Time is divided into hours, days, weeks, months and years. The earth performs a complete revolution in its orbit about the sun, in 365 days 05 hours 48 minutes and 47.4624 seconds or nearly 365¼ days. In ordinary year consist of 365 days and to make up for the fraction, every fourth year is taken to be 365 days. This is called the Leap year. The method of distribution time into hours, says, weeks, months, and years etc. is called __CALENDAR__.

The modern form of calendar is due to Julius, Caesar as modified by Augustus. The year adopted by Julius Caesar is too long by eleven (11) minutes 24 seconds. Therefore, the error would amount to 3 days in 400 years. Hence Pope Gregory VIII carried out a further reform by which the century year is not considered a leap year unless it be divisible by 400. Thus 400, 800, 200, 1600 & 2000 are leap year but not 1700, 1800, 1900. The calendar was then set right in 1582. The “New Style” was adopted by the whole of Europe (except Russia) in the year 1752.

The week consists of 7 days. Hence the days on the 8^{th}, 15^{th}, 22^{nd}, & 29^{th} of a month shall be the same as on the I^{st}.

#### The fallowing facts should be remembered.

__In the month of.__ __The difference of the days.__

28 days (4 weeks) 0 days

29 days (4 weeks 1 day) 1 day

30 days (4 weeks 2 days) 2 days

31 days (4 weeks 3 days) 3 days

__Similarly, in a year of:__

365 days (52 weeks 1 day) 1 day

366 days (52 weeks 2 days) 2 days

In Hundred years, there are seventy-six ordinary years and twenty-four Leap years.

Therefore, there will be a difference of (24×2) +76 = 124 days, 7 weeks and 5 days.

Thus in 100 years, there is a difference of 5 days

Thus in 200 years, there is a difference of 3 days

Thus in 300 years, there is a difference of 1 day

Thus in 400 years, there is a difference of 0 days

Thus in 800, 1200, 1600 years, there is a difference of 0 days

**Note: –**

i) In these calculations remember that the century year in an ordinary year expect when divisible by 400.

ii) For the purposes of calculation JAUARY Ist. 1 AD us to be taken as falling on Monday

__Example 1:__

Find the day of the week on March 26^{th}, if March Ist was a Friday total member of days from March I^{st} to 26^{th} is 25^{th} days = 3 weeks 4 days 7/25/3-4 March 26^{th} was Tuesday. (4 days after Friday = Tuesday.

__Example 2__:

What day of the week was June 23^{rd} if the 2^{nd} March fell on Saturday.

** **Total number of days from 2^{nd} March to 23^{rd} June.

March 31-2 = 29 days

April = 30 days

May = 31 days

June = 23 days

113 days

113 days = 16 weeks and 1 day, so it was Sunday. (1 day after Saturday)

__Example 3__:

A certain leap year began on Sunday. Find the day of the week on August 9^{th}.

January (31-1) = 30 days

February = 29 days from January 1^{st} to August

March = 31 days 9^{th} total No days 221 =31

April = 30 days week and 4 days.

May = 30 days

June = 30 days August 9^{th} will be Thursday

July = 31 days (four day after Sunday)

August = 09 days

Total = 221 days. (221/7=31-4).

__Example 4__:

Find the day of the week on the 8^{th} October 1954.

During 1600 years there will be complete weeks + 0 days

300 + 1 day

53 + 4 days

13 Leap years I (53 years) + 6 days

from January to 8^{th} October = 281 days + 1 day

Total days = 12

Center from Monday (12/7=1-5)

So, October 8^{th} 1954 was Friday.

__RULE[adsense]__

The number of days to be counted beginning from Monday will given by the remainder of the formulas.

__Y + L –C +D __

** 7 **

Where Y = the number of years (excluding the year under reference)

Where L = the number of leap years (the ebullient of y/4 integral part only)

Where C = the number of centuries. Those were not leap years.

Where D = the number of days of the given year up to day.

__Example 5:__

Find the day of the week on 20^{th} August 1957.

Here Y= 1956 + L= 489 + C= -15 + D=232 = 2662. 2662/7= 38 weeks and 2 days. Which gives a remainder 2 in 20^{th} August 1957 in TUESDAY.

__Example 6:__

What was the day of the week when the Great European War Commence on August 4, 1914.

Jan = 31 days

Fab = 0 day

Mar = ———-

(Here Y= 1913 + L= 489 + C = -15 + D = 216 = 2662)

2592/7= 370 weeks & 2 days.

In 4^{th} August 1914 was __TUESDAY.__

**Note: –**

The formula given above would apply to all cases after the year 1752 for all dates before 1752 and for all Julian years it (Y+L+D/7) but days are to be counted from Saturday.

__Example 7:__

The Holy Prophet of Islam was born on April 20, A.D. 571 what was the day of the week it?

Hear Y = 570 Jan. = 31

L = 142 Feb. = 28

D = 110 Mar. = 31

822/7 = 110

Remainder 3.

Then country form Saturday. The 20^{th} April AD 571 was __MONDAY.__

__THE MUSLIM ERA__

__THE MUSLIM ERA__

The year at Hijra are purely lunar, this era began on the first day of the month preceding the departure of the Holy Prophet of Arabic from Mecca to Medina. This was on 15^{th} July AD 622. The length of lunar year is 354 11/30 days and that of the solar year 365.2422.

__Year of Hijra__ = __354 11/30 __ = 0.970224

Solar year 365.2422

Also, the year Al-Hijra began after 621.5774 year of the Christian Era. Hence the date of the commencement of the year Al-Hijra according to the New Style Christian Era may be calculated by the following.

__RULE__

__RULE__

Multiply the year of Al-Hijra by 0.970224 and add 621.5774 to the product Era whole number of the sum will given the year of the Christian Era and the day of the multiplying the decide figures by 365.

__Example 8:__

Find the date on which the year 1375 at Al-Hijra began, multiply 1375 by 0.970224 we get 1334.058 adding 621.5774, we get 1955.6354.

Thus, the year was AD 195 multiplying by 0.6354 by 365, we get 231.902 or 232 nearly thus the 1^{st} day of Al-Hijra 1375 was the 232^{nd} day of 1955 AD.

That if fell on 20^{th} August 1955.

Y = 1954, L = 488, C = 15, D = 232

Y+L-C+D/7 = 1954+488+232-15/7 = 3659/7

Which gross the remainder as 6 on 1^{st} Muharram 1375 Al-Hijra, the day was __THURSDAY.__

To convert Al-Hijra year to A.D., divide No. of days by 365 add year to be converted into Al=-Hijra subtract 621.5774 divided the result so ultimate by 0.97022416.

OR year Al-Hijra = {No. of days/365 + year (AD)} -621.5774

0.97022416