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 AC. This distance can be measured by comparing the two end rulings with an intermediateFIG. 69 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, i. e., one-half 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