2. In 7 casks of prunes, each weighing 3cwt. 1qr. 5lb. gross, tare 17 lb. per cwt. and trett as usual, how much net? Ans. 18cwt. 2qrs. 25lb.

3. What is the net weight of 3 hogsheads of sugar weighing as follows: the first, 4cwt. 5lb. gross, tare 73lb. the second, 3cwt. 2qrs. gross, tare 56lb. and the third, 2cwt. 3qrs. 17lb. gross, tare 47lb. and allowing trett to each as usual? Ans. 8cwt. 2qrs. 4lb.

CASE 4.

When tare, trett, and cloff are all allowed.

RULE.

Deduct the tare and trett, as before, and divide the suttle by 168, and the quotient is the cloff, which subtract from the suttle, and the remainder is the net.

EXAMPLES.

1. What is the net weight of a hhd. of tobacco, weighing 15cwt. 3qrs. 20lb. gross, tare 7lb. per cwt. and trett and cloff as usual?

2. In 19 chests of sugar, each containing 13cwt. 1qr. 17b. gross, tare 13lb. per cwt. and trett and cloff as usual, how much net, and what is the value at 5 d. per pound?

Ans. 215cwt. 17lb. and value 5771. 6s. 5 d.

COMPOUND PROPORTION,

OR

DOUBLE RULE OF THREE.

COMPOUND PROPORTION teaches how to resolve such questions, as require two or more statings in Simple Proportion.

In these questions there is always given an odd number of terms, as five, seven, or nine, &c. These are distinguished into terms of supposition, and terms of demand, the number of the former always exceeding that of the latter by one, which is of the same kind with the term or answer sought.

This rule is often named the Double Rule of Three, because its questions are sometimes performed by two operations of the Rule of Three.

RULE FOR STATING.

1. Write the term of supposition, which is of the same kind with the answer, for the middle term.

* The reason of this rule for stating, and of the methods of operation, may be easily shown from the nature of Simple Proportion; for every line in this case is a particular stating in that rule. And therefore with respect to the second method, it is. evident, that, if all the separate dividends be collected into one dividend, and all the divisors into one divisor, their quotient must be the answer sought.

X

2. Take one of the other terms of supposition, and one of the demanding terms of the same kind with it; then place one of them for a first term, and the other for a third, according to the directions given in the Rule of Three. Do the same with another term of supposition and its correspondent demanding term; and so on, if there be more terms of each kind; writing the terms under each other, which fall on the same side of the middle term.

METHOD OF OPERATION.

1. By several operations.-Take the two upper terms and the middle term, in the same order as they stand, for the first stating of the Rule of Three; then take the fourth number, resulting from the first stating, for the middle term, and the two next terms in the general stating, in the same order as they stand, for the extreme terms of the second stating; and so on, as far as there are any numbers in the general stating, always making the fourth number, resulting from each simple stating, the second term of the next. So shall the last resulting number be the answer required.

2. By one operation. Multiply together all the terms in the first place, and also all the terms in the third place. Then multiply the latter product by the middle term, and divide the result by the former product; and the quotient will be the answer required.

NOTE 1. It is generally best to work by the latter method, namely, by one operation. And after the stating, and before the commencement of the operation, if one of the first terms, and either the middle term, or one of the last terms, can be exactly divided by one and the same number, let them be divided, and the quotients used instead of them; which will much shorten the work.

NOTE 2. The first and third terms of each line, if of different denominations, must be reduced to the same denomination.

EXAMPLES.

1. How many men can complete a trench of 135 yards long in 8 days, provided 16 men can dig 54 yards in 6 days?

2. If 1001. in one year gain 51. interest, what will be the interest of 750l. for seven years?

Ans. 2621. 10s.

3. What principal will gain 2621. 10s. in 7 years, at Jl. per cent. per annum? Ans. 7501.

4. If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, may he travel 360 miles? Ans. 98 days.

5. If 120 bushels of corn can serve 14 horses 56 days; how many days will 94 bushels serve 6 horses?

Ans. 1021 days.

6. If 7oz. 5dwts. of bread be bought at 42d. when corn is at 4s. 2d. per bushel, what weight of it may be bought for 1s. 2d. when the price of the bushel is 5s. 6d. ?

Ans. 1lb. 4oz. 3479dwts.

7. If the carriage of 13cwt. 1qr. for 72 miles be 21. 10s. 6d. what will be the carriage of 7cwt. 3qrs. for 112 miles ? Ans. 21. 5s. 11d. 1779.

8. A wall, to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days; how many men must be employed to finish the wall in 4 days, at the same rate of working? Ans. 36 men.

9. If a regiment of soldiers, consisting of 939 men, can eat up 351 quarters of wheat in 7 months; how many soldiers will eat up 1464 quarters in 5 months, at that rate? Ans. 54833.

10. If 248 men, in 5 days of 11 hours each, dig a trench 230 yards long, 3 wide and 2 deep; in how many days of 9 hours long, will 24 men dig a trench of 420 yards long, 5 wide and 3 deep? Ans. 2887