Remarks on Ancient Eclipses. 443 



tpoch most convenient for calculating the lunar periods and cycles 

 to anv extent. The place of the moon's ascending node and 

 apogee in September of that year coincided with points in the 

 heavens not occurring during many ages, at least for upwards of 

 nine centuries. 



In 912 solar years there are 48 lunar cycles of 19 years, and 

 exactly 49 revolutions of the nodes : therefore if you divide this 

 period by 48, the precise measure of one cycle is obtained ; and 

 if you divide the same period by 49, you will ascertain the period 

 of one revolution of the nodes. The whole of these calculations 

 depend upon the just quantity of the solar year, any augmenta- 

 tion or diminution of which, beyond or short of its true and ab- 

 solute measure, affects all the lunar calculations founded on it. 

 A difference of one minute in the quantity of a solar year will 

 amount to 15 hours 12 minutes for a whole period, and a dif- 

 ference of but one second in a lunation will amount to three 

 hours in that space of time; a difference of eight seconds will 

 amount to one day ; and one hour and a half in a cycle will 

 amount to three days. 



In 912 solar years there are 228 bissextiles and seven inter- 

 calary days, in all 235 days; and in one lunar cycle ave 12 x 19 

 = 228 lunations, and seven intercalary; in all 235 lunations: 

 also in a lunar cvcle are 940 changes of the moon, and in 912 

 solar years are 940 lunations : this harmony really subsists, and 

 is confirmed bv every evidence of observation. 



The lunar cycle is computed at 19 solar years, and constitutes 

 one fundamental principle of the Paschal Tables puldished in all 

 editions of the book of Common Prayer. The fractional quantities 

 belong to the pure astronomy, and which can only affect the ec- 

 clesiastical and calendar reckoning in a lapse of some centuries. 

 This cycle comprehends a regular series of eclipses ; and when 

 expired, a new series begins, with a variation which requires a 

 whole period to exhaust ; so that forty-eight such cycles must 

 elapse before such period terminates. This arises from the motion 

 of the moon's ecliptic points or nodes, whose revolutions pro- 

 duce these admirable variations. 



The precise measure of this cycle is variously estimated, but 

 the following method will nearly approximate to the truth. 

 Days. H. M. Diivs. H. AT. 



365 X 19 = 6935 

 6 X 19= 4 18 



G939 IS .Julian time 

 11 X 19- 3 29 



G939 14 31 Solar time. 

 S s 2 Tiiere- 



