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Bradley was more fortunate; being an excellent observer, as well as a learned geometrician, he pursued the same research, at the same place, with a constancy, which led him at length to a perfect knowledge of all these singular phenomena. He perceived, that certain stars appeared, in the space of a year, to have a kind of libration in longitude, without changing their latitude in the least; and that others varied their latitude alone; while a still greater number appeared to describe in the heavens, during the same period, a small ellipsis, more or less prolate.
This period of a year, to which all these motions answered, though so different in other respects, was a certain indication, that they had some connection with the motion of the Earth in it's orbit round the Sun: but this was no more than a general hint, insufficient to give a precise and complete reason for the phenomena. Bradley made a new step, which decided the question. He conceived the happy idea, that the apparent aberration of the fixed stars was produced by the progressive motion of light, com-. bined with the annual motion of the Earth: and he arrived at this by reasoning with himself as follows.
The theory of Roemer teaches me, that the velocity of light is not instantaneous, and that it has a definite ratio, of about 10000 to 1, to the velocity of the Earth in it's orbit. Consequently a ray of light, issuing from a star, and conveying the impression of that star to my eye, does not arrive, till the Earth has undergone a sensible change of place since the instant when the ray departed: accordingly, when my eye receives the impression, it must refer the star
to a place different from that, to which it would have referred it, had I remained still in the same place. An observer on the Earth, therefore, does not see the stars in their real places in the heavens, and must ascribe to them different motions, which depend on the different positions they have with respect to him.' Furnished with this key, Bradley explained all the apparent aberrations of the fixed stars in an exact and precise manner, conformable to his own observations and those of all other astronomers. Thus all these uncertainties were removed; and to the proofs already adduced in support of the copernican system he added a new one, which may be called a mathematical demonstration.
Not contented with having laid the foundation of this theory by observations, he reduced it into trigonometrical formulæ, the results of which he published, without demonstrations, in the Philosophical Transactions for 1717.
The novelty and interesting nature of the subject attracted the attention of all astronomers and geometricians. Clairaut gave the demonstrations, which Bradley had suppressed: and he added to them several other easy and commodious theorems; an important service, which contributed not a little to accelerate the progress of this new branch of astronomy.
About ten years after, the same geometrician applied the theory of aberration to the motions of the planets and comets; to which, it is evident, it must equally apply. The time, which light takes in coming from a planet or a comet to the Earth, neces
sarily produces some apparent change in the situation of the comet or planet. The problem therefore is of the same nature as for the stars; with this difference however, that, the stars being fixed, while the planets and comets have motions to be taken into the account, the formulæ of aberration for these are of course more complex. To this must be added the difficulty in the calculation, which arises from the eccentricity of the orbits of the planets and comets.
Modern astronomy is indebted to Bradley for another discovery not less remarkable, that of the nutation of the Earth's axis, to which geometry smoothed his way, by pointing out the observations he must make to arrive at it.
Having the general knowledge, that the inequalities of the attractions of the Moon and the Sun, on different parts of the terrestrial spheroid, must occasion different motions in it's axis with regard to the plane of the ecliptic, Bradley applied himself to discover and unravel these motions, by a long series of laborious and delicate observations, made in those positions of the Sun and Moon, which were best calculated to show the effects he sought. Accordingly he found, 1st, that the axis of the Earth has a conical motion, by which it's extremities describe round the poles of the ecliptic, and contrary to the order of the signs, a complete circle in 25000 years, or about an arc of 50 seconds in a year, which produces the precession of the equinoxes: 2dly, that this axis has a libratory motion with regard to the plane of the ecliptic, or an alternate preponderation of each extremity, by which it is inclined about 18 seconds
seconds during one revolution of the lunar nodes; which make their circuit, contrary to the order of the signs, in a period of about nineteen years: after which period the axis returns to it's former position, to incline again new. These observations, which are consistent with the newtonian theory of attraction, constitute an additional demonstration of it, as I shall more particularly observe farther on.
Since these discoveries, the nutation of the Earth's axis forms as essential a part of astronomical calculations, as the precession of the equinoxes, the quantity of which was pretty nearly known before.
As the fixed stars are points, to which the motions of the planets are referred, astronomers at all times have bestowed great pains on augmenting their number, and fixing their respective positions. These are the two chief objects of catalogues of the stars. It has been seen, that Hipparchus had made an accurate enumeration of the stars known in his time; and Ptolemy and the arabian astronomers afterward improved his labours. In the preceding period notice was taken of Flamsteed's catalogue of the stars visible in our climates, and of that drawn up for the stars of the southern hemisphere from the observations made by Halley at St. Helena. La Caille, one of the best and most indefatigable astronomers that ever lived, after having calculated the positions of a great number of stars in France, undertook a voyage to the Cape of Good Hope in 1751, in order to enlarge and improve the catalogue of southern stars. I shall not enter into a minute account of the means he employed, and the precautions he adopted, to execute
this grand work so useful to astronomy, and at présent one of it's grand foundations: but I shall ob serve, that he brought to Europe an accurate cata→ logue, carefully verified, of more than 9800 stars, included between the south pole and the tropic of Capricorn.
During the course of these principal observations, la Caille occasionally made others on different interesting points of astronomy, as on refractions, the elevation of the pole, the length of the pendulum, and the longitude of the Cape of Good Hope, on which the opinions of the ablest geographers differed more than three degrees. He took particular pains to observe the meridian altitudes of Mars, Venus, and the Moon, which enabled him to determine their parallaxes with precision, by comparing his observations with those made at the same time in France, England, Sweden, and Prussia. Lastly he measured a degree of the Earth, of which I shall have occasion to speak more at large in the succeeding article.
The question of the figure of the Earth is of the highest importance to Astronomy and Navigation. Hence attempts have been made in all ages to solve it; but it is only since the measure taken by Picard, that we have begun to obtain results, on the accuracy of which dependance may reasonably be placed..
This astronomer found in 1669, that the length of a degree of the meridian was 57060 toises [121569 yards], in the latitude of 49° 23′ north. Though this determination was considered as incomparably more accurate than any that had preceded it, some