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 observation's, 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.[1] 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[2] 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
- ↑ His observations as a matter of fact point to a value rather greater than 18", but he preferred to use round numbers. The figures at present accepted are 18"⋅42 and 13"⋅75, so that his ellipse was decidedly less flat than it should have been.
- ↑ Recherches sur la précession des équinoxes et sur la nutation de l'axe de la terre.
