94 TO MEASURE STONE IN A WELL. TO MEASURE STONE IN A WELL. In taking the diameter of the wall, measure from centre to centre, or to the clear add the thickness of the wall. And when the diameter is taken or obtained, find the circumference, which is the length of the wall. RULE. As 7 is to 22, so is the diameter (taken) to the circumference required : having found the length of the wall and measured its thickness and depth, it is then prepared for calculation as has already been explained. EXAMPLES. 1. A certain well, near the compiler's door, walled with stone 1 foot 2 inches thick, its diameter in the clear 2 feet 4 inches, and depth 50 feet-required the length of the wall and the quantity of stone. As 7:22 :: 3.5 : 11ft. circumference, or length. 1ft. 2in.=1.1666+6 thickness 11 length 1.1666 +6 50 depth 12.8332 50 11 24.75)641.6600(25.925+ per. Ans. thick Ift. 2 in. Diameter 3 1 2 To what the well measures in the clear, (inside the walls) add the thickness of the wall, and you have the diameter of the wall, or circle. 2. Required the number of perches of stone in a well, whose diameter is 4 feet 9 inches in the clear, the depth of the well 20 feet, and the thickness of the wall 15 inches. Ans. 19.047 perches, or 19 perches + FELLOWSHIP. FELLOWSHIP is a general rule by which merchants and others, trading in partnership, compute their several shares of gain or loss, in proportion to each one's share of the stock, and time of its continuance in trade. By this rule a bankrupt's estate may be divided amongst the creditors, or legacies adjusted, when there is a deficiency of effects. CASE 1. When the several stocks in company are considered without regard to time. RULE 1. RULE 2. 1. Divide the whole gain, or loss, by the whole stock, and the quotient will be the gain, or loss, per dollar. 2. Multiply the gain, or loss, per dollar, by each particular stock, and the product is the proportional gain, or loss, required. EXAMPLES. 1. Three merchants trading together, gained 800 dollars. A's stock was 1200 dollars, B’s 4800 dollars, and C's 2000 dollars—what is each man's share of the gain ? A $1200 As 8000 : 1200 :: 800 : 120 A's share 8000 By second rule. 800-8000=.l per $ Then 1200 x.l=120 A's share, 4800 x.l=480 B's share, 2000X.1=200 C's share. 2. Three partners, D, E, and F, trading together, gained 120 dollars ; D's stock was $280, E's $600, and F's $320required the share of each. Ans. D $28, E $60, F $32. 3. A person failing in trade, is indebted to A $539, to FELLOWSHIP. 96 B $756.80, to C $854.16, to D $1200; his property, when disposed of, amounts to $837.49—how much will they severally lose ? Ans. A $404.25, B $567.60, C $640.62, D $900. 4. A, B, C, and D freighted a ship with wine, of which A had 25 tons, B 36, C 40, and D 43; but the crew threw overboard, in a storm, 36 tons—what part of the loss must they severally bear? Ans. A 6.25 tons, B 9, C 10, and D 10.75. 5. A man died leaving 3 sons, to whom he bequeathed his estate, in the following manner, viz. to the eldest he gave 184 dollars, to the second 155 dollars, and to the third 96 dollars; but when his debts were paid, there was but $184 left-what is each one's proportion of the estate ? Ans. $77.8298855+ 65.563218+ shares. 40.606896+ 6. A legacy of $3050.25 is to be divided among A, B, and C, in proportion to the number of their children; now A has 6, B 7, and C 8-required their respective shares. Ans. A $871.50, B $1016.75, and C $1162. 7. Four men traded with a stock of 800 dollars, and they gained (in two years? time) twice as much and 40 dollars over: A's stock was 140 dollars, B's 260 dollars, C's 300 dollarsI demand D's stock, and what each man gained by trading. Ans. D's stock was $100; A gained $287, B $533, C $615, and D $205. CASE 2. When the stocks in trade are increased or diminished, while the partnership continues : or difference of continuance. RULE 1. Multiply each man's stock by the time it was in trade. Then, as the sum of the products Is to the product of each stock and time, So is the whole gain or loss to be divided, To each partner's share or dividend. RULE 2. 1. Multiply each man's stock by the time it was in trade, for its product. 2. Divide the gain or loss, by the sum of the products, for the gain or loss per dollar. 3. Multiply the gain or loss per dollar (or pound) by each product, for each man's (proportional) gain or loss. EXAMPLES 1. A, B, and C join stocks for 12 months; A puts in 100 dollars, and on the first of the 5th month, 150 dollars more ; and on the first of the 9th month takes out 30 dollars. - B puts in at first 250 dollars, and on the first of the 6th month 60 dollars more, and on the first of the 11th month 100 dol. lars more. C puts in 300 dollars ; on the first of the 4th month takes out 200 dollars, and on the first of the 8th month takes out 50 dollars more. At the end of the year, their gain is found to be $149—required their several shares. $100 X 4= 400 $250 x 5=1250 250 X4=1000 310 x 5=1550 220 x 4= 880 410X2= 820 $ c. As 7450 : 2280 :: 149 : 45.60 A’s gain 7450 : 3620 :: 149 : 72.40 B's gain Operation by Rule 2. 7450)149.000.02 Then 2280 X.02=$45.60 A's gain 149.00 3620X.02= 72.40 B’s gain 1550 X.02= 31.00 C's gain 2. Three graziers, M, N, and P, rent a tract of pasture in common, for 120 dollars, into which M puts 80 oxen for 35 days, N 75 oxen 50 days, and P 90 oxen 45 days-what| rent must they severally pay? Ans. M $31.37=$31.69,8+; N $42.94=$42.45,3 nearly; and P $45.44=$45.85 nearly. 3. A, with a capital of 1000 dollars, began trade, January 1st, 1820, and meeting with success in business, took in B as a partner, with a capital of 1200 dollars, on the 1st of March following. Two and a half months after that, they admit C as a third partner, who brought sufficient stock in LOSS AND GAIN. 98 to entitle him to share equal profits the first of the following year with his partners; at which time they found they had gained 1200 dollars—required C's stock, and each man's just share, including his stock and gain. Ans. C's stock $payy; A's share $ptyy, B's $payy, and C's $eyyy. 4. D and E enter into partnership ; D puts in 40 dollars for three months, and E 75 dollars for four months, and they gained 70 dollars—what is each man's share of the gain? Ans. D's 20 dollars, E's 50 dollars. LOSS AND GAIN. Loss AND GAIN is a rule which enables merchants or traders to estimate the profit or loss per cent. in buying and selling goods; also to advance or reduce the price of any article, so as to gain or lose so much per cent., &c. CASE 1. The prime cost given, and price sold for, to find the loss or gain, and the loss or gain per cent. (Per cent. means per 190 dollars, &c. : thus, 6 per cent. loss or gain, is 6 dollars loss or gain on every 100 dollars expended.) RULE. Subtract the less price from the greater, the remainder will be the loss or gain. Annex two ciphers to the loss or gain, and divide by the prime cost, the quotient will be the loss or gain per cent. required. Or, As the prime cost EXAMPLES. C. 1. If I buy coffee at 20cts. per lb. and sell it again at 25cts. per lb., what do I gain per lb., and what per cent. ? Price sold for 25 Proof. If 20 : 100 :: 5 : 25 Ans. 25 per cent. gain |