8 2 8 THE POPULAR SCIENCE MONTHLY. 



moon and the positions of the sun in the heavens do not recur in a 

 full number of days, and that a solar year does not contain a full num- 

 ber of months ; the various phases of the moon requiring a little more 

 than 29^ days, and the positions of the sun somewhat less than 365 

 days ; thus making the solar year contain about 12 months and 11 

 davs. 



To illustrate : if months of 29 and 30 days be alternated, if 365 

 days be allotted to each solar year, and after 99 6uch months (equiva- 

 lent to eight years), the counting of the months be made from the same 

 date of the year, a tolerable agreement with celestial signs could, in- 

 deed, be attained, but after a number of years the date of the month 

 would differ from that indicated by the moon, and with a greater lapse 

 of time the accepted solar year would show a decided variation from 

 the annual position of the sun and moon, and, in fact, from the yearly 

 heating effects of the sun. An improvement could, indeed, be made 

 if, in the alternation of months of 29 and 30 days, two months of 30 

 days each be allowed to succeed each other at intervals of 33 months ; 

 also, if each fourth solar year were to contain 365^ days instead of 365, 

 and if, finally, once in nineteen years, the so-called golden cycle, the 

 reckoning of the lunar months began with the same date of the sun ; 

 but a uniform and perfect coincidence of these cycles of days, months, 

 and years would also, in this manner, be unattainable. In short, the 

 problem was purely an arithmetical one, especially difficult so long as 

 it was sought to make the minor divisions of the year agree with the 

 appearances of the moon, and it is, accordingly, no matter of wonder 

 that many fruitless attempts at improvement were made before a 

 judicious and adequate method was discovered. The founder of 

 Islam clearly recognized the danger which the unsuccessful attempts 

 to construct a calendar for future time engendered for the authority 

 of the leaders in that religion, and hence arose the fear that the un- 

 avoidable conflict of different calendars would promote the formation 

 of religious sects. Mohammed forbade, therefore, the establishment of 

 any connection of the lunar month with the solar year, and ordered all 

 calculations to be made from the observation and proclamations of the 

 new light of the moon. While the peculiar difficulties of the chrono- 

 logical problems had afforded, on the one hand, advance in the ob- 

 servation and understanding of the movements of the heavenly bod- 

 ies, and, on the other, had brought calculations of time into discredit, 

 these astronomical inquiries produced still other important results at 

 an early date, as in Babylon, many centuries before the conquest of 

 Alexander the Great. These results, extending beyond the limits 

 of chronology, secured to astronomers a mighty influence over the 

 minds of the people, notwithstanding the repeated inaccuracies oc- 

 curring in the calendar. This was attained through the teachings of 

 astrology. 



The systematic and long-continued recording of the celestial phe- 



