8I> Light Waves and Their Uses upon the supposition that our standard is absolutely correct. But the length of the standard decimeter itself has to be determined by means of microscopic measurements, and since the temperature plays a considerable role, it is difficult to avoid errors very much larger than those due to the microscope. If we combine all these errors, we can probably attain at best an accuracy in all measurements involved of the order of one part in 100,000. Finally, we have to measure the angle ACB, and it is very much more difficult to measure angles than lengths. All these errors—the measurement of the angle, the error in the determination of the distance AC, that in the comparison of the intermediate standard which we use, and that in the distribution of these spaces—may combine in such a way that the total error may amount to very much more than one part in 100,000; it may be one in 20,000 or 30,000. This degree of accuracy, however, is greater than that attained by either of the other two methods w The first of these proposed standards was the length of the pendulum which vibrates seconds at Paris. Such a pendulum may be obtained by suspending from a knife edge a steel rod upon which a large lens-shaped brass bob is fastened. The steel rod carries another knife edge near the other end, so that the pendulum can be turned over so as to be suspended from this low^er knife edge. The pendulum must then be adjusted so that its time of vibration is exactly the same in either position, which can bo done with but little difficulty. When such a pendulum vibrates seconds in either position, the distance between the knife edges is the length of a simple seconds pendulum. We may also construct a simple pendulum by-fastening a sphere of metal to the end of a thin, fine wire. It is then necessary to measure the time of oscillation, and the distance | LiCxHT Waves as Standards of Length 87 between the point of suspension and the center of gravity of the spherical bob. This distance can be measured to a very fair degree of accuracy. Unfortunately the different observations vary among themselves by quantities even greater than the errors of the diffraction method. The second of these proposed standards was the circumference of the earth measured along a meridian, as it was believed that this distance is probably invariable. There are, however, certain variations in the circumference of the earth, for we know that the earth must be gradually cooling and contracting. The change thus produced is probably exceedingly small, so that the errors in measuring this circumference would not be due so much to this cause as to others inherent to the method of measuring the distance itself. For suppose we determine the latitude of two places, one 45° north of the equator and one 45° south. The difference in latitude of these places can be determined with astronomical precision. The distance between the places is one-fourth of the entire circumference of the earth. This distance must be measured by a system of tri-angulation— a process which is enormously expensive and requires considerable time and labor; and it is found that the results of these measurements vary among themselves by a quantity even greater than do those reached with the pendulum. So that none of these three methods is capable of furnishing an absolute standard of length. While it was intended that one meter should be the one forty-millionth of the earth’s circumference, in consequence of these variations it was decided that the standard meter should be defined as the arbitrary distance between two lines ruled on a metal bar a little over a meter long, made of an alloy of platinum and irridium. It was made of these two substances principally on account of hardness and durability. In order to bring the metal as nearly as possible |