62 DISPLACEMENT INTERFEROMETRY BY 



of the apparatus which is not adapted for brass rods as thick as this, as well 

 as the sectional irregularity of stress. If % be the true micrometer displace- 

 ment and %' that due to apparent yielding of the apparatus and sectional 

 discrepancies, and if C is a constant and io 12 the modulus of brass, we may 

 write (since A7V = # 



C/AN 



E=io lz or x = EAN/io l * = o. 00009 cm. per kg. 

 C/x 



while the yield, etc., of parts is thus equivalent to 0.00007 cm - P er kg. In any 

 case, therefore, the individual fringes would have to be used in a rigid appa- 

 ratus for rods of this relative thickness (0.375 cm.). But there is, of course, 

 no difficulty in inserting thin brass rods, taking advantage of the con- 

 venience of displacement interferometry. We may also conclude that the 

 insufficiency of the apparatus lies well within the smallest division (io~ 4 cm.) 

 of the micrometer. 



Further experiments were now made by loading the rod with 2.5 kg. and 

 making observations in triplets between 2.5 and 4.5 kg. The results came 

 out equally unsatisfactory, being 



io 5 AAYAP = 18 26 25 26 



io- n = 5.1 3.4 3-5 3-4 



Between these and the preceding results there may have been some dislo- 

 cation, such that a smaller part of the sectional area was strained in the latter 

 case, resulting in a decrease of E; but an error in reading of io~ 4 cm. would 

 also account for it. 



To test the preceding values experiments were now made on a hard drawn- 

 brass rod much thinner than the preceding. Its dimensions were 



L = 2.scm. 27 = 0. 205 cm. ^ = .033 cm. 2 



To accommodate this rod a sleeve was turned, telescoping into the larger 

 sheath b, figure 34, and holding the new brass rod within loosely. From trip- 

 lets of observations between loads of 2.5 and 4.5 kg. the values of E came out 

 as follows : 



io 5 A./V/AP = 149 161 123 120 

 io~ u E= 4.2 3.9 5.1 5.2 



As this is but half the usual modulus of brass, and as AN/AP is relatively 

 large, the discrepancy must be attributed to yielding or other dislocation 

 within the apparatus. 



Tests made for hysteresis showed no effect beyond the possible errors of 

 observation. The mean results obtained from rising and falling loads were, 

 for instance, 



AP=i.s 2.5 3.5 4-5 kg. 

 io 5 AAf=i37 128 121 114 

 io~ 12 = 0.33 0.44 0.52 



i-5 2.5 3.5 4-5 kg. 

 136 127 121 114 cm. 

 0.34 0.47 0.48 



