Light Waves as Standards of Length 85 itself, so that there can be no error in determining the number of rulings. This number is usually very large, between 50,000 and 100,000. Since this number of lines is accurately known, we know also the number of spaces in the whole distance A C. This distance can be measured by comparing the two end rulings with an intermediate standard of length, which ^ has been compared with the standard yard or the standard meter with as high a degree of accuracy as is possible in mechanical measurements. If, now, we know also the angle ACB, we can calculate the distance AB; and since we know the number of waves in this distance, which is the same as the number of apertures, we have the means of measuring the length of one wave. It will be observed, in making such an absolute determination of wave length by this means, that we have to depend entirely upon the accuracy of the distance between the lines on the grating—a distance which is measured by a screw advancing through a small proportion of its circumference for each line ruled. If the intervals between the lines are not exactly equal, then there will be an error introduced, notwithstanding every precaution taken, which it is extremely difficult, if not impossible, to correct. Another error may be introduced in making the comparison of the two extreme lines on the grating with the standard decimeter. This error may, roughly, be said to amount to something like one-half a micron, /. e., one-lialf of one-thousandth of a millimeter. If, then, the entire length of the ruling is fifty millimeters, and the error, say, one ten-thousandth of a millimeter, the wave length may be measured to within one part in 500,000. This is the error | 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 |