SINGLE FELLOWSHIP. Q. What is SINGLE FELLOWSHIP? A. Single Fellowship is a rule by which merchants, &c., trading in company with a joint stock, are enabled to ascertain each person's particular share of the gain or loss, in proportion to his share in the joint stock, each share of which stock having been in trade an equal term of time. EXPLANATIONS. As was stated on page 168, Single and Double Fellowship is only an application of the Rule of Three Direct, and has this name given to it merely as applicable to its application and use in this particular transaction of business. By this rule also, legacies are adjusted, and the effects of bankrupts divided among their creditors; for, as the sum due to the creditors is to the bankrupt's estate, so is each creditor's demand to his share of the bankrupt's estate. RULE. Q. How do you state and work the terms to find each man's share of the gain or loss? A. As the whole stock is to the whole gain or loss, so is each man's stock to his share of the gain or loss. EXAMPLES. 1. Three merchants trading in company, gained $120: A's stock was $140, B's $300, and C's $160; what was each man's share of the gain? Ans. $28 A's share, $60 B's share, $32 C's share. EXPLANATIONS. You first add together the different sums which compose the stock in trade, which amounts to $600; then say, as $600, the whole stock in A's stock $140 B's stock $300 whole stock, $600 60 B's share. whole gain, so is each man's 600: 120: 300 stock to his share of the gain, or $120. It is per fectly plain that each man's share of the gain is, by this operation, in proportion to his stock. 2. Three merchants, in company, have a stock, of which A put in £20, B £30, and C £40, and they gained £360; what was each man's share of the gain? Ans. A £80, B £120, C £160. 3. A and B loaded a vessel with 500hhd. of sugar; A owned 350hhd., and B 150hhd.; in a storm, the captain of the vessel was under the necessity of throwing 100hhd. ́overboard; how many hogsheads must each man lose? Ans. A 70hhd. and B 30hhd. 4. Three merchants F, L, and M, traded together; F put in stock amounting to $500, L $400, M $300, and by misfortune they lost $300; what is each man's share of the loss? Ans. F $125, L $100, M $75. 5. A bankrupt is indebted to A $345, to B $255, and to C $400, and his whole property is only $250; what will be each share of the creditor's property? Ans. A $86,25c. B $63,75c. C $100. COMPOUND FELLOWSHIP. Q. What is COMPOUND FELLOWSHIP? 4. Compound Fellowship is when the several stocks are continued for different lengths, or unequal terms of time. RULE Q. How do you state and work the terms to find the share of each man's gain or loss? A. First multiply each man's stock by the time it was continued in trade, and add the several products together then, as the whole sum of the products is to the whole gain, or loss, so is each man's product, to his share of the gain or loss. EXAMPLES. 1. Three merchants, A, B, and C, traded in company; A put in $600 for 9mo., B $700 for 12mo., and C $800 for 15mo., and they gained $212,10c.; what is each man's share of the gain? Ans. A $44,39,3m., B $69,05,5m., C $98,65,Im. 2. Three merchants traded in company; D put in $88 for 3mo., E $120 for 4mo., and F $300 for timo., and they gained $181; what was each man's share of the gain? Ans. D's $19,09,4m., E's $34,71,6m., F's $130,18,8m. 3 A and B tra led; A put in $390 for 9mo, and B put in $215 for 6mo., and by misfortune they lost $200; what share of the loss must each man sustain? Ans. A $146,25c., B $53,75c. 4. Two merchants traded in company; A put in $100 for 6mo., and then put in $50 more; B put in $200 for 4mo, and then took out $80; at the end of 12mo. they had gained $95; what was each man's share of the gain? Ans. A's $43,71,1m., B's 51,28,8m. ALLIGATION. Q. What is ALLIGATION? A. Alligation teaches how to compound or mix together several simples of different qualities, so 1 that the composition may be of some middle or intermediate quality or price. EXPLANATIONS. As was stated on page 168, Alligation is only an application of the Rule of Three Direct. It consists of two kinds; Alligation Medial and Aliigation Alternate. ALLIGATION MEDIAL. Q. What is ALLIGATION MEDIAL? A. Alligation Medial teaches, when the quantities and prices of several things are given, to find the mean price or quality of the mixture composed of those materials. RULE. Q. How do you state and work the terms to find the mean price or quality of any part of the composition, when the several quantities and their prices or qualities are given? A. The quantity of each ingredient must first be multiplied by its price or quality; then all the products must be added together, and all the quantities must also be added together into another sum. Then, as, the whole composition is to the whole value, or sum of the products, so is any part of the composition to its mean price or quality. EXAMPLES. 1. A farmer mixed 12bu. of rye at 70c. a bushel, 15bu. of corn at 54c. a bushel, and 20bu. of barley at 40c. a bushel; what is a bushel of this mixture worth? Ans. 526. Im. EXPLANATIONS. In this example, you must first multiply each number of bushels by the price per bushel, and then add the amount together, and also the amount of the bushels contained in the mixture; and then say, as 47 bushels, the whole amount of bushels in the mixture, is to $24 50c., the value of the whole composition, or materials, so is lbu. to the mean price or value of one bushel of the composition. The principle of this operation is very plain; for it is perfectly evident, that as the whole number of bushels is to the money it cost, so is Ibu. to the value or cost of Ibu. 2. A grocer mixed three kinds of tea; 2016. at 5s., 35lb. at 8s., and 25lb. at 4s.; what is a pound of the mixture worth? Ans. 6s. 3. A silversmith melted 4oz. of silver worth 75c. an ounce, with 8oz. of silver worth 60c. an ounce; what is an ounce of this mixture worth? Ans. 65c, 4. A wine merchant mixed three kinds of wine; 16 gal. at $1,10c. a gallon, 12gal. at 75c. a gallon, and 24 gal. at 90c. a gallon; what is a gallon of this mixture worth? Ans. 92c. 6m. 5. A refiner mixed 2lb. of gold of 17 carats fine, with 4lb. 23 carats fine; what was the fineness of the mixture? Ans. 21 carats. ALLIGATION ALTERNATE. Q. What is ALLIGATION ALTERNATE? A. Alligation Alternate teaches to find what quantity of each of any number of ingredients or simples, |