Of the numerous irregularities of this class which are now known, and which may be referred to generally as =nutation=, that indicated by Bradley in the passage just quoted is by far the most important. As soon as the idea of an irregularity depending on the position of the moon’s nodes occurred to him, he saw that it would be desirable to watch the motions of several stars during the whole period (about 19 years) occupied by the moon’s nodes in performing the circuit of the ecliptic and returning to the same position. This inquiry was successfully carried out between 1727 and 1747 with the telescope mounted at Wansted. When the moon’s nodes had performed half their revolution, _i.e._ after about nine years, the correspondence between the displacements of the stars and the changes in the moon’s orbit was so close that Bradley was satisfied with the general correctness of his theory, and in 1737 he communicated the result privately to Maupertuis (§ 221), with whom he had had some scientific correspondence. Maupertuis appears to have told others, but Bradley himself waited patiently for the completion of the period which he regarded as necessary for the satisfactory verification of his theory, and only published his results definitely at the beginning of 1748. [Illustration: 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.