Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c23: Chapter XVIII. The Muhammadan Year
Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c23
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Chapter XVIII. The Muhammadan Year
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123. The Muhammadan Era, commonly called Hejra or Hijra, is dated from Friday, 16 July, 622 A.D., the day of the Flight of the Prophet.
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The Muhammadan calendar is not luni-solar like the Indian Calendar, but strictly lunar. The length of the synodical month according to the Muhammadan calendar is 29 days 12 hours 44 minutes. The 3 seconds reckoned in addition in the Hindu calendar are neglected in the Muhammadan. The months are alternately 29 and 30 days long, which, again, if carried out uniformly, would result in an error of 44 minutes per month, which, in 360 months, or 12 lunar years, would amount to (360 × 44)/(60 × 24) = 11 days. These 11 days are accordingly added to the last month of the calendar in 11 out of every 30 years, and the year containing an extra day is, from analogy, sometimes called a leap year.
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124. Every 30 years form a cycle in the Muhammadan calendar. The years which have 355 days, instead of 354, are in some countries the 2nd, 5th, 7th, 10th, 13th, 15th, 18th, 21st, 24th, 26th and 29th. Elsewhere, the 2nd, 5th, 8th, 10th, 13th, 15th, 19th, 21st, 24th, 27th and 29th are kept as leap years.
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It will be noticed that the difference of usage is as regards the 8th, 19th and 27th years in each cycle.
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Our Muhammadan Calendar (Table XV) assumes that the 8th, 19th and 27th years in each cycle are leap years, and in paragraph 4 of the explanation at page 197 of the Tables we have shown clearly how Table XV should be used by those who observe the 7th, 18th and 26th years in each cycle as leap years.
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125. All the books that deal with the Muhammadan Calendar mention the above difference of usage, but they do not give the reason of it. The reason is, however, not far to seek.
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If we write down the accumulated error which remains at the end of each year by reason of the neglect to take account of 44 minutes, which we adverted to in the first section of this chapter, we obtain the following result under the system of reckoning the 8th, 19th and 27th as leap years:—
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| Year. | Error. | How error is corrected by leap year. | Year. | Error. | How error is corrected by leap year. |
| 1st year, | 8 hrs. 48' | | 16th year, | *Nil.* | |
| 2nd year, | 17 hrs. 36' | 1st day added by leap year. | 17th year, | 5 hrs. 36' | |
| 3rd year, | 2 hrs. 24' | | 18th year, | 14 hrs. 24' | 7th day added by leap year. |
| 4th year, | 11 hrs. 12' | | 19th year, | 23 hrs. 12' | |
| 5th year, | 20 hrs. 0' | 2nd day added by leap year. | 20th year, | 8 hrs. 0' | 8th day added by leap year. |
| 6th year, | 4 hrs. 48' | | 21st year, | 16 hrs. 48' | |
| 7th year, | 13 hrs. 36' | | 22nd year, | 1 hr. 36' | |
| 8th year, | 22 hrs. 24' | 3rd day added by leap year. | 23rd year, | 10 hrs. 24' | 9th day added by leap year. |
| 9th year, | 7 hrs. 12' | | 24th year, | 19 hrs. 12' | |
| 10th year, | 16 hrs. 0' | 4th day added by leap year. | 25th year, | 4 hrs. 0' | |
| 11th year, | 0 hrs. 48' | | 26th year, | 12 hrs. 48' | 10th day added by leap year. |
| 12th year, | 9 hrs. 36' | | 27th year, | 21 hrs. 36' | |
| 13th year, | 18 hrs. 24' | 5th day added by leap year. | 28th year, | 6 hrs. 24' | 11th day added by leap year. |
| 14th year, | 3 hrs. 12' | | 29th year, | 15 hrs. 12' | |
| 15th year, | 12 hrs. 0' | 6th day added by leap year. | 30th year, | *Nil.* | |
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We see that by observing the 8th, 19th and 27th as leap years, a day is added by means of a leap year in order to avoid the error accumulating to more than 1 day at the end of the following year.
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Those that observe the 7th, 18th and 26th as leap years add a day by means of a leap year in order to avoid the error accumulating to more than half a day at the end of the following year. This in fact is what is done by both the schools at the end of the 15th year.
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126. The months and the number of days in each are as follows:—
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| Month. | | No. of days. | Day of Commencement reckoning from beginning of year. | Month. | | No. of days. | Day of Commencement reckoning from beginning of year. |
| 1. Muharram | ... | 30 | ... | 7. Rajab | ... | 30 | 177 |
| 2. Safar | ... | 29 | 30 | 8. Shaban | ... | 29 | 207 |
| 3. Rabi-ul-awwal | ... | 30 | 59 | 9. Ramzan | ... | 30 | 236 |
| 4. Rabi-ul-akhir or Rabi-us-sani | ... | 29 | 89 | 10. Shawwal | ... | 29 | 266 |
| 5. Jumadal-awwal | ... | 30 | 118 | 11. Zilkada | ... | 30 | 295 |
| 6. Jumadal-akhir or Jumad-us-sani | ... | 29 | 148 | 12. Zil-hijja Do. (when intercalary). | ... | 29 30 | 325 |
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All readers are familiar with the names of two of the Muhammadan months, Muharam and Ramzan, and all are equally familiar with the fact (due to the strictly lunar character of the year) that Muharram is liable to occur at any part of the solar year.
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127. The Muhammadan day is reckoned from sunset to sunset, and the first day of Muharram is that on which the moon is for the first time visible at sunset after new moon. This is called the heliacal rising of the moon. Our readers are familiar with the Muhammadan usage of observing the heliacal rising of the moon from eminences of any sort, and passing word as soon as she is seen, so as to give notice that Muharram has commenced.
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To the reader who is by this time quite at home among tithis and their ending moments, we would quote the following rule from Messrs. SEWELL & DIKSHIT'S *Indian Calendar*:—
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"It is well to note that where the first tithi of a month ends not less than 5 ghatikas before sunset, the heliacal rising of the moon will probably take place on the same evening; but where the first tithi ends 5 ghatikas or more after sunset, the heliacal rising will probably not take place till the following evening. When the first tithi ends within these two periods between 5 ghatikas before and 5 ghatikas after sunset, the day of the heliacal rising can only be ascertained by elaborate calculations".
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Where so much depends upon sunset and moonrise, it is obvious that places with different longitudes and latitudes will often not agree in regard to the exact date of commencement of the Muhammadan year.
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N.B.—Further directions for the use of our Table XV relating to the Muhammadan year are given as a concluding note to that table, *vide* Tables, p. 197.
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Before commencing Part II of our work, which gives special hints with examples regarding the use of each of the more important tables, we take the opportunity to insert a note on Broken Periods:—
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Note on Broken Periods.—It is very important that the reader, dealing with the Indian or any other calendar, should know thoroughly how to reckon broken periods. It is generally a question of addition or subtraction, but unless one goes through the process with reflection, there is always a danger of adding or subtracting 1 too much.
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To take the simplest case, how many days are there from Friday in one week to Tuesday in the next? Most people would use their fingers in such a case and answer '4' or '5' according as they began the reckoning with Friday or with Saturday. Now, such uncertainty is fatal to exact reckoning, and we should therefore follow certain rules whereby we may avoid all uncertainty.
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First of all, we must always note the meaning of the question with reference to the *next sub-division of the broken period*: that is, in this case whether the meaning is from a particular hour on Friday to the same hour on Tuesday. This makes the meaning quite clear. From 6 a.m. on Friday to 6 a.m. on Tuesday following, there are 4 days: and the proper way to answer the question is to convert Friday and Tuesday into week-day figures 6 and 3, and to add a whole period (7) to 3 before deducting 6. Thus, 7+3=10. From 10 take 6, and we have the answer, 4 days. Some exercise is necessary in order to do even these simple week-day problems correctly.
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The rule about adding a whole period when you have taken to reckon from a fraction of one period to a fraction of the next is very important. How many days are there from 23rd October in one year to 15th March in the next, the second being a leap year. If we refer to Table VIII we shall find that 23rd October is 296 days from 1st January, and 15th March (where we have had to pass 29th February) is 75 days. Add 365 to 75. Total 440. Deduct 296. Answer, 144 days.
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If the 1st of a Tamil month be the 15th July, what will be the 7th of the Tamil month? In such cases we must make the same addition to or the same deduction from the one side as we make in regard to the other. In the example before us, the addition to be made is 6, and the answer, 21st July.
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If the 1st of a Tamil month be the 15th July, what will be the 29th of the Tamil month? We add 28 to each side. Therefore the answer is 15+28=43rd July, from which we deduct the whole of the completed period (July=) 31 days. Final answer, 43 minus 31=12th August.