This may now be considered as done; and the next step is to increase it 2 per cent., and that is done by multiplying by 102, and dividing by 100. Then we shall have, as here represented.

We must now give interest on this money, at 4 per cent. for 9 months; that is, multiply by 103, and divide by 100. After that, we must increase it 15 per cent., and we shall have the whole amount of dollars to be received for the 300 yards of cloth. We then divide hy 300, and we shall have the sum corresponding to one yard, and the work is done, all but the canceling. When completed, in form it stands thus:

This will cancel in part, and as far as it will cancel, it is so much labor saved; but the chief merit insisted upon, is the plan, going through the entire operation in form without multiplying or dividing, going through the solution as a reasoner, and not as a mechanical operator only.

Let this be a pattern or a rule for all other problems

of the like kind.

2. A merchant bought 280 yards of sheeting in Liverpool for 25 pounds, and duties and transportation cost 7 pounds 10 shillings more; what shall be the price per yard in cents, to gain 20 per cent. on first cost?

Ans. 66 cents 8 mills.

3. Received 600 yards of Irish linen, the whole cost, including transportation, duties and commission, was 75 pounds 10 shillings, Irish currency; what must be my retail price per yard, in Federal Money, to gain 20 per Ans. 60,4 cents, nearly.

cent.?

4. A merchant bought sugar in New York at 6 pence per pound, New York currency; and while on his hand the wastage was estimated at 5 per cent., and interest on the first cost to the time of sale, at 2 per cent.; how many cents shall he ask per pound to gain 25 per cent.? Ans. 81 cents.

5. A merchant bought 3 hogsheads of Lisbon wine at of a milree per gallon: on arrival at New York, it was found that one hogshead had lost 21 gallons by leakage; the duties and transportation amounted to 18 per cent. on the original cost; what shall he sell it per gallon, to gain 20 per cent.? Ans. 79 cents.

6. Received from Malaga six hogsheads of wine, which, including duties and transportation, cost me 175 Spanish dollars: it has suffered a leakage of about 4 per cent.; how must I sell it per gallon to gain 12 per cent.? Ans. 54 cents.

7. I bought 560 yards of Irish linen, which cost me, including all expenses, 90 pounds Irish currency, and I sold it at 75 cents per yard; what was my gain per cent.? Ans. 14 per cent. nearly. sale.

cost.

Solution: as 90X410: 560X75 :: 100: 4th term. 8. If 108 dollars were given for 9 hundred weight of sugar, nett weight, tare 16 pounds per hundred weight, what must be the price per pound, to gain 12 per cent.? Ans. 14 cents.

9. Received from my agent, 300 barrels of flour, which cost me 1400 dollars, and 75 dollars incidental expenses; I now ship the same to Brazil, and pay $1,25 per barrel for transportation; what must it bring in that market to yield me 15 per cent., exclusive of duties at that port? Ans. $7,09 +

10. A merchant bought, in the British West Indies, 3 casks of molasses, each containing 54 gallons, for 12 pounds 13 shillings 6 pence; transportation and duties, £3 4 s. 6 d. in addition; he then estimates a wastage of 4 per cent.; what shall be his price per gallon, in federal money, to gain 20 per cent.? Ans. ,58 cts. 11. What is the cost of 15 chests of tea, each contain

ing 147 pounds gross, at 4 shillings 6 pence, New York currency, per pound, tare 16 pounds on every 112 pounds? Ans. $1063,121.

12. Sold cloth at 12 shillings 6 pence, New York currency, and gained 15 per cent.; what would have been the price per yard, in dollars and cents, had I gained 27 per cent.? Ans. $1,725 +

Solution:

12,5 X 100

8X115

: []: 100 : 127

Dividing by 8, reduces shillings to dollars, New York cur

rency.

13. A merchant received from Amsterdam, 620 yards of carpeting, whole cost 2480 guilders; what must be the retail price per yard, in federal money, to gain 15 per cent.? Ans. $1,84.

14. New York, March 30, 1842. This day received from Liverpool, 900 yards of broadcloth, whole cost 1200 pounds sterling; how must I sell it per yard, in federal money, to gain 20 per cent.? Ans. $7,68.

15. Boston, July 1, 1843. This day received from France, 1200 bottles of Champagne, for which I paid 400 French guineas, each $4,60; how must I sell this wine per bottle, to gain 35 per cent.? Ans. $2,07.

16. "Received 300 ells of cloth from Hamburg, which cost 1500 marks banco; how must the same be sold per yard, in federal money, to gain 12

Hamburg being 2 qr."

per cent., the ell Ans. $3,00.

17. A man shipped flour to Dublin: whole cost, including purchase, transportation, commission, and duties, was 4500 dollars; he directs his agent to sell it not under an advance of 10 per cent.; how many pounds, Irish currency, could he draw for? Ans. £1207 6 s. 4 d.+

(ART. 113.) Connected with the higher order of exchanges, is a certain class of problems which trace a result through several proportions: yet different from compound proportion, as that which is generally considered compound proportion, is, in reality, in respect to things, single proportion, and compound only, in respect to numerical factors; but the proportions we are about

to introduce, change from one thing to another, in fact, and, after being condensed and properly linked together, the single operation is called Conjoined Proportion: or, The Chain Rule. We shall treat it, however, as simple reduction; but reduction is proportion, as we may see by the following example:

Reduce 3 tons to pounds, by proportion; thus,

Thus we perceive that reduction is proportion; but the formal statements, one by one, step by step, render all such simple problems complex. It is obvious that these three proportions are linked together; they are conjoined, or enchained; but, as a whole, are entirely unlike compound proportion. We call particular attention to this, as some authors have made the sad mistake of placing problems in conjoined, under rules of compound, proportion.

Let us return to our example again. We observe that the first terms of the several proportions are units: hence there will be no dividing; the whole operation will be

actual multiplication, and, by Art. 24, the entire operation will stand thus:

This may be read as follows: * What number of pounds in 3 tons, if 1 ton=20_cwt., 1 cwt.=4 quarters, and 1 quarter=28 pounds ? We may render this same question much more complex, without changing its nature. It will still be reduction, stated thus:

If 2 tons in London make 40 hundred weight in New York, and 3 hundred weight in New York make 12 quarters in Havana, and 4 quarters in Havana are equal to 112 pounds in Brazil, how many pounds in Brazil are equal to 3 tons in London?

This solution will stand thus:

3 tons, term of demand. If tons, 2= 40 hundred weight;

Divide or cancel out the numbers on the left hand side of the line, and it will be the same as before expressed.

This is rendered complex, by mentioning places, which need not, yea, should not be mentioned in connection with this problem, but which must be mentioned in connection with some others; we mention them here, to show how mere names of places, or different names to things, will throw confusion into the mind, when in reality the problem may be simple.

For a further illustration, let us take the following well known problem.

* In view of these equalities, and the subsequent arrangements of the terms each side of a perpendicular line, some have been led to say that this perpendicular line, in all cases, represents equality-an unphilosophical assertion. Indeed, it is to be apprehended that this whole system of canceling may, for a time, suffer in the estimation of the public, by the immodest pretensions of some of its professors.