62 Bronson — Transverse Vibrations of Helical Springs. 



Figure 4 gives the length-tension and length-frequency curves 

 plotted from the values given in Table III. The full and 

 dotted lines represent respectively the observed and calculated 

 curves; the observed points are surrounded by circles, and the 

 calculated points are indicated by crosses. In case the observed 

 and calculated curves agree too closely to show both, the calcu- 

 lated curve will be given, and the observed points indicated by 

 circles. 



4 



It is evident from the plot that the relation between the 

 length and tension is practically linear through nearly the 

 entire range used. This relation is most simply expressed by 

 the equation 



(1) T ^ ml* + x 



where m is the slope of the line, and x is the point at which, if 

 continued, it would intersect the T axis. 



In order to find the relation between length and frequency, 

 it seemed most natural to take the usual expression for a 

 vibrating string, which for the present purpose is most con- 

 veniently written in the form 



