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

20
gold constitutes, having given that a cubic inch of water weighs
252-458 grains, and that gold is 19-362 times as heavy as water.
XXI.
1. Reduce 11 lbs. 11 oz. 11 drams to the decimal of a hundredo
weight; and reverse the operation.
2. What decimal of 5 cwt. 1 qr. 17 lbs. 3 oz. is 4 cwt. 23 lbs. 3 oz.
Avoirdupois?
3. Determine the exact value of -03456 of one ton and 'i7 of one
hundredweight.
4. If the unit be -0064 ounce Avoirdupois, what is the smallest
number of such units which can be represented by an integer?
5. Add -24 to 5-03, subtract from this sum 3-002, multiply the
difference by 40. Divide this product by -007; and supposing the
original unity to have been a hundredweight, find the value of
the resulting decimal in tons, cwts., &c.
XXII.
1. Express a pound Troy as the decimal of a pound Avoirdupois;
and conversely, express a pound Avoirdupois as the decimal of a
pound Troy.
2. If the Roman pound contained 63460-6 French grains, find
how many grains Troy are contained in the Roman pound if the
French grain is equal to -8202 of the grain Troy.
3. If 40,443,495 sovereigns weigh 10,386,772 ounces, and
150,291,456 pennies weigh 1,442 tons 12 cwt., find to three places of
decimals the weight of a sovereign and of a penny in grains.
4. If gold be sold to the mint at ~3 17s. 9d. per ounce, of which
11 parts are pure gold and one part alloy, and be coined into
sovereigns; what is the difference of the mint profit on 10,000
sovereigns, if the alloy be silver worth 5s. 2d. an ounce Troy, or
copper worth Is. 9d. per pound Avoirdupois, supposing each sovereign
to weigh 123-247 grains?
5. At the English mint 1869 sovereigns are coined from 40 lbs.
Troy of standard gold -i fine. At the French mint, 155 Napoleons
are coined from one kilogramme (2-2 pounds Avoirdupois) of standard
gold -9 fine. A Napoleon being equivalent to 20 francs, find how
many francs are equivalent to an English sovereign.
XXIII.
1. Find the value of '7854 mile in yards, feet, and inches.
2. Find the exact value of -0123 of 2,- miles; and reverse the
process.
3. Express in the fraction of a foot, the remainder after '012 of a.
yard has been subtracted as often as it is possible from 1-087 yard.