EXAMPLES. 1. Gross 173 cwt. 3 qr. 17 lb. tare 16lb. pr. cwt. how m utch neat? 3. In 25 barreis of figs, each 2 cwt. 1 qr. gross, tare 16 pr. cwt.; how much neat? CASE III. Ans. 48 cwt. 24lb.. When Trett is allowed with Tare. RULE. Divide the suttle by 26, and the quotient will be the Trett, which subtract from the suttle, the remainder is the net weight. EXAMPLES. 1. In 9 cwt. 2 qr. 17 lb. gross, tare 37 lb. and trett as usual; how much neat? Deduct the tare and trett as before, divide the suttle by 168, the quotient will be the cloff, which subtract from the sattle; the remainder is the neat weight. EXAMPLES. 1. What is the neat weight of a hhd. of tobacco, weighing 15 cwt. 3. qr. 20lb. gross, tare 7 lb. pr. cwt. and trett and cloff as usual? Teaches to solve, at once, such questions, as require two, or more statings in simple proportion, whether Direct, or Inverse. In this rule, their are always five terms given, to find a sixth. The three first terms of which, are a supposition, the two last a demand, RULE. In stating the question, place the terms of supposition, so that the principal cause of loss, gain, or action, possess the first place; that which signifies time, distance of place, in the second place, and the remaining term in the third place. Place the terms of demand under those of the same kind, in the supposi tion. If the blank place, or term sought, fall under the third term, the proportion is direct; then multiply the first and second Note. The following method of stating compound proportion is, by some, prefered, 1. Place that number, or term, which is of the same name, or kind with the answer, in the third place. 2. Then take one term from the supposition, and one from the demand, both of the same name, or kind, and place them with the third term. 3. Then proceed in the same manner with the two remaining terms. terms together for a divisor, and the other three for a dividend but if the blank fall under the first, or second term, the proportion is Inverse; then multiply the third and fourth term together for a divisor, and the other three for a dividend; and the quotient will be the answer. 4. Reduce the similar terms to the same denomination, if necessary. 5. Multiply the terms in the second and third place together, and divide their product by the product of those in the first place; the quotient will be the answer. EXAMPLE. If 7 men can build 36 rods of wall in 3 days, how many rods ean 20 men build in 14 days? In compound proportion, there are always five numbers given to find a sixth, which multiplied into the product of the two first, shall be equal to the product of the other three. And it may be shown in compound, as in simple proportion, that the product of the extremes, is equal to the product of the means; thus 2 X 3: 12: : 3X4: 24; here the extremes are 2 X 3 and 24, and the means are 12 and 3 X 4; now the product of 2 X 3X 24 the extremes, is 144; and the product of 12 X 3 X 4 the means, is also 144; whence it is evident that dividing either the product of the three extremes, or means, by any two of the means gives the other mean; thus, 144 divided by the product of the two means 3 X 4, gives 12 for the other mean; and it is also manifest, that by dividing the product of the three extremes, or means, by the product of any two of the extremes, the other extreme is obtained; thus dividing 144 the product of the means, by 2 X 3 the product of two of the extremes, gives 24 for the other extreme: hence the propriety of the rule in multiplying the 3d. 4th. and 5th. terms, or means together, and dividing by the product of the two first terms, or extremes, to obtain the other extreme. EXAMPLES. If 7 men can build 36 rods of wall in 3 days, how many rods Can 20 men build in 14 days? 7: 336 terms of supposition. In compound, as in simple proportion, the term required may be found by logarithms, if we substitute addition for multiplica¬ tion, and subtraction for division. RULE. Add together the logarithms of those terms which in common arithmetick are to be multiplied together for a dividend, and from the sum, subtract the sum of the logarithms answering to these terms, which in common arithmetick, are multiplied for a divisor; and the remainder will be the logarithm of the answer. Or more fully; find the arithmetical complement of the logarithms to be subtracted, and then add all the terms together; the sum will be the logarithm of the answer. EXAMPLES. 2. If 4 men in 12 days, mow 48 acres; how many acres can & men mow, in 16 days? a. c. 9. 3979400 Two first terms 54 * It must be observed, that each arithmetical compliment increases the index of the logarithm by 10; as often therefore, as the a. c. is used, the index of the sum of the logarithms, must be made less by so many tens.. 1. If 10 bushels of oats, be sufficient for 18 horses 20 days,. how many bushels will serve 60 horses 36 days? Three last terms { 60 log. 1. 7781513 36 1. 5563025 3. What principal will gain £262 10s. in cent? 7 years, at₤5 pr. Ans. £750 4. If the interest of 365 82 13 cts. what will be and 6 months ? 5. If £100 in 12 months, gain £6 interest; how much will £75 gain in 9 months? dollars for 3 years and 9 months, be the interest of 8 8 940 for two years Ans. 340 Ans. £3 7s. 6d. 6. If £16 18s. be the wages of 16 men, for 8 days; what sum will 32 men earn in 24 days? Ans. 01 8s. Ans. £75 7. If £100 in 12 months, gain 7 interest; what principal will gain £3 18s. 9d. in 9 months? 8. If 200lb. be carried 40 miles, for 40 cents; how far may 20200lb. be carried for $ 60 60 cts. Ans. 60 miles. COMPOUND INTEREST. In calculating compound interest, the amount for the first year, is made the principal for the second year; and the amount for the second, the principal for the third, &c. As the Logarithmickal method of computing compound interest, is by mutch the most expeditious, it is thought unnecessary to subjoin the old one in this place. Therefore, To calculate Compound Interest by Logarithms. RULE. 1. Find the amount of 1 dollar for 1 year; multiply its logarithm by the number of years, and to the product add the loga |