178 HISTORY OF PHYSICAL ASTRONOMY. 



Newton says, " 4 minutes by the Tables, 6f by our 

 calculation." He boldly adds, "I suspect this differ- 

 ence 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 observations 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 rules which they educe. 



The same theory which gave these Inequalities 

 in the motion of the Moon produced by the dis- 

 turbing force of the sun, gave also corresponding 

 Inequalities in the motions of the Satellites of other 

 planets, arising from the same cause ; and likewise 

 pointed out the necessary existence of irregularities 

 in the motions of the Planets arising from their 

 mutual attraction. Newton gave propositions by 

 which the Irregularities of the motion of Jupiter's 

 moons might be deduced from those of our own 15 ; 

 and it was shown that the motions of their nodes 

 would be slow by theory, as Flamsteed had found 

 it to be by observation 16 . But Newton did not 

 attempt to calculate the effect of the mutual action 

 of the planets, though he observes, that in the case 

 of Jupiter and Saturn this effect is too considerable 

 to be neglected 17 ; and he notices, in the second 



" B. i. Prop. 66. ' 6 B. iii. Prop. 23. 



17 B. iii. Prop. 13. 



