NOTE. Here it appears that feet multiplied by feet produce feet; feet 60 by inches 66 inches; seconds; inches 66 by inches inches" by seconds" thirds; seconds" by seconds" fourths. OBS. The above operation is the ordinary method of solving questions in Duodecimals: but the result is evidently the same, if we begin by multiplying the lowest denomination of the multiplicand, and divide each product by 12, and place each remainder under its like name, as will be seen by comparing the same example, performed according to the directions just given; which is preferable, as it is more strictly conformable to what takes place in the multiplication of numbers accompanied by decimals. This mode of operation is much easier for the pupil. It was taken from Lacroix. 1st. Example by Lacroix's Method. Multiply 7 ft. 3in. 2′′ 2. Multiply 9 feet 6 inches, by 4 feet 9 inches. Ans. 45 ft. 1 in. 6′′ 3. Multiply 8 feet 11 inches, by 7 feet 10 inches? Ans. 69 ft. 10 in. 2′′ 4. Multiply 9 feet 8 inches, 6", by 7 feet 9 inches, 3" Ans. 75 ft. 5 in. 3′′ 7''' 6''' 5. How many square feet in a board 10 feet 8 inches long, and 1 foot 5 inches broad? 6. How many square feet in a and 2 feet 6 inches wide? Ans. 15 ft. 1 in. 4′′ board, 14 feet 9 inches long, Ans. 36 ft. 10 in. 6" 7. What are the contents of a door 6 feet 9 inches 3" long, and 3 feet 5 inches wide? 8. How many square feet in a long, and 4 feet 7 inches broad? 9. Find the square feet in a board 1 foot 5 inches wide? Ans. 23 ft. 1 in. 7′′ 3′′′′ flag stone, 5 feet 10 inches Ans. 26 ft. 8 in. 10′′ 17 feet 7 inches long, and Ans. 24 ft. 10 in. 11′′ 10. What is the price of a marble slab, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at one dollar per foot? Ans. $10:23'5 11. What will the painting of a floor come to, at 10 cts. per square yard, allowing the floor to be 21 feet 8 inches long, and the breadth 14 feet 10 inches? Ans. $3: 57 NOTE. Divide the square feet by 9, and the quotient will be square yards. 12. What is the contents of 12 windows, each measuring 3 feet 10 inches long, 2 feet 8 inches broad; what will the glaz ing come to at 25 cents per foot. Ans. 122 ft. 8 in. $30: 66'6 amount, OBS. In computing solid measure, the given length must be multiplied by the given breadth, and that product by the given height; the last product will be the answer. 1. How many solid feet in a pile of wood 8 feet long, 3 feet wide, and 2 feet 8 inches high? Ans. 64 ft. 2. A. bought a load of wood, which was 9 feet 6 inches long, 8 feet 4 inches wide, and 3 feet 7 inches high; what did it want of a cord? Ans. 14 ft. 6 in. 4′′ 3. How much wood in a pile 3 feet, 8 inches wide, 3 feet 5 inches high, and 6 feet 7 inches long? Ans. 82 ft. 5 in. 8′′ 4′′′′. 4. What are the contents of a solid stick of timber, 7 feet 6 inches long, 1 foot 3 inches wide, and 1 foot 10 inches thick? Ans 17 ft. 2 in. 3′′ MENSURATION. MENSURATION has reference to that branch of common arithmetic which treats of the admeasurement of surfaces, and the relative magnitude of bodies. RULE :-- When the length of a board or plank is in feet, and the width in feet, multiply them for the contents in feet. When the length is in feet and the width in inches, multiply the length by the width, and divide the product by 12 for feet. When the length of timber or joist is in feet, and the side or sides in inches, multiply the product of the sides by the length, and divide by 12 for feet, board measure. Ex. 1. In a board or plank 19 feet long, and 2 feet wide, how many feet? Ans. 38 OPERATION. 2. In a board or plank 23 feet long, and 17 inches wide, how many feet? Ans. 32 ft. 7 in. OPERATION. 23X17=391+12=32 7 in. 3. How many feet in a joist, 8 inches square and 30 feet long? Ans. 160 OPERATION. 8x8=64x30=1920+12=160 Require the superficial feet in the following lot of boards, Require the contents of the following pieces of timber in board measure, the length and side of the square being given. To calculate interest on notes, bonds, &c. on which partial payments have been made.—The following Rule was established by the Superior Court of Connecticut, in 1784. RULE:" Compute the interest to the time of the first payment, if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and, in like manner from one payment to another, till all the payments are absorbed; provided, the time between one payment and another be one year or more. But if any payment be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation for one year, add it to the principal; and compute the interest on the sum paid, from the time it was paid, up to the end of the year; add it to the sum paid, and deduct that sum from the principal and interest added as above. If any payment be made of a less sum than the interest arisen at the time of such payment, no interest is to be computed, but only on the principal sun, for any period."-Kirby's Reports, p. 49. 1. Suppose a note was given on demand for 1000 dollars, dated February 1, 1825. On which were the following indorse What was the balance due on the note, Oct. 1, 1828, at 6 per cent? $1000 Principal. Ans. $263:93 70 Interest to the 1st ind't., being 1 year and 2 mo. 1070 Amount. 80 1st Indorsement. 990 Principal remaining due, April 1, 1826. 99 Interest to the 4th ind't., being 1 yr. and 8 mo 1089 Amount to do. 2:40 Interest to the 4th Indorsement. 32:40 10: 600: 3d Ind't., which does not bear in't. because I y's. in't. has accrued on new principal. 4th Indorsement. 642:40 Deduct from 1089 dollars. 446:60 Principal remaining due, Dec. 1, 1827. 200 5 5th Indorsement. do. Interest to Oct. 1, 1828, being 5 months. 205 Amount deduct from 468: 93 cts. $26393 cts. Balance due, Oct. 1, 1828. 2. Suppose a bond or note dated May 10th, 1824, was given for 2000 dollars, interest at 6 per cent, upon which were the following indorsements, viz: 1. March 10, 1825, Received, 2. May 10, 1826, 3. Sept. 10, 1827, $800 400 300 What remained due January 10, 1829? Ans. $831:57'5 The following Rule was established by the Superior Court of the State of Massachusetts in 1821. RULE:"Cast the interest up to the first payment, and if the payment exceed the interest, deduct the excess from the principal, and cast the interest. unon the remainder to the time of the INTEREST ON NOTES AND BONDS 193 second payment. If the payment be less than the interest, place it by itself, and cast on the interest to the time of the next payment, and so on, until the payments exceed the interest, then deduct the excess from the principal, and proceed as before."Mass. Reports, Vol. 17, page 418. EXAMPLES. 1. Suppose a note was given on demand for $1000, dated February 1, 1825, on which were the following indorsements. 1. April 1, 1826, Received, 2. August 1, 1826, 3. October 1, 1827, 4. December 1, 1827, 5. May 1, 1828, $80 30 10 600 200 What remained due on the note, Cct. 1, 1828, at 6 per cent? $1000 Principal. Ans. $265: 87'2 70 Interest to the first ind't., being 1 yr. 2 months. 990 Principal remaining due, April 1, 1826. 1980 Interest to the 2d Indorsement, being 4 mo. 979: 80 Principal remaining due, Aug. 1, 1826. 9:798 Interest to the 4th ind't., on same principal; 1058 18'4 Amount to the 4th Indorsement. 10 600 610 3d Indorsement. 4th Indorsement. Sum of the 3d and 4th Ind't., deducted. 448 18'4 Principal remaining due, Dec. 1, 1827. 259: 388 Principal remaining due, May 1, 1828. $265: 87'2 Balance due on note, Oct. 1, 1828. 2. Suppose a bond or note was given for 1200 dollars, at 6 per cent interest, dated Oct. 15th, 1826, on which were the following payments, viz. Oct. 15th, 1827, Received 1000 dollars, April 15th, 1828, Rec'd. 200 dollars. What remained due Oct. 15th, 1828? Ans. $82:56'4 |