On the Lunar Cycle. 35? 



The period of the moon's ascending node, which is the hniar 

 pquinoctial point, if I may ])e allowed so to express myself, seemg 

 very fairly to confirm my hypothesis in fixin?? on 912 years for 

 the completion of the moon's motion. Mr.Whiston's Collection 

 of Tables annexed to his Lectures gives the mean motion of the 

 moon, apogee, and node, as follows : 



These numbers bring ev^ry period within 31 days of the ca- 

 lendar time, and so far answer to the observed dates of the cor- 

 responding eclipses as to leave little doubt of their correctness. 

 Subtract and add equal to Sf days. 



Years. S. D. M. S. S. D. M. S. S. D. M. S. 



912 = 1 12 51 12 1 59 25 11 29 47 39 

 3idays 1 16 7 2 23 23 11 8 



3 5 50 1 p 36 2 11 29 58 47 



The mean motion of the node for 19 complete years is 7 deg. 

 27 min. 22 sec. by Whiston's Tables ; but if we say 7 deg. 30 

 min. in every cycle, the whole ecliptic motion is performed in 

 912 years ; the mean motion for four cycles or 76 years is equal 

 to one sign, and in 12 x 76 years the node revolves through the 

 whole of the signs. 



There is no difference between the Chaldean period and the 

 Metonic lunar cycle, but the method of calculation. The Chal- 

 dean period is one lunar year shorter than the Metonic, and 

 consists of 223 lunations according to Dr. Halley's account, and 

 the Metonic consists of 235 lunations : and hence it is, that the 

 Chaldean periods and eclipses follow in the order of the signs. 

 The same celestial pliaenomcna are common to both these periods; 

 so that in every eclipse found by one method the same is to be 

 found by the other also, but the method of calculation is different. 

 The Chaldean period runs through all the signs in about 612 

 years, including 34 revolutions in order from the date of any 

 assigned new or full moon, adding 18 .Julian years 1 1 days 

 7 hours 43 seconds when four leap-years are included, and 

 10 days 7 hours 43 minutes when five leap-years come in the 

 period. 



Pcripd 



