The method shown calculates the number of days that have elapsed to any given Rosh Hashannah since the year 1H.
The Hebrew date for Rosh Hashannah 1H is corresponds to Monday 7 September -3760g.
The Gregorian calendar has a perfectly repeatable cycle of 146,097 days. This cycle corresponds to the fact that in every 400 years there are 100 packets of 4 years which include the leap day, less the 3 days which account for the 3 century years that are not evenly divisible by 400, and so non-leap.
Moreover, the number 146,097 also represents a whole number of weeks.
The above implies that 7 September -3760g will, after every 400 years, certainly fall on a Monday. Hence, 7 September 1840g fell on a Monday, as will 7 September 2240g. It is assumed here that no calendar changes will be taking place.
Concerning the year 1840g, it is 5600 Gregorian years later than the year -3760g. Since there are 14 cycles of 400 Gregorian years in 5600 years that means that 14*146,097 = 2,045,358 days have elapsed until 7 September 1840g.
It is necessary to add two days to this value to get the number of days that have elapsed since day 0 of the actual count. Hence, this value now becomes 2,045,360 days elapsed since day 0 of the primordial lunar event.
The time of the MOLAD for Tishrei 5759H is
Sutracting the number of days to the 1840g point leaves us with
Again subtracting 100 years, which in this case have 36500 + 24 leap days, leaves 21,198 days from 7 September 1940g to Rosh Hashannah 5759H.
By continuing the remaindering process the date of Monday 21 September 1998g is eventually derived.
In his book "The Calculated Confusion of Calendars", Wolfgang Alexander Shocken makes the excellent suggestion to begin with March 1 as the start date of the year and end with February 29. This alignment has the advantage of placing the leap day out of calculation's way.
The following sites map Hebrew calendar dates to their equivalent Gregorian and Julian calendar dates (and vice versa).
First Paged 8 Jun 1997 Next Revised 13 Feb 2000