In pre-Islamic times, the Arabs had various eras, such as the building of the Ka'bah, and the sovereignty of Omar* b. Rabíi'a to whom was due the rise of idolatry in Ḥijáz, and this continued in use till the year of the Elephant,* which they, in turn, observed as a fresh epoch. Every Arab tribe constituted any important event in their history, an era. In the time of the prophet this thread of custom had no coherence, but from the date of the Hijra, they gave each year a special name. Thus that year was called the ‘year of Permission,” that is, the permission to go from Mecca to Medina. The second year was named the “year of Command,” i. e, to fight the unbelievers.* At the accession of the second Caliph (Omar), Abú Músa Asha'ri,* governor of Yaman made the following representation: “Your despatches have arrived dated the month of Shạbán. I cannot dis­cover what date is understood by Shạbán.” The Caliph summoned the learned. Some of the Jews advised the use of their era. The sage Húr­muzán* said; “the Persians have a computation which they call Máhroz” and this he explained. But as there were intercalations in both, and their skill in calculation was slight, he did not accept either but adopted the era of the Hijrah. The month according to their system is reckoned from the sight of one new moon, after the sun has completely set, till the next is visible. It is never more than 30 nor less than 29 days. It sometimes occurs that four successive months are of 30 days, and three of 29. Chronologers put­ting aside calculations based on the moon's appearance, reckon lunar months in two ways, viz., Natural, which is the interval of the moon's departure from a determinate position, with the sun in conjunction or opposition or the like, to its return thereto; 2ndly, Artificial; since the motions of the moon are inconstant and their methodisation as well as an exact discrimination of its phases difficult, its mean rate of motion is taken and thus the task is facilitated. In the recent (Gurgáni) tables, this is 29 days, 12 hours and 44 minutes.* The rule is this, that when the fraction is in excess of half, it is reckoned as one day. Thus when the excess is over a half, they take the month of Muharram as 30 days, and the second month 29, and so on alternately to the last. In common years, therefore, Dḥi'l Ḥijjah is 29 days. The mean lunar year consists of 354 d. 8. h. 48 m.* which is less than a solar artificial year by 10 d. 21 h. 12 m. Mirza Ulugh Beg has based his new Canon on this era of which 1002 years have elapsed to the present time.*