24 



DISPLACEMENT INTERFEROMETRY. 



12. Conclusion. The present experiments, made with a totally dissimilar 

 apparatus and in a different manner, are nevertheless (notwithstanding the 

 relative simplicity of the present design) not markedly superior to the earlier 

 experiments, as a whole. The misgiving felt regarding the force couples 

 entering into the earlier method was not therefore justified. Both apparatus 

 function admirably so far as the optics of the method are concerned ; particu- 

 larly is this so when one considers the admissibility of the rather rough treat- 

 ment needed in work of the present kind. Both apparatus are liable to give 

 misleading results from the same cause, i.e., from an insufficiently uniform and 

 continuous contact of the two ends of the rod with the abutments. From this 

 results appreciably unequal distribution of stress in the sections of the rod 

 and possibly flexure. There seems to have been no serious yield in the abut- 

 ments, etc., of either apparatus. 



The values of the modules as a consequence come out too small. There 

 can therefore (tapping admitted) have been no serious discrepancy from fric- 

 tion in the application of stress; for this would have made E too large. More- 

 over, all slight dislocations within the interferometer, as the result of the 

 tapping or jar, were finally eliminated, so that the cycles are practically closed, 

 or merely give evidence of a difference of slope in the outgoing and return 

 series. Such an effect would be expected from viscosity and hysteresis. 



I was at first inclined to regard the small values of the modulus E as an 

 actual or trustworthy result, in keeping with the peculiar crushing stress 

 applied. But inasmuch as E may be increased to the normal value by succes- 

 sively decreasing the diameter of the rod in the case of glass and even of brass, 

 the small values of E must be associated with the lack of contact at the abut- 

 ments of the rod. Rods about i to 2 cm. in length should not be thicker than 

 i or 2 mm. (ratio about 10 to i) if the results are to be correct in their absolute 

 values. And here again a thin rod, r, with two thick ends, as in figure fd, if 

 both ends are firmly clutched (without strain), is the ultimate desideratum. 

 Figures ;&, "jc, 70 (sheath, s), are admissible expedients, the latter being par- 

 ticularly convenient. The relative results are almost always smooth and 

 admirable to a fraction of a wave-length; but for relatively large sections 

 they can not be interpreted, owing to the sectional discrepancy in question. 

 This also is relative in its character; at least for moduli markedly above io 10 . 

 Thus it is as difficult to obtain the true modulus for a glass rod as for a brass 

 rod, although the latter body is far more rigid. 



It is not easy to interpret the apparent hysteresis in many of the above 

 graphs; for this is always associated with possible changes in a complicated 

 train of apparatus. Similarly the different rates in the outgoing and the 

 return series may be variously explained. If the measurements are made in 

 triplets between definite steps of pressure, this difference soon vanishes. 

 Hence such a procedure is to be preferred. 



