A Short History of Astronomy

by Arthur Berry

Fig. 77.—Precession and nutation.

214. Bradley’s observations established the existence of certain alterations in the positions of various stars, which could be accounted for by supposing that, on the one hand, the distance of the pole from the ecliptic fluctuated, and that, on the other, the precessional motion of the pole was not uniform, but varied slightly in speed. John Machin (?-1751), one of the best English mathematicians of the time, pointed out that these effects would be produced if the pole were supposed to describe on the celestial sphere a minute circle in a period of rather less than 19 years—being that of the revolution of the nodes of the moon’s orbit—round the position which it would occupy if there were no nutation, but a uniform precession. Bradley found that this hypothesis fitted his observations, but that it would be better to replace the circle by a slightly flattened ellipse, the greatest and least axes of which he estimated at about 18″ and 16″ respectively.[119] This ellipse would be about as large as a shilling placed in a slightly oblique position at a distance of 300 yards from the eye. The motion of the pole was thus shewn to be a double one; as the result of precession and nutation combined it describes round the pole of the ecliptic “a gently undulated ring,” as represented in the figure, in which, however, the undulations due to nutation are enormously exaggerated.

215. Although Bradley was aware that nutation must be produced by the action of the moon, he left the theoretical investigation of its cause to more skilled mathematicians than himself.

In the following year (1749) the French mathematician D’Alembert (chapter XI., [§ 232]) published a treatise[120] in which not only precession, but also a motion of nutation agreeing closely with that observed by Bradley, were shewn by a rigorous process of analysis to be due to the attraction of the moon on the protuberant parts of the earth round the equator (cf. chapter IX., [§ 187]), while Newton’s explanation of precession was confirmed by the same piece of work. Euler (chapter XI., [§ 236]) published soon afterwards another investigation of the same subject; and it has been studied afresh by many mathematical astronomers since that time, with the result that Bradley’s nutation is found to be only the most important of a long series of minute irregularities in the motion of the earth’s axis.

216. Although aberration and nutation have been discussed first, as being the most important of Bradley’s discoveries, other investigations were carried out by him before or during the same time.

The earliest important piece of work which he accomplished was in connection with Jupiter’s satellites. His uncle had devoted a good deal of attention to this subject, and had drawn up some tables dealing with the motion of the first satellite, which were based on those of Domenico Cassini, but contained a good many improvements. Bradley seems for some years to have made a practice of frequently observing the eclipses of Jupiter’s satellites, and of noting discrepancies between the observations and the tables; and he was thus able to detect several hitherto unnoticed peculiarities in the motions, and thereby to form improved tables. The most interesting discovery was that of a period of 437 days, after which the motions of the three inner satellites recurred with the same irregularities. Bradley, like Pound, made use of Roemer’s suggestion (chapter VIII., [§ 162]) that light occupied a finite time in travelling from Jupiter to the earth, a theory which Cassini and his school long rejected. Bradley’s tables of Jupiter’s satellites were embodied in Halley’s planetary and lunar tables, printed in 1719, but not published till more than 30 years afterwards ([§ 204]). Before that date the Swedish astronomer Pehr Vilhelm Wargentin (1717-1783) had independently discovered the period of 437 days, which he utilised for the construction of an extremely accurate set of tables for the satellites published in 1746.

In this case as in that of nutation Bradley knew that his mathematical powers were unequal to giving an explanation on gravitational principles of the inequalities which observation had revealed to him, though he was well aware of the importance of such an undertaking, and definitely expressed the hope “that some geometer,[121] in imitation of the great Newton, would apply himself to the investigation of these irregularities, from the certain and demonstrative principles of gravity.”

On the other hand, he made in 1726 an interesting practical application of his superior knowledge of Jupiter’s satellites by determining, in accordance with Galilei’s method (chapter VI., [§ 127]), but with remarkable accuracy, the longitudes of Lisbon and of New York.

217. Among Bradley’s minor pieces of work may be mentioned his observations of several comets and his calculation of their respective orbits according to Newton’s method; the construction of improved tables of refraction, which remained in use for nearly a century; a share in pendulum experiments carried out in England and Jamaica with the object of verifying the variation of gravity in different latitudes; a careful testing of Mayer’s lunar tables ([§ 226]), together with improvements of them; and lastly, some work in connection with the reform of the calendar made in 1752 (cf, chapter II., [§ 22]).