transition period of ten years in merchandising, leaving manufacturers to adopt the new measures as they please. It is certain that if given a footing metric standardization will approve itself and the existing measures will be abandoned without serious disarrangements or expenditures within a comparatively short time. The metric system is now used by most modern advanced peoples, ourselves and the British being the important exceptions. It gives easier and in practice more accurate measure than the Anglo-American traditional units of measure, as many an American soldier discovered during the war. But even if it were not more scientific, its adoption would be advisable for us because it is the standard in use in the markets which Americans hope to enter throughout the world. Our present system is a substantial handicap for our foreign trade, in South America for example. Differences in measure of length, capacity, and weight are annoying to our customers and a deterrent to the purchase of American goods. In proportion as the development of foreign trade is essential to our prosperity the need for accepting the international standard becomes urgent. This is important in peace. In case of war it is even more important. In the late conflict our system of measures was a serious obstacle to prompt and effective coöperation and exchange of resources with our allies. In consequence, men like General Pershing urge adoption of the metric standards. In fact, soldiers, scientists, educators, manufacturers, and commercial men of the highest standing are the emphatic advocates of international standardization upon the metric basis. But the reform is of importance to all of us in proportion as we are all affected, directly or indirectly, by the expansion and efficiency of our trade, both domestic and foreign. The reform has been on the way too long. Our foreign commerce cannot afford any handicap of which it can rid itself. It will take time to put the system in operation and make the necessary adjustments and it is therefore bad policy to postpone action longer. EXERCISES 1. In our reading we find mention of such units as: cubit, pace, , hand, ell. Find out what these units mean and how they originated. 2. Using the metric scale on your ruler, measure the length of the page of the textbook to the nearest tenth of a centimeter. 3. Change 268 mm. to centimeters; 3764 mm. to meters; 8 m. to decimeters; 15 m. to decimeters; 2486 mm. to centimeters. 4. The distance between two cities in France is 132 kilometers. How many miles are they apart? 5. The height of an airplane is 800 meters. Express this in feet. 6. The speed of an airplane is 98 kilometers an hour. Express the speed in miles. 7. By means of the compass determine to the nearest sixteenth of an inch the number of inches contained in 3 centimeters; 5 centimeters; 6 centimeters; 8 centimeters. Arrange your results in the form of a table. 8. The distance between two cities in France is 153 kilometers. Express this in miles. MEASURING LINE SEGMENTS WITH SQUARED PAPER 10. Squared paper. Fig. 31 represents a part of a sheet of squared paper. It is ruled with east-west and north-south lines. They divide the paper into large and small squares. By measuring with the ruler we find the sides of the large squares to be one FIG. 31 centimeter long, the sides of the small squares to be .2 of a centimeter. Thus the lines on the paper are divided according to the metric system. 11. How to measure with squared paper. Squared paper may be used to measure segments. It is con venient to select as a unit a segment 2 centimeters long, as AB (Fig. 32). A +1 В Then the length of CD is one-tenth of that of AB, or .1. GED With a little practice we shall be able to estimate the FEFF length of a segment which is shorter than CD. Thus EF is less than CD, but greater than one-half of CD. To determine FIG. 32 the length of EF with a fair degree of accuracy imagine CD divided into 10 equal parts. Each of these parts is one-tenth of CD, and therefore equal to one-hundredth of AB, or .01. Similarly, one-half of CD is equal to .5 of CD, or .05. By examining the segment EF we find that it is greater than .05, but less than .1. It seems to be about .08. Thus, we have seen that if AB=1, then CD=.1, and EF =.08 approximately. We shall now learn to measure segments, using a unit 2 cm. long. EXERCISES 1. Measure AB (Fig. 33). Directions: Open the compass placing the sharp points at A and B respectively. Place the metal point of the compass on one of the corners of a large square, such as C. With the pencil point make a mark on one of the heavy lines passing through C. This locates the point D. Then CD is of the same length as AB, and the length of AB may now be found by measuring CD. Show that CE is equal to 1. Show that EF is equal to 1. Hence CF is equal to 2. Show that FG is equal to .2. Fig. 33 Show that CD is approximately 2.28. After measuring a segment write the length on the segment, as shown in Fig. 33. Notice that in this result the first and second figures in the number 2.28 are exact, but that the last figure is uncertain. We say that AB has been measured to three figures or to two decimal places. 2. Show that the length of AB (Fig. 34) is 0.84, when measured to three figures. This result is stated in the form AB=0.84 approximately. 3. Draw a segment and measure it to three figures. State the result in the form shown in Exercise 2. 4. Measure to three fig Fig. 34 ures the segment AB (Fig. 35). Let one pupil write the results of several others on the blackboard. Let each pupil find the average of these results. Which results differ least from the average? Measure AC and BC (Fig. 35) each to three figures. 5. Measure to three figures each of the segments AB, BC, CD, and DA (Fig. 36). State the results as in Exercise 2. 6. Draw segments AC C and DB (Fig. 36), and measure each to three D figures. 7. Measure to three figures the distances from A to B (Fig. 37), from B A B to C, from B to D, from A to C. State the results as Fig. 36 in Exercise 2. 12. Symbols of equality and inequality. In $11 we used the statements is equal D C C to, is greater than, and is less than. In mathematics it is convenient and customary to use symbols to denote A B briefly such verbal state ments. Thus, Fig. 37 |