PREFACE. 



The present report is chiefly devoted to the investigation of methods of 

 research in which displacement interferometry, conducted by the aid of the 

 achromatics discussed in the preceding report, gives promise of fruitful 

 applications. Thus, in Chapter I the method of measuring small angles 

 hitherto suggested is given a practical test. The general theory of the sub- 

 ject in its bearing on the two possible methods is developed at some length 

 and a variety of interferometer devices, with mirror, ocular, and collimator 

 micrometers, are instanced. Unfortunately, it was not till after the end of 

 these experiments that I detected the method of reducing the fringes to the 

 smallest number possible, practically to a single fringe; otherwise the work 

 would have been more satisfactory throughout. 



As the achromatic fringes can not (in general) be found without first 

 finding the corresponding spectrum fringes and, conversely, since for each 

 type of spectrum fringes (direct or reversed) a corresponding group of achro- 

 matic fringes may be associated, I have devoted Chapter II to spectrum 

 fringes differing in their manner of production. The endeavor here has 

 been to obtain interferences from distant slender luminous objects, without 

 the aid of a slit. Partially at least the work has succeeded, but not as 

 far as I hoped. The experiments are very difficult. 



The work in the third chapter was undertaken at the request of Prof- 

 W. G. Cady, of Wesleyan University, in the endeavor to obtain the elastic 

 constants of small bodies. The application of the displacement method 

 proved at once to be astonishingly easy in a case where a degree of rough 

 handling is inevitable; but there lurked in the elastic apparatus some dis- 

 crepancy, both of viscosity and hysteresis, the nature of which escaped 

 detection even after many attempts to locate its origin. 



Chapter IV contains applications of the rectangular interferometer using 

 achromatic fringes to geophysical problems. A method for the determina- 

 tion of the Newtonian constant is worked out. Again, the same interfero- 

 meter is associated with the horizontal pendulum for the detection of small 

 changes in the inclination of the earth's surface. Series of observations 

 extending between January and August are recorded. 



Finally, in the last chapter, I have investigated corresponding methods for 

 the interferometry of vibrating systems. The luminosity of the achro- 

 matic fringes lends itself easily to this purpose and it was merely necessary to 



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