Application of Interference Methods 55
a quantity requiring a good microscope to perceive; but such a quantity is very readily measured by the interferometer. It means a displacement amounting to several fringes, and this displacement may be measured to within a fiftieth of a fringe or less; so that the whole displacement may be measured to within a fraction of 1 per cent. Of course, with long bars the attainable degree of accuracy is far greater.
Figs. 50 and 51 represent a piece of apparatus designed by Professors Morley and Rogers,1 based on this principle, b and c (Fig.
50) are the two plane-parallel plates of the interferometer, and the two mirrors are at a and a'. Each mirror is divided into two halves as at an, so that a motion of each end of the bar to be tested can be observed. The jackets gg serve to keep the bars at any desired temperatures. One side of the instrument, as aa, being kept at a constant temperature, a change in the temperature of a'a' will cause the fringes to move, and from this motion of the fringes the change in length, which is caused by the change in temperature, can be very accurately determined. Fig. 51 shows a perspective view of the apparatus.
Evidently the same kind of instrument is suitable for experiments in elasticity, and one of these was shown in the last lecture, where a steel axle was twisted (c/. Figs. 30 and
i Morley and Rogers, Physical Review, Vol. IV (1896), pp. 1,100.
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.