2. If 1001. in one year gain 51. interest, what will be the interest of 7501. for 7 years? Ans. 2621. 10s. 3. What principal will gain 2621. 10s. in 7 years, at 51. per cent. per annum? Ans. 7501. 4. If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, may he travel 360 miles? Ans. days. 5. If 120 bushels of corn can serve 14 horses 56 days; how many days will 94 bushels serve 6 horses?

Ans. 1021 days. 6. If 7oz. 5dwts. of bread be bought at 44d. when corn is at 4s. 2d. per bushel, what weight of it may be bought for 1s. 2d. when the price of the bushel is 5s. 6d. ?

Ans. 1lb. 4oz. 479 wts. 7. If the carriage of 13cwt. 1qr. for 72 miles be 21. 10s. 6d. what will be the carriage of 7cwt. 3qrs. for 112 miles? Ans. 21. 5s. 11d. 179.

8. A wall, to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days; how many men must be employed to finish the wall in 4 days, at the same rate of working? Ans. 36 men.

9. If a regiment of soldiers, consisting of 939 men, can eat up 351 quarters of wheat in 7 months; how many soldiers will eat up 1464 quarters in 5 months, at that rate? Ans. 5483 23

143

10. If 248 men, in 5 days of 11 hours each, dig a trench 230 yards long, 3 wide and 2 deep; in how many days of 9 hours long, will 24 men dig a trench of 420 yards long, 5 wide and 3 deep? Ans. 2887

CONJOINED PROPORTION.

CONJOINED PROPORTION is when the coins, weights, or measures, of several countries are compared in the same question; or it is the joining together of several ratios, and the inferring of the ratio of the first antecedent and the last consequent from the ratios of the several antecedents and their respective consequents.

NOTE 1. The solution of questions, under this rule, may

freque

when

atly be much shortened by cancelling equal numbers, In both the columns, or in the first column and third term, and abbreviating those, that are commensurable.

NOTE 2. The proof is by so many statements in the single rule of three, as the nature of the question requires.

CASE I.

When it is required to find how many of the last kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the first.

RULE.

1. Multiply continually together the antecedents for the first term, and the consequents for the second, and make the given number the third.

2. Then find the fourth term, or proportional, which will be the answer required.

EXAMPLES.

1. If 10lb. at Boston make 9lb. at Amsterdam; 90lb. at Amsterdam, 112lb. at Thoulouse; how many pounds at Thoulouse are equal to 50lb. at Boston?

Ant. Cons.

10 :- 9

90 : 112

In performing this example, the first abbreviation is obtain

2. If 20 braces at Leghorn be equal to 10 vares at Lisbon; 40 vares at Lisbon to 80 braces at Lucca; how many braces at Lucca are equal to 100 braces at Leghorn? · Ans. 100 braces.

CASE II.

When it is required to find how many of the first kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the last.

RULE.

Proceed as in the first case, only make the product of the consequents the first term, and that of the antecedents the second.

EXAMPLES.

.1. If 100lb. in America make 95lb. Flemish; and 19lb. Flemish, 25lb. at Bolognia; how many pounds in America are equal to 50lb. at Bolognia?

ed by dividing 90 and 9 by their common measure 9; the second by dividing 10 and 50 by their common measure 10; the third by dividing 10 and 5 by their common measure 5; and the fourth, or answer, by dividing 2 and 112 by their common meas

ure 2.

2. If 25lb. at Boston be 221b. at Nuremburg; 88lb. at Nuremburg, 921b. at Hamburgh; 46lb. at Hamburgh, 491b. at Lyons; how many pounds at Boston are equal to 98lb. at Lyons? Ans. 100lb. 3. If 6 braces at Leghorn make 3 ells English; 5 ells English, 9 braces at Venice; how many braces at Leghorn will make 45 braces at Venice? Ans. 50 braces.*

FELLOWSHIP.

FELLOWSHIP is a general rule, by which merchants, &c. trading in company, with a joint stock, determine each person's particular share of the gain or loss in proportion to his share in the joint stock.

By this rule a bankrupt's estate may be divided among his creditors; as also legacies adjusted, when there is a deficiency of assets or effects.

SINGLE FELLOWSHIP.

Single Fellowship is when different stocks are employed for any certain equal time.

* Barter is the exchanging of one commodity for another, and directs traders so to proportion their goods, that neither party may sustain loss.

Loss and Gain is a rule, that discovers what is got or lost in the buying or selling of goods; and instructs merchants and traders to raise or lower the price of their goods, so as to gain or lose a certain sum per cent. &c.

Questions in these rules are performed by the rule of Three. Vol. I...

Q

RULE.*

As the whole stock is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or loss.

METHOD OF PROOF.

Add all the shares together, and the sum will be equal to the gain or loss, when the question is right.

EXAMPLES.

1. Two persons trade together; A put into stock $130 and B $220, and they gained $500; what is each person's share thereof?

130 220

350 : 500 :: 130:

500

35,0)6500,0(185*71

35

300

280

200

175

250

245

50

35

15

* That the gain or loss, in this rule, is in proportion to their stocks is evident: for, as the times the stocks are in trade are equal, if I put in of the whole stock, I ought to have of the whole gain; if my part of the whole stock be, my share of the