PRELUDE TO THE EPOCH OF HIPPARCHUS. 141 



marchus, an intimate friend of Eudoxus, they went together to Athens, 

 and communicated to Aristotle the invention of Eudoxus, and with 

 his help improved and corrected it. 



Probably at first this hypothesis was applied only to account for the 

 general phenomena of the progressions, retrogradations, and stations 

 of the planet ; but it was soon found that the motions of the sun and 

 moon, and the circular motions of the planets, which the hypothesis 

 supposed, had other anomalies or irregularities, which made a further 

 extension of the hypothesis necessary. 



The defect of uniformity in these motions of the sun and moon, 

 though less apparent than in the planets, is easily detected, as soon as 

 men endeavor to obtain any accuracy in their observations. We have 

 already stated (Chap. I.) that the Chaldeans were in possession of a 

 period of about eighteen years, which they used in the calculation of 

 eclipses, and which might have been discovered by close observation 

 of the moon's motions ; although it was probably rather hit upon by 

 noting the recurrence of eclipses. The moon moves in a manner 

 which is not reducible to regularity without considerable care and 

 time. If we trace her path among the stars, we find that, like the 

 path of the sun, it is oblique to the equator, but it does not, like that 

 of the sun, pass over the same stars in successive revolutions. Thus 

 its latitude, or distance from the equator, has a cycle different from its 

 revolution among the stars ; and its Nodes, or the points where it cuts 

 the equator, are perpetually changing their position. In addition to 

 this, the moon's motion in her own path is not uniform ; in the course 

 of each lunation, she moves alternately slower and quicker, passing 

 gradually through the intermediate degrees of velocity; and goes 

 through the cycle of these changes in something less than a month ; 

 this is called a revolution of Anomaly. When the moon has gone 

 through a complete number of revolutions of Anomaly, and has, in the 

 same time, returned to the same position with regard to the sun, and 

 also with regard to her Nodes, her motions with respect to the sun 

 will thenceforth be the same as at the first, and all the circumstances 

 on which lunar eclipses depend being the same, the eclipses will occur 

 in the same order. In 6585 J days there are 239 revolutions of anom- 

 aly, 241 revolutions with regard to one of the Nodes, and, as we have 

 said, 223 lunations or revolutions with regard to the sun. Hence this 

 Period will bring about a succession of the same lunar eclipses. 



If the Chaldeans observed the moon's motion among the stars with 

 any considerable accuracy, so as to detect this period by that means, 



