452 Astronomical and JVautical Collections, 



Egyptian year 

 of Nabonassar. 



tercalary, and 2924 days. The solar year containin*^ 365j 

 days, and the lunar 354, they observed, that the lunar year was 

 11 J days shorter than the solar, and they inquired what mul- 

 tiple of this time would give them complete months. Now, 

 8 times 11 J are 90 days, or 3 months: and these months they 

 introduced in the 3d, 5th, and 8th years of each cycle : leaving 

 two years unaltered between two of the pairs of intercalations, 

 and one between the other pair : and since two Ivmar months 

 make 59 days, they reckoned the months alternately of 29 and 

 30 days, or deficient and complete, as they were called. 



** The octaeterid, thus constituted, agreed sufficiently well 

 with the course of the sun, but not so accurately with that of 

 the moon : for the true month consists of ^^3- of a day more 

 than 29 J, so that the 99 true months made 2923^ days : while 

 the 8 solar years gave only 2922 days : and the lunar period 

 was a day and a half greater than the solar, two octaeterids 

 wanting 3 days of the corresponding 198 months : of course 

 in 20 octaeterids, the difference amounted to a month ; and it 

 was necessary to omit an intercalary month once in 160 years, 

 and to make only 29 instead of 30 intercalations in that period. 



•' These proportions, however, are still in want of further 

 correction, and instead of omitting an intercalation in 20 oc- 

 taeterids, it is more accurate to omit one in 19 : and instead of 

 3x19 or 57 intercalations in this time, to make only 56, that 

 is 7 in each period of 19 years. 



*' On this last correction the periods of [Meton] Euctemon, 

 Philippus, and Calippus, were founded. They first took the 

 solar year as containing 365^y^ days, making 6940 days in 19 

 years, and of the 235 months in this period they made 125 

 complete and 110 defective ; the complete and defective months 

 not being always alternate : and 110 being [about] the 63d part 

 of 6940, they left out one day of a complete month every 63d day 

 of the period. Calippus afterwards found that the year, thus 

 measured, was y^- of a day too short ; he therefore established 

 a period of 76 years, in which he corrected the error by divid- 

 ing it into 940 months, of which 28 are intercalary ; the whole 

 containing 27759 days.'' 



This arrangement of Calippus was admirably adapted for 

 preserving the order of the true lunar months ; but it must 

 have deviated very considerably from that of the solar years : 

 and we have no positive evidence of the manner in which the 

 seven intercalary months were distributed among the 19 years 

 into which each quarter of the period was divided. 



The same period of nineteen years is still of considerable use 

 in modern chronology : for in the present century, if we divide 

 the date of the Christian year by 19, multiply the remainder 

 by 11, and divide by 30 ; the last remainder will be the epact, 



