34 PHILOSOPHICAL TRANSACTIONS. [aNNO 1750. 



between one mean conjunction of the moon with the sun and the next following, 

 or a mean Synodical month, is equal to 29'' 12^ 44" 3' 2* 56', according to Mr. 

 Pound's tables of mean conjunctions. The common lunar year consists of 12 

 such months. The intercalary or embolimaean year consists of 13 such months. 

 In each cycle of 19 lunar years, there are 12 common, and 7 intercalary or em- 

 bolimaean years, making together 235 synodical months. 



It was thought, at the time of the general council of Nice, which was holden 

 in the year of our Lord 325, that IQ Julian solar years were exactly equal to 

 such a cycle of IQ lunar years, or to 235 synodical months ; and therefore that at 

 the end of IQ years, the new moons or conjunctions would happen exactly at 

 the same times as they did 1 9 years before: and on this supposition it was, that 

 some time afterwards, the several numbers of that cycle, commonly called the 

 golden numbers, were prefixed to all those days in the calendar, on which the 

 new moons then happened in the respective years corresponding to those num^ 

 bers ; it being imagined, that whenever any of those numbers should for the 

 future be the golden number of the year, the new moons would invariably happen 

 on those days in the several months, to which that number was prefixed. 

 But this was a mistake : 



For 19 Julian solar years contain 6939"* 18*' O™ 0» O* 



Whereas 235 synodical months contain only 6939 16 31 56 30 



And are therefore less than I9 Julian solar years by O 1 28 3 30 



This difference amounts to a whole day very nearly in 310.7 years, the new 

 moons anticipating, or falling earlier, by 24 hours in that space of time, than 

 they did before: and therefore now in the year 1750, the new moons happen 

 above 4-^ days sooner, than the times pointed out by the golden numbers in the 

 calendar. 



In order therefore to preserve a sort of regular correspondence between the 

 solar and the lunar years, and to make the golden numbers, prefixed to the days 

 of the month, useful for determining the times of the new moons, it would be 

 necessary, when once those golden numbers should have been prefixed to the 

 proper days, to make them anticipate a day at the end of every 310.7 years, as 

 the moons will actually have done ; that is to set them back one day, by prefixing 

 each of them to the day preceding that against which they before stood. 



But as such a rule would neither be so easily comprehended or retained in me- 

 mory, as if the alteration was to be made at the end or at the beginning of com- 

 plete centuries of years ; the rule would be much more fit for practice, and keep 

 sufficiently near to the truth, if those numbers should be set back 9 days in the 

 space of 2800 years ; by setting them back one day, first at the end of 400 years, 

 and then at the end of every 300 years for 8 times successively : by which they 

 would be set back, in the whole, 9 days in 2800 years. After which they must 



