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 frequently be much shortened by cancelling equal numbers, when 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 1.

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 ?

10: 9:50 10: 1 :: 50 1: 1 :: 5

90: 112

10: 112*

10: 112

2 : 112 :: 1:56. 56 the answer.

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 2.

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.

*In performing this example, the first abbreviation is obtained 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 com mon measure 2.

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?

25:

5: 100

5:4

19:50 25 : 1:50 1: 1 :: 50 1: 4 :: 10:

4

Ans. 40lb.

2. If 25lb. at Boston be 221b. at Nuremburg; 88lb. at Nuremburg, 92lb. 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.

for

SINGLE FELLOWSHIP.

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

RULE.*

As the whole stock is to the whole gain or loss, so is each

* 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 ør lose a certain sum per cent. &c.

Questions in these rules are performed by the Rule of Three. That the gain or loss, in this rule, is in proportion to their

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?

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