Michelson A. A. Light waves and their uses (1903)

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Light Waves and Their Uses

37, p. 39). If we measure the couple producing the twist, and the number of fringes which pass by, we can find the corresponding angle of twist, and a simple calculation gives us the measure of our coefficient of rigidity.

The interferometer in this second form has also been

applied to the balance. Fig. 52 shows such an arrangement. The mirrors of the interferometer are on the upright metal plate, the two movable mirrors being fastened to the ends of the arms of a balance which is just visible within the horizontal box. The object of this particular experiment was to determine the constant of gravitation; in other words, to find the amount of attraction which a sphere of lead exerted on a small sphere hung on an arm of the balance. The amount of this attraction, when the two spheres are as close together as possible, is proportional to the diameter of the large sphere, which was something like eight inches. The attraction on the small ball on the end of the balance was thus the same fraction of its weight as the diameter of the large ball was of the diameter of the earth, ?. r., something like one twenty-millionth.1 So the force to be measured was one twenty-millionth of the weight

• This ratio takes into account the increased attraction duo to the greater density of the load sphere.

Application of Interference Methods 57

of this small ball. This force is so exceedingly small that it is difficult to measure it by an ordinary balance, even if the microscope is employed. But by the interference method the approach of the large ball to the small one produced a displacement of seven whole fringes. The number of fringes can be determined to something of the order of one-twentieth of the width of one fringe.

We therefore have with this instrument the means of measuring the gravitation constant, and thence the mass of the whole earth, to within about T* T of the whole. By still more sensitive adjustment it would be possible to exceed this degree of accuracy.

An instrument in which the interferometer is used for testing the accuracy of a screw is shown in Fig.

53. The screw which was to be tested by this device was intended to be used in a ruling engine for the manufacture of ditfraction gratings. Now, it is necessary, in ruling gratings, to make the distance between the lines the same to within a small fraction of a micron. The error in the position of any of the lines must be less than a ten-millionth part of an inch. Ordinarily a screw from the best machinists has errors a thousand times as great. The screw must then be tested and corrected. The testing is often done with the microscope, but here the microscope is replaced by the inter

FIG. 52