partners in company; or the effects of bankrupts, or legacies in case of a deficiency of assets or effects; or the shares of prizes; or the numbers of men to form certain detachments; or the division of waste lands among a number of proprietors. Fellowship is either Single or Double. It is Single, when the sharer or portions are to be proportional each to one single given number only; as when the stocks of partners are all employed for the same time: And Double, when each portion is to be proportional to two or more numbers; as when the stocks of partners are employed for different times. SINGLE FELLOWSHIP. GENERAL RULE. ADD together the numbers that denote the proportion of the shares. Then say, As the sum of the said proportional numbers, Or, as the whole stock, is to the whole gain or loss, To his particular share of the gain or loss. TO PROVE THE WORK. Add all the shares or parts together, and the sum will be equal to the whole number to be shared, when the work is right. EXAMPLES. 1. To divide the number 240 into three such parts, as shall be in proportion to each other as the three numbers 1, 2 and 3. Here 1+ 2+ 36, the sum of the numbers. 40 the 1st part, 80 the 2d part, 120 the 3d part, Sum of all 240, the proof. Ex. 2. Three persons, A, B, C, freighted a ship with 340 tuns of wine; of which, a loaded 110 tuns, в 97, and c the rest : in a storm the seamen were obliged to throw overboard 85 tuns; how much must each person sustain of the loss? 3. Two merchants, c and D, made a stock of 1201, of which c contributed 75l, and D the rest gained 301; what must each have of it? by trading they by trading 4. Three merchants, E, F, G, made a stock of 7001, of which E contributed 1231, F 3581, and & the rest they gain 125 10s; what must each have of it? Ans. E must have 221 1s Od 2339. 64 3 8 03. 39 5 3 1. 5. A General imposing a contribution* of 7001 on four villages, to be paid in proportion to the number of inhabitants contained in each; the 1st containing 250, the 2d 350, the 3d 400, and the 4th 500 persons; what part must each village pay? Ans. the 1st to pay 116/ 13s 4d. 6. A piece of ground, consisting of 37 ac 2 ro 14 ps, is to be divided among three persons, L, M, and N, in proportion to their estates: now if L's estate be worth 500l a year, и's 3201, and N's 75l; what quantity of land must each one have? Ans. must have 20 ac 3 ro 391ps. 13 1 30,4%. 23178. M 3 0 7. A person is indebted to o 571 15s, to P 108 3s 8d, to a 221 10d, and to R 731; but at his decease, his effects Contribution is a tax paid by provinces, towns, villages, &c. to excuse them from being plundered. It is paid in provisions or in money, and sometimes in both. VOL. I. 17 are are found to be worth no more than 170l 14s; how must it be divided among his creditors? Ans. o must have 371 15s 5d 2,5302 104301 7498 270430 4720 10439 3358 10439 Ex. 8. A ship worth 9001, being entirely lost, of which belonged to s, to T, and the rest to v; what loss will each sustain, supposing 5401 of her were insured? Ans. s will lose 451, т 901, and v 2251. 9. Four persons, w, x, y, and agree that w shall pay is, their shares are to be in proportion as, 1, 1, and : what are their shares ? Ans. w must pay 9s 8d 3449. and z, spent among them 25s, of it, x, y, and z ; that X Y Ꮓ 6 5 344. 4 10 144. 3 10 3 10. A detachment, consisting of 5 companies, being sent into a garrison, in which the duty required 76 men a day; what number of men must be furnished by each company, in proportion to their strength; the first consisting of 54 men, the 2d of 51 men, the 3d of 48 men, the 4th of 39, and the 5th of 36 men ? Ans. The 1st must furnish 18, the 2d 17, the 3d 16, the 4th 13, and the 5th 12 men.* DOUBLE FELLOWSHIP. DOUBLE FELLOWSHIP, as has been said, is concerned in cases in which the stocks of partners are employed or continued for different times. Questions of this nature frequently occurring in military service, General Haviland, an officer of great merit, contrived an ingenious instrument, for more expeditiously resolving them; which is distinguished by the name of the inventor, being called a Haviland. RULE. RULE.*-Multiply each person's stock by the time of its continuance; then divide the quantity, as in Single Fellowship, into shares, in proportion to these products, by saying, As the total sum of all the said products, Is to the whole gain or loss, or quantity to be parted, To the correspondent share of the gain or loss. EXAMPLES. 1. A had in company 501 for 4 months, and в had 601 for 5 months; at the end of which time they find 24/ gained: how must it be divided between them? 93 =91 12s 143 = 14 8 A's share.. B's share. Then, as 500: 24: 200 and as 500 24 300 2. C and D hold a piece of ground in common, for which they are to pay 541. c put in 23 horses for 27 days, and D 21 horses for 39 days; how much ought each man to pay of the rent? Ans. c must pay 231 5s 9d. D must pay 30 14 3 4. Three persons, E, F, G, hold a pasture in common, for which they are to pay 391 per annum; into which E put 7 oxen for 3 months, F put 9 oxen for 5 months, and & put in 4 oxen for 12 months; how much must each person pay of the rent? Ans. must pay 5l 10s 6d 19. 11 16 10 0. 12 12 7 25. 4. A ship's company take a prize of 1000l, which they agree to divide among them according to their pay and the time they have been on board: now the officers and midshipmen have been on board 6 months, and the sailors 3 months; The proof of this rule is as follows: When the times are equal the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal, the shares as the times; therefore, when neither are equal the shares must be as their products. the the officers have 40s a month, the midshipmen 30s, and the sailors 22s a month; moreover there are 4 officers, 12 midshipmen, and 110 sailors; what will each man's share be? Ans. each officer must have 231 2s 5d 07¶· each midshipman 17 6.9 33. each seaman 6 72 013 173 Ex. 5. H, with a capital of 10001, began trade the first of January, and, meeting with success in business, took in 1 as a partner, with a capital of 1500l, on the first of March following. Three months after that they admit к as a third partner, who brought into stock 28001. After trading together till the end of the year, they find there has been gained 17767 10s; how must this be divided among the partners? 6. x, y, and z made a joint-stock for 12 months; x at first put in 201, and 4 months after 20 more; y put in at first 301, at the end of 3 months he put in 20 more, and 2 months after he put in 40 more; z put in at first 601, and 5 months after he put in 10 more, 1 month after which he took out 301; during the 12 months they gained 501; how much of it must each have? Ans. x must have 10l 18s 6d 3419. 22 8 1 01 16 13 4 0. INTEREST is the premium or sum allowed for the loan, or forbearance of money. The money lent, or forborn, is called the Principal. And the sum of the principal and its interest, added together, is called the Amount. Interest is allowed at so much per cent. per annum; which premium per cent. per annum, or interest of 100l for a year, is called the rate of interest :-So, When |