4. How high must a box be made, to contain 24 cu. ft., the length of the box being 4 ft. and its width 3 ft.? Ans. 2 ft. 5. How high must it be, if its length is 8 ft. and its breadth 3 ft.? 6. If its height is 22 feet, what must be the area of its base? 7. How long must a pile of wood be, which is 4 ft. wide, 3 ft. 6 in. high, to contain a cord? 8. There are 144 square inches on one side of a block containing a cubic foot; what is the length of the edge of the block? 9. There being 112 cubic feet in a stick of timber which is 12 feet square at the end, what is the length? Ans. 50 ft. MEASURES OF CAPACITY. 180. LIQUID MEASURE. The denominations are gallons, quarts, pints, and gills. TABLE. 252 sho.. 4 gills (gi.) = 1 pint, 2 pts. 4 qts. =1 quart, =1 gallon, marked pt. NOTE.-The denominations tierce, barrel, hogshead, pipe, butt, and ton, are sometimes used, but their size is variable. Barrels generally contain 31 or 32 gall.; hogsheads, 63 gall. Casks are generally gauged and marked accordingly. They are called hogsheads, pipes, butts, or tuns, without distinction. EXAMPLES. 1. Reduce 3 gall. 3 qt. 1 pt. 2 gi. to gills. 2. Reduce 5 gall. 1 qt. 0 pt. 3 gi. tọ gills. 3. Reduce 23684 gills to gallons. 4. Reduce 984324 gills to hogsheads. Ans. 126 gi. Ans. 740 gall. 1 pt 5. What will 27 gall. 3 qt. of milk cost at 4 cents per qt.? 181. DRY MEASURE. The denominations are bushels, pecks, quarts, pints, and gills. 9.309+ gal. in a bu. EXAMPLES. 1. Reduce 5 bu. 3 pk. 3 qt. 1 pt. to pints. 2. Reduce 2641 pt. to bu., etc. Ans. 375 pt. Ans. 41 bu.1 pk. 0 qt. 1 pt. 3. Reduce 10 bu. 1 pk. 2 qt. 0 pt. 3 gi. to gills. 4. Reduce 8765432 gi. to bu., etc. 5. What will 4 bu. 1 pk. 2 qt. of cherries cost at 8 cts. per quart? 6. Sold 3 bu. 3 pk. 5 qt. of peaches for $7.50; what did I receive per quart? 182. COMPARISON OF LIQUID AND DRY MEASURES. Liq. Meas. Dry Meas. Cu. in. 1. I have a dish that contains 2 cu. ft.; how many quarts of blackberries will it hold? 2. How many quarts of water? Ans. 51. Ans. 599 qt. 3. How many gallons of water will a cistern hold that is 3 ft. long, 3 ft. wide, and 24 ft. high? 4. How many bushels of apples can be put into a bin 8 ft. long, 3 ft. 2 in. wide, and 2 ft. high? CIRCULAR OR ANGULAR MEASURE. 183. This measure is used principally in astronomy, gengraphy, navigation, and surveying. Fig. 1. 184. A Circle is a plane surface bounded by Circumference. a line, every part of which is equally distant from a point within called the centre. Arc.. Circle. Fig. 2. Radius. Diameter. 185. The bounding line is called the Circumference of the circle. Any part of the circumference is called an Arc. 186. A straight line passing from the centre of the circle to the circumference, is called a Radius (plural, radii). 187. A straight line passing from one point in the circumference, through the centre, to an opposite point, is called a Diameter. 188. The circumference of any circle is supposed to be divided into 360 equal parts, called Degrees, each degree into 60 Minutes, and each minute into 60 Seconds. 189. A Semi-circumference is half a circumference, a Quadrant one fourth, and a Sextant one sixth. A Sign, used only in astronomy, equals 30°. Fig. 3. 190. An Angle is the opening between two lines which meet each other. The point of meeting is called the Vertex of the angle. The angle in the annexed figure may be read "the angle a bc," or simply "the angle b." An angle is measured by that part of the circumference of a circle included between its sides, the centre of the circle being at the vertex of the angle; thus, Fig. 4. h e C m f In fig. 4, the angle def is measured by the arc mn; that is, if the arc mn contains 70°, the angle def is an angle of 70°. 191. An angle which includes 90°, or of a circumference, is a Right Angle, the sides of which are said to be perpendicular to each other; in fig. 4, the angle g eh is a right angle. An angle greater than a right angle is an Obtuse angle. An angle less than a right angle is an Acute angle; he d is an acute angle and ged is an obtuse angle. NOTE. As arcs are measurements of angles, the table for angular measure is the same as the table for circular measure. 192. EXAMPLES. 1. Reduce 148° 54′ 18" to seconds. 2. Reduce 354° 0′ 16′′ to seconds. Ans. 536058 A cicle has 21600 0212960081 3. Reduce 53684" to numbers of higher denominations. 4. Reduce 359° 59′ 59′′ to seconds. 5. Reduce 1 quadrant to seconds. Ans. 14° 54' 44" 8. Reduce 35467′′ to numbers of higher denominations. TIME MEASURE. 193. The length of an Astronomical or Sidereal Day is the time the earth takes to turn once upon its axis; the length of a Solar Day is the time the earth takes to turn so as to bring the sun to the same meridian again. The solar day is divided into 24 hours, each hour into 60 minutes, and each min. ute into 60 seconds. The denominations of time are centuries, years, months, weeks, days, hours, minutes and seconds. 194. The time which the earth takes to revolve around the sun is 365 d. 5 h. 48 m. 50 s. nearly. The common year (365 days) thus loses nearly one day in 4 years. Hence the leap year of 366 days was established, which occurs once in 4 years. But this adds too much by about 11 m. a year, which in 100 years amounts to nearly 183 h. To balance this error, every 100th year is not regarded as a leap year. But this drops too much by a little more than 53 h., which in 4 centuries amounts to nearly 1 d. Hence every four-hundredth year is a leap year. This leaves an error which is less than 1 d. in 3600 years. Hence the RULE for ascertaining when any year is a leap year. When the number denoting the year is divisible by 4, and not by 100, it is a leap year; and any year that is divisible by 400 is a leap year. 195. A year is divided into four seasons, of three calendar months each, and commences with January, the second winter month. The succession of the seasons, quarters and months, and the number of days in each month, are shown by the following diagram: NOTE. In the following examples, common and leap years are under stood unless the Julian is specified. Leap year. 29 d. |