Engineers have adopted the decimal plan in connection with the English system by using scales and steel tapes with inches divided latadata.data.datadadadadadadadadad Fig. 2. Comparison between Centimeter and Inch Scales. into tenths. They also use Surveyors' long measure in making land surveys. (See Appendix.) 44. Square Measure. A surface has two dimensions, length and breadth. The area of a surface is defined as the number of units of surface it contains, and is equal to the product of its two dimensions expressed in the same linear units. The unit of surface is a square, which is a plane figure bounded by four equal sides and having four right angles, Fig. 3. A square, each side of which is one inch in length, is called a square inch. Squares formed with sides of 1 foot, 1 meter, 1 mile, etc., are called respectively, 1 square foot, 1 square meter, 1 square mile, etc. Fig. 3. A Foot Square. A distinction should be clearly made between the terms square Fig. 4. A 2-Foot foot and foot square or between square mile and mile square. If Fig. 3 may be supposed to represent a square 1 foot on a side, it may be called either 1 sq. ft. or 1 ft. square. On the other hand, Fig. 4 measures two feet on a side and hence it is 2 ft. square, but, as may readily be seen, it has not 2 sq. ft. but 4 sq. ft. of area. Therefore a cattle ranch covering an area 3 miles square has really 9 square miles of surface. Square measure, therefore, involves units whose names are the same as those used in linear measure with the term square in front of each. The English system has an extra unit used in measurements of land, which is called the acre, equal to the area of a square about 209 ft. on a side. In the metric system, the square centimeter and square meter— the latter being about 20% larger than the English square yard— are used for small areas. The larger surfaces are measured in ares and hectares, the former being 10 meters square (acre) and the latter equal to 100 ares or 2 acres. 45. Cubic Measure. The volume of any solid is obtained by cubic measure. The unit of volume is a cube, Fig. 5, each edge of which is some unit of length; for example, the cubic inch, cubic centimeter, cubic foot are common units of volume. The volume of a body of rectangular figure is Fig. 5. A 1-Foot equal to the product of its three dimensions, each expressed in the same linear unit. Cube. In the case of an irregular body, however, the volume although still expressed in cubic measure, must be measured by displacement of water. Liquids are classed as irregular bodies but in the English system are measured by a different unit, giving rise to the classification as given in Sec. 46. In Sec. 44 it was proved that the area of a square surface increases as the second power of the side of the square; i. e., a surface 2 feet square was found to cover 2 X 2 or 4 sq. ft. of area. In the same manner, Figs. 5 and 6 show that a 2-foot cube has 2 X 2 X 2 or 8 cubic feet of volume; i. e., the volume of a cube increases as the third power of the length of the side. Fig. 6. A 2-Foot Cube. NOTE. The use of the multiplication sign in finding the volume has given rise to its use in indicating the dimensions of surfaces and solids. Thus a 2 X 12 joist means a joist 2 inches thick and 12 inches wide; or a room 15' x 12' x 10' means a room 15 feet long, 12 feet wide, and 10 feet high. The units of cubic measure in the English system are the same as those in long measure with the prefix cubic; for example, cubic inch, cubic yard. The cord (128 cu. ft.) for wood and the perch (24} cu. ft.) for stone or masonry are also used. In the metric system, the cubic centimeter and cubic meter are common, the latter being 30% larger than the cubic yard and used in place of it in measuring earth and rock excavations, as well as in measuring timber, stone, etc., where the English cord and perch are used. MEASURES OF CAPACITY 46. Capacity signifies the extent of volume or space. In the English system a lack of unity exists in the measurement of capacity Dry Quart Liter Liquid Quart because of the use of several kinds of measure. For example, the common liquid measure and the apothecaries' fluid measure are used for liquids, and still another kind called dry measure for grains, vegetables, etc. This complication is avoided in the metric system by having the same units for all measurements of capacity. 47. Liquid Measure. Liquid measure is used in measuring liquids and in estimating the capacity of cisterns, reservoirs, etc. In the English system, the most common liquid In the metric system the unit is the liter, which is 5% larger than the liquid Fig. 7. Comparison of Liter, Dry quart and 10% smaller than the dry Quart, and Liquid Quart. (actual size) quart, Fig. 7. Note the following: 1000 cubic centimeters (c.c.) = 1 liter (1.) = 1 hectoliter. 48. Dry Measure. Dry measure is used in measuring dry substances such as grain, vegetables, salt, etc. In the English system the quart, peck, and bushel are used. In the metric system the hectoliter serves the same purpose as the United States bushel and is equal to about 3 bushels. The common units in dry measure are: 8 quarts* = 1 peck (pk.) 4 pecks = 1 bushel (bu.) MEASURES OF WEIGHT 49. Weight is a measure of the force of the earth's attraction for a body. In the English system several units of weight are used, viz, the standard Troy weight, which is used in weighing gold, silver, and jewels; the more common avoirdupois weight, used in general trade; and the apothecaries' weight, used by druggists and physicians. The student is referred to the Appendix for the Troy and apothecaries' measure. 50. Avoirdupois Weight. Avoirdupois weight is used to measure the weight of objects in general trade. The most useful units are as follows: The ton just given is the short ton and is more generally used than the gross ton which is equal to 2,240 lbs. This latter unit is now mainly used in the United States custom house and in weighing coarser articles, such as coal at the mines. 51. Metric Weight. In the metric system the unit of weight is the gram which is equal to the weight of 1 cubic centimeter of pure water at a temperature of 38° F. The following are the most impor *The dry quart is about 15% larger than the liquid quart, Fig. 7. 30 grams approximately equal one ounce, and one kilogram equals 2.2 pounds, hence the gram is used wherever the ounce, pennyweight, etc., would be used, while the kilo and half kilo replace the pound. The metric ton serves the same purpose as the short or gross tons. MEASURE OF TIME 52. Time is measured in the same manner and by the same unit throughout the civilized world, the unit being the mean solar day. This mean solar day is obtained by taking the average of all of the days of the year, a day being measured from noon of one day to noon of the next day. This process is necessary because the position of the earth relative to the sun changes as the year advances, and, therefore, no one day can be taken as the true day. Evidently the time when it is noon, i. e., the instant the sun is passing the north and south line, will be different as we pass from east to west. London has her noon five hours earlier than New York. This has led to the adoption in the United States of four standard times, the Eastern, Central, Western, and Pacific, each one hour later than the preceding. Therefore, when it is noon in Washington it is 11 o'clock For example, |