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. 4d. per milree, between Lisbon and Paris, at 460 rees for 3 francs, and between Paris, and Amsterdam, at 54d. Flemish for 3 francs 2 123. 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 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 appreheud enough has been said io enable the pupil to apply the foregoing princi. les to the practice of any merchant's countimig-house in which he may placed. Those who wish for o information on the subject, are referred to Doctor Kelly's Uuiversal Caubist. - UNLIMITED QUANTITIEs. Ry 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, *nd again by the difference between the lowest rate and third highest, &c, so that there may be a remainder, into which the *UNLIMITED quantities, 251 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 qmantitity 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. *. Cramples. A merchant has different parcels of wheat, which stand him in 18d., 200. 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 P o Solution : 24 – 18 = 6 difference between highest and lowest rate 22 — 18 = 4 difference between 2d highest and lowest. 20 – 18 = 2 difference between 3d highest and lowest. 1000 x 21 = 21000 1000 x 18 = 18000 6) 3000(400 - 4) 600(100 2)200(100 Answer, 400 at 24 pence = 9600 pence, 1000 1000)21000(21 proof. 1. A grocer has sugars at 10d. and at 7%d. per lbs. and has a mind to mix 200lb so as to stand in 84 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 2701bs. so as to stand him in 10d. per lb. 3. Spirits of 7s. and 11s. 3d. per gallon are so mixed that an lhd, qt 63 gallons may be sold for 25l 4s. how many gallons of each were taken P 4. A merchant has spirits at 8s., 9s., 10s. and 1 1s. per gallon, and has a mind to fill a puncheon containing lzo gallons Therefore 17 gallons at 11s., 17 gallons at 9s. 6d. and 7 gal: 1ons 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 1191, to consist of 119 bank notes or pieces of money, viz. bank notes of 30s., sovereigns of 213s. 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 2 *li. It is required to pay a bill of 1671 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 91, cows at 51, sheep at ll, and lambs at 5s. ; how many of each must I buy? POSITION, Position, though not so much practised as formerly, on ae. 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. f Position admits of two varieties, Single Position and Double Position; and takes its name, because by working with a supposed number or numbers, according to the conditions of the Fo proposed, the true answers are discovered. In Single osition, 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 th; 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. A person after paying away # and 4 of his money, had 1001 left; how much mdney had he at first 7 - * - Suppose he had sel at first, he paid away { s and also.... + Sum paid away, or of the whole. t *1 — or = Y, And as or ; +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 ° r 2. What number is that, which being increased by +, + and + of itself, the sum shall be 80 : , - * 3. Divide 1801 between two persons, in proportion as 4 to 1. * Note-Any number would do as well as o ; and if a number had been chosen, which could be evenly divided by 12, the work would *PPear without fractions, - o - * 4. Divide £150 between A, B, and C, so that A may have 301 more than B, and B 15, more than C 2. * : 5. Suppose 8s. 8d. was distributed between some poor people, consisting of men, women, and children; 3d to each man, 2d to each woman, and ld to each child; now if there were twice as many women as there were men, and three times as many children as there were women; how many were there of each? - 6. A captain after an engagement, finds + of his company either killed or missing ; + are sent wounded to hospital, or are on duty, and 51 are on parade ; what was the strength of his company before the engagement? * -- **** 7. If I wish to divide 600 between some poor people, consisting of an equal number of men, women, and children, and gave to each man 6d, each woman 4d, and each child 3d, and had 8d to spare ; how many were there of each P 8. Suppose I lent at interest a certain sum, at 6 per cent, per an. simple interest, and at the end of 8 years both principal and interest amounted to 512! what was the sum lent? .9. What number is that, whose third exceeds its fourth part by 24? 10. What sum of money is that whose +, +, + and parts added together, shall make 281 10s, 2 - 11. Required a number, which being multiplied by 8, the product divided by 5, the quotient increased by twice the required number, and by 6, will make 60? . . 12. Required a number, to which if + of itself be added, half the sum shall be 15? ‘. . 13. A person after spending + his yearly income, and 45l, had left 4 of it, together with 51; what was his income? . 14. A sum of money which had been put out to interest, is increased by + of the original sum, which is now 1441; what was the sum lent? 15. What number is that, to which if its 4 and its + be added together with half the sum thus produced, the whole shall be 484 P - * DOUBLE POSITION Is the method of resolving certain questions by means of two suppositions, ** |