512 PHILOSOPHICAL TRANSACTIONS. £aNNO 1788. 



by the appearance of the moon, or the calculated period of conjunction, but 

 according to a certain division of a cycle of 30 years, adopted for this purpose.* 

 Particular attention is due to the explanation of this mode, both as being more 

 artificial and complex, and because it serves to regulate the dates in matters of 

 historical record, and indeed of all writings where pretension is made to accu- 

 racy. On this the Turkish, Moorish, and every systematic Mahometan 

 calendar are founded. 



The lunar month, or mean synodic revolution, according to the computation 

 of the Arabian astronomers, consists of 2Q days, 12 hours, and 792 scruples or 

 parts in 1080; and the year of 354 days, 8 hours, and 864 scruples. But, as 

 the purposes of mankind require that the year should contain an integral number 

 of days, it became expedient to collect and dispose of these fractional exceedings 

 in a consistent and practical manner; and with this view, a cycle or period of 30 

 lunar years was chosen, as the lowest number that admitted of their being 

 formed into days, without sensible deficiency or remainder. Their sum being 1 1 

 days, it was determined that IQ of those 30 years should be composed of 354 days, 

 and 11 of 355 days each. The justness of this proportion will equally appear, 

 if it be observed, that 8 hours and 864 scruples, or 48 minutes, constitute 1 1 

 parts in 30 of 24 hours, and consequently in 30 years produce an excess of 11 

 whole days.-j- It remained next to be considered in what order and method these 

 additional or intercalary days should be inserted, so as to affect the compensa- 

 tion required with as much equability as possible, and maintain a correspondence, 

 as near as circumstances would admit, with the periods marked by the phases of 

 the moon. The following are the years to which, for reasons that shall be 

 afterwards assigned, it was judged proper to annex an extraordinary day, and 

 which, in contradistinction to those 19 that have only 354 days, are termed 

 years of excess, viz. the 2d, 5th, 7th, 10th, 13th, l6th, 18th, 21st, 24th, 

 26th, and 29th, of the cycle of 30 years. 



Their months, conformably with those of the Hebrew calendar, it was deter- 

 mined should consist alternately of 30 and 29 days; and therefore, in an ordi- 



• A passage in Alfraganus (who wrote about the year of Christ 950) would lead us to infer^ that 

 besides the 2 ways of computing time here distinguished, the astronomers were accustomed to follow 

 a 3d, whose periods were marked by the conjunction of the luminaries : but, as this learned Maho- 

 metan was a professed student of Ptolemy's works, which in this place he quotes, we may conclude 

 that, when he speaks of astronomers, he does not mean to confine the expression to those of his own 

 country or religion. — Orig. 



-f The mean synodic revolution being SP"* 12" 44"" and nearly 3% this cycle falls short of 30 com- 

 plete lunar years, by something more than 17", and consequently advances I day in about 2500 years. 

 The Chaldaeans, who made the time of the revolution to consist of I scruple, or 1080th part of an 

 hour, more than the Arabs thought fit to allow, were wonderfully near to the truth. If, instead of 

 30 years, a cycle of 19 had been chosen, and 7 days intercalated, there would have been an excess of 

 » 30th part of a day, which would have caused the reckoning to retrograde 1 day hi 570 years. — Orig, 



