Elementary arithmetic, with brief notices of its history... by Robert Potts.

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XXXIV.
1. The sun appears to a person on the earth to move through 360~
in 365-24 days; shew it moves through 59' 8" -351... in one day.
2. Assuming the length of the Julian year at 365 days 6 hours, find
the decimal which represents one hour to 10 places of figures.
3. Find what time in hours, minutes, and seconds corresponds to
230 27' 53" in the revolution of the earth on its axis; and conversely.
4. If the circumference of a circle be 3-14159 times the diameter,
find at what rate per hour a body moves at the equator by the rotatory
motion of the earth, supposing the equatorial diameter of the earth to
be 7925-648 miles.
5. The longitude of Calcutta is 88~ 20' east, and of Barbados
59~ 50' west of London. Convert these longitudes into time, and shew
how much the clocks of London are before or behind those of Barbados and Calcutta; also how much the clocks of Calcutta are before
or behind those of Barbados.
6. A lunar month is 29-530588 days. How many lunar months are
there in 19 solar years, calculated at 365-242264 days?
7. There was a full moon on the 26th June, 1858, at 9.13 a.m. The
interval between successive full moons has since been on the average
29 days 12 hours 47~ minutes; how many full moons have there been
between the 26th June, 1858, and 26th June, 1875?
XXXV.
1. Describe the Julian and Gregorian adjustments of the calendar,
and explain why only every 400th year is a leap year.
2. How many days elapsed between the epoch of the correction of
the calendar by Julius Caesar, January 1, B.c. 45, and September 14,
A.D. 1752, the date of the adoption of the Gregorian correction in
England?
3. The solar year contains 365-242218 days, and the average
Julian year 365-25 days. In the year 1582 Pope Gregory corrected
the Julian calendar; how many days in roundnumbers did he add or
omit in that year to make it coincide with solar time?
4. The length of the tropical year being 365-242264 days, compare
the accuracy of the Gregorian intercalation with that of the Persian,
in which 8 days were intercalated in 33 years.
5. If the year be divided into eighteen months of twenty days
each, and five intercalary days be added at the end of each year, and
also 12 intercalary days at the end of each cycle of 52 such years, in
how long a time will the error in reckoning amount to one day, the
true length of a year being 365-242264 days?
6. The true length of the year is 365-242264' days, and the
calendar as corrected by Julius Csesar supposed it to be 3651 days; in
how many years will the error caused by this discrepancy amount to
one week?