72 



DISPLACEMENT INTERFEROMETRY. 



an even more sensitive micrometer, with the advantage that the telescope 

 may be shifted, there being no fiducial line within it. If Ae refers to dis- 

 placement of fringes measured along this scale, the standardization showed 

 that io 3 AW/Ae = 101. Triplets for the loads 1-2-1 kg. gave a mean value of 

 Ae/AP = o.25 cm., whence io 4 A7VYAP = 2.5i cm. and = 0.39 Xio~ 12 as above. 

 The change is cyclic, the graphs are curved. The mean E, even above 3 kg. 

 of load, will not exceed o.3X io 12 . Triplets gave in succession 



P=I-2-I 



i o 3 A/AP = 27 

 EXio 12 /AP= 0.20 



2-3 2 



17 

 0.29 



3-4-3 



13 

 0.38 



4-5-4 kg. 



9 cm. 



0.54 cm. 



which is no marked improvement over what has preceded. 



There seems to be little hope of further increasing the effective rigidity 

 of the apparatus. Measurements for E will therefore have to be made differ- 

 entially. For this purpose the constants of the apparatus (here with elas- 

 tic brass bifilar) are to be determined by a relatively thick steel rod, as has 

 just been done. An example of this has been put 

 in figure 51, a, showing the behavior of a fresh, 

 hard-rubber rod treated in successive cycles of 

 loads between i and 5 kg. Hysteresis and viscous 

 deformations appear very clearly, as usual. The 

 mean moduli for the ascending branches will not 

 much exceed 2Xio 10 , and in triplet observations 

 they ran from this to about 6Xio 10 for loads up 

 to about 50 kg. per cm. 2 , also in the manner found 

 above. As a contrast to these results the behavior 

 of the steel rod of the same dimensions (zL= 5 cm., 

 2r = o.37 cm., nearly), for which data have just 

 been given, is also inserted in the lower curve b of the same figure. Both 

 curves are cyclic, but on an enormously different scale, even though the true 

 steel moduli can not be approached to more than one-quarter. The true 

 steel line is shown at c. We admit that the hysteresis in curve 6 is possibly 

 in the apparatus, which is a compound elastic body; but it is hardly plausible 

 that the hysteresis of curve a can be similarly explained away. The apparatus 

 discrepancy is given in b. 



1 2, 



