30-i HISTORY OF FORMAL ASTRONOMY. 



times ; and the motion of the Node had been supposed uniform. He 

 found that the inclination increased and diminished by twenty minutes, 

 according to the position of the line of nodes ; and that the nodes, 

 though they regress upon the whole, sometimes go forwards and some- 

 times go backwards. 



Tycho's discoveries concerning the moon are given in his Progym- 

 fiasmata, which was published in 1603, two years after the author's 

 death. He represents the Moon's motion in longitude by means of 

 certain combinations of epicycles and eccentrics. But after Kepler 

 had shown that such devices are to be banished from the planetary 

 systern, it was impossible not to think of extending the elliptical theory 

 to the moon. Horrox succeeded in doing this ; and in 1638 sent this 

 essay to his friend Crabtree. It was published in 16*73, with the nu- 

 merical elements requisite for its application added by Flamsteed. 

 Flamsteed had also (in 1671-2) compared this theory with observa- 

 tion, and found that it agreed far more nearly than the Philolaic Ta- 

 bles of Bulliaklus, or the Carolinian Tables of Street (Epilogus ad 

 Tabulas). Moreover Horrox, by makiDg the centre of the ellipse re- 

 volve in an epicycle, gave an explanation of the evection, as well as of 

 the equation of the centre. 3 



Modern astronomers, by calculating the effects of the perturbing 

 forces of the solar system, and comparing their calculations with ob- 

 servation, have added many new corrections or equations to those 

 known at the time of Horrox ; and since the Motions of the heavenly 

 bodies were even then affected by these variations as yet undetected, 

 it is clear that the Tables of that time must have shown some errors 

 when compared with observation. These errors much perplexed astron- 

 omers, and naturally gave rise to the question whether the motions of 

 the heavenly bodies really were exactly regular, or whether they were 

 not affected by accidents as little reducible to rule as wind and weather. 

 Kepler had held the opinion of the casualty of such errors ; but Hor- 

 rox, far more philosophically, argues against this opinion, though he 



3 Horrox (Eorrocies as he himself spelt his name) gave a first sketch of his theory 

 in letters to his friend Crabtree in 1638 : in which the variation of the eccentricity 

 is not alluded to. But in Crabtree's letter to Gascoigne in 1642, he gives Horrox*s 

 rule concerning it ; and Flamsteed in his Epilogue to the Tables, published by Wallis 

 along with Horrox's works in 1673, gave an explanation of the theory which made 

 it amount very nearly to a revolution of the centre of the ellipse in an epicycle. 

 Halley afterwards made a slight alteration ; but hardly, I think, enough to justify 

 Newton's assertion (Princip. Lib. iii. Prop. 35, Schol.), "Halleius centrum el- 

 lipseos in epicyclo locavit." See Baily's Flamsteed, p. 6S3. 



