140 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



We may further write for abbreviation 



+ ( wco 



and 



a = tan^^ 



moo 



CO 



dyne sec /cm (8) 



radians (9) 



The quantities entering in the above equations, and their analogous 

 electrical cjuantities, are tabulated below. 



Circular Graph of Velocity. — By equation (6) x is seen to be 



F 



sinusoidal, with amplitude i , and lagging by an angle a behind the 



\^\ 



impressed force. A geometrical representation of the amplitude and 

 phase of x is given in Figure 14. In the left hand part of the figure 

 Oy is a representation of the vector mechanical impedance z. As w 

 changes from zero to infinity, the point y moves along the straight 

 line Xy from minus infinity to plus infinity, parallel to OY. In the 

 right hand part of the figure, the circle is the vector graph of F /z, 

 which is given in magnitude and direction by OP. This circle is 

 obtained by taking the reciprocal of the straight line locus of the vector 



