56 DISPLACEMENT INTERFEROMETRY BY 



In all this work the initial loads of i kg. each were not removed. The elon- 

 gations between i kg. and 4 kg. were consistent, though naturally with definite 

 evidence of apparent hysteresis. For instance, on the last series with brass 

 caps the individual contractions were 



AP= 4 3 212 3 4 kg. 



io 4 A/V=i2o 94 55 o 40 78 141 cm. 



and in the last series with the mushroom-shaped solid, 



AP = 4 3 2 i 2 3 4 kg. 

 89 68 38 o 34 64 89 cm. 



As the values AAf are proportional to the decrements of length, the rod is 

 shorter on unloading and longer on loading, c&t. par. In other words, the 

 hard-rubber rod is influenced by its immediately antecedent history. The 

 curved lines obtained may, however, also be influenced by gradual dislo- 

 cation or decreased firmness in the seating of the rod. Thus the modulus 

 in the last example decrease from about io g E = g between the two highest 

 loads (3 to 4 kg.) to id 9 E = 6 between the two lowest loads (i to 2 kg.). 

 Of the two the former (high loads) is unquestionably the more trustworthy 

 and least influenced by imperfections of apparatus. 



Results of the same nature were obtained for brass, though here, from the 

 much greater rigidity, the effect of dislocation at small loads is much more 

 apparent. The first experiments were made with a relatively thick rod, of 

 the dimension L = 2.2 cm., A =0.70 cm. 2 , for which E = 4.5Xio 10 was ob- 

 tained. This is enormously too low and the result is a mere indication of 

 the yield of the apparatus or inequalities of stress. The rod was now turned 

 down on the lathe to a mushroom-shaped solid (fig. 33), the dimensions 

 L = 2.i cm., A=o.ii3 cm. 2 . With this the values EXio n = i, 2, 5, were 

 found, according as the rod was unloaded or loaded from 4 to 3 kilo- 

 grams. Clearly this is a case of dislocation of parts of the adjustment. The 

 rod was then further diminished to diameter of but 0.2 cm., so that L= 1.8 

 cm. and ^=0.035 cm. 2 now obtained. With this, for the highest loads, 

 values =i.4Xio n followed under like conditions. This is no improve- 

 ment and shows that the apparatus yields seriously for moduli as large as 

 that of brass (say io 12 ). Thus in the series with largest values of E the in- 

 dividual contractions were 



4 3 2 i 2 3 4 kg. 



io 4 A7V=i.6 1.4 0.9 o .9 1.5 2.1 



30. Rods in metallic sheath. In the data thus far obtained the value of 

 E is throughout too low, showing that the section of the rod has not been 

 uniformly stressed. A final modification was therefore made as shown in 

 figure 34, in which the rod r (to be tested) is rather loosely surrounded by 

 a rigid metallic tube or sheath rigidly screwed into the bar FF of the inter- 



