THE COMPARISON OF WEIGHTS AND MEASURES. The operations are performed by the Single Rule of Three Direct. EXAMPLES. 5. If 60 pounds in America make 56 pounds at Amsterdam, how many pounds in America are equal to 350 pounds at Amsterdam? Ans. 375 pounds. 6. If 112lbs, in America be equal to 106 lbs. at Lyons, how many lbs. at Lyons are equal to 1 ton in America? Ans. 2120lbs. 7. If 100 English ells make 125 yards in the United States, how many English ells are equal to 1000 yards in the United States? Ans. 800 English ells. CONJOINED PROPORTION,* OR, THE RULE OF CONJUNCTION.† Conjoined Proportion, or the Rule of Conjunction, is a comparison of the coins, weights, or measures, of several countries in the same question; or, it is the joining of many proportions together, and by the relation which several antecedents have to their consequents, the proportion between the first antecedent and the last consequent is discovered, as well as the proportion between the others in their several respects. CASE 1. When it is required to find how many of the first sort of coin, weight, or measure, mentioned in the question, are equal to a given quantity of the last sort. RULE. Place the antecedents on the left hand and the consequents on the right, and let the last number stand on the left hand; then, multiply all the numbers in the left hand column together for a dividend, * See Thomas Dilworth's Arithmetic. t See William Gordon's Arithmetic. and those in the right hand column for a divisor: the quotient thence arising will be the answer required. N. B.-Equal antecedents and consequents cancel each other; the others may be divided by any number that will divide both without a remainder, and the quotients used in their stead. EXAMPLES. 1. Suppose 100 yards of America make 100 yards of England, and 100 yards of England 50 canes of Thoulouse, and 100 canes of Thoulouse 160 ells of Geneva, and 100 ells of Geneva 200 ells of Hamburg; how many yards of America are equal to 379 ells of Hamburg? Antecedents. Consequents. 100 yards of America=100 yards of England. 100 x 100 x 100 x 100×379-37900000000 dividend/ 236yds. 3qrs. 2na. answer. yds. grs. na. =236 3 2 Answer Ant. Con 0 2 5 1 2. If 20lbs. at Richmond, in Virginia, make 25lbs. at Antwerp, and 150lbs. at Antwerp make 180lbs. at Leghorn, how many pounds at Richmond, in Virginia, are equal to 144lbs. at Leghorn? Ans. 96lbs. at Richmond, in Virginia. 3. If 12lbs at Boston make 10lbs. at Amsterdam, and 100lbs. at Amsterdam 120lbs. at Paris, how mary pounds at Boston are equal to 80lbs. at Paris? Ans. 80lbs. at Boston are=80lbs. at Paris. 4. If 25lbs. at London make 22bs. at Nuremburg, and 88lbs. at Nuremburg 92lbs. at Hamburg, and 46lbs. at Hamburg 49lbs. at Lyons, how many pounds at London are equal to 98lbs. at Lyons? Ans. 100 pounds. 5. If 100lbs. English make 95lbs. Flemish, and 19lbs. Flemish 25lbs. at Bologna, how many pounds English are equal to 50lbs. at Bologna ? Ans. 40lbs. English. 6. If 6 braces at Leghorn make 3 ells English, and 5 ells English 9 braces at Venice, how many braces at Leghorn are equal to 45 braces at Venice? Ans. 50 braces at Leghorn. 7. If 3 dozen pair of gloves are equal in value to 2 pieces of ribbon, and 3 pieces of ribbon to 7 dozen of points, and 6 dozen of points to 2 yards of Flanders lace, 3 yards of Flanders lace to 81 shillings, how many dozen pair of gloves may be bought for 28 shillings? Ans. 2 dozen pairs. CASE 2. When it is required to find how many of the last sort of coin, weight, or measure, mentioned in the question, are equal to a given quantity of the first sort. RULE. Place the numbers alternately, as before, beginning on the left hand with the antecedents, and let the last number stand on the right hand; then multiply all the numbers in the left hand column together for a divisor, and those on the right for a dividend; the quotient thence arising will be the answer required. EXAMPLES. = 1. If 20 braces at Leghorn 10 vares at Lisbon, and 40 vares at Lisbon 80 braces at Lucca, how many braces at Lucca are=100 braces at Leghorn? Antecedents.. Consequents. 20 braces are= -10 vares. 40 vares are 80 braces. Contracted. 10)20=10 |2|1 100 braces as before. Ans. 100 br. at Lucca. 2. If 12lbs. at Boston=10lbs. at Amsterdam, and 100lbs. at Amsterdam=120lbs. at Paris, how many pounds at Paris are to 80 pounds at Boston? Ans. 80lbs. at Paris. 3. If 10lbs. at London are=9lbs. at Amsterdam, and 90lbs. at Amsterdam=112lbs at Toulouse, how many pounds at Thoulouse 50lbs. at London? are Ans. 56lbs. 4. If 96lbs. at Richmond, in Virginia, are=144lbs. at Leghorn, and 180lbs. at Leghorn=150lbs. at Antwerp, how many pounds at Antwerp are=20lbs. at Richmond, in Virginia? Ans. 25lbs. 5. If 40lbs. English are=50lbs. at Bologna, and 25lbs. at Bolog na 19lbs. Flemish, how many pounds Flemish are 100 pounds English? Ans. 95lbs. Flemish. 6. If 50 braces at Leghorn are=45 braces at Venice, and 9 braces at Venice=5 English ells, how many English ells are equal to 6 braces at Leghorn ? Ans. 3 English ells. Practice is a short way of finding the value of any quantity of goods, or other mercantile articles, when the price of one integer and the number you wish to find the value of, are both known. The questions may be proved by varying the parts, by Compound Mul. tiplication, or by the Single Rule of Three Direct. When the price of an integer is less than a dollar, and also an aliquot part of it. RULE. Divide the given number by the said aliquot part, and the quotient will be the answer in dollars-but if there should be a remainder, proceed with it according to the rule given in Division of Federal Money. EXAMPLES. When the price of an integer is less than a dollar, and not some aliquot part of it. RULE. Find the aliquot parts of the given price contained in one dollar, by which divide the given number of things, and the sum of the quotients will be the answer in dollars, &c. Parts may be taken out of parts very conveniently, as may be seen in the following EXAMPLES. What will 56 yards cost, at 933 cents per yard? C. 50 yds. 56 |