172 THE GREEK ASTRONOMY. 



ity was greatest also." He then adds some further remarks on the 

 circumstances according to which the moon's place, as affected by this 

 new inequality, is before or behind the place, as given by the epicy- 

 clical hypothesis. 



Such is the announcement of the celebrated discovery of the moon's 

 second inequality, afterwards called (by Bullialdus) the Evection. 

 Ptolemy soon proceeded to represent this inequality by a combination 

 of circular motions, uniting, for this purpose, the hypothesis of an epi- 

 cycle, already employed to explain the first inequality, with the hy- 

 pothesis of an eccentric, in the circumference of which the centre of the 

 epicycle was supposed to move. The mode of combining these was 

 somewhat complex ; more complex we may, perhaps, say, than was 

 absolutely requisite ; 33 the apogee of the eccentric moved backwards, 

 or contrary to the order of the signs, and the centre of the epicycle 

 moved forwards nearly twice as fast upon the circumference of the 

 eccentric, so as to reach a place nearly, but not exactly, the same, as 

 if it had moved in a concentric instead of an eccentric path. Thus 

 the centre of the epicycle went twice round the eccentric in the course 

 of one month : and in this manner it satisfied the condition that it 

 should vanish at new and full moon, and be greatest when the moon 

 was in the quarters of her monthly course. 34 



The discovery of the Evection, and the reduction of it to the epi- 



33 If Ptolemy had used the hypothesis of an eccentric instead of an epicycle for 

 the first inequality of the moon, an epicycle would have represented the second in- 

 equality more simply than his method did. 



34 I will insert here the explanation which my German translator, the late distin- 

 guished astronomer Littrow, has given of this point. The Eule of this Inequality, 

 the Evection, may be most simply expressed thus. If a denote the excess of the 

 Moon's Longitude over the Sun's, and b the Anomaly of the Moon reckoned from 

 her Perigee, the Evection is equal to 1. 3. sin (2a-J). At New and Full Moon, a 

 is or ISO , and thus the Evection is 1. 3. sin 5. At both quarters, or dichot- 

 omies, a is 90 or 270, and consequently the Evection is + 1. 3 . sin I. The 

 Moon's Elliptical Equation of the centre is at all points of her orbit equal to 6. 3 . 

 sin b. The Greek Astronomers before Ptolemy observed the moon only at the 

 time of eclipses; and hence they necessarily found for the sum of these two great- 

 est inequalities of the moon's motion the quantity 6 . 3 . sin 51 . 3 . sin J, or 5 . 

 sin I : and as they took this for the moon's equation of the centre, which depends 

 upon the eccentricity of the moon's orbit, we obtain from this too small equation 

 of the centre, an eccentricity also smaller than, the truth. Ptolemy, who first ob- 

 served the moon in her quarters, found for the sum of those Inequalities at those 

 points the quantity 6 . 3 . sin 5 + 1 . 3 . sin , or 7 . 6 . sin I ; and thus made the 

 eccentricity of the moon as much too great at the quarters as the observers ol 

 eclipses had made it too small. He hence concluded that the eccentricity of the 

 Moon's orbit is variable, which is not the case. 



