VIBRATING TELEPHONE DIAPHRAGMS. 455 



of Xa is the distorted velocity graph ; also ab'c'd'h' of Xn is the ab- 

 sorption velocity graph, reckoned negatively. At any impressed 

 angular velocity, such as 4,450 radians per second, the nndistorted 

 or primary velocity Xm would be OD cm. per sec, leading the im- 

 pressed V.M.F. by the angle EOD. The observed velocity Xa, in 

 the presence of distortion, is Od; while the vector difiference between 

 the Xm and Xa, or Dd, is equal to x.^^ — Od' or Od' reversed. 



It will be observed that the graph of .r., a'b'c'h' is only approxi- 

 mately a circle. It may be regarded, in the light of (29), as the 

 graph of a vector fraction of a motional circle. 



It should also be noted from (28) that when the primary and 

 secondary resonant frequencies differ, the resultant velocity .r„ will 

 not come into phase with the V.M.F. at either resonance frequency, 

 but will trace a dissymmetrical loop. The absorption velocity graph 

 a'b'c'h' will be likewise dissymmetrical. 



Fig. 6 shows the observed graph Oabch of motional impedance, 

 and therefore of velocity, with reference to an impressed force in 

 the vector direction OE. The heavy circle OABCH is the inferred 

 nndistorted or primary graph, as deduced from the segment AOH. 

 The foliate graph Oa'b'c'h' is the vector difference, or secondary 

 graph of absorption. It will be observed that except for a slight 

 difference in the primary and secondary resonant frequencies, the 

 case presented in this test agrees closely with the geometrical rela- 

 tions indicated in Fig. 20. 



Referring to Figs. 7 and 8, it will be observed that the angle 

 AOC is approximately equal to the angle COF. This means that, 

 at secondary resonance, the absorption velocity OF lies nearly as 

 far in angle beyond the vector OC, of that frequency on the nndis- 

 torted circle, as OC lies from OA the mean diameter. Formula 

 (29) gives a ready explanation for this; because at secondary reso- 

 nance Sa = r.-,, so that 



xo = Xm ( — ~— I , kines Z . (31) 



If, as in the cases represented by Figs. 7 and 8, n is small by com- 

 parison with z, this becomes approximately 



.To = A-,„ I -- , kines Z . (32) 



