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 E.-$404.444. to Federal Money. Can. . $364. N. E., $303.333. Ans. $85.833. N. Y. $227.50, &c. Ans. 4. Reduce £125, N. E. to 10. In £227 17s. 5 d. N. E.. Federal Money. how many dollars, cents and Ans. $416.666. mills ? Ans. $759 57cts. 3m. 5. Change $100 to each of the foregoing currencies. 11. In $1.612, now many $100=£22 10s. Eng.=£25 shillings, pence and farthings? Can.-£30 N. E.-£40 N. Y. =£37 10s. Penn. $ 9s. Ed. N. E. Ans. 12s. 104d. N. Y. 6. In: $1111.111, how many pounds, shillings, pence and 12. Reduce £33 13s. N. Y., farthings? to Federal Money. £333 6s. 8d. N. E. Ans. $84.125. Ans. £444 8s. 10 d. N. Y. 13. In £1 Is. 104d. Penn., 7. In £1 ls. 10d. N. E., how dollars ? how inany dollars ? Ans. $2.917. Ans. $3.646. 8. In £1 13. 10.d. N. Y., 14. In £1 ls. 103d. Can., how many dollars ? how many dollars ? Ans. $2.735. Ans. $4.376. 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 }, N. E. to N. Y. add }, N. Y. to N. E. subtract 4, N. E. to Penn. add 4, Penn, to N. E. subtract }, N. Y. to Penn. subtract It, Penn. to N. Y. add 1'5, N. E. to Can. subtract ļ, Can. to N. E. add }, &c. 15. In $255.406, how inany 16. Change £240 15s. N. pounds, shillings, pence and E. to the several other curfarthings? rencies. £76 125. 5d. N. E. £321 Os. Od. N. Y. Ans. £102 33. 3d. N. Y. £300 18s. 9d. Penn. £95 15s. 6 d. Penn. Ans. £200 12s.6d, Can. £63 178. 01. Can. $802.50 Fed. Mon. TABLE 303. Of the most common gold and silver coins, containing their weight fineness, and intrinsic value in Federal Money. Country. | Names of coins. | Weight. | Fineness. I Valuc. SIIVER COINS. 416. 41.6 92.90 451.62 386.18 418.47 418.47 450.90 225.45 432.93 216.46 265.68 504.20 162.70 413.80 301.90 oz. pwt. 1.000 0.500 0.250 0.100 1.111 0.556 0.222 1.06 0.898 0.991 0.972 1.037 0.519 0.926 0.463 0.615 1.222 0.375 1.009 0.602 Portugal. Note-The current values of several of the above coirs differ somewhat from the:r intr.nsic value, as expressed in the table, SECTION II. MENSURATION. 1. Mensuration of Superäicies. 304. The area of a figure is the space contained within the bounds of its surface, without any regard to thickness, 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. I crer 5 4. What is the area of a Ans. 25 ft. rhomboid 24 inches long, and 8 wide ? Ans. 192 inches. 5 5. How many acres in a 2. What is the area of a rectangular piece of ground, rectangle, whose length is 9, 56 rods long, and 26 wide ? and breadth 4ft.? Ans. 36ft. 56X26-160=970. Ans. 306. To find the area of a triangle. (64) : RULE 1.-Multiply the base by half the perpendicular height, and tne product will be the area. RULE 2.-If the three sides only are given, add these togethe: and take half the sum ; from the half sum subtract each side separately ; multiply the half sum and the three remainders continually together, and the square root of the last product will be the area of the triangle. 1. How many square feet | 3. What is the area of a in a triangle, whose basc is 40 triangle, whose three sides are feet, and height 30 feet? 13, 14 and 15 feet? 40 base. 13+14+15-12 155$ perpend. height. and 42:2—21-half sum. 21 21 21 200 13 14 15 and 21X6X7X 40 [=7056. rem. 8 7 6 600 feet. Ans. Then 70561–84 feet, Ans. 2. The base of a triangle is 4. The three sides of a tri6.25 chains, and its height 5.20, angle are 16, 11 and 10 rods, chains; what is its area? what is the area ? Ans. 16.25 square chains. Ans. 54.299 rods. 307. To find the area of a trapezoid. (65) ROLE.--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 in a plank 12 feet 6 inches chairs, and the other 12.25, long, and at one end, 1 foot and the perpendicular distance and 3 inches, and, at the other, between them is 154 chains; | 11 inches wide ? what is the area Ans. 1314 feet. 12.25 7.5 3. What is the area of piece of land 30 rods Long, 2)16.75 and 20 rods wide at one end, and 18 rods at the other? 9.875 Ans, 570 rods. 15.4 4. What is the area of a 39500 hall 32 feet long, and 22 feet 49375 wide at one end, and 20 at the 9875 other? Ans. 672 feet 152.0750 sq. chains. Ans. 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. i. A trapezium is divided 2. What is the area of a into two triangles, by a diago- trapezium whose diagonal is nal 42 rods long, and the per- 1083 feet, and the perpendicupendiculars let fall from the lars 561 and 60 feet? opposite anglez of the two tri Ans. 63474 feet. angles, are 18 rods and 16 rods; what is the area of the trape 3. How many square yards zium ? in a trapezium whose diagonal 42 42 336 is 65 feet, and the perpendicu8 378 lars let fall upon it 28 and 33.5 feet? 378 336 714 rods, Ans. Ans. 222 ! yds. 309. To find the diameter and circumference of a circle, either from the other. (67) RULE 1.--As 7 is to 22, so is the diameter to the circumference, and as 22 is to 7, so is the circumference to the diameter. RULE 2.-As 113 is to 355, so is the diameter to the circumference, and as 355 is to 113, so is the circumference to the dia ameter. RULE 3.-As 1 is to 3.1416, so is the diameter to the circumference, and as 3.1416 is to 1, so is the circumference to the diameter. 1. What is the circumfer 3. What is the diameter of ence of a circle whose diame a circle whose circumference ter is 14 feet? is 50 rods? By Rule 1. As 22:7::50 : 15.9090, Ans. By Rule 2. As 113 : 355 :: 14:4311}, Ans. As 355 : 113 :: 50 : 15.9155, Ans. By Rule 3. By Rule 3. As 1 :3.1416 :: 14:43.9824, Ans. As 3.1416 :1::50 : 15.9156, Ans. 2. Supposing the diameter 4. Supposing the circumfer. of the earth to be 7958 miles, ence of the earth to be 25000 what is its circumference ? miles, what is its diameter ? Aas. 25000.8528 miles. Ans. 7957nearly. 310. To find the area of a circle. RULE.--Multiply half the circumference by half the diameter,--or the square of the diameter by .7854, ,-- or the square of the circumference by .07958,—the product will be the area. |