5. The radius of a sphere is 18 inches. ference of a great circle? The surface? What is the circumThe volume? 6. What is the weight of an iron cannon-ball 12 inches in diameter, considering the weight of a cubic foot of water as 1,000 ounces, and considering iron 7.5 times as heavy as water? 7. Find the ratio between the volume of a sphere 4 inches in diameter, and that of a cylinder 4 inches in altitude, radius of base 4 inches. NOTE.- Indicate the volume of each, and cancel. 8. A man has a cubical block of hard wood, its side measuring one foot, which he wishes made into a sphere one foot in diameter. What decimal part of the block is cut away? The volume of the sphere is about what fraction of the volume. of the cube? ANNUAL INTEREST. 1171. Slate Problems. DETROIT, MICH., June 1, 1890. Four years after date, without days of grace, I promise to pay to the order of Daniel W. Lawler, Six Hundred Dollars, value received, with annual interest at six per cent. $600,00 GEORGE OXNARD. 1. Find the amount due June 1, 1894, no payments of principal or interest having been made. 1172. When the maker of a note fails to keep his contract to pay interest annually, the laws of some states, including Michigan, permit the collection of simple interest on the deferred payments of interest. Principal, Interest, 4 years, at 6%, 3 years' interest, at 6%, on the 1st year's interest, $36, $600.00 6.48 2. Find the amount due, at 5%, for 5 years, on a note for $1,200, annual interest being unpaid. 3. What is the amount of a note for $720, at 4 years, at 4%, annual interest unpaid after the first year? 4. The maker of a note for $900, with annual interest at 7%, makes the first and the second interest payments when due. How much will he owe at settlement, 6 years after the date of the note? 5. Find the difference between the amount due at 6% for 3 years on a note for $300, annual interest unpaid, and the amount of the same sum placed at compound interest for the same time at the same rate. 6. Find the amount due March 1, 1899, on a note for $500, dated March 1, 1893, with interest at 6%, annual interest unpaid after the third year. U.S. GOVERNMENT LANDS. 1173. In surveying government lands, a line is run east and west, called the base line, and one perpendicular to it, called the principal south of base line, in the second range east of the principal meridian). 1174. A township, which contains 36 square miles, is divided into sections one mile square, numbered as in the diagram, No. 1 being found at the northeast corner. Each section contains 640 acres. 1175. Sections are divided into half-sections (320 A.) and quarter-sections (160 A.), and the latter are subdivided into half quarter-sections (80 A.) and quarter quarter-sections (40 A.). 1176. Slate Problems. 1. Find the cost of the S.W. of the N. of sec. 13, T. 7 N., R. 4 E., at $1.87 per acre. 2. What will be the cost of fencing, at 75¢ per rod, the W. of the N.W. of sec. 36? 3. Mr. Thompson owns sec. 1, and his brother owns sec. 30 of the same township. What is the length of the shortest line. between the boundaries of the two farms? 4. A road runs east and west between townships 4 and 5, south. Another road runs north and south between R. 7 and 8 east. How far is it by road from the north-east corner of T. 5 S., R. 10 W., to the north-west corner of T. 7 N., R. 8 E.? 5. How many feet of boards, 6 inches wide, would be needed to build an open fence, 4 boards high, around the N. ✈ of the S.W. of sec. 16? 6. The owner of secs. 19 and 20 has sold the W. of N.W. of sec. 19; also the N., the N. of S.E. 4, and the S.E. of the S.E. of sec. 20. Draw a map of the land he still owns, and calculate its area. METRIC SYSTEM. 1177. The metric system, which is used in nearly all the countries of continental Europe, is based upon the meter. The length of the meter is one ten-millionth part of the length of the meridian from the equator to the poles — about 39.37 inches. 1178. The subdivisions of the meter are denoted by the Latin prefixes milli (1), centi (1), deci (). For the multiples, the Greek prefixes deka (10), hecto (100), kilo (1,000), and myria (10,000) are used. 1179. It will be noticed, in the table below, that small letters are used for the abbreviations of the Latin prefixes of the subdivisions, and capital letters for the Greek prefixes of the multiples. The following is the table of 1180. Measures of Length. 10 millimeters (mm.) 10 centimeters 10 decimeters 10 meters 10 dekameters 10 kilometers 1 centimeter (cm.) 1 decimeter (dm.) 1 dekameter (Dm.) 1181. The units of this table in common use are the centimeter, the meter, and the kilometer. 1182. A person who wishes to buy 124 meters of cloth, would not ask for 1 hectometer 2 dekameters 4 meters, any more than a New York merchant would tell a person who owes him $38.75 that his bill is 3 eagles 8 dollars 7 dimes 5 cents. 1183. Long distances are expressed in kilometers. The thickness of wire is given in millimeters. 1184. Problems. 1. What will be the cost in francs of 380 m. 75 of dress goods at 2 f. 60 per meter? (380.75 meters @ 2.60 francs.) 2. How many square meters in a piece of carpet 26 m. 50 long, 85 cm. wide? 3. How many square meters in a circle whose diameter is 15 meters? 4. An are is a surface 10 meters long, 10 meters wide. How many ares in a field 135 meters long, 69 meters wide? 5. Find the area in ares of a right-angl base is 245 meters, hypotenuse 875 meters. triangle whose |