THE AID OF THE ACHROMATIC FRINGES. 97 



produced. They do not, however, increase in size in proportion to the de- 

 crease of variable resistance, a result attributable to the amount of resistance 

 and inductance necessarily in circuit, the effect of which is relatively large 

 when the additional resistance is small. 



To obtain some idea of the smallest average current appreciable, the Siemens 

 dynamometer may be put in circuit, though unfortunately it has a resistance 

 as high as about 1,000 ohms. With the magneto inductor running at a speed 

 of r = o.i7 sec., the Siemens showed a deflection of but 0.02 cm. on the given 

 scale, owing to this resistance. 



Estimating the average current i asi = C V <p, where C is the dynamometer 

 constant and <p is the deflection in centimeters, the value of C as found by 

 Clarke's cell and resistances was C=5Xio~ 4 , so that_the average magneto 

 current corresponding to <p = o.o2 cm. is i= $X io~ 4 X V 0.02 = 7 X io~ 5 ampere. 

 The resistance in circuit was here about 1,500 ohms. If an additional 10,000 

 ohms is inserted and the magneto reduced in speed to T= 0.2 5 sec., the current 

 is still appreciable at the interferometer and would be of the average value of 

 t = 6Xio~ 6 ampere. Although no account has been taken of self-induction, 

 it is improbable that the smallest average current here observable by the 

 interferometer apparatus in the earlier form could have been much within a 

 microampere. In this respect the device was somewhat disappointing. 



In a later and more refined adjustment the ellipses obtained with an in- 

 sertion 10,000 were found to fill (as to their vertical or current axes) fully 

 one-quarter of the field of the telescope. As little as one-tenth to one- 

 hundredth of this would be easily appreciable with certainty, so that the 

 minimum average current capable of detection may be estimated as a few 

 io~ 7 amperes. It must be remembered, however, that the above mirrors 

 (mm') and appurtenances are unnecessarily heavy, and the bifilar too robust. 

 The improvement would therefore consist in constructing a very light needle 

 and delicate bifilar. 



If the dampers p,p r are removed, the ellipses, even at high resistance, are 

 apt to pass out of the field of the telescope. Even if the principles of forced 

 vibrations are applicable, the system in the absence of current is too mobile 

 for convenience. 



When the magneto was run at maximum speed (without pulleys) a deflection 

 of about 0.12 cm. was obtained on the dynamometer, corresponding to an 

 average current, therefore, of about = i.sXio~ 4 ampere. In this case the 

 even band a (fig. 72) takes the definite shape of a train of waves (fig. 68) of 

 short wave-length, with amplitude of but 10 or 20 fringe-breadths. These 

 also admit of the additional insertion of several thousand ohms before they 

 are reduced to the linear band. 



If one of the telephones is reversed, the fringes showing marked vibration 

 (bed, fig. 72) in the first position frequently cease to show any vibration 

 (a, fig. 72) until the ellipses in the former case are very large (small resistance 

 in circuit). The results in such a case are uniformly consistent. Thus, for 



