PHILOSOPHICAL TRANSACTIONS. 



513 



VOL. LXXVIII.] 



naty or simple year of 354 days, the 12th and last month, Dulhajee, would 

 have only 2Q ; but, in the years of excess, the intercalary day is added to this 

 month, which is then made to consist of 30 days, and the year, consequently, 

 of 355 days. Thus, for example, in the year of Christ 622, the Hejera com- 

 menced on the l6th of July, with the Arabian month 



It*, year. 



Moharram, which had days 30. . . 



Safar 29- . 



Rabee prior 30. . 



Rabee posterior 29- • 



Joomad prior 30. . 



Joomad posterior 29- . 



ad year. 

 ..30 

 ..29 

 , . . 30 

 ...29 

 , ..30 

 ...29 



Carried over 177 



1st year ended 5 July 623. 



177 



1st year. 

 Brought over. . 177. . 



Rajab 30. . , 



Saban 29. . , 



Hamadan 30. . , 



Sawal 29. . 



Dulkaidat 30. . 



Dulliajee 29. . 



354 

 2d year ended 25 June 624. 



2d year. 



. . 177 



.. 30 



.. 29 



.. 30 



...29 



...30 



... 30 



355 



It may not be uninteresting to examine the rule by which the Arabians appear 

 to have been guided, in placing the intercalary day at the end of those particular 

 years which have been specified. It was observed that the annual excess is cal- 

 culated to be 11 parts in 30 of a day. At the commencement of the first year 

 of their first cycle, they appear to have assumed the fact, somewhat capriciously, 

 that there was an excess of 1 1 parts, belonging to the preceding year, to be 

 accounted for, or brought on. At the end of the first year there would conse- 

 quently be 22 such parts; and at the end of the 2d year 33 parts. Here then, 

 the first intercalary day was applied; that 2d year was made to consist of 355 

 days, and there remained 3 parts, over and above, to be carried on to the next. 

 At the expiration of the 3d year, the parts amounted to 14: of the 4th year, 

 to 25; and of the 5th, to 30; when the intercalation was again applied, and a 

 balance of 6 parts carried on. From this it will be understood in what manner 

 the fractional exceedings of each year were combined and disposed of through the 

 succeeding years of the cycle; and it will be necessary only further to remark, 

 that, when the aggregate of the fractions falls short no more than 2 or 3 parts 

 of the number of 30, they still add the intercalary day, and deduct the defi- 

 ciency from the excess of the following year, which, in the course of 1 cycle, 

 takes place only 3 times. At the end of the 29th year, the accumulated frac- 

 tions, amounting exactly to 30, are commensurate with the intercalation then 

 applied; and the excess of the 30th, or last year, is accounted for in the first 

 intercalation of the succeeding period. The operation would doubtless have 

 appeared more methodical, if the first intercalary day were not to have been 

 added till the end of the 3d year, and the 1 1 th, or last, till the end of the 30th 

 year or termination of the cycle. From this consideration some commentators 

 have been led to dissent from the more general idea, as above given, and to 



VOL. XVI. 3 U 



