to their consequents the proportion between the first antecedent and the last consequent is discovered. This rule may often be abridged by cancelling equal quantities on both sides, and abbreviating commensurables. NOTE. The first numbers in each part of the question are called antecedents, and the following consequents. 1. If 20lb. at Boston make 23lb. at Antwerp, and 155lb. at Antwerp make 180lb. at Leghorn, how many pounds at Boston are equal to 144lb. at Leghorn? RULE. 20 X 155 X X44 23 × 180 9 248010713lb. Ans. Write the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right; and, if the last number stands at the left hand, multiply the numbers of the left-hand column continually together for a dividend, and those at the right for a divisor; but, if the last number stands at the right hand, multiply the numbers of the righthand column continually together for a dividend, and those at the left for a divisor; and the quotient will be the answer. NOTE. The demonstration for this rule is the same as for Compound Proportion. 2. If 12lb. at Boston make 10lb. at Amsterdam, and 10lb. at Amsterdam make 12lb. at Paris, how many pounds at Boston are equal to 80lb. at Paris ? Ans. 80lb. 3. If 25lb. at Boston are equal to 22lb. at Nuremburg, and 881b. at Nuremburg are equal to 921b. at Hamburg, and 46lb. at Hamburg are equal to 491b. at Lyons, how many pounds at Boston are equal to 98lb. at Lyons? Ans. 100lb. NOTE. The pupil may cancel all the following questions in a similar manner. 4. If 24 shillings in Massachusetts are equal to 32 shillings in New York, and if 48 shillings in New York are equal to 45 shillings in Pennsylvania, and if 15 shillings in Pennsylvania are equal to 10 shillings in Canada, how many shillings in Canada are equal to 100 shillings in Massachusetts ? Ans. 83 shillings. 5. If 17 men can do as much work as 25 women, and 5 women do as much as 7 boys, how many men would it take to do the work of 75 boys? Ans. 36 men. 6. If 10 barrels of apples will pay for 5 cords of wood, and 20 cords of wood for 4 tons of hay, how many barrels of apples will it take to purchase 50 tons of hay? Ans. 500bbl. 7. If 100 acres in Bradford be worth 120 in Haverhill, and 50 in Haverhill be worth 65 in Methuen, how many acres in Bradford are equal to 150 in Methuen ? Ans. 96 acres. 8. If 10lb. of cheese are equal in value to 7lb. of butter, and 11lb. of butter to 2 bushels of corn, and 11 bushels of corn to 8 bushels of rye, and 4 bushels of rye to one cord of wood, how many pounds of cheese are equal in value to 10 cords of wood? Ans. 4324lb. SECTION LV. PARTNERSHIP, OR COMPANY BUSINESS. PARTNERSHIP is the association of two or more persons in business, with an agreement to share the profits and losses in proportion to the amount of the capital stock contributed by each. EXAMPLES. 1. Three men, A, B, and C, enter into partnership for two years, with a capital of $1080. A puts in $240, B $ 360, and C $480. They gain $54. What is each man's share of the of gain? 240 As the whole stock in trade is $1080, of which $240 be longs to A, A's share of the stock, therefore, will be and as each man's gain is in proportion to his stock, of $54, which is $12, is A's gain. B's stock in trade is $360; there fore 3 of $54, which is $18, is B's gain. C's stock is $480; therefore his part of the whole stock is 360 ; consequently C's share of the gain is of $54, which is $24. Hence, to find any man's gain or loss in trade we have the fol lowing RULE. Multiply the whole gain or loss by each man's fractional part of the stock. NOTE. The pupil who may be desirous of performing the questions of this rule in the "old way will adopt the following RULE. As the whole stock is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or loss. The following is the statement of the first question, with the answers and proof. th As the stock $1080 $54:: $240: $12 A's gain. $1080 $1080 $54 :: $360: $18 B's gain. Proof, $12+$18 + $ 24 = $ 54 whole gain. 2. A, B, and C enter into partnership, with a capital of $1100, of which A put in $ 250, B put in $ 300, and C $ 550; they lost by trading 5 per cent. on their capital. What was each man's share of the loss? A's loss, $12.50. 3. Two merchants, C and D, engaged in trade; C put in $6780, and D put in $12,000; they gain $1000. What is each man's share? C's share, $361.02,21††. D's share, $ 638.97,719. 4. M, P, and Q trade in company, with a capital of $10,000; M put in $3000, P $2000, and Q $5000; they gain $500. What is each man's share of the gain? 5. A, B, and C enter into partnership; M's gain, $150. Q's gain, $250 A put in $500, B $350, and C put in 320 yards of broadcloth; they gain $ 332.50, ich C's share is $120. What were A's and B's shares of A's gain, $125.00. B's gain, $87.50. C's cloth per yd. $1.50. A, B, and C trade in company; A put in $5000, B put in 500, and C put in $7500; they gain 40 per cent. on their ital, but receive the whole amount of their gains in bills, which they are obliged to allow a discount of 10 per cent. w much was each man's net gain? A's gain, $1800. B's gain, $2340. C's gain, $2700. 7. A merchant, failing in trade, owes A, $455.00. B, $576.334. C, $ 637.00. D, $606.66. 8. A bankrupt owes $5000. His effects, sold at auction, amount to $4000. What will his creditors receive on a dollar? Ans. $0.80. 9. A merchant, having sustained many losses, is obliged to become a bankrupt. His effects are valued at $1728, with which he can pay only fifteen cents on the dollar. What did he owe? Ans. $11,520. SECTION LVI. PARTNERSHIP ON TIME. WHEN merchants in partnership employ their stock for unequal times, it is called Partnership on Time. EXAMPLES. 1. Two men, A and B, trade in company. A puts in $420 for 5 months, and B puts in $350 for 8 months; they gain $ 84. What is each man's share of the gain? . METHOD OF OPERATION BY ANALYSIS. $420 for 5 months is the same as 5 × $420 = $2100 for 1 month; and $350 for 8 months is the same as 8 x $ 350 = $2800 for 1 month. The question, therefore, is the same as if A had put in $2100 and B $2800 for 1 month each. whole stock would then be $4900. A's share of the gains, therefore, will be 2188 = 4 of $84 = $36. And B's share will be 4988 800 = # of $84 900 $48. The RULE. Multiply each man's stock by the time it continued in trade, and consider each product a numerator to be written over the sum of all the numerators, as a common denominator; then multiply the whole gain or loss by each fraction, and the several products will be the gain or loss of each man. NOTE. It might be well for the student to be acquainted with the "old way" of performing these questions. The following is the RULE. - Multiply each_man's stock by the time it was continued in trade; then, as the sum of all the products is to the whole gain or loss, so is each man's particular product to his share of the gain or loss. The first question would be performed thus: $420 × 5 $350 × 8 2100 4900 84: 2100: $36 A's gain. Proof, $36+$ 48 = $84 = A and B's gain. 2. A commenced business, January 1, with a capital of $ 3200; May 1, he took B into partnership, with a capital of $4200; and at the end of the year they had gained $240. each man's share of the gain? What was $128, A's gain. $112, B's gain. 3. A, B, and C traded in company. A put in $300 for 5 months, B put in $400 for 8 months, and C put in $500 for 3 months; they gain $100. What is the gain of each ? $24.19, A's gain. $51.61, B's gain. $24.19, C's gain. 4. Three men hire a pasture in common, for which they are to pay $26.40. A put in 24 oxen for 8 weeks, B put in 18 oxen for 12 weeks, and C put in 12 oxen for 10 weeks. ought each to pay? What A should pay $ 9.60. 5. Two men in Boston hire a carriage for $25, to go to Concord, N. H., the distance being 72 miles, with the privilege of taking in three more persons. Having gone 20 miles, they |