The following exhibits the face of an account in the ledger, and the time (date) at which it averages due is required. 1850. Due Oct. 10, $301 66 EXAMPLE.-Practical method of stating and working. COMPOUND AVERAGE consists in finding the time at which the balance of an account or demand averages due, whose sides. the debit and the credit - average due at different dates. RULE. Multiply the less sum or side by the difference in days between the two dates -that at which the debit side averages due and that at which the credit side averages due — and divide the product by the difference of the sums or sides; the quotient will be the number of days that one of the dates must be set back, or the other forward, to mark the time sought; for which last, SPECIAL RULE. Earlier date with larger sum, set back from earlier. EXAMPLE. The debit side of an account in the ledger foots up $400, and averages due Oct. 12, 1850; the credit side of the same account foots $300, and averages due Nov. 16, 1850. At what date does the balance or difference between the two sides average due? = 100) 10500 (105 days earlier than Oct. 12, June 29, 1850. Ans. EXAMPLE. The debit side of an obligation foots $250, and averages due May 17, 1850; the credit side of the same obligation foots $175, and averages due May 1, 1850. At what date does the difference of the sides average due? 250 175 75 175 ) 2800 ( 37 days later than May 17, = June 23, 1850. Ans. - NOTE. AVERAGE gives no "interest on interest" to the creditor. It does not give him his just due. It estimates by way of the interest on both sides, on the sums falling due prior to the average date, and on those falling due subsequently, and not by the interest on those falling due prior, and by the discount on those falling due subsequent, as would be strictly correct. The practice is against the creditor or holder of the demands, in like manner, and relative extent, as shown in note under DISCOUNT. FELLOWSHIP. FELLOWSHIP calls for the distribution of a given effect to each of the several causes associated in its production, proportional to their respective magnitudes one with another. It is a rule, therefore, adapted to the use of partners associated in business, in achieving a pro rata distribution among themselves as individuals, of the profits or losses pertaining to the company. RULE.-Multiply each partner's investment or share of the capital stock, by the whole gain or loss, and divide the product by the sum of all the shares, or gross capital. EXAMPLE. Three men, A, B, and C, enter into partnership. A invests $500, B $700, and C $300. They trade and gain $400. What is each partner's share of the profits? $133.33 A's share. = = A, $500 500 X 400 186.663 B's 66 $1500 = gross capital. $400.00 Proof. EXAMPLE.-D's investment of $600 has been employed eight months; E's, of $500, five months; and F's, of $300, five months; the profits of the company are $500, and are to be divided pro rata among the partners. What is each partner's share? D, $600 X 8 E, 500 X 5 EXAMPLE. Of $120 distributed, there were given to A, ; to B, ; to C, ; and to D, , and there was nothing remaining. What sum did each receive? EXAMPLE. Divide the number 180 into 3 parts, which shall be to When it is required to know the gain or loss per cent. RULE. Multiply the difference of the two sums (the cost and the price sold at) by 100, and divide the product by the cost; the quotient will be the per cent. gained, if the cost be the less sum; lost, if it be the greater. EXAMPLE. - Paid $1.88 for an article, and sold it for $2.34; what per cent. did I gain? 2.34 1.88 .46 X 100 = 461.88 = 24 per cent. Ans. EXAMPLE. Paid $2.34 for an article, and sold it for $1.88; what per cent. did I lose? 2.34 1.88 .46 X 100 46.00 2.34 = 19 per cent. Ans. When it is required to know at what price a commodity must be sold to gain or lose a given per cent. RULE. -1. If a gain be intended, multiply the cost by the contemplated per cent., and add the product to the cost; the sum will be the price to sell at. RULE. 2. If a loss be intended, multiply the cost by the contemplated per cent., and subtract the product from the cost; the remainder will be the price to sell at. The sales price, and the profit or loss per cent. involved, being known, to ascertain the cost. RULE.-Multiply the sales price by 100, and divide by 100, plus the per cent. gain, or minus the per cent. loss involved; the quotient I will be the cost. EXAMPLE.What cost me that article, whose price, involving a profit of 25 per cent., is $5? EXAMPLE. What cost me that article, whose price, involving a loss of 25 per cent., is $3? 100 - 25 = 75. ALLIGATION Medial is a method by which to find the mean price of a mixture or compound, consisting of two or more articles or ingredients, the quantity and price of each being given. RULE.-Multiply each quantity by its price, and divide the sum of the products by the sum of the quantities; the quotient will be the price per unity of measure of the mixture; and, having found the price of the given quantities as mixed, any quantities of the same materials, taken in like proportions, will be at the same price. EXAMPLE.If 20 lbs. of sugar at 8 cents, 40 lbs. at 7 cents, and 80 lbs. at 5 cents per pound, be mixed together, what will be the mean price, or price per pound, of the mixture? The several kinds, then, at their respective prices, taken in the proportion of 1 at 8, 2 at 7, and 4 at 5 cts., will form a mixture worth 6 cts. a pound. EXAMPLE.If 10 lbs. of nickel are worth $2, and 24 lbs. of copper are worth $4, and 8 lbs. of zinc are worth 40 cts., and 1 lb. of lead is worth 5 cts., what are 5 lbs. of pretty good German silver worth? (200+450+40 +5) X 5 = 81 cents. Ans. 43 ALLIGATION Alternate is a method by which to find what quantity of each of two or more articles or ingredients, whose prices or qualities are given, must be taken to form a mixture or compound that shall be at a given price or of a given quality between the two extremes. It also applies to the finding of relative quantities when the quantity of one or more of the articles is limited. Connect the given prices or qualities RULE. - a less than the given mean with that one or either one that is greater-and to the extent that all be thus connected; then place the difference between each given and the given mean opposite, not the given, or the given mean, but the given with which it is alligated; the number standing opposite each price or quality will be the quantity that must be taken at that price, or of that quality, to form a mixture or compound at the price or of the quality desired. And, being proportions respectively to each other, they may be taken in ratio greater or less, as desired. EXAMPLE. In what proportions shall I mix teas at 48 cents a pound and 54 cents a pound, that the mean price may be 50 cents a pound? In the proportions EXAMPLE. In what proportions shall I mix teas at 48, 54, and 72 cents a pound, that the mixture may average 60 cents a pound? EXAMPLE. A wine dealer has received an order for a quantity of wine at 50 cts. a gallon. He has none ready manufactured at that price. He has it at 40 cts., at 56 cts., and at 80 cents a gallon, and he has water that cost him nothing. He wishes to fill the order with a mixture composed of the four materials-the water and the three different priced wines. In what proportions must he mix them, that the mean or average price may be 50 cents? If, now, having found the proportions desired, it is wished to limit one of the articles in quantity-say the best wine to 8 gallons in the |