COMPARISON OF WEIGHTS AND MEASURES. EXAMPLES. 1. If 78 pence Massachusetts be worth 1 French crown, how many Massachusetts pence are worth 320 French crowns? F. cr. d. F. cr. As 1 78 :: 320 78 2560 2240 24960 Ans. 2. If 24 yards at Boston make 16 ells at Paris, how many ells at Paris will make 128 yards at Boston? As 24yds. 16ells. :: 128yds. : 85 ells, Ans. 3. If 60lb. at Boston make 56lb at Amsterdam, how many lb. at Boston will be equal to 350 at Amsterdam? Ans. 375lb. Boston. 4. If 95lb. Flemish make 100lb. American, how many American lbs. are equal to 550lb. Flemish ? Ans. 578 lb. American. CONJOINED PROPORTION IS when the coins, weights or measures of several countries are compared in the same question; or, in other words, it is joining many proportions together, and by the relation, which several antecedents have to their consequents, the proportion between the first antecedent and the lost consequent is discovered, as well as the proportion between the others in their several respects. This rule may generally be so abridged by cancelling equal quan tities on both sides, and abbreviating commensurables, that the whole operation may be performed with very little trouble, and it may be proved by as many statings in the Single Rule of Three, as the nature of the question may require. CASE I. 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. RULE. Place the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right, and let the last number stand on the left hand; then multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer. EXAMPLES. : EXAMPLES. 1. Suppose 100 yards of America=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 Hamburgh How many yards of America are equal to 379 ells of Hamburgh? Antecedents. 100 of America 100 of England 100 of Thoulouse 100 of Geneva 379 of Hamburgh? Therefore, 379X5 Consequents. = 160 of Geneva. 200 of Hamburgh. Abriged. Ant. Con. 5 8 379 =236 yds. of America=379ells of Hamburgh. ILLUSTRATION. Let the last cy The two 100s of both sides cancel each other. phers of the three next antecedents and consequents be cancelled, which is dividing by 10. Then divide the second antecedent and consequent by 5, and the quotients will be 2 on the side of the antecedents, and 1 on the side of the consequents; then 2 will measure the third antecedent and consequent, and the quotients will be 5 and 8. 10 will measure the 4th antecedent and consequent, and the quotients will be 1 and 2. Now, there being 2 left on each side, they cancel each other, and as there is no farther room for abridg ing by reason of the odd number 379, the operation is finished, and the answer found, as before. 2. If 20lb at Boston make 231b at Antwerp, and 155 at Antwerp make 180 at Leghorn: How many at Boston are equal to 144 at Leghorn ? Ans., 107 lb. 3. If 12lb. at Boston make 10lb. at Amsterdam, 10lb at Amsterdam 120lb. at Paris: How many lb. at Boston are equal to 80lb. at Paris ? Ans. 80lb. 4. If 140 braces at Venice be equal to 150 braces at Leghorn, and 7 braces at Leghorn be equal to 4 American yards: How many Venetian braces are equal to 32 American yards? Ans. 52 5. If 40lb. at Newburyport make 36 at Amsterdam, and 90lb. at Amsterdam make 116 at Dantzick: How many lb. at Newburyport are equal to 260lb. at Dantzick? CASE II. Ans. 224 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. RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the right hand; then multiply the first row for a divisor, and the second for a dividend. EXAMPLES. EXAMPLES. 1. Suppose 100 yards of America=100 yards of England, and 100. yards of England 5 canes of Thoulouse, and 100 canes of Thoulouse-160 ells of Geneva, and 100 ells of Geneva-200 ells of Hamburgh How many ells of Hamburgh are equal to 236 yards of America? Ant. Con. 100 Amer = 100 Abridged. Eng. 100 Thoul. = 160 100 Gen. = 200 236 Hamb. 236 × 8 = 379 Ham. Ans. This needs no further illustration. The learner will readily see, that, this case being the reverse of the former, they are proofs to each other. 2. If 20lb. at Boston make 231b at Antwerp, and 155 at Antwerp make 180 at Leghorn: How many at Leghorn are equal 144 at Boston ? Ans 144lb. 3. If 12lb. at Boston make 10lb. at Amsterdam, and 100lb. at Amsterdam 120lb at Paris: How many at Paris are equal to 80lb. at Boston ? Ans. 80lb. 4 If 140 braces at Venice be equal to 150 braces at Leghorn, and 7 braces at Leghorn be equal to 4 American yards: How many American yards are equal to 52 Venetian braces? Ans. 32 yards. 5. If 40lb. at Newburyport make 36 at Amsterdam, and 90lb. at Amsterdam make 116 at Dantzick: How many lb. at Dantzick are equal to 244 at Newburyport? Ans. 283lb. ARBITRATION OF EXCHANGES. By this term is understood how to choose, or determine the best way of remitting money from abroad with advantage; which is performed by conjoined proportion: Thus, Suppose a merchant has effects at Amsterdam to the amount of 3530 dollars, which he can remit by way of Lisbon at 840 rees per dollar, and thence to Boston, at 8s. 1d per milree (or 1000 rees :) Or, by way of Nantz, at 53 livres per dollar, and thence to Boston at 6s. 8d. per crown, It is required to arbitrate these exchanges, that is, to choose that which is most advantageous? 1 dollar at Amsterdam 1000 rees at Lisbon 840X97x3530 1000X1 = = 840 rees at Lisbon. = 97d. at Boston. 3530 dollars at Amsterdam. 1198 8s. 8d. by way of Lisbon. 1 dollar at Amsterdam = 5 livres at Nantz. Here it may be observed that the difference is £139 8s. 8d. in favour of remitting by way of Lisbon rather than by Nantz, which depends on the course of exchange, at that time; but the course may vary so, that, in a short time by way of Nantz may be better; hence appears the necessity and advantage of an extensive correspondence, to acquire a thorough knowledge in the courses of exchange, to make this kind of remittance. ने FELLOWSHIP. THE Rules of Fellowship are those by which the accompts of several merchants or other persons, trading in partnership, are so adjusted, that each may have his share of the gain, or sustain his share of the loss, in proportion to his share of the joint stock, together with the time of its continuance in trade. SINGLE FELLOWSHIP Is, when the stocks are employed for any certain equal time. 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. PROOF. Add all the particular shares of the gain or loss together, and, if it be right, the sum will be equal to the whole gain or loss. EXAMPLES. 1. Divide the number 360 into four such parts, which shall be to each other, as 3, 4, 5 and 6. 2. A, B, C and D companied; A put in .145; B, £.219; C, .378, and D,.417, with which they gained .569: What was the £. s. d. 11058 A's sha. 145: 71 382 1139 375 B's dit. 378: 185 116 552 C's dit. 1139 13 3 D's dit. 417: 204 14 54 1139 That their gain or lofs, in this rule, is in proportion to their flocks is evident: For, as the times, in which the stocks are in trade, are equal, if I put in of the whole ftock, I ought to have of the gain: If my part of the stock be, my fhare of the gain or lofs ought to be alfo. And generally the fame ratio that the whole ftock has to the whole gain or loss, must each perfon's particular stock have to his refpective gain or lofs. 3. A, B, C and D are concerned in a joint stock of D.1000; of which A's part is D. 150; B's D. 250 ; C's D.275, and D's D.325.— Upon the adjustment of their accompts, they have lost D.337 50c. What is the loss of each? Ans. A's loss D.50 624c. B's D.84 374c. C's D.92 814c. and D's D.109 684c. 4. A and B companied ; A put in £.45, and took of the gain; What did B put in ? 5-3-2. Then, As 3: 45:: 2 : 30 Ans. 5. A, B and C freighted a ship with 68900 feet of boards: A put in 16520 feet; B 28750; and C the rest; but, in a storm, the Captain threw overboard 26450 feet: How much must each sustain of the loss? Ans. A, 63414 feet. B, 110364 and C, 90714 do. he 6. A gentleman died, leaving three sons and a daughter, to whom he bequeathed his estate in the following manner: To the eldest son gave 312 moidores, to the second 312 guineas, to the third 312 pistoles, and to the daughter 312 dollars; but when his debts were paid, there were but 312 half joes left: What must each have in proportion to the legacies which had been bequeathed them? Ans. 1st son £.293 Os... -2d. son .227 17s. 104d.- 2d. son £.179 is. 2 d. and the daughter .48 16s. 81d. 7. A ship, worth D.3000, being lost at sea, of which belonged to A, to B, and the rest to C: What loss will each sustain, supposing D.450 to have been insured upon her? 8. A and B venturing equal sums of money, cleared by joint trade D.140: By agreement, as A executed the business, he was to have 8 per cent. and B was to have 5 per cent.: What was A allowed for his trouble? D. D. D. D. D. D. D. D. D. D. As 8+5: 140 :: 8: 86, And, as 8+5: 140 :: 5 : 5311. Ans. D.32 30c. 73m. 9. A bankrupt is indebted to A.120, to B.230, to C .340, and to D.450, and his whole estate amounts only to £.560: How must it be divided among the creditors? Ans. A, £.58 18s. 114d. B, L.112 19s. 74d. C, £.167 Os. 4d. and D, .221 1s. Od. 10. A, B and C put their money into a joint stock; A put in D.40; B and C together, D.170: They gained D.126, of which B took D.42; What did A and C gain, and B and C put in respectively? As D.210 the whole stock: D.126 the whole gain :: D.40 A's stock: D.24 A's gain. As D.24 A's gain: D.40 A's stock :: D.42 B's gain: D.70 B'6 stock. Then D.170-D.70 D.100 C's stock; and whole gain D.126-D.66 A's and B's gain=D.60 C's gain. 11. A, B and C companied ;-A put in .40; B 60, and C a suma unknown: They gained .72; of which C took £.32 for his share : What did A and B gain, and C put in? The |