136 DISPLACEMENT INTERFEROMETRY APPLIED TO 



For the given needle p = o. 65/22 =0.03 gram per linear cm., /=n cm., 

 4.2 cm., m = 0.58 gram. Thus 



Hence the discrepancy due to the attraction of stem of needle actually amounts 

 to nearly 15 per cent of excess in 7. 



If now we write T=yT f , t = yt', and if T is the modulus of torsion and y' 

 the above approximate constant, 



T== 

 whence 



where y' = KAy. For K the more accurate mean value of 104 should be in- 

 serted, viz, K = io~ 7 X i .73 ; while i/T = o. 145 and Ay = 0.437 (means in preceding 

 paragraph) . Hence 





1+0.145 



This is within i per cent of a normal result, and in comparison with the orig- 

 inal errors supplies the strongest evidence in favor of the exhaustion method 

 pursued. But to rate the last result as to its trustworthiness, it is nevertheless 

 necessary to consult figure 168 or the corresponding table on the individual 

 values of Ay, which are quite variable. It seems, however, that in a series of 

 results extending over a long time interval the radiation error is eliminated in 

 the vacuum experiments. 



103. Contemporaneous experiments. To accentuate the importance of the 

 vacuum method, a series of parallel observations were made at the same time 

 with apparatus V and the old apparatus II (closed chamber of waxed wood) . 

 In the work with No. V, the glass case of No. I was again utilized in its old 

 position, but a new quartz fiber was inserted. This was, unfortunately, thicker 

 than was desirable. Tested with a small brass cylinder (mass 1.774 grams, 

 diameter 0.474 cm.) of moment of inertia N = 0.0498, the period was found to 

 be 7 = 2.51 seconds. Using the preceding equation, where now L = 378 cm., 

 is the scale-distance from needle and /= n cm. the semi-length of the latter, 

 M= 1,490 grams, ^ = 4.24 cm., 



9.87X0.0498 (4.24)' 



37 8XiiX(2.5i) 2 1490X0.59 



Hence a deflection of only 2 mm. was to be expected. 



The results in figure 169 are very much larger, the old straw-shafted needle 

 of apparatus No. / being used. In fact, in the experiments of the first three 

 days there was so much drift that they were thrown out. There is even an 



