DOUBLE FELLOWSHIP. § 168. When several persons who are joined together in trade employ their capital for different periods of time, the partnership is called Double Fellowship. For example, suppose A puts $100 in trade for 5 years; B $200 for 2 years, and C $300 for 1 year: this would make a case of double fellowship. Now it is plain that there are two circumstances which should determine each one's share of the profits: 1st, the amount of capital he puts in; and 2ndly, the time which it is continued in the business. Hence each one's share should be proportional to the capital he puts in, multiplied by the time it is continued in trade. Therefore we have the following RULE. Multiply each man's stock by the time he continues it in trade: then say, as the sum of the products is to the whole gain or loss, so is each particular product to each man's share of the gain or loss. Q. What is Double Fellowship? What two circumstances determine each one's share of the profits? Give the rule finding each one's share? EXAMPLES. 1. A and B enter into partnership: A puts in £840 for 4 months, and B puts in £650 for 6 months: they gain £300: what is each one's share of the profits? A's stock £840 × 4=3360 B's stock £650 × 6=3900 £7260: 300 :: { 3360: £138 16s 10d. 3900: £161 3s 1d. 2. A put in trade £50 for 4 months, and B £60 for 5 months they gained £24: how is it to be divided between them? Ans. A's share=£9 12s; B's=£14 8s. 3. C and D hold a pasture together, for which they pay £54: C pastures 23 horses for 27 days, and D 21 horses for 39 days: how much of the rent ought each one to pay? Ans. C, £23 5s 9d; D, £30 14s 3d. TARE AND TRET. § 169. Tare and Tret are allowances made in selling goods by weight. Draft is an allowance on the gross weight in favour of the buyer or importer: it is always deducted before the Tare. Tare is an allowance made to the buyer for the weight of the hogshead, barrel or bag, &c., containing the commodity sold. Gross Weight is the whole weight of the goods, together with that of the hogshead, barrel, bag, &c., which contains them. Suttle is what remains after a part of the allowances have been deducted from the gross weight. Net Weight is what remains after all the deductions are made. Q. What are Tare and Tret? What is Draft? What is Tare? What is Gross Weight? What is Suttle? What is Net Weight? EXAMPLES. 1. What is the net weight of 25 hogsheads of sugar, the gross weight being 66cwt. 3qr. 14lb.; tare 11lb. per hogshead? cwt. qr. lb. 66 3 14 gross. 23 tare. 2. If the tare be 4lb. per hundred, what will be the tare 3. What is the net weight of 32 boxes of soap, weighing 31550lb., allowing 4lb. per box for draft and 12 per cent for tare? Ans. 3770,64lb.=1T. 13cwt. 2qr. 18lb. 10oz. + 4. What will be the cost of 3 hogsheads of tobacco at $9,47 per cwt. net, the gross weight being of 5. At £1 5s per cwt. net; tare 4lb. per cwt.: what will be the cost of 4 hogsheads of sugar weighing gross, cwt. qr. lb. 6. At 21 cents per lb., what will be the cost of 5hhd. of coffee weighing in gross, 7. At £7 5s per cwt. net, how much will 16hhd. of sugar come to, each weighing 12lb. per cwt.?. gross 8cwt. 3qr. 7lb.; tare Ans. £912 14s 53d+. 8. What is the net weight of 18hhd. of tobacco, each weighing gross 8cwt. 3qr. 14lb.; tare 167b. to the cwt.? Ans. 6T. 16cwt. 3qr. 20lb. 9. In 4T. 3cwt. 3qr. gross, tare 20lb. to the cwt., what is the net weight? Ans. 3T. 8cwt. 3qr. 5lb. 10. What is the net weight and value of 80 kegs of figs, gross weight 7T. 11cwt. 3qr., tare 14lb. per cwt., at $2,31 per cwt.? 6T. 12cwt. 3qr. 3lb. 8oz. Ans. {Value $306,72 4+. DUODECIMALS. $170. Duodecimals are denominate fractions in which 1 foot is the unit that is divided. The unit 1 foot is first supposed to be divided into 12 equal parts, called inches or primes, and marked '. Each of these parts is supposed to be again divided into 12 equal parts, called seconds, and marked ". Each second is divided in like manner into 12 equal parts, called thirds, and marked ""'. This division of the foot gives 1' inch or prime . =of a foot. =1 of a foot. of 12 of 12-1728 of a foot. Duodecimals are added and subtracted like other denominate numbers, 12 of a lesser denomination making one of a greater, as in the following 1. In 185', how many feet? 2. In 250", how many feet and inches? 3. In 4367"", how many feet? Ans. 15ft. 5'. Ans. 1ft. 8' 10". Ans. 2ft. 6' 3" 11" Q. In Duodecimals what is the unit that is divided? How is it divided? How are these parts again divided? What are the parts called? How are duodecimals added and subtracted? How many of one denomination make I of the next greater? EXAMPLES IN ADDITION AND SUBTRACTION. 1. What is the sum of 3ft. 6′ 3′′ 2′′''` and 2ft. 1'10" 11""? Ans. 5ft. 8′ 2′′ 1′′". 2. What is the sum of 8ft. 9′ 7′′ and 6ft. 7′ 3′′ 4′′"? Ans. 15ft. 4' 10" 4"". 3. What is the difference between 9ft. 3′ 5′′ 6′′" and Ans. 1ft. 11'10" 11′′. 7ft. 3' 6" 7""? 4. What is the difference between 40ft. 6′ 6′′ and Ans. 11ft. 6' 5" 5"". 29ft. 7""? MULTIPLICATION OF DUODECIMALS. § 171. It has been shown (§ 64) that feet multiplied by feet give square feet in the product. EXAMPLES. 1. Multiply 6ft. 6' 6" by 2ft. 7'. Set down the multiplier under the multiplicand, so that feet shall fall under feet, inches under inches, &c. It is generally most convenient to begin with the highest denomination of the multiplier, and then multiply first the lower denominations of the multiplicand. OPERATION. ft. 6 6' 6" 2 7' 13 1' 3 9' 9" 6"" 16 10′ 9′′ 6 6". 44 of The 6" of the multiplicand is of an inch, or a foot. Therefore when we multiply it by 2 feet, the product is 12", equal to 1 inch. Multiplying 6', or of a foot, by 2 feet, the product is 12', to which add 1 inch from the last product, making 13'. Set down 1' under the column of inches and carry 1 foot to the product of the 6 by 2, making 13 feet. Then multiply by 7'. The product of 7' by 6"-42′′": for, 7' of a foot, and 6" of a foot: hence 7' x 6" 6 =12×14=1138=42"-3"6"". Then |