THE AID OF THE ACHROMATIC FRINGES. 



61 



induced current in the secondary. This is in keeping with theory, which de- 

 mands an angular phase difference of the form tan" 1 (Leo//?). On changing 

 the resistance R, these ellipses showed little tendency to oscillate. They 

 rather expand or contract. A measurement of their extent between the tan- 

 gents ab and kg is difficult, because of the initial displacement corresponding 

 to hf, for the difference ah-\-fg only is effective. The full ranges may be 

 stated as 



at R = 1,250 ohms, 25 scale-parts, 



2,200 



4,200 



10,200 



tc 

 it 



1C 



20 



13 



10 



(t 



(f 

 <e 



With lower or higher resistances the change of size necessarily (Ohm's law) 

 increases or decreases asymptotically; at 20,000 ohms the effect of breaking 

 the circuit is still quite observable. In fact, the bands for R= are slightly 

 overcompensated, as though they corresponded to an electrostatic capacity, 

 so that truly linear fringes were obtained on inserting high resistances. 



The auxiliary telephone in circuit was now nearly silent. If at 2,000 ohms 

 the net range of elliptic displacement is taken as 10 scale-parts, the current 

 would be (an average of io~ 2 volts being impressed) 



10 



,-2 



IOX2XI0 3 



= 5 X io~ 7 ampere per scale-part. 



But much less than this is observable in the 

 changes of form and disposition of fringes. 



The conditions of figure 62 , in which for R = < 

 the bands hf appear, merely make a special case. 

 Figure 63 shows another of many similar cases 

 observed. Here, when R= , the symmetrical 

 ellipses hf, implying a phase difference of 90, 

 due to the so-called mechanical coupling, was 

 observed. On decreasing R from oo , kf passed 

 into the oblique ellipse e, the range of which, bg, increases as R decreases. At 

 25,000 ohms no change was observed; but at 20,000 ohms there was definite 

 change of inclination apparent. At 5,000 ohms the ellipse showed a new 

 increase of range of over 10 scale-parts. The occurrence of a variety of con- 

 ditions, exemplified by figures 62 and 63, shows that a very variable cause 

 is productive of phase difference between the vibrating objective and the 

 vibrator of the interferometer. 



44. Capacity and sehMnduction in the secondary. The phase differences 

 thus far observed are attributable to the self-induction of the secondary. 

 It is interesting, therefore, to test whether the lead of the form tan. \i/CRa)) 

 due to capacity can be equally well observed. The circuit (fig. 59) was there- 

 fore provided with a condenser C, containing up to one microfarad, in steps 



