18 PHILOSOPHICAL TRANSACTIONS. [aNNO 1755. 



the worth of any performance of that kind. The first essay is a Theorj' of the 

 Precession of the Equinoxes, and the Nutation of the Earth's Axis ; which, 

 as is indebted to you for the discovery of the cause on which it is founded, 

 as it also for settling of the effects with which its result is to be compared, 

 ought to be laid before you as a homage, that of right is due. You ex- 

 pressed a desire of a theory on that subject; I have therefore examined, ac- 

 cording to the principle of gravity, what motions may be produced in the 

 globe of the earth by the actioits of the sun and moon, and have endeavoured to 

 determine their precise quantity and laws of variation. You observed yourself, 

 that the supposition you made use of, of the earth's pole moving round the pe- 

 riphery of a circle, whose centre represented the mean place of the pole, was not 

 exact : and in effect, as theory shows there are 2 equations arising from the sun's 

 action, and as many from the action of the moon, to be used in settling the true 

 place of the pole, the simple motion in the circle cannot answer accurately to 

 the composition of these several motions ; and has hence proceeded that surpriz- 

 ing difference you found between the polar distances calculated on that supposi- 

 tion, and those observed, in the star « Cassiopea, in the year 1738, and in r> 

 Ursae Majoris in the year 1740 and 1741; which distances, if computed from 

 the theory, as here laid down, agree with the obser\'ations as nearly as the others. 

 You also insinuated that it would be proper to examine, whether the position of 

 the moon's apogee had not a share of influence in these apparent motions of the 

 stars. I therefore considered that pomt, but found, as you will see in the 5th 

 prop, that the diminution of the moon's action in the higher part of its orbit, is 

 so compensated by the increase of the same action in the lower part, that in the 

 whole revolution of the moon no alteration arises, whatever be the situation of 

 the nodes. 



The second essay is a Theory of the Irregularities, that may be occasioned in. 

 the annual Motion of the Earth by the Actions of Jupiter and Saturn. I was 

 led into this research by reflecting on that question, debated among the astrono- 

 mers for so many ages past, whether the mean inclination of the two planes of 

 the ecliptic and equator suffers any change, or remains invariable. Considering 

 then what cause could produce a change in this inclination, I easily conceived, 

 that if the action of Jupiter had sufficient power to alter the plane of the earth*s 



he published several separate works, both on mathematics and theology : as, 1. Analyse des Mesures 

 des Rapports et des Angles, 4to, 1749; being an extension and explanation of Cotes' s Harmonia 

 Mensurarum. 2. Theorie du Mouvement des Apsides, 8vo, 1749- 3. De Inaequalitatibus Motuum 

 Lunarium, 4to, 1758. An Explanation of the Apocalypse, Ezekiel's Vision, &c. By the fire at 

 Bath, at the time of the riots, several valuable manuscripts, which he had been compiling during a 

 well-spent life of labour and travelling through many countries, before bit return to England, were 

 irretrievably lost. 



