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

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posing these rents to be ~500, ~350, ~800, and ~160, how many
~acres must be allotted to each?
XXIII.
1. On measuring a distance of 32 yards with a rod of a certain
length, it was found that the rod was contained 41 times with half an
inch over. What is the distance approaching nearest to 77 yards
which can be measured exactly by the same rod?
2. If.- of an inch on a map corresponds to 7 miles of a country,,what distance on the map represents 20 miles?
3. Two scales 9 and 10 inches long respectively are each divided
into 10 equal parts; the points of division being marked 1, 2, 3... 10;
if the scales are applied to one another so that the points marked
2 coincide, what is the distance between the points marked 9?
4. If 35 metres are equal to 39 yards, 17 metres to 9 toises, and 5
plethra to 124 toises, how many yards are there in 1,575 plethra?
5. The relative distances of three trees are 3, 4, and 5, and a rope
492 feet long just goes round them; find the respective distances.
6. If a yard measure be incorrect by one-eighth of an inch, find
the error in measuring a distance of 500 yards 2 feet 6 inches. Explain,
if there is any difference, whether the error be in excess or defect.
7. What fraction of the Earth's diameter is a mountain 51 miles
high, if the radius of the Earth be 3,963 miles? Determine by what
fractional parts of an inch could be represented (1) the highest point
of Mont Blanc, which is about 15,700 feet above the level of the sea,
on a globe of 16 inches in diameter; and (2) the highest peak of the
Himalayas, Kunchinjunga, 28,178 feet above the level of the sea, on
a globe of 30 inches diameter.
XXIV.
1. How many square yards, square feet, and square inches are
there in a rectangle 34 yards 2 feet 11 inches long and 29 yards 1 foot
10 inches wide?
2. The length of one side of a rectangular field is 572 yards, and
its area 50 acres, 2 roods, 32 poles; find the length of the other side.
3. How many yards of stuff 3 quarters broad will line a cloak
65 yards long and 1- yards broad?
4. What must be the width of a floor which is 17 feet 7 inches
long, in order that it may contain the same area as another of 13 feet
4 inches by 22 feet 11 inches?
5. How many plots of ground containing 33|- square yards can be
cut off from a field containing 4 acres, 3 roods, 9 poles, 191 square
yards, whose breadth is 135 yards; and what will be the width of the
remaining strip, after the plots are marked off?
6. A piece of land whose length is 151 yards 1 fee',, and breadth
35 yards, is to be exchanged for part of a strip of land of the same