THE AID OF THE ACHROMATIC FRINGES. 



63 



The current induced in the primary controls the objective of the vibration 

 telescope, which thus moves with a lag a subject to 



(2) 



*=*'o sin (wt a) 



and this may be modified by the resistance and inductance in the primary. 

 The objective is, as stated, either mechanically or magnetically coupled 

 with the vibrator on the interferometer in a way yet to be ascertained. Hence 

 the vibrator displacements s are subject to an equation with a lag or lead 



(3) 



5 = So sin (ut 



in the absence of current in the secondary (R = ) . 



Finally, the secondary, if carrying current, has its own lag or lead 7, depend- 

 ing on the R, L, C, there inserted, and is thus subject to an equation 



(4) 



= s sin (at 7) 



where 7 is essentially associated with /3, as seen in the preceding paragraphs. 



If we suppose the coupling implied in equation (3) to be uniform, the lag 

 in equation (2) may be made obvious. In this way vibration figures were 

 obtained, examples of which are given in figures 68 

 and 69. Calling the two nearly equal auxiliary self- 

 inductions in the primary L and U (R= in the 

 secondary) , in the case of figure 68, the bands obtained 

 in the absence of L or L' changed to ellipses of about 

 the same range for either the L or L' insertion, and 

 these to nearly horizontal bands when both L and L' 

 were inserted. On removing the L+L' the first figure 

 returned. In figure 69 the initial form (L = o) was 

 an ellipse, changing to bands with but little differ- 

 ence of phase between the L and 2L insertions. 



In all these cases the vibration figures were very 

 large and very definite in the successions of their changes with L, however 

 frequently repeated. 



The insertion of L (choking coil) naturally somewhat reduces i and there- 

 fore the amplitude of the objective of the vibration telescope. It appears 

 from figures 68 and 69 that at the same time the vibration of fringes is lessened 

 and ceases practically under 2L (horizontal bands). Here, in other words, 

 the apparently mechanical coupling has been eliminated; but by closing the 

 secondary with a resistance R, the effect of C and L in the secondary (which 

 might now be investigated without the mechanical discrepancy) proved to be 

 insignificant. There was no appreciable induced current left in the secondary. 

 Again, since these vibration figures appear and are modified when R = , 

 the coupling roughly called mechanical must be magnetic. In other words, 

 all the quivering stray magnetic fields in the room directly influence the 

 vibrator cc', figure 59. Further corroboration will be found in 48. 



