INDUCTIVE EPOCH OF NEWTON. 409 



whether Newton's reasoning was sufficient to establish this part of his 

 theory ; namely, that her actual motions arise from her gravitation to 

 the sun. And to this we may reply, that it was sufficient for that 

 purpose, — since it showed that, from Newton's hypothesis, inequalities 

 must result, following the laws which the moon's inequalities were 

 known to follow ; — since the amount of the inequalities given by the 

 theory agreed nearly with the rules which astronomers had collected 

 from observation ; — and since, by the very intricacy of the calculation, 

 it was rendered probable, that the first results might be somewhat 

 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 Inequal- 

 ity, an inequality, following the law of the Evection, or second 

 inequality discovered by Ptolemy ; another, following the law of the 

 Variation 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. 10 The Mean Motion of the 

 Nodes in a year agreed within less than one-hundredth of the whole." 

 The Equation of the Motion of the Nodes also agreed well. 12 The 

 Inclination of the Plane of the Orbit to the ecliptic, and its changes, 

 according to the different situations of the nodes, likewise agreed. 13 

 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 Quad- 

 ratures, is, Newton says, " 4^ minutes by the Tables, 6f by our calcu- 

 lation ." He boldly adds, "I suspect this difference to be due to the 

 fault of the Tables." In the second edition (1711) he added the 

 calculation of several other inequalities, as the Annual Equation, also 

 discovered by Tycho ; and he compared them with more recent obser- 

 vations made by Flamsteed at Greenwich ; but even in what has 

 already been stated, it must be allowed that there is a wonderful 

 accordance of theory with phenomena, both being very complex in the 

 rales which they educe. 



The same theory which gave these Inequalities in the motion of the 

 Moon produced by the disturbing force of the sun, gave also corres- 



io B. iii. Prop. 29. » Prop. 32. 12 Prop. S3. 13 Prop. 35. 



