DAVIS. LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 723 



nodes at the middle of the string are coming out more and more strongly, 

 nearly in the same proportion, as the howing-point approaches the mid- 

 dle of the string. This is also brought out by the envelopes of these 

 surfaces which are shown in Figure 9. As before, the surface at the 

 limit (A) is quite different from the limit of the surfaces. It is possible 

 to get a series converging toward h from the other side by means of the 

 formula m/(2 m — V) as is indicated in Table IV ; the approach is through 



TABLE IV. 



Showing, the serial relations among the surfaces of the first and second plates. 



essentially the same set of surfaces, and the same set of partials come 

 out strongly, but in the opposite phase. 25 



Parts of similar series converging toward ^ are shown on the second 

 plate, the formula being m/(B m ± 1). They show very prettily Krigar- 

 Menzel's change of phase in the 3d, 6th, 9th, etc. partials. The envel- 

 opes of the first of these series are shown in the upper half of Figure 11, 

 and those of the second series on a reversed scale in the lower half of 

 that figure. It should be compared with Figures 9 and 1, and espe- 

 cially with Figure 10, which is Young's representation of essentially 

 the same fact. Finally, in the lower line of the second plate are 

 two surfaces belonging to the convergences upon *, the formula being 

 2 m (5 m ± 1). In them the oth, 10th, etc., partials are beginning to 

 come out strongly, and are, as usual, in opposite phases. 



Notwithstanding this essential difference, the surfaces for T 5 o and -fy 

 are, in general appearance, very much alike, and a comparison of either 

 of them with the surface for % itself seems to show that each of them is 



25 See the preceding footnote. 



