70 DISPLACEMENT INTERFEROMETRY BY 



a vertical or a horizontal axis normal to the rays from the interferometer 

 would also contribute to the error in question. Yet the method of loading 

 does not seem to admit of such stress, unless the weight supported on the 

 single leveling-screw g of the base (figs. 28, 29) nearer the interferometer, 

 is at a disadvantage as compared with the load supported on two 

 screws remote from the interferometer. Moreover, this apparent yield 

 is consistent, increasing proportionately to the load, so that it is difficult 

 to separate it from the true strains. The only way of counteracting these 

 difficulties is to remodel the apparatus, casting it as a single massive piece 

 of metal, and providing other means (precision slides) of applying 

 stress. The pulley-offset device used must be regarded as im- 

 provised, for it is here that fictitious strains undoubtedly enter. 



Apart from these considerations and in view of the consistent 

 presence of the discrepancy, its cause might be sought in the un- 

 equal sectional distribution of stress from end to end of the rod. 

 Such an effect, moreover (i. e., any unevenness of the seat of the rod r, fig. 50), 

 is not unlikely to produce flexure. Thus the stresses PP' in the figure, act- 

 ing on the left edge, would tend to bend the rod to the right at the middle. 

 This would also be a purely elastic deformation and behave as such. Again, 

 if in figure 50, P and P' act at diagonally opposite corners, the rod is subject 

 to shear. 



There is still another possible explanation of the discrepancy in terms of 

 friction, which may be adduced. Appreciable friction effects at the pulleys 

 are improbable ; but at the conical points of the offsets, as they engage the 

 corresponding conical sockets, displacement involving marked friction is not 

 excluded. If, therefore, c is the coefficient of friction and W the weight ap- 

 plied, and if we write N = CW, where C is a constant, the effect of additional 

 weight dW may be written 



when the load is increased ; and similarly, 



when the load is being gradually decreased. If the effective coefficients 

 are not equal, the observations would therefore correspond to two lines of 

 different slopes and the passage from one to the other would invariably be 

 hysteresis-like, even if there is no such quality appreciable in the elastic solid 

 under observation. Also, the phenomenon would increase in magnitude as 

 the deformations are greater, giving a result very similar to the above 

 observations. True, whether the friction effect occurred in a symmetrical or 

 regular fashion or not, it would not have been eliminated in the triplets of 

 observations made. It is quite conceivable that if a weight W added has 

 produced cW less stress than is implied, the removal of that weight would 

 deduct c'W less stress than implied, or even for larger c' deduct no stress at 

 all. Hence in such triplets AW would be much too large or AN" much too small 



