EXAMPLE II. If 23 pound of lead cost 5s. 44d. what will 1cwt. 3qrs. IF DEFINITION. any effect performed depend on two or more proportional causes, then it is called compound proportion. VOL. I. PROBLEM PROBLEM XI. To resolve a question in compound proportion. I. Say, as the product of all the given causes put for the first term, is to the given effect performed by these causes in the second term, so is the product of any other causes in the third term, to the effect performed by the last causes in the fourth term. II. If the number sought be in the extremes, multiply all the means together for a dividend, and the extremes together for a divisor, and the quotient will be the answer. III. But if the number sought is in the means, multiply the extremes together for a dividend, and the means together for a divisor, and the quotient will be the answer. Note. It will be necessary to put some mark or letter where the term is wanting. If 4 men, in 36 days, can lay 24 squares of flooring, how many squares will 12 men lay in 21 days? Here it is evident that the squares is the effect, or the work done. 4×36=144)6048(42 squares the answer. 576 288 In this Example, because the unknown terms fall in the extremes, I multiply the means together for a dividend, and the extremes for a divisor; then the work is performed as in simple proportion. EXAMPLE II If 4 men, in 36 days, can lay 24 squares of flooring, how many men must be employed to complete 42 squares in 21 days? In this Example, because the unknown term is in the means, I therefore multiply the extremes together for a dividend, and divide by all the terms of the means multiplied together according to the Problem. EXAMPLE III. If 1001. in 12 months gain 51. interest, what principal will gain the same sum in 8 months? In this Example, because the second and fourth terms are the same, it will be of no use to multiply and divide by the same number. There was a certain building completed by 150 workmen in 9 months, but by some accident it took fire, and was burnt down: how many men must be employed to complete a house twice as good as the former, so that it shall be finished in 12 months? If the carriage of 150 feet of wood, that weighs three stone a foot, for 40 miles, comes to 31. how much will the carriage of 54 feet of stone, that weighs & stone a foot, cost for 25 miles? 150X3X40 18,000)32,400(11. 16s. Ans. 18 14400 18)288,000(16 18 108 108 The reason of all operations in compound proportion, will appear in a similar manner to the following: thus, in Example V. the expence of the carriage will be in proportion to the number of feet, if the weight and distance carried are the same; and if the weight vary, and the number of feet and distance carried be the same, then will the expence be as the weight: but if the number of feet and the weight be the same, then the expence of the carriage will be as the number of miles; therefore, when neither of them are constant, the expence of the carriage will be as their product. To contract an operation performed by compound proportion. State the question as directed before, find a number that will divide any two terms, one of which must be in the extremes, and the other in the means; then scratch out the terms, and place their respective quotients above instead of them, and proceed in this manner as long as you can; then multiply and divide as directed by the problem, and you will have the answer. EXAMPLE I. If 4 men in 36 days can lay 24 squares of flooring, how many squares will 12 men lay in 21 days? 3 6 1 7 4x38: 47× then 6x7=42 sqrs, the ans. EXPLANATION. It is easy to observe that 4 will divide 4 in the extremes, and also 24 in the means, therefore I place the quotient of |