416. Apothecaries' weight is used by apothecaries and physicians in compounding dry medicines. 1. Medicines are bought and sold in quantities by Avoirdupois weight. 2. The pound, ounce, and grain are the same as those of Troy Weight, the ounce being differently divided. 419. Time is a measured portion of duration. The calendar year is divided as shown in the diagram. 420. Circular or angular measures are used in measuring angles, determining latitude and longitude, etc. The unit for measuring angles is the degree. 421. A Circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the centre. 1. A semi-circumference is one-half of a circumference, or 180°. 2. A quadrant is one-fourth of a circumference, or 90°. 3. A sextant is one-sixth of a circumference, or 60°. 4. A sign is one-twelfth of a circumference, or 30°. 5. A degree (1°) is one ninetieth of a right angle. 6. The length of a degree varies with the size of the circle; thus, a degree of longitude at the Equator is 69.16 statute miles, at 30° of latitude it is 59.81 miles, at 60° of latitude it is 34.53 miles, and at 90°, or the poles, it is nothing. 7. A minute of the earth's circumference is called a geographic, or nautical mile, and is about 1 common miles. WRITTEN EXERCISES. 423. To change higher to lower denominations, Reduce Change 1. 3 mi. 51 ch. 6 1. to links. 5. 10 S. 10° 10' 10" to ". 2. b 16 37 33 to 9. 6. 3. Cong. 4 0. 5 f 38 to f3.7. 75 A. 4 sq. ch. 18 P. to sq. 1. 2 common years to hours. 4. 4 fath. 3 ft. 8 in. to in. 8. 16° 24′ 26′′ to seconds. Find the value, in integers of lower denominations, of 21. A field 17 ch. 31 1. long, 12 ch. 87 1. wide, is enclosed by a board fence. What is the length of the fence in feet? 23. How many acres in a piece of land 105 ch. 85 l. long, and 40 ch. 15 l. wide? To change a compound number to a fraction of a higher denomination: What part of 7. f31 is f35 m 36? 8. 1 mi. is 18 fathoms? 9. 1 chain is 4 feet. What decimal of 10. 1 lea. is 2 mi. 3 rd. 1 yd.? 13. In what time will a heavenly body move through a quadrant, if it move at the rate of 3′ 12′′ per minute? 14. What will be the cost of a farm containing 4550000 sq. 1., at $50 an acre? 15. How many rods of fence will enclose a farm 60 chains square? 16. In a storm at sea, a ship changed her longitude 423 geographic miles. How many degrees and minutes? GOVERNMENT LANDS. 425. Government Lands are usually surveyed into rectangular tracts, bounded by lines conforming to the cardinal points of the compass. A base line on a parallel of latitude, and a principal meridian intersecting it, are first established. Other parallel lines are then run six miles apart, each way. The tracts thus formed are called townships, and are designated by their number N. or S. of the base line. A range is a line of townships extending north and south of the base line, and is designated by its number E. or W. of the principal meridian. A township is divided into 36 equal squares, called sections, each 1 mile square, and containing 640 acres. The U. S. Land Office recognizes the following divisions of a section WRITTEN EXERCISES. 426. 1. If a township of land is equally divided among 288 families, what does each receive? What part of a section? 2. What number of rails will enclose a quarter section of land with a fence 6 rails high, and 3 lengths for every 2 rods; and what will be the cost of the rails, at $40 per thousand? 3. A man bought the S. of a section of land at $24 an acre, and afterward sold the E. of what he bought at $4.371 an acre. What was his gain on the part sold? 4. If I buy the N. E. and the E. of N. W. of a section of land, how many acres do I purchase? What part of a whole section? Locate the parts in a diagram. of Sect. 4, 5. A man bought of the Ill. Cent. R. R. Co., the S. Tp. 10 N., range 6 E., at $2 an A. He sold the E. of S. E. at $2.75 an A.; the N.W. of S. E. 1 at $34 an A.; and the N. of S. W. at $3.84 an A. How many A. has he left? What was his gain on the cost of the whole? Draw diagram. 6. From a section of land bought of the U. S. Government at sold the S. of S. W. at $2.50 an A. t at $1.75 an A.; the W. of S. W. 1 of N. E. at $3 an A. $1.25 an A., was N. E. of N. W. A.; and the W. A. remained, and of S. E. ; the at $2 an How many what was the gain, if the remainder sold at $21 an acre? Draw diagram and explain. |