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

36
Is.; 4-s.=12 carlini, and Is. =-72 of 1 carlini. Hence 1 scudi=2 — of - of f2 of
1 carlini, and therefore 500 scudi =500 X 21 X 4 X 7- = 6048 carlini. 6. 7055- carlini.
7. 620-43- thalers. 8. 100 francs. 9. ~6 in London is equivalent to 85 marks in
Hamburgh.
XVIII.
1. 17s. n64 4Wd. in the pound, and they lose wl6l7 of their debt. 2. He loses
U of ~5342 5s. 3. i lost, whole debt ~120 8s. 44d. 4. The creditors lose 8 7 part.
The whole debt was ~2440. 5. ~178 Is. 6d. 6. ~810, ~621, ~729. 7. 137
~784, ~58. Each receives 392 per cent. of his debt. 8. First, ~664 was to gain
2 1
~166, or ~ of the capital employed, which is ~25 in the ~100, or 25 per cent.
Secondly, ~830 lost ~166, or - of the capital employed, or 20 per cent. 9. By
dividing ~195 into three parts, 7, *T, and 39. 10. ~180, ~320, ~500. 11.
Here +I+-1 _ -62+ +-ls2- 1 of the whole, of which -I- share is not assigned.
4r 6'T' ' — ' TT ' I "- IL'
The gain ~125 for their share must be deducted from ~1,500, which leaves ~1,375 to
be divided. Their three capitals are denoted by 6, 3, 2, and the first takes 7 per
cent. on his 6, the second 5 per cent. on his 3, and the third 3 per cent. on his 2
and the sums of these 42+15+6=63, or -+ +-2 — 1l, which gives the shares of
the gains ~916-, ~327-, ~13010. 12. ~200x161, ~200X371, ~200x531,
3) 2 11 '2 1 2 ~ 00X ' 60
~200 X 6390.
XIX.
1. The questions are one the reverse of the other. 2. ~333 6s. 21d. 3. 5-dwts.
of pure gold. 4. The supposition gives 96 grains of pure gold, neglecting the alloy.
5. 8~ out of 100 parts, or 8~ per cent. 6. The true weight of a sovereign is 5dwts.
2}grs. The loss on 100 light sovereigns is to be calculated on the supposition of a
loss of lid. on ~3 17s. 10Dd., the value of one ounce of standard gold. 7. Neither
gain nor loss. 8. lObs. of jewellers' gold consists of 5%1bs. of pure gold, and 471bs.
of alloy, of which alloy.. of llb. added to 5]lbs. pure gold, makes 6A4-lbs. standard
gold; the rest of the alloy, 3 —lbs., is neglected. The question now requires the
price of 6y4Tlbs. of standard gold at ~3 17s. 10~d. per ounce. 9. 17 carats pure gold
implies 7 carats alloy, 2- ounces of pure gold. 10. The sum of ~3 17s. 10cd.
could have paid ~4 13s. 6d. in 1815; but in 1821 the depreciation was 15s. 7dc. on
~4 13s. 6d., or A of ~4 13s. 6d. Hence the depreciation on ~100 will be ~16., or
162 per cent. 11. If the number of grains in one ounce Avoirdupois be divided by
the number of grains in the weight of one sovereign, the quotient will give the
number of sovereigns required. 12. The alloy in a sovereign is 10-l- grains. The
difference will be the excess in value of 10F-b grains of silver at 5s. 6d. an ounce, and
10-' grains of copper at Is. 6d. a pound Avoirdupois of 7,000 grains.
XX.
1. 12dwts. 2. 5s. 3*d. 3. 8dwts. 11 6 grains of pure silver, and 13-o grains
alloy. 4. 516 — farthings.
5. Supposing the value of the alloy neglected. 80 per cent. of pure silver
implies 20 per cent. of alloy, so that 1.oi + 2o =1 or -4+I=1. And if the unit be
taken as one ounce, one ounce of alloyed silver is in value 4 of an ounce of pure
silver, or 4s. And 15 times the value of one ounce of alloyed silver is ~3, and ~3
is i of the value of 1 ounce of pure gold. But three parts of pure gold and one part
of copper make up the ounce of alloyed gold. 4 of an ounce of copper, or 25 per
cent., must be mixed with 75 per cent. of pure gold.
6. Estimating the coins by the pure silver in them, 1 sestertium = 250 X 54 grains
of pure silver, and 4 of 20 X 24 grains =-37 X 12 grains, which are worth 5s. 2d. The
sestertium is worth ~7 17s. l-;rcd.