80 DISPLACEMENT INTERFEROMETRY BY 



in the micrometer. The displacement of mirrors is now virtually parallel 

 to the rays and no difficulty in finding the fringes need occur. Naturally the 

 mirrors must be good, there being now four additional reflections in each 

 ray; and this V-micrometer must be accurately adjusted for parallelism of 

 mirrors. 



With the fringes found, there is now no difficulty in showing the attraction 

 of gravitation. In fact, an iron brick moved on a small truck, near the shot 

 at one end of the needle, grips these balls very much like a magnet acting 

 on the pole of a magnetic needle. By approaching and withdrawing the iron 

 mass on one side, the fringes could be put in regular and uniform vibration 

 over enormous (relatively speaking) arcs as measured by fringes. Thus 

 in an incidental experiment the micrometer reading was 0.255 cm - w ith an 

 iron mass near and slow vibration and 0.026 cm. (eventually) with iron 

 mass remote. 



Throughout the whole of the experiment the fringes were under the perfect 

 control of the micrometer. 



A more systematic experiment was then made by testing the attraction 

 of a lead ball 5.43 cm. in diameter and weighing about M = Q5o grams 

 for the shot (at the end of the needle) weighing w = o.6i gram. M was 

 moved on a circular track with stops to a distance of ^ = 4.24 cm. (between 

 centers of balls) from the ball of the needle, alternately. The position of 

 the large ball M was reversed every 10 minutes, but the period of the air- 

 damped needle can not have been less than 18 minutes. The case is, then, 

 that of a forced vibration under constant force and a large logarithmic decre- 

 ment. The observations are given in table 4, the reading being made 

 every minute, beginning with the equilibrium position (M in the neu- 

 tral position). If these data of the displacement x of the mass m are con- 

 structed graphically it will be seen that the motion of the needle is nearly 

 dead-beat. The successive arcs of vibration increase, and from the limiting 

 distance between elongations the attracting force could be computed, if the 

 torsion coefficient of the quartz fiber and the logarithmic decrement were 

 known. The limiting arc was not reached, owing to incidental reasons. 

 From static experiments made during hour intervals this elongation was 

 found to be about 0.116 cm., or a departure of the shot in at the end of the 

 needle from its position of equilibrium of 0.058 cm. in response to the attrac- 

 tion of M. If I is the semi-length of the needle (between centers of shots), 

 the micrometer displacement A/V and the displacement A# of the mass m 

 are given by the equation 



cos i/b = 0.89 AAT 



where b is the breadth of the ray parallelogram and * = 45 the angle of in- 

 cidence of the interferometer. Thus the micrometer displacement is of the 

 same order as the displacement of m, and if the latter is 0.116 cm., we should 

 have 



o.i cm. 



