62 



DISPLACEMENT INTERFEROMETRY BY 



of tenths. An auxiliary telephone T" was also inserted as a detector. The 

 results were successful at once, as shown in figures 64 and 65. In figure 64, 

 R= co , or the symmetrical ellipse is obtained on open circuit. This changed 

 rapidly into the oblique ellipse C when 0.5 microfarad is inserted, and the latter 

 into the bands L (with a range of 30 scale-parts) when the circuit was closed 

 with about 3,000 ohms. In another adjustment (fig. 65) of primary, R= 

 gave normal bands (i.e., the fringes do not vibrate); the capacity 0.5 micro- 

 farad now gave the oblique bands C and the self-induction (R= 5,000 ohms) 

 the nearly symmetrical ellipses L. 



66 



67 



The passage from L to C was always through bands, thus indicating the 

 probability of an opposition of phase change of the relation of lag to lead. This 

 is instanced in figures 66 and 67, where the direction of fringes (like the vibra- 

 tion of the objective) happens to be horizontal, and the displacement of fringes 

 therefore vertical. L is obtained by closing the circuit with ^ = 3,000 ohms. 

 When 0.5 microfarad was then inserted, the oblique bands L changed into the 

 ellipse C by first passing through nearly horizontal bands of duplicated fringes. 

 In figure 67 (owing to a change in the primary) L has the elliptical form and 

 C is banded or duplicated. In both cases the detecting telephone was audible 

 to about the same degree. On breaking circuit (7?= ) the telephone was 

 silent; but the fringes vibrated, as shown in the figure. It is not unusual for 

 these patterns to occupy the greater part of the field of view. The ellipses 

 are sharply visible at the ends of maximum curvature, where there is partial 

 cessation of motion. The connecting lines may escape detection. It is fre- 

 quently necessary to re-focus the vibration telescope. 



45. Self=induction in the primary. The present experiments contain an 

 element of uncertainty, owing to the so-called mechanical (possibly magnetic) 

 coupling of the vibrator cc', on the interferometer (fig. 59), and the objective 

 of the vibration telescope V. Some relevant information, it was thought, 

 would be gained by inserting additional self-induction into the primary. The 

 two small electromagnets e" (fig. 59; about an inch long), which could be used 

 either separately or in series, were available for this purpose. 



The different elements of harmonic motion involved in the experiment may 

 therefore be analyzed as follows : The whole is fundamentally subject to the 

 vibration period of the spring at the interruptor of the primary, which gives 

 the impressed electromotive force 



(i) e = eo sin w* 



