NOTE. CIRCULAR MEASURE. 29. 8. 1 23 37 39 9 15 38 47 4 7 58 5 2 - In Circular Measure, the minuend is sometimes less than the subtrahend, as in Ex. 29, in which case it must be increased by 12 signs. 103. To find the difference of dates. Ex. 1. What is the difference of time between October 16th, 1852, and August 9th, 1854? Ans. 1y. 9mo. 23da. FIRST OPERATION. y. mo. da. 9 16 Min. 1854 7 9 1 9 23 SECOND OPERATION. Commencing with January, the first month in the year, and counting the months and days in the later date up to August 9th, we find that 7mo. and 9 da. have elapsed; and counting the months and days in the earlier date, up to October 16th, we find that 9mo. and 16da. have elapsed. We, therefore, write the numbers for subtraction as in the first operation. The same result can be obtained by reckoning the number of the given months instead of the number of months that have elapsed since the beginning of the year, and writing the numbers as in the second operation; written either way, Min. 1 8 5 4 8 9 1 9 23 The earlier date being placed under the later, is subtracted, as by the preceding rule. NOTE. In finding the difference between two dates, and in computing interest for less than a month, 30 days are considered a month. In legal transactions, a month is reckoned from any day in one month to the corresponding day of the following month, if it has a corresponding day, otherwise to its end. EXAMPLES FOR PRACTICE. 2. What is the time from March 21st, 1853, to Jan. 6th, 1857 ? Ans. 3y. 9m. 15da. 3. A note was given Nov. 15th, 1852, and paid April 25th, 1857; how long was it on interest? Ans. 4y. 5mo. 10da. 4. John Quincy Adams was born at Braintree, Mass., July 11th, 1767, and died at Washington, D. C., Feb. 23, 1848; to what age did he live? Ans. 80y. 7mo. 12da. 5. Andrew Jackson was born at Waxaw, S. C., March 15th, 1767, and died at Nashville, Tenn., June 8th, 1845; at what age did he die? Ans. 78y. 2mo. 23da. 103. From what period do you count the months and days in preparing dates for subtraction? How do you arrange the dates for subtraction? How subtract? How many days are considered a month in business transactions? What is the second method of preparing dates for subtraction? MISCELLANEOUS EXERCISES. 1. What is the amount of the following quantities of gold: 4lb. 8oz. 13pwt. 8gr., 5lb. 11oz. 19pwt. 23gr., 8lb. Ooz. 17pwt. 15gr., and 181b. 9oz. 14pwt. 10gr.? 2 Ans. 371b. 7oz. 5pwt. 8gr. 2. An apothecary would mix 7b 33 23 29 1gr. of rhubarb, 103 03 19 13gr. of cantharides, and 2tb 33 73 29 17gr. of opium; what is the weight of the compound? Ans. 12b 53 33 09 11gr. 3. Add together 17T. 11cwt. 3qr. 11lb. 12oz., 11T. 17cwt. 1qr. 19lb. 11oz., 53T. 19cwt. 1qr. 17lb. 8oz., 27T. 19cwt. 3qr. 18lb. 9oz., and 16T. 3cwt. 3qr. Olb. 13oz. Ans. 127T. 12cwt. 1qr. 18lb. 5oz. 4. A merchant owes a debt in London amounting to 7671£; what remains due after he has paid 1728£ 17s. 9d.? Ans. 5942£ 2s. 3d. 5. From 73lb. of silver there were made 26lb. 11oz. 13pwt. 14gr. of plate; what quantity remained? Ans. 46lb. Ooz. 6pwt. 10gr. 6. From 71lb 83 13 19 14gr. take 7b 93 13 19 17gr. Ans. 63lb 103 73 29 17gr. 7. From 28T. 13cwt. take 10T. 17cwt. 19lb. 14oz. Ans. 17T. 15cwt. 3qr. 5lb. 2oz. 8. A merchant has 3 pieces of cloth; the first contains 37yd. 3qr. 3na., the second 18yd. 1qr. 3na., and the third 31yd. 1qr. 2na.; what is the whole quantity? Ans. 87yd. 3qr. Ona. 9. Sold 3 loads of hay; the first weighed 2T. 13cwt. 1qr. 171b., the second 3T. 17lb., and the third 1T. 3qr. 11lb.; what did they all weigh? Ans. 6T. 14cwt. 1qr. 20lb. 10. What is the sum of the following distances: 16m. 7fur. 18rd. 14ft. 11in., 19m. 1fur. 13rd. 16ft. 9in., 97m. 3fur. 27rd. 13ft. 3in., and 47m. 5fur. 37rd. 13ft. 10in.? Ans. 181m. 2fur. 18rd. 9ft. 3in. 11. From 76yd. take 18yd. 3qr. 2na. Ans. 57yd. Oqr. 2na. 12. From 20m. take 3m. 4fur. 18rd. 13ft. 8in. Ans. 16m 3fur. 21rd. 2ft. 10in. 13. From 144A. 3R. take 18A. 1R. 17p. 200ft. 100in. Ans. 126A. 1R. 22p. 71ft. 80in. 14. From 18 cords take 3 cords 100ft. 1000in. Ans. 14 cords 27ft. 728in. 15. A gentleman has three farms; the first contains 169A. 3R. 15p. 227ft., the second 187A. 1R. 15p. 165ft., and the third 217A. 2R. 28p. 165ft.; what is the whole quantity? Ans. 574A. 3R. 20p. 12ft. 16. There are 3 piles of wood; the first contains 18 cords 116ft. 1000in., the second 17 cords 111ft. 1600in., and the third 21 cords 109ft. 1716in.; how much in all? Ans. 58 cords 82ft. 860in. 17. From 17T. take 5T. 18ft. 765in. Ans. 11T. 21ft. 963in. 18. From 169gal. take 76gal. 3qt. 1pt. Ans. 92gal. Oqt. 1pt. 19. From 17ch. 18bu. take 5ch. 20bu. 1pk. 7qt. Ans. 11ch. 33bu. 2pk. 1qt. 20. From 83y. take 47y. 10mo. 27d. 18h. 50m. 14s. Ans. 35y. 1mo. 2d. 5h. 9m. 46s. 21. From 11S. 15° 36′ 15" take 5S. 18° 50′ 18′′. Ans. 5S. 26° 45' 57". 22. John Thomson has 4 casks of molasses; the first contains 167gal. 3qt. 1pt., the second 186gal. 1qt. 1pt., the third 108gal. 2qt. 1pt., and the fourth 123gal. 3qt. Opt.; how much is the whole quantity? Ans. 586gal. 2qt. 1pt. 23. Add together 17bu. 1pk. 7qt. 1pt., 18bu. 3pk. 2qt., 19bu. 1pk. 3qt. 1pt., and 51bu. 3pk. Oqt. 1pt. Ans. 107bu. 1pk. 5qt. 1pt. 24. James is 13y. 4mo. 13d. old, Samuel is 12y. 11mo. 23d., and Daniel is 18y. 9mo. 29d.; what is the sum of their united ages? Ans. 45y. 2mo. 5d. 25. Add together 18y. 345d. 13h. 37m. 15s., 87y. 169d. 12h. 16m. 28s., 316y. 144d. 20h. 53m. 18s., and 13y. 360d. 21h. 57m. 15s. Ans. 436y. 290d. 20h. 44m. 16s. 26. A carpenter sent two of his apprentices to ascertain the length of a certain fence. The first stated that it was 17rd. 16ft. 11in., the second said it was 18rd. 5in. The carpenter finding a discrepancy in their statements, and fearing they might both be wrong, ascertained the true length himself, which was 17rd. 5yd. 1ft. 11in.; how much did each differ from the other? 27. From a mass of silver weighing 106lb., a goldsmith made 36 spoons, weighing 5lb. 11oz. 12pwt. 15gr.; a tankard, 3lb. Ooz. 13pwt. 14gr.; a vase, 7lb. 11oz. 14pwt. 23gr.; how much unwrought silver remains? Ans. 881b. 11oz. 18pwt. 20gr. 28. From a piece of cloth, containing 17yd. 3qr., there were taken two garments, the first measuring 3yd. 3qr. 2na., the second 4yd. 1qr. 3na.; how much remained? Ans. 9yd. 1qr. 3na. 29. Venus is 3S. 18° 45′ 15" east of the Sun, Mars is 7S. 15° 36′ 18′′ east of Venus, and Jupiter is 5S. 21° Mars; how far is Jupiter east of the Sun? 38′ 27′′ east of Ans. 4S. 26°. 30. The longitude of a certain star is 3S. 18° 14′ 35′′, and the longitude of Jupiter is 11S. 25° 30′ 50"; how far will Jupiter have to move in his orbit to be in the same longitude with the star? Ans. 3S. 22° 43′ 45′′. MULTIPLICATION. 104. Multiplication of Compound Numbers is the process of taking a compound number any proposed number of times. 105. When the multiplier is 12 or less. Ex. 1. If an acre of land cost 14£ 5s. 8d. 2far., what will 9 acres cost? OPERATION. 8. d. far. Multiplicand 14 5 8 9 128 11 4 2 Ans. 128£ 11s. 4d. 2far. We write the multiplier under the lowest denomination of the 2 multiplicand, and then say 9 times 2far. are 18far., equal to 4d. and 2far. We write the 2far. under the number multiplied, reserving the 4d. to be added to the next product. We then say 9 times 8d. are 72d., and the 4d. make 76d., equal to 6s. and 4d., and write the 4d. under the column of pence, reserving the 6s. to be added to the next product. Then, 9 times 5s. are 45s., and 6s. make 51s., equal to 2£ and 11s., and write the 11s. under the column of shillings, reserving the 2£ to be added to the next product. Again, 9 times 14£ are 126£, and 2£ make 128£, which we write under the column of pounds; and have 128£ 11s. 4d. 2far. for the answer. 105. Explain the 104. What is multiplication of compound numbers? operation. By what do you divide the product of each denomination? What do you do with the quotient and remainders thus obtained? |