DAVIS. LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 699 



drawn from the ends of the base line in the manner indicated. 9 In 

 the general case, Ik, the envelope would be k straight lines similarly 

 determined. When the speed of the rubbing wheel was varied, all other 

 conditions remaining the same, the amplitude was found to vary directly 

 as the peripheral velocity of the wheel, a fact which was tested for a 

 considerable range of velocities in each of the four cases considered. 

 This fact is an obvious consequence of Helmholtz's two laws. 



In all, 331 amplitudes were measured, each observation involving, in 

 general, six settings of a filar micrometer. The results are summarized 

 in Table I. The first column gives the position of the point rubbed, and 



TABLE I. 



the second, the position or range of positions of the point observed, in 

 fractions of the length of a vibrating segment ; the third gives the pe- 

 ripheral velocity of the rubbing wheel in cms. per second. In the fourth 

 column is given a mean standard amplitude M, obtained from the actually 

 observed amplitudes m, first, by multiplying each of them by an appro- 

 priate factor obtained directly from the geometry of Figure 1, giving a 



9 The distance A A l having been arbitrarily assumed, the points B 1( C lt and T> x 

 on the line O' A 1 are determined by the bowing points B, C, and D, and themselves 

 determine the rays through O. The symmetry of the figure determines the corre* 

 sponding rays through O'. 



