If AB and BD are each divided into ten equal parts and lines drawn parallel to AB and BD, as shown, the unit area is divided into 100 equal squares, each of which is a square decimetre. FIG. 4.-Representing a square metre divided into 10 decimetres. Scale 20 In scientific work the centimetre is the unit of length usually selected, and the unit of area is then one square centimetre. British Measures of Area or Surface. [Unit area=1 square yard. Larger and smaller units obtained by multiplying by 4840 and dividing by 27 and 3888.] 144 square inches =1 square foot. 1296 square inches or 9 sq. ft. 1 square yard. 640 acres Metric Measures of Area. =1 acre. =1 square mile. Units of Volume.-In the British system an arbitrary unit, the gallon, is the standard unit of volume, and is defined as the volume occupied by 10 lbs. of pure water at a temperature of 62° F. A larger unit is the capacity of a cube the base of which, ABCD (Fig. 5), is a square the side of which is 1 foot and the height BE also 1 foot. The volume of such a cube is 1 cubic foot. As the base contains 144 square inches, the volume is 1728 cubic inches. Ꭰ A B As already mentioned in the case of the unit of length, with one or two exceptions, bodies expand by heat and contract when cooled; hence the temperature of the water must be given. The weight of a cubic foot of water depends upon its tempera FIG. 5.-Cubic foot. ture. Thus at 32° F. the weight is 62-418 lbs., at 62° F. the weight is 62.355 lbs., and at 212° is 59-64 lbs. A good average value is 62.3 lbs. For convenience in calculations a cubic foot is sometimes taken to be 6 gallons, its weight 1000 oz., or 62.5 lbs. Hence the weight of a pint is about 14 lbs. When the unit of length is one inch, the unit of volume is one cubic inch. In Fig. 6 a cubic yard is shown. If ABCD represent a square having its edge 1 yard, the area of the square is 9 square feet. If the vertical sides, one of which is shown at DE, be divided into three equal parts, and the remaining lines be drawn parallel to DE and the base respectively. Then, as will be seen from the figure, there are nine perpendicular rows of small cubes, the sides being 1 foot in length, area of base 1 square foot, and volume 1 cubic foot. Also there are three of these cubes in each row, making in all 3 x9=27. Thus 1 cubic yard = 27 cubic feet, i.e. 3x3x3=27, and the weight of a cubic yard of pure water would be 27 × 62.3 lbs. = 1682.1 lbs. In this example and also in considering the weight of a gallon, A B E FIG. 6. Showing a cubic yard and a cubic foot. the student should notice that the specification "pure" water is necessary, for if the water contains matter either in solution or mixed with it, its weight would be altered. Thus, the weight of a cubic foot of salt water is 64 lbs., and the weight of a gallon of muddy water may be 11 or 12 lbs. instead of 10 lbs. FIG. 7.-Cubic decimetre (1000 cubic centimetres) holds 1 kilogram or 1000 grams (1 litre) of water at 4° C. Metric System.-In the Metric System the unit of volume is the volume occupied by a Kilogram of pure water at 4° C. and is called a Litre. It is very nearly a cubic decimetre or 1000 cubic centimetres (Fig. 7), and is equal to 1.76 English pints. We have found that the unit of area is, for convenience, taken to be one square centimetre, and the corresponding unit of volume will be the cubic centimetre (c.c.). MEASURES OF VOLUME OR CAPACITY. British. Unit Volume is the volume occupied by a gallon, or 10 lbs. of water at a temperature of 62° F. One fourth part of a gallon is a quart, and an eighth part of a gallon is a pint. 1728 cubic inches = 1 cubic foot. 27 cubic feet = 1 cubic yard. Metric. Unit Volume. The Litre is the volume occupied by 1 Kilogram of water at 4° C. 1000 cubic centimetres=1 litre. The standard temperature 4° C. is not very convenient, and the temperature 62° F., or 163 C., may be used instead; a suitable correction for expansion must be made if necessary. Units of Mass and Weight.-The mass of a body is the quantity of matter it contains. The British Unit of Mass is the Pound Avoirdupois. The mass of a body is ascertained by comparing it with the Standard. The British Pound is defined as the quantity of matter in a platinum cylinder (Fig. 8) deposited in the offices of the Board of Trade. Accurate copies of the Standard, as well as multiples and sub-multiples of it, are to be found in various parts of the country. The sub-multiples of the unit are obtained by dividing the unit into sixteen equal parts, each called an ounce. A smaller measure of weight is obtained by dividing the pound avoirdupois into 7000 equal parts, each of which is called a grain. Thus, one-sixteenth part of the unit is an ounce, and one seventhousandth part a grain. FIG. 8.-Imperial Standard Pound. From Aldous's Course of Physics (Macmillan). By the operation of weighing very accurate copies of the standard can be made. The choice of platinum as a suitable material for the standard is made on account of its being a substance not liable to be affected by atmospheric influences. The Metric Unit of Mass is the Kilogram. The metric standard of mass is conveniently obtained from the corresponding unit of volume. The kilogram, for such the standard is called, was originally defined to be the quantity of matter in a cubic decimetre, or litre, of pure water, at its temperature of maximum density 4° C. It is now defined to be the mass of a platinum cylinder (Fig. 9) deposited in the French Archives. For all practical purposes a litre of pure water at 4° C. weighs 1 kilogram or 1000 grams. Hence, since, as has been seen, the litre contains 1000 cubic centimetres (c.c.) a gram is the weight of a cubic centimetre of water at a temperature of 4° C. The |