78 DISPLACEMENT INTERFEROMETRY BY 



filament (r=io~ 3 cm.) should still hold 4.5 grams, or much more than the 

 weight of the above needle (within 2 grams.) 



As the moment of inertia of the needle is2Xo.75Xi3 2 = 253, and if the mod- 

 ulus of torsion be computed from the slide modulus w = 5Xio n , the periods 

 would be as given above, the second being nearly 8 minutes. The period 

 of the above needle was estimated at about 2 minutes. This would give a 

 modulus of torsion about 0.7 and make AN = 6fXio~ 5 cm. per attracting 

 kilogram; i. e., about 17 achromatic fringes per kilogram were to be expected. 



Having mounted the needle as stated, the fringes were found without 

 much difficulty and the image of the wide slit (i. e., the reflected beam seen 

 in the telescope) was almost quite stationary, the light needle being thus 

 adequately damped. But within this virtually stationary slit-image, the 

 fringes (preferably made horizontal) continually wandered up and down, 

 showing that micrometric vibration had not been eliminated. The experi- 

 ment is a very impressive one, but as the drift is still much larger than the 

 17 fringes per kilogram to be anticipated, any attempt at measurement is 

 again idle. Whether this drift is due to temperature or to the tremors of 

 the laboratory would be difficult to state. Cutting down the intensity 

 of the interfering rays (which need not be strong) made no difference. 



When the case is open above, there is no difficulty in finding the position 

 of equilibrum of the needle symmetrically to the glass walls of the case. This 

 position is assured by the parallelism of the images of the needle in both faces 

 with the needle itself, and their distance from it. When, however, the 

 wooden boards are inserted, the needle does not seem to be in stable equi- 

 librium in the symmetrical position. It tends to move either into one or the 

 other extreme of oblique positions at which the balls touch the plates of the 

 case. Believing the phenomenon to be electrical, I placed a radium tube in 

 the vicinity of the case for some time, but this made no difference. Damp 

 cloth did not change the result. This was particularly true in the earlier 

 experiment, where >^-inch plates were used for the case in the absence 

 of thin plates, and in which one plate was thicker than the other. One 

 would thus be inclined to interpret the instability as possibly due to the 

 gravitational attraction of the residual disk. Considering the case as that 

 of a point mass confronting an infinite disk, the potential would be y(Cd=x) 

 27ro- and the force 2^70- per gram attracted, which is a little above the mass 

 of the ball. Thus, if <r = Pt (a being the density and t = 0.1 cm. the residual 

 thickness of plate corresponding to the surface density a} , the force should be 



Since the lever arm is 13 cm., this makes the torque i-7X io" 6 dyne cm. ; and 

 if the modulus of torsion of the quartz fiber is 0.7, as estimated above, the 

 deflection should be 



0=i.7Xio~ 6 /-7 = 2 -4Xicr 6 radian 



i. e., about half a second of arc and therefore quite ineffective so far as 

 instability is concerned. Neither does it seem plausible that the needle 



