DAVIS. — LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 713 



velocity, followed by a descent with another constant velocity, the ratio 

 of the lesser velocity to the greater being l/(q — 1). It follows that the 

 duration of the greater velocity is 1/^th of a complete period, or, speak- 

 ing geometrically, that the length of the projection on the t axis of the 

 steeper of the two straight lines which make up a typical segment of the 

 curve y = $ (t) for the point in question, is 1 /qih of the length of that 



Figure 5. The case \. The upper figures show configurations at intervals of 

 7712, the first from to T/4, and the second from T/i to T/2; the return to 

 equilibrium is through forms symmetric to those of the ascent. The lower figures 

 show the motion of the points J, |, \, and \. 



segment. A number of measurements of this ratio for the various 

 rational cases up to and including q — 10 are presented in Table III. 

 The observations summarized in this table were made with a Gaertner 

 comparator whose stage was driven by a half-millimeter screw with a 

 head reading to thousandths of a millimeter. Each slide was oriented so 

 that the curve to be measured lay along the axis of the micrometer 

 screw and readings were made of the settings necessary to bring 



