concerned, the following rule, usually called the Chain Rule, is generally preferable. RULE.-Distinguish the several courses of exchange into antecedents and consequents; place the antecedents in one column, and the consequents in another, to the right-hand of the antecedents, in such a manner, that the first consequent may be of the same name and denomination as the second antecedent, and the second consequent as the third antecedent &c. through the whole. Then multiply all the antecedents together for a divisor, and all the consequents together for adividend; the quotient produced by this division will be the value of the sum required. The operation may be often abridged by striking out any antecedent and consequent that are alike, and by reducing to their lowest terms such as admit of a common divisor. Examples. 120. When the exchange between Dublin and London is 9 per cent, and between London and Amsterdam 36s. 6d. Flem. per pound sterling; how many guilders will be received for 3817 10s. Irish, remitted from Dublin by way of London, allowing the merchant in London per cent? Antecedents Irish 109... London 1 How many Sti.Amsterdam = 99×219×381. Consequents 99 London. 219 Sti. Amsterdam 381 Irish. 8313075 109 109 20) Answer,.... G. 3813 6 12 pen. 121. A banker at Paris remits to his correspondent in Amsterdam, 4684 francs, 75 centimes, first to London, at 23 francs, 75 centimes per pound sterling; thence to Lisbon, at 5s. 4d. per milree; thence to Leghorn, at 810 rees per pezza of 8 reals; and thence to Amsterdam, at 100 pezze for 237 florins or guilders; how many guilders will be received at Amsterdam, and what will the banker gain, supposing the direct exchange between Paris and Amsterdam to be 51 pence Flemish for 3 francs ? 122. A merchant in England is indebted 1000 to one in Amsterdam; whether is it better for the merchant in Amster dam to have a direct remittance, at 36s. 4d. Flemish per pound sterling, or a circular one through Lisbon and Paris; exchange. between London and Lisbon, at 5s. 44d. per milree, between Lisbon and Paris, at 460 rees for 3 francs, and between Paris and Amsterdam, at 54d. Flemish for 3 francs? 123. A merchant in Amsterdam owes one in Paris, 2000 florins, which the latter orders to be remitted to London, at 36s. 8d. Flemish per pound sterling; thence to Spain at 42d. sterling per piastre; thence to Leghorn, at 130 piastres for 100 pezze; and thence to Paris, at 5 francs, 4 centimes per pezze; whether did he gain or loose by the circular course, the direct exchange between Paris and Amsterdam being 54d. Flemish for 3 francs? To treat on the doctrine of Exchange in its full extent, would far exceed my limits, as it is a subject which might be dilated to a much greater extent than is possible in a work of this nature, but I apprehend enough has been said to enable the pupil to apply the foregoing principles to the practice of any merchant's counting-house in which he may be placed. Those who wish for complete information on the subject, are referred to Doctor Kelly's Universal Cambist. UNLIMITED QUANTITIES. By this title I denote such questions as have more than one answer, such are generally solved by alligation, and as this rule is of little use, I thought it better, wholly to omit it, substituting the following, which will answer all that is necessary in such cases. When the prices of several ingredients are given to find how much of each will be required to make up a given quantity, at a mean rate. Multiply the proposed quantity by the mean rate, and again by the lowest given rate, aud find the difference between both products; subtract the lowest given rate from each of the other rates, and note their differences; divide the difference of the products by the difference between the highest and lowest rate, in such a manner, that there may be a remainder: divide this remainder by the difference between the lowest rate and second highest, so that there may be a remainder, and again by the difference between the lowest rate and third highest, &c. so that there may be a remainder, into which the last difference will go evenly; the different quotients thus found will be the required quantities of each of the rates whose differences were divided, the sum of these subtracted from the proposed qnantitity will give the required quantity at the lowest rate. NOTE.-If a remainder cannot be found, into which the last difference will go evenly, the answer cannot be found in whole numbers, therefore must have a mixed number in it. Examples. A merchant has different parcels of wheat, which stand him in 18d., 20d. 22d., and 24d. per stone; having an order to ship 1000 barrels, so as to stand in 21d. per stone; how many barrels of each sort must he take? 22225 20 18 18 24 18 6 difference between highest and lowest rate 4 difference between 2d highest and lowest. 2 difference between 3d highest and lowest. 1000 × 21 = 21000 1000 × 18 = 18000 1. A grocer has sugars at 10d. and at 74d. per lbs. and has a mind to mix 200lb so as to stand in 8 per lb. how many pounds of each sort must he take? 2. A grocer has sugar of 12d. and of 7 per lb. how many lbs of each sort must he take to make a mixture of 270lbs. so as to stand him in 10d. per lb. 3. Spirits of 7s. and 11's. 3d. per gallon are so mixed that an 1hd. qt 63 gallons may be sold for 251 4s. how many gallons of each were taken? 4. A merchant has spirits at 8s., 9s., 10s. and 11s. per gallon, and has a mind to fill a puncheon containing 120 gallons so that the mixture may stand in 9s. 6d. per gallon ; how many gallons of each must he take? 15. Certain goods of 9d., 12d., 24d. and 30d, per lb. are so mixed that 198lbs. stand in 21d. per lb; how many pounds of each were taken ? ↑ 6. Teas of 7s., 8s. and 10s. per bare mixed so that 30lbs. stand in 88. 8d. per ; how many pounds of each were taken? 7. It is required to mix spirits at 98.6d and at 11s. gallon with water, so that a cask containing 41 gallons may stand in 8s. 6d. per gallon. Solution: 1100 19 16 10 11 Therefore 17 gallons at 11s., 17 gallons at 9s. 6d. and 7 galė lons of water will form the mixture required. 8. Rums at 9s., 10s. and 11s. per gallon are so mixed, that a cask of 30 gallons stands in 8s. per gallon; how many gallons of water, and of each kind were taken? 9. It is required to make up 1197, to consist of 119 bank notes or pieces of money, viz. bank notes of 30s., sovereigns of 21s. and 6s. pieces; how many of each sort were taken? 10. Having in store 4 different parcels of oats which I would sell at 11s., 12s. 6d., 13s. and 15s.per barrel, I have an order to ship 1000 barrels, so as to stand in 14s. per barrel; how many barrels of each must I take? 11. It is required to pay a bill of 167 with 334 pieces of money, sovereigns of 21s. 8d., 6s., 2s. 6d. and 10d. pieces; how many of each must be taken? 12. Pay 2731 with exactly twice as many pieces as pounds sterling, and use some of each of the following descriptions, and no other, viz. guineas, sovereigns, half sovereigns, 7s. or rather 7s. 7d. pieces and shillings? 13. It is required to purchase 51 live stock or cattle to stand in 40s. each, viz. horses at 94, cows at 51, sheep at 17, and lambs at 5s.; how many of each must I buy? POSITION. POSITION, though not so much practised as formerly, on ac count of the knowledge of Algebra becoming more general, still continues to be of considerable use; I will therefore give the learner a specimen of such parts of it as are most useful, and which he can readily understand, without recourse to the Extraction of Roots, or Algebra. Position admits of two varieties, Single Position and Double Position; and takes its name, because by working with a sup posed number or numbers, according to the conditions of the question proposed, the true answers are discovered. In Single Position, one number only is used, and the answer is found by one operation; in Double Position, two different numbers are assumed, and a double operation performed before the answer can be found. SINGLE POSITION, Take or assume any number for that which is required, and perform the same operations with it as are described to be performed in the question. Then, as the result of this operation is to the result in the question, so is the position or assumed number, to a fourth number, which will be the number sought. Examples. A person after paying away and of his money, had 1002 left; how much money had he at first? *1. Sum paid away, of the whole. 1 And as ** : +4 or 1 :: 100: 240 the answ. 1. What number is it which being multiplied by 7, and the product divided by 6, the quotient may be 21 ? 2. What number is that, which being increased by 4, 4 and of itself, the sum shall be 80 ? 3. Divide 1,80/ between two persons, in proportion as 4 to 1? NOTE-Any number would do as well as one; and if a number had been chosen, which could be evenly divided by 12, the work would appear without fractions, |