In performing this question, we arrange the numbers, that would be the second and third terms in the regular statement of the question on the right hand of a perpendicular line, and the numbers, that would be the first term, on the left. We then divide the product of the uncancelled numbers on the right by the product of the uncancelled numbers on the left. 8 9 2. If 6 men in 16 days of 9 hours 24 6 each build a wall 20 feet long, 6 feet high, and 4 feet thick, in how many days of 8 hours each will 24 men build a wall 200 feet long, 8 feet high, and 6 feet thick ? 3. If $100 gain $ 6 in 12 months, how much would $800 gain in 8 months? 6 4 16 The Chain Rule consists in joining many proportions together; and by the relations which the several antecedents have 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 20 lbs. at Boston make 23 lbs. at Antwerp, and 150 lbs. at Antwerp make 180 lbs. at Leghorn, how many pounds at Boston are equal to 144 lbs. at Leghorn ? RULE. Write the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right hand; 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 hand for a divisor; but, if the last number stands at the right hand, multiply the numbers at the right hand column continually together for a dividend, and those at the left for a divisor; and the quotient will be the answer. 2. If 12 lbs. at Boston make 10 lbs. at Amsterdam, and 10 lbs. at Amsterdam make 12 lbs. at Paris, how many pounds at Boston are equal to 80 lbs. at Paris? 3. If 25 lbs. at Boston are equal to 22 lbs. at Nuremburg, and 88 lbs. at Nuremburg are equal to 92 lbs. at Hamburg, and 46 lbs. at Hamburg are equal to 49 lbs. at Lyons, how many pounds are equal to 98 lbs. at Lyons? 10 12 80 80 lbs. Ans. 22125 49 46 100 lbs. Ans. 5 7. If 100 acres in Brad-6 120|100 ford be worth 120 in Ha- 13 6550 10 verhill, and 50 in Haver hill worth 65 in Methuen, how many acres in Brad ford are equal to 150 in Methuen ? 8. If 10 lbs. of cheese are equal in value to 7 lbs. of butter, and 11 lbs. 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? 150 25 1250 500 bls. Ans. 96,2 acres, Ans. 432; lbs. Ans. 7 |