PART III. PRACTICAL EXERCISES SECTION 1. Exchange of Currencies. 299. In £13, how many dollars, cents and mills? Now, as the pound has different values in different places, the amount in Federal Money will vary according to those values. In England, $1=4s. 6d. 4.5s.££0.225, and there £13-13÷0.225 $57.777. In Canada, $1=5s. £0.25, and there £13=13÷0.25=$52. In New England, $1=6s. ££0.30, and there, £13-13-0.3=$43.333. In New York, $1=8s. £0.4, and there, £13-13-0.4 32.50. In Pennsylvania, $1=7s. 6d. 7.53.£7£0.375, and there, £13 13÷0.375 $34.666. And in Georgia, $1= 4s.8d. 4.6+s. £20.0=£0.2333+, and there, £13-13-0.2333 =$55.722. 4.6+ 300. In £16 7s. 8d. 2qr., how many dollars, cents and mills? Before dividing the pounds, as above, 7s. 8d. 2qr., must be reduced to a decimal of a pound, and annexed to £16. This may be done by Art. 143, or by inspection, thus, shillings being 20ths of a pound, every 23. will be 1 tenth of a pound: therefore write half the even number of shillings for the tenths £0.3. One shilling being 1 20th £0.05; hence, for the odd shilling we write £0.05. Farthings are 960ths of a pound, and if 960ths be increased by their 24th part, they are 1000ths Hence 8d. 2qr.(34qr.+1) £0.035; and 16+0.3+0.05-0.035 =£16.385, which, divided as in the preceding example, give for English currency, $72.822, Can. $65.54, N. Y. $40.962, &c. Hence, 301. To change pounds, shillings, pence and farthings Federal Money, and the reverse. RULE. Reduce the shillings, &c. to the decimal of a pound; shen, if it is English currency, divide by 0.225; if Canada, by 0.25; if N. E., by 0.3; if N. Y., by 0.4; if Penn., by 0.375, and if Georgia, by 0.23; -the quotient will be their value in dollars, cents and mills. And to change Federal Money into the above currencies, multiply it by the preceding decimals, and the product will be the answer in pounds and decimal parts. 3. In £91, how many dol-| 9. Reduce £25 15s. N. E., lars ? £91 Ε. $404.444. to Federal Money. Can. $364. N. E., $303.333. N. Y. $227.50, &c. Ans. 4. Reduce £125, N. E. to Federal Money. Ans. $416.666. 5. Change $100 to each of the foregoing currencies. $100 £22 10s. Eng. £25 Can. £30 N. E. £40 N. Y. £37 10s. Penn. 6. In $1111.111, how many pounds, shillings, pence and farthings? Ans. { £333 63. 8d. N. E. £444 83. 10d. N. Y. Ans. $85.833. 10. In £227 17s. 5łd. N. E, how many dollars, cents and mills ? Ans. $759 57cts. 3m. 11. In $1.612, now many shillings, pence and farthings? Ans. 9s. 8d. N. E. 12s. 10 d. N. Y. 12. Reduce £33 13s. N. Y., to Federal Money. Ans. $84.125. 13. In £1 1s. 101⁄2d. Penn., 7. In £1 1s. 10td. N. E., how many dollars? how many dollars? Ang 2017 302. The following rules, founded on the relative value of the several currencies, may sometimes be of use: To change Eng. currency to N. E. add 4, N. E. to N. Y. add 4, N. Y. to N. E. subtract 4, N. E. to Penn. add 1, Penn. to N. E. subtract 1, N. Y. to Penn. subtract T's, Penn. to N. Y. add T's, N. E. to Can. subtract 4, Can. to N. E. add 4, &c. TABLE 303. Of the most common gold and silver coins, containing their weight fineness, and intrinsic value in Federal Money. NOTZ-The current values of several of the above coins differ somewhat from their uner.asic value, as expressed in the table SECTION II. MENSURATION. []. Mensuration of Superficies. 304. The area of a figure is the space contained within the bounds of Its surface, without any regard to thiekness, and is estimated by the number of squares contained in the same; the side of those squares being either an inch, a foot, a yard, a rod, &c. Hence the area is said to be so many square inches, square feet, square yards, or square rods, &c. 305. To find the area of a parallelogram (65), whether it be a square, a rectangle, a rhombus, or a rhomboid. RULE.-Multiply the length by the breadth, or perpendicular height, and the product will be the area. 1. What is the area of a square whose side is 5 feet? 5 Ans. 25 ft. 5 5 2. What is the area of a rectangle, whose length is 9, and breadth 4ft.? Ans. 36ft. د 3. What is the area of a rhombus, whose length is 12 rods, and perpendicular height 4? Ans. 48 rods. 4. What is the area of a rhomboid 24 inches long, and 8 wide? Ans. 192 inches. 5. How many acres in a rectangular piece of ground, 56 rods long, and 26 wide? 56×26-160-9. Ana 306. To find the area of a triangle. (64) RALE 1.-Multiply the base by half the perpendicular height, and the product will be the area RULE 2.-If the three sides only are given, add these togethez and take half the sum; from the half sum subtract each side separately; multiply the half sum and the three remaindern continually together, and the square root of the last product will be the area of the triangle. 307. To find the area of a trapezoid. (65) RULE.-Multiply half the sum of the two parallel sides by the perpendicular distance between them, and the product will be the area. 1. One of the two parallel | 2. How many square feet sides of a trapezoid is 7.5 chairs, and the other 12.25, and the perpendicular distance between them is 154 chains; what is the area 12.25 2)16.75 9.875 39500 49375 9875 in a plank 12 feet 6 inches long, and at one end, 1 foot and 3 inches, and, at the other, 11 inches wide? Ans. 1314 feet. 3. What is the area of a piece of land 30 rods long. and 20 rods wide at one end. and 18 rods at the other? 152.0750 sq. chains. Ans. I 308. To find the area of a trapezium, or an irregular polygon. RULE. Divide it into triangles, and then find the area of these triangles by Art. 306, and add them together. |