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NOTE.-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.

ART. 103.

To find the time between two different dates. Ex. 1. What is the difference of time between October 16th 1852, and August 9th, 1854 ? Ans. ly. 9mo. 23da.

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, however, could be obtained, as some prefer, 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. 1854

Sub. 1852

9 16

Rem. 1 9 23

mo. da.




Min. 1854 8 9
Sub. 1852 10 16

Rem. 1 9


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 same day of the following month.


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.

QUESTIONS. Art. 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?


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.?

Ans. 371b. 7oz. 5pwt. 8gr. 2. An apothecary would mix 7 33 23 29 1gr. of rhubarb, 21 103 03 19 13gr. of cantharides, and 21 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. 191b. 11oz., 53T. 19cwt. 1qr. 171b. 8oz., 27T. 19cwt. 3qr. 18lb. 9oz., and 16T. 3cwt. 3qr. Olb. 13oz.

Ans. 127T. 12cwt. 1qr. 181b. 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 261b. 11oz. 13pwt. 14gr. of plate; what quantity remained?

Ans. 461b. Ooz. 6pwt. 10gr. 6. From 71 83 13 19 14gr. take 7b 93 13 19 17 gr. Ans. 63 103 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. 57yd. Oqr. 2na.

Ans. 181m. 2fur. 18rd. 9ft. 3in. 11. From 76yd. take 18yd. 3qr. 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. farms; the first contains 169A 187A. 1R. 15p. 165ft., and the what is the whole quantity? Ans. 574A. 3R. 20p. 121ft.

15. A gentleman has three 3R. 15p. 227ft., the second third 217A. 2R. 28p. 165ft.;

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. 765 in.

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. 8h. 44m. 16s.

26. A carpenter sent two of his apprentices to ascertain the length of a certain fence. The first stated 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. 1lin.; how much did each differ from the other?

27. From a mass of silver weighing 1061b., 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

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