$ 2i 4 -2i6] Nutation 269 



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.* 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 XL, 232) published a treatise t 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 du_e to t|iejittraction 

 o the moon on the protuberant parts ^)f the ^arth round 

 trie v ~equator (cf. chapter ix., 187), while Newton's ex- 

 planation of precession was confirmed by the same piece 

 of work. Euler (chapter XL, 236) published soon after- 

 wards 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 t 

 of minute irregularities in the motion of the earth's axis. 



216. Although aberration and nutation have been dis- 

 cussed 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 i8"'42 and 13"'75, so that his ellipse 

 was decidedly less flat than it should have been. 



t Recherches sur la precession des equinoxes et siir la nutation de 

 I axe de la terre. 



