INDUCTIVE EPOCH OF NEWTON. 177 



mers had collected from observation; and since, 

 by the very intricacy of the calculation, it was ren- 

 dered probable, that the first results might be some- 

 what inaccurate, and thus might give rise to the 

 still remaining differences between the calculations 

 and the facts. A Progression of the Apogee; a 

 Regression of the Nodes ; and, besides the Elliptical' 

 or first Inequality, an inequality, following the law' 

 of the Ejection, or second inequality discovered by 

 Ptolemy ; another, following the law of the Varia- 

 tion discovered by Tycho ; were pointed out in the 

 first edition of the Principia, as the consequences 

 of the theory. Moreover, the quantities of these 

 inequalities were calculated and compared with 

 observation with the utmost confidence, and the 

 agreement in most instances was striking. The 

 Variation agreed with Halley's recent observations 

 within a minute of a degree 11 . The Mean Motion 

 of the Nodes in a year agreed within less than one- 

 hundredth of the whole 12 . The Equation of the 

 Motion of the Nodes also agreed well 13 . The In- 

 clination of the Plane of the Orbit to the ecliptic, 

 and its changes, according to the different situations 

 of the nodes, likewise agreed 14 . The Evection has 

 been already noticed as encumbered with peculiar 

 difficulties: here the accordance was less close. 

 The Difference of the daily Progress of the Apogee 

 in syzygy, and its daily Regress in Quadratures, is, 



11 B. iii. Prop. 29. ' Prop. 32. 



13 Prop. 33. M Prop. 35. 



VOL. II. N 



