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

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XXXI.
1. The inscription on the congius of Vespasian preserved at
Dresden, states that it contains 10 Roman pounds. When this
measure was filled with water and carefully weighed, the weight of
the water was found to be 63460*6 French grains; find how many
grains Troy are contained in one Roman pound, if the French grain is
equal to -8202 of the English grain.
2. By the statute of William III. the Winchester bushel is declared
to be round with a plain bottom, 18~ inches wide throughout, and
'8 inches deep. How many cubic inches is the content, the area of a
circle being equal to 3'14159 times the square of the radius?
3. If the Roman modius contained three congii, and the congius
of Vespasian preserved at Dresden contains ten Roman pounds of
water, how many English gallons make a modius?
4. Pliny states that a modius of the corn of Clusium weighed
twenty-six Roman pounds. Suppose that a congius and a gallon are
filled with the same grain, and that the former weighs as many Roman
pounds as the latter weighs pounds Avoirdupois, and if a modius be
three congii, what would be the weight of an imperial bushel of the
corn of Clusium?
XXXIL
1. Reduce 23~ 15' 11" to the decimal of a degree in circular
measure.
2. Express 13~ 17' 8" as the decimal of a right angle.
3. Reduce 1. --- of a degree to degrees, minutes, and seconds.
4. If 90 English degrees correspond to 100 French degrees, how
many French degrees are there in 36-45 English?
XXXIII.
1. What decimal of a day is 13 hours 12 minutes 10 seconds?
2. What decimal of a day of twelve hours is 5 hours 48 minutes
49-7 seconds? Find the value of -85714 of a calendar month.
3. Reduce 3 days 5 hours 48 minutes 57 seconds to the decimal of
a Julian year.
4. Divide 3 weeks 4 days 5 hours 6 minutes 7 seconds by 5 days,6 minutes 40 seconds, expressing the result as a decimal and stating
its nature.
5. Divide -375 of a calendar month by -7854 of a week, and state
<the nature of the quotient.
6. Find the sum of '123 of a Julian year, -565 of a week, '0125 of
an hour, in days.
7. Find the decimal of a week which differs from a day by less
than the millionth part of a week.
8. For what unit of time can 108-8 and 8-28 hours be represented by numbers prime to each other?