disappears when the spots on the solar surface are least numerous. The zodiacal light is not rigorously parallel to the ecliptic, but rather to that of the solar equator, which is somewhat inclined to the former. Putting all these circumstances together, Cassini was led Mém. de l'Acad. tom., viii., p. 122. to imagine that this phenomenon indicated the existence of a solar atmosphere of very rare and luminous matter and immense extent, since it reaches far beyond the orbit of Venus, and even perhaps as far as the earth. There are, however, difficulties in this explanation, which have caused it to be rejected by La Place; the subject is one of those regarding which we must be compelled to confess our ignorance. Finally, Cassini has the honour of having completed the theory of the moon's libration. Galileo had explained the diurnal libration, and that in latitude. Hevelius had led the way in explaining the libration in longitude, by observing that the moon always presented the same face to the centre of her orbit, and not to the earth, which is in the focus of the ellipse. This Newton showed to be equivalent with supposing her rotation on her axis to be uniform, while her motion round the earth was unequal. Lastly, Cassini showed that the axis of rotation was not perpendicular to the ecliptic, but slightly inclined, and that the nodes of the lunar equator always coincided with those of the orbit. This explained satisfactorily what had been before observed, that the period of the inequalities of the libration coincided with the revolution of the nodes of the orbit. This long list of discoveries sufficiently shews Cassini to have been one of the greatest observers who have ever existed: perhaps in this respect he is second only to Herschel. Yet we must confess with Delambre, that he has been in France the object of exaggerated eulogium; and several astronomers, whose labours were of a nature less generally appreciated, have in reality done more for the advancement of science. The observer who has devoted himself to forming a catalogue of the fixed stars, or the correction of the solar, lunar, and planetary tables, if he succeeds in his object, has rendered a more essential service than he who has added to the number of satellites of Saturn, or taught us the rotation of the planets on their axes. Yet the latter will enjoy a popular reputation, for which the former must not hope, contented to be properly appreciated by the scientific few. We must now revert to Römer, whose invention of the transit instrument we have before noticed. But it is by a discovery of higher importance that his name is immortalized. It required a genius of no common order to detect the interval of time occupied by light in traversing the planetary orbits; or even to conceive the possibility that its transmission was not instantaneous. This bold idea was not the result of a mere fanciful speculation, like those which so often led Kepler to stumble upon a sublime truth, and so often to plunge into the wildest errors; it was founded upon a series of careful and systematic observations: and Römer deserves equal credit for his assiduity in following the phenomena, and his acuteness in generalizing from them. Careful observation of the eclipses of Jupiter's satellites, and more particularly of the first, led him to remark, that sometimes these eclipses occurred from ten to twelve minutes later than was indicated in the tables of Cassini, while at other times no such retardation was perceptible. The quantity of this retardation was found to be constant for the same time, and to be the same for all the four satellites. It could not, then, depend upon the inequalities of the motions of these satellites; nor even upon that of Jupiter, for these would affect differently the different satellites. The cause then being extraneous to Jupiter and his system, Römer endea voured to ascertain upon what other circumstances the fact could depend. In this he was led to the fortunate remark that the retardation was the greatest when Jupiter was farthest from the earth, and that its period varied with the distance of the planet. We can thús see the train of ideas that guided him to the theory of the successive propagation of light; for what other cause could make the eclipses occur later as Jupiter receded from us? The eclipse is determined by the satellite entering the cone of shadow cast by the primary planet. The position of this cone and of the satellite at a given moment evidently cannot depend upon the distance to the earth: there is, then, nothing left for us but to suppose that we see them later when we are farther removed; or that light is not transmitted instantaneously, but successively. The time taken by it to traverse the diameter of the earth's orbit was estimated by Romer first at eleven and then at fourteen minutes: modern astronomers have fixed it at sixteen minutes and a quarter. It is remarkable that an explanation so simple and beautiful of a phenomenon at first sight so perplexing should not have extorted at once general assent and eulogy. But this was far from being the case: it was not admitted even by the great Cassini; it was spoken of by the acute Fontenelle as a seductive error: and though the truth ultimately overcame all opposition, it remained sterile till the beautiful application of it made by the immortal Bradley*. CHAPTER XV. Picard-Measure of a Degree-Length instruments. The care and skill with The principle of this measure was, it is hardly necessary to say, exactly the same as that of Snellius; to connect two points by a series of triangles, and thus ascertaining the length of the arc of a meridian intercepted between them, to compare it with the difference of latitudes found from celestial observations. The extreme points of the arc of Picard were Malvoisine in the vicinity of Paris, and Sourdon near Amiens: the base was measured between Ville-Juif and Juvisy, and found to amount to 5663 French toises. In order to verify the observations, another base, of 3902 toises, was measured near Sourdon, and its length found to agree with that deduced from calculation. The difference of latitudes was determined by observing the zenith distances of Cassiopeia: this was found to be 1° 11′ 57′′. The arc of the Römer's discovery was announced to the Aca demy of Sciences in 1676. V. Hist. de l'Acad., tom. i. p. 213. terrestrial meridian between the two was 68430 toises, giving for the length of the degree 57064 toises. But the system of triangles having been subsequently extended to Amiens, and the latitude observed there, the length of the degree was found to be 57057; and by a mean between this and the former, 57060 toises. If the arc of Snellius was the first that was measured upon scientific principles, that of Picard was the first that was executed with sufficient accuracy in the details, to bear a comparison with modern determinations of the same kind. It involved however two small errors, which fortunately were of such a nature as to compensate each other. Though the base had been measured twice over, and the difference between the two measurements only amounted to two feet; yet it was found by Clairault and Maupertuis, who verified the operations of Picard in the next century, that an error of six toises had been committed on this length. Again, in determining the latitudes, no allowance was made for the aberration of the fixed stars, a phenomenon at that time unknown; but this error fortunately acted in a contrary direction to the former. This operation of Picard is interesting, among other reasons, for having been the first in which instruments furnished with telescopes were employed. The terrestrial angles were measured with a quadrant of 38 inches radius; the zenith distances with a sextant of ten feet radius, both fitted with telescopest. A novel and excellent part of the operation of Picard, consisted in comparing the length of the toise he made use of, with that of the pendulum beating seconds of time at Paris. The length of this pendulum was found to be 36 inches 84 lines, the toise being supposed to contain six feet. The determination of the length of the seconds pendulum is so very delicate an operation, that perhaps no great reliance is to be placed upon the measure of Picard, but the idea is in the highest degree philosophical, and has received a splendid extension in later times. Mouton first proposed the length of the pendulum as a standard measure, but he complicated the idea so much by connecting it with the erroneous measure of a degree taken from Riccioli, as to Equal to 122943 English yards. For Picard's account of his operations, see Mémoires de l'Acad. des Sciences, tom. viii. make it impracticable. The advantage of an invariable physical standard, susceptible of being verified, or recovered if lost, is so great as to have engaged the attention of the most enlightened governments in Europe for some time past: and no standard seems, on the whole, better to satisfy the conditions required than the seconds pendulum. But on this point we shall have more to say in a subsequent part of this treatise. In the preceding chapter it was mentioned that Richer had been sent to Cayenne to observe the parallax of Mars. While engaged with these observations, an unexpected phenomenon presented itself to his notice*. The pendulum that he used made, in the course of twenty-four hours, 148 vibrations less than it had done at Paris. Yet its length remained unaltered; and it was found necessary to shorten it, at least one line and a quarter, to make it beat seconds, as it had done at Paris. Picard had already perceived that a difference of temperature, by causing the metal to expand or contract, would affect the duration of an oscillation; but it was not possible to explain from this cause the phenomenon observed by Richer. For the change of temperature in this case could not at the utmost have affected the pendulum more than the third of a line. It was impossible then to assign any cause for the fact, which observations, carried on during ten months, had indisputably established, except the diminution of gravity towards the equator. The cause of this diminution was perceived by Newton and by Huyghens. We shall defer giving any account of the explanation of the former till we come to consider his theory of universal gravitation. The reasoning of the latter was founded on his own theorems regarding centrifugal force. Without entering into geometrical details, the nature of his theory may be thus briefly conceived:-Supposing the earth spherical, and to have a motion of rotation on its axis, the centrifugal forces which act on different points of the surface, will be different, according to the velocity with which they revolve in their different circles. A body at the equator revolves with the greatest velocity, and the centrifugal force soliciting it is the greatest; at the latitude 45°, both the velocity and the centrifugal force are much less; at Hist. de l'Acad., tom. i. p. 176. the Pole the body is immoveable, and the force vanishes. Also the centrifugal force acts in the plane of the circle in which the body revolves, gravity in the direction of the centre of the sphere; the compound force resulting from these two will then not tend to the centre, except under the equator or the pole. The direction of the compound force must be perpendicular to the earth's surface at every given point; for the fall of heavy bodies must take place in this direction, and the surfaces of fluids at rest be perpendicular to it. But since this force does not tend to the surface of the sphere, and yet the earth's surface must be perpendicular to it, the earth cannot be a sphere. Under the equator the whole centrifugal force goes to diminish gravity, and this force is, at the same time, at its maximum; at any other place it is only a certain resolved part of the force in question, which counteracts gravity, and this force also diminishes towards the Pole. We see then the reason of the diminution of gravity from the Pole to the equator: a diminution which Huyghens from theory estimated at th part of the whole. He proceeded to determine from theory the ratio of the equatorial to the polar semi-axis*. Following the example of Newton, he supposed two cylindrical canals, reaching from the centre of the earth, the one to the pole, the other to the equator. These canals he supposed filled with water; and it is evident that they must be in state of equilibrium. The quantity by which the weight of the equatorial branch is diminished, is equal to half the product of the length of this branch into the centrifugal force. The whole weight of this branch then will equal the product of the absolute gravity into its length, minus half the product of this length into the centrifugal force. This must equal the weight of the polar branch, which is represented by the product of its length into the absolute gravity. Equating these two expressions, we get the ratio of the length of the equatorial to the polar branch, or which is the same, of the length of the equatorial to the polar axis of the earth. This ratio is that of the absolute gravity, to the same diminished by half the centrifugal force. But Huyghens had found before the centrifugal force at the equator equal to th part of gravity: De vi Gravitatis, 1690. the half would be. The ratio in question then which is the ratio of the two semi-axes, is 578 577. Though subsequent observation has fully established the spheroidal figure of the earth, it has made the difference of the axes much greater. Yet these early attempts to determine theoretically this important question are too interesting to be passed over without notice. The foundation of the Royal Observatory at Greenwich, in the year 1675, has been already mentioned. The first person upon whom the office of astronomer at this observatory was conferred was John Flamstead, who had already distinguished himself by two small but excellent Treatises on the Equation of Time, and the Lunar Theory, which were published with the posthumous works of Horrox. It may justly be a matter of surprise, that the subject of the equation of time should not have been completely understood by the astronomers of Modern Europe, long before the work of Flamstead appeared. Yet such seems not to have been the case. Kepler had perceived, as indeed Hipparchus had done before him, that this equation was composed of two parts, the one resulting from the reduction to the equator of the sun's path in the ecliptic, the other from the inequality of the sun's motion in his orbit: but to these he had added a third, which had no real existence, a pretended acceleration of the earth's rotation on its axis. Tycho had only admitted the first part of the equation; and the opinions of scientific men were still divided, when the treatise of Flamstead first put the question in its proper light. The numerous lunar inequalities have, in all times, given much trouble to astronomers. Besides the inequality depending upon the eccentricity of the orbit, Ptolemy had discovered another, the Evection, which appeared to be connected with the eccentricity, and which he attempted to represent in the way that we have seen in a preceding part of this treatise. Horrox, with great sagacity, perceived that it depended upon a periodical change of the eccentricity of the lunar orbit. To represent this, he supposed the centre of the lunar ellipse to revolve in a small circle, the earth remaining always in the focus. The least distance of the centre from the earth gave the first inequality alone, the greatest gave this inequality increased by the whole evection. In detecting the connection between these two inequalities, Horrox showed great sagacity; and Flamstead adopted the theory in his own work on the subject. But these geometrical hypotheses have ceased to possess any interest: for those who wish to construct lunar tables, it is sufficient to determine empirically a certain sine or cosine which represents the variations of any given inequality, and its maximum value. Hence its value, at any given moment, is found with the greatest facility. Kepler seems to have given the first idea of this method in the lunar theory, by remarking that the variation discovered by Tycho, was proportional to twice the distance from the moon to the sun. When promoted to the place of Astronomer Royal, which he filled for many years, Flamstead devoted himself to observation with most meritorious zeal and constancy. The fruit of his long labours was ultimately published in three folio volumes, under the name of " Historia Coelestis Britannica," containing a great mass of observations, and an extensive and accurate catalogue of the fixed stars. The Greenwich observations begin in the year 1676: at this time, Flamstead followed the method of Tycho and Hevelius; that of determining with a sextant the distances of the observed body from two given fixed stars; the only difference between his instrument, and that of the astronomers just mentioned, being that it was furnished with a telescope. But seven years afterwards he abandoned this system for that introduced by Picard, namely, the observing the transits and meridian altitudes simultaneously by means of a mural quadrant placed in the plane of the meridian. In this way the declinations of the stars may be obtained with considerable accuracy; but the right ascensions must be rather uncertain, from the difficulty of adjusting the plane of the instrument exactly to the meridian, or, at all events, of estimating the deviation. It is remarkable that the transit instrument did not come into use, at the observatories of Greenwich and Paris, till fifty years after its first invention by Römer. Bradley and La Caille have the merit of its introduction. It is still more curious that Halley, the successor of Flamstead, adopted it for a short time, and then abandoned it again, to confine himself to the mural quadrant. In the transits observed by Flamstead, * Horrox, Lunæ Theoria, Nova Opera Posthuma, London, 1673, with his mural instrument (and this may well excite our surprise), he employed only one wire: the time is generally given to whole seconds, very rarely to the half. From all these circumstances, these observations are now of little use to science: a tenth part of this mass made with the same care and skill as those contained in the triduum of Römer* would be a valuable treasure. Yet we must not undervalue the merits of this first Greenwich Catalogue: it was an important addition to the astronomical knowledge of the age; and its merits are sufficient, in the opinion of the best judges, to place its author by the side of Tycho among the most illustrious of the benefactors to science. To accompany his catalogue, Flamstead undertook to construct a celestial Atlas on a large scale. This, indeed, had been done before by Bayer, of Augsburg, but with a very inferior degree of accuracy: the only happy idea in his atlas was that of distinguishing the different stars of a constellation by the letters of the Greek alphabet. The constellations, by a curious mistake, he had drawn as seen from the outside of the sphere. This was rectified in the charts of Flamstead, who invented a new me thod of projection for laying down the arcs of the meridian and the parallels. This method consisted in developing the arcs of parallels in parallel straight lines, perpendicular to a given meridian, also represented by a straight line: the degrees of right ascension measured on these parallels diminish as the cosine of the declination. The successor of Flamstead, at the Greenwich Observatory, was Edmund Halley, one of the greatest names in the whole history of ancient and modern discovery. His brilliant career commenced at an unusually early age. At twenty he undertook a voyage to the southern hemisphere, for the purpose of forming a catalogue of those stars which were too remote from the North Pole to be visible to European observers. For the execution of this project he selected the island of St. Helena, a choice which turned out singularly unfortunate, as the climate of that island, which had been represented to him as well adapted to observation, proved cloudy and unfavourable in the extreme. During a year's residence (1676-7) he was not able to determine the places of more ⚫ V. Page 71. |