The limited success of the French Republican calendar is testimony to the enduring simplicity of the calendar handed down to the Western world by Julius Caesar and Pope Gregory XIII. However, many individuals since 1582 have recognised the failings of the Gregorian calendar and suggested solutions.
The lengths of the months are a haphazard sequence. The four quarters of the year are not of equal length - in a normal year, they are 90 days, 91 days, 92 days and 92 days.
The year, whether 365 days or 366, does not contain a whole number of weeks, and so each day in the year can fall on any day of the week. The number of working days (i.e. not weekends) in a month varies from one year to the next. A phrase such as "the last Sunday in October" does not define a fixed day of the month.
Proponents of the "World Calendar" suggest a scheme which would eliminate all of these problems. They split the year into four quarters, beginning in January, April, July and October. The first month of each quarter would have 31 days, whilst the second and third months would have 30 days each, making exactly 13 weeks.
There would be an extra day at the end of the year, called Year End Day, to bring the total to 365, and in leap-years the additional day would be placed in the middle of the year, between June and July.
Each quarter would begin on a Sunday. Since each quarter contains exactly 13 weeks, the sequence of days of the week would not be broken during the year, except in leap-years. Neither Year End Day and Leap Year Day would have a day of the week, in the same way that in the French Republican calendar, the five or six year-end days had their own names.