440 PHILOSOPHICAL TRANSACTIONS. [aNNO 1754. 



moon, of the quantity of the earth's flatness, of the quantity of the terrestrial 

 matter, and indeed of every thing of a physical nature that can enter into the 

 problem. 



We are content to examine the motions of the pole of the earth produced by 

 the sun and the moon. The same method, and the same formulae, will give 

 likewise the motions of the terrestrial pole arising from any other planet, as Sa- 

 turn, Jupiter, &c. but these motions are too minute to merit attention. 



Whatever has been said of the action of the sun on the redundant matter 

 about the earth's equator, is also applicable to his action on a simple ring placed 

 at the ec)uator, without adhering to the terrestrial globe ; and the motion of the 

 pole of such ring may be determined by the same method, and consequently the 

 motion of its nodes on the plane of the ecliptic, and the alteration of the incli- 

 nation of its axe to the same plane. And since these motions are the same, 

 whether the ring be supposed entire, or a small portion of it only be considered, 

 or a mere point of it, the motions of the nodes, and the alteration of the incli- 

 nation of a moon, or a satellite of a planet, may thereby be known. And the 

 formulae differ in nothing from those of the motion of the nodes of the earth's 

 equator, and of the alteration of the obliquity of the earth's axe to the plane of 

 the ecliptic, but in this, that the action of the sun on the ring to make it turn, 

 is exerted entirely on it ; whereas, in the problem of the precession, this force 

 must necessarily be distributed throughout the whole mass of the earth, on ac- 

 eount of the adherence of the ring to the globe of the earth. 



As to the division of the work, this memoir is divided into 4 sections. The 

 1st section treats of the motion of the pole of the terrestrial equator caused by 

 the sun. The 2d section treats of the motion of the pole of the terrestrial 

 equator caused by the moon. The 3d section treats of the motion of the pole 

 of a ring, or of the orbit of a moon, caused by the sun. The 4th section con- 

 tains the application of the formulae found in the other sections. 



But as there are some inaccuracies in this very long and intricate treatise, and as 

 its objects may be better answered by the first part of Mr. Thomas Simpson's 

 Miscellaneous Tracts, on the same subject, printed in 1757, it is deemed unne- 

 cessary to reprint this treatise, which will not admit of abridgment. 



LIX. On the Ages of Homer and Hesiod. By George Costard, M. A, in a 

 Letter to the Earl of Macclesfield, F.R.S. p. 441. 



It seems to be an opinion pretty generally received, that Homer and Hesiod 

 lived much about the same time. What that age was, is indeed not at all agreed 

 on among writers ; the only thing in which they conspire being, as Mr. C. thinks, 

 to place both of them much earlier than they ought to have done. 



Among the ancients, Velleius Paterculus says, that Homer lived 950 years 



