In the third example, the whole amount of the bankrupt's debt is to be made the first number; the value of his effects the second number; and any creditor's real due the third number, and the fourth number is that creditor's share. Fellowship with time, or double fellowship, is when the different stocks are employed for different times. Rule. Multiply each man's particular stock by the time it is employed for; then fay, by the rule of three, as the total of all these products is to the whole gain or lofs, fo is each man's particular product to his particular fhare of the gain or lofs. Thus the rule of three must be repeated as often as there are products or perfons concerned, as in the single rule. Example 1. A put 2007. in a certain trade; B five months after put 300l.; at the end of one year they find they have gained 350%. profit, what is each person's share? The method of proof in this rule is the fame as in the fingle rule, as may be seen above. Qu. 2. A, B, and C rent a pafture in common, at 40%. per annum; A puts in it 3 oxen for 8 months in the year, B puts in 7 for 4 months, and C puts in 2 for the whole year; what muft each perfon pay towards the rent? Anfwer, A 12/. 125. 7 d. 4; B 147. 145. 8d. 28; C 127. 125. 74d.38. Example 3. A, B, and C make a ftock for 12 months, A put in at first 7281. at the end of 2 months he put in 201. more; B put in at first-2001. and at the end of 5 months he took out 150%.; C put in at firft 40l. and at the end of 6 months 50%. more, and at the end of 10 months 10% more; at the year's end they find they have gained 500l.; what is each perfon's profit? In thefe examples, and all others of the like nature, where the different parts of the stock of each perfon are employed for a different time, the different parts of each person's stock are to be multiplied by their own separate times, and these products added together to make up the product of each perfon; and then each perfon's product added together to make the total product. Thus, in the last example, I first multiply the 7281. put in by A, by 2, the number of months it is employed alone, and the product is Then A put in 201. more, which, added to the 728%. is 7481. and which multiplied by 10 months, the product is And which two added together gives A's produ 7480 89,6 1000 B put in 2001, for 5 months, which product is 350 The two products of B-added together are his true one 1350 C put in at firft 40%. which continued alone 6 months, that product therefore is At the end of 6 months he put in gol. more, which, added to the former fol. is gol. which multiplied by 4 months, gives The laft 2 months he had 100/. in the stock, which, multiplied by 2 months, gives 240 360 200 Therefore the product of C is The total fum of all the products 11086 6826 Then the work is wrought as before, faying, as 11086 (the fum of the products). is to 500%. (the total gain), so is 89364, (the product of A) to 403/. os. 744, 62, the share of A of the profits; and repeat the operation twice more, to, find the fhares of B and C, The rule of alligation teacheth how to mix différent fubftances together, and to difcover the value of any part of fuch mixture; or to make a mixture from known fubftances of any value.. Alligation is either medial or alternate. Alligation medial is that which teacheth how to find the rate or price of any mixture or compound, from having the rates or prices, and the quantities of the feveral fubftances given. Rule. Multiply each quantity by its rate or price, and add the products together for a dividend; add the fums of the feveral quantities together for a divifor; and divide the fum of the products by the sum of the quantities, and the quotient will be the rate or price of the componnd. Example 1. A mealman mixes 20 buthels of flour, worth 53. per bushel, with 12 Buthels worth 3s. 48. per bushel; what is 1 bushel of this mixture worth ? In this example the price of the bufhel is reduced into pence (as it mostly fhould). The anfwer is the price of the quantity, which is of the fame denomination with the divifor, which here is bufhels. ›i Proof. Find the value of the whole mixture from the value of any part, and if it be equal to the value of the original fimples, the work is right. Thus, to prove the foregoing example, I multiply the price of one bushel of the mixture by 4 and 8, or 32, the number of bushels in the whole, and the product, I find, is 71.; then I find the value of the feveral fimples, by multiplying the number of bushels in each by the number of pence in al bushel (which is already done in the example), and the product 1680 brought into pounds, gives 74. as follows |