To find the value of this remainder. 1. In shillings, &c. 136 6 216)816(3s. 648 168 12 216) 2016(9d. +72 4. 216)288(1 qr. 72 216=3 2. In Federal money. Annex cyphers, as in division of decimals; the two quotient places next to dollars, will be cents ; the third mills; the others, decimals of a mill; or the remainder with the divisor will form a fraction of a mill. 216)1360(62c. 9m. 640 432 2080 1944 136 17 PROB. 3. To ascertain the weight of gold equivalent to any given sum, currency. Rule 1. If the given sum be in pence, reverse Rule 1. Theorem 1. that is; As the numerator 8 is to the given sum in pence; so is the denominator 3 to the weight required, in grains. What weight of gold is equal to 4s. ? Rule 2. If the given sum be in pounds, shillings and pence. As is equal to ; therefore, divide the given sum by 8, and that quotient by 2; add the two quotients together, double the last denomination, and you will have the answer. What quantity of gold is equivalent to 451 13s 4d. PROB. 4. To find the value of gold equivalent to any given sum in Federal money. R Rule. Rule. As the numerator 8 is to the number of dollars; so is the denominator 9 to the answer in pennyweights: Or, divide the dollars by the numerator 8, and add the quotient to the dividend. Or, divide as before, and multiply the quotient by the denominator 9. In either case you will have the answer. 1. Required the weight of gold equal to 76 dollars. As 8: 76: 9 9 8)684 Or thus, 8)76 Or, 94x9-851pwt. Ans. 85 pwt.= 4 2. Required the weight of gold equal D.159. 75c. Or, 159.75-8 x 9-179pwt. 171gr. as before. RULE OF THREE DIRECT IN DECIMALS. RULE. Having reduced your fractions to decimals, and stated your question as in whole numbers, multiply the second and third together; divide by the first, and the quotient will be the answer. EXAMPLES. 2. If loz. of silver cost 6s. 8d. what is the price of a bowl, which weighs 1lb. 7oz. 13gr.? Ans. £.6 6s. 10d. 3. If 9 yards cost D.11 25c. what will yard come to? Ans. 57c. 613m. 4. If 1hhd. sugar, weighing 9cwt. 3qrs. 14lb. cost £.27 13s. 7d. what will 3cwt. 1qr. 171b. come to? Ans.9 10s. 81d. 5. A tobacconist bought 5hhds. of tobacco, each weighing 8cwt. 2qrs. 19lb. for D.534 5c. what was it per ounce ? Ans. 63m. 6. There is a cistern, which has 3 cocks, the first will empty it in of an hour, the second in, and the third in 11⁄2 hour in what time will it be emptied, if all three run together? h. Cist, h. Cist. Cist. h. Cist. S:25:11:4 : As 6: 1 :: 1 :·1667-10 min. Ans. As 75: 1 :: 1: 1·333+ 1·5 : 1 :: : 0·667— 6 Cist. 7. A conduit has a cock, which, running into a cistern, will fill it in 12 minutes: This cistern has three cocks; the first will empty it in 14 hour, the second in 371⁄2 minutes, and the third in an hour: In what time will the cistern be filled, if all four run together? 8. If 19 yards cost 25 7 5 what will 485 yards come to ? yds. D. d. c. yds. As 19: 25 7 5 :: 435.5 25.75 217 75 3048 5 21775 8710 D. d. c. m. 19)11214-125(590 2 1 7,2 Ans. 9. If 345 yards of tape cost D.5. 1d. 7c. 5m. what will 1 yd. cost? yds. D. d. c. m. yds. c. m. As 345: 5 1 7 5 :: 1 :·0 15 Ans. 10. If I give D.12. 8d. 2c. 5m. for 675 tops, how many tops will 19 mills buy? Ans. I top. RULE RULE OF THREE INVERSE, OR RECIPROCAL PROPORTION, Teaches, by having three numbers given, to find a fourth, which shall have the same proportion to the second, as the first has to the third. Therefore, the greater, the third term is, in respect to the first, the less will the fourth term be, in respect to the second; or, the less the third term is in proportion to the first, the greater the fourth must be in proportion to the second; and this is called reciprocal, inverted, or indirea Proportion. The principal difficulty that will embarrass the learner will be, to distinguish when the proportion is direct, and when indirect. This is done by an attentive consideration of the sense and tenour of the question proposed: For if thereby it appears that, when the third term of the stating is less than the first, the answer must be less than the second; or when the third is greater than the first, the answer must be greater than the second; then the proportion is direct: But, if the third be less than the first, and yet the sense of the question requires the fourth to be greater than the second; or if the third, being greater than the first, the answer must be less than the second, the proportion is inverse. RULE.* State and reduce the terms as in the Rule of Three Direct; then, multiply the first and second terms together, and divide the product by the third; the quotient will be the answer in the same denomination as the middle term was reduced into. If there be fractions in your question, they must be stated as before directed, and if they be vulgar, invert the third term: Then multiply the three terms continually together, and the product will be the answer, EXAMPLES. 1. How much shalloon, that is yard wide, will line 6 yards of eloth which is 14 yard wide? yd. yds. qrs. As 14 64 3 qrs. qrs. qrs. As 5: 27 :: 3 5 3)135 4)4.5 114 yards, Ans. The The reafon of this rule may be explained from the principles of Compound Multiplication and Compound Division, in the same manner as the direct rule.— For example, If 4 men can do a piece of work in 12 days, in what time will 8 men do it? 4X12 As 4 men: 12 days :: 8 men: 6 days, the Answer. 8 And here the product of the first and fecond terms, that is, 4 times 12, or 48, is evidently the time in which one man would perform the work. Therefore, 8 men will do it in one eighth part of the time, or 6 days, The same by Vulgar Fractions. 5×27X4 As: 4. And xX1X1X3=4=4=114 Answer. 27 :: 48 The same by Decimal Fractions. 11=1.25, 63-6.75 and 3qrs.=75. As 1.25: 675 :: 75 Then, 3. How many yards of carpet, 2 feet wide will cover a floor, which is 18 feet long and 16 feet wide? ft. ft. ft. ft. yds. As 16 18 :: 21×3:3449 Ans. Note, I multiply 2 by 3, because 3 feet=1 yard. 4. Suppose I lend a friend (.350 for 5 months, he promising the like kindness; but, when requested, can spare but .125, how long may I keep it to balance the favour? . Mo. . Mo. As 350: 5 :: 125 : 14 Ans. 5. Suppose 450 men are in a garrison, and their provisions are calculated to last but 5 months; how many must leave the garrison, that the same provisions may be sufficient for those who remain 9 months? M. Mo. M. Mo. M. 250-200 men, Ans. 6. If a man perform a journey in 15 days, when the day is 12hours long, in how many days will he do it, when the day is but 10 hours? Ans. 18 days. If a piece of land, 40 rods in length, and 4 in breadth, make an acre, how wide must it be, when it is but 19 rods long to make an acre? " Ans. Srods 6ft. 117,in. 8. If when wheat is D.1 per bushel, the two penny loaf weigh 96oz. what ought it to weigh, when wheat is D 1 25c. per bushel ? Ans. 7oz. 13pwt. 14-4gr. 9. If |