DAVIS. — LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 711 



Figure 3. The case f . The upper figure shows the configurations of the string 

 at the times 0, 7712, 2T/12, . . . 6T/V2, 2T being the period; the string returns 

 to equilibrium through the same forms ; in this, and in the following cases, the 

 configurations during the second half of a complete vibration can be obtained by 

 turning the page upside clown. The lower figures show the curves u = <f> (t) for the 

 points \ and \. The dotted lines in this, and in the similar figures to follow, show 

 the motion due to the major vibration alone. It is interesting to notice that this 

 mode of vibration is identical with that of a string plucked at its middle point. 



§ 4. Rational Points — Krigar-Menzel's Law. 



The experimental method described in section 2 has two disadvantages. 

 In the first place, it is not easy, especially in a complex case, to discover 

 any vibration form that corresponds to a given envelope ; and in the 

 second place, an envelope is sometimes, and perhaps always, not enough 

 to determine its vibration form uniquely. For example, in the case of 

 the struck string, if the initial conditions be taken in the form 



u = when t = 0, 

 3 it 

 Jt 

 9 u 

 Jt 

 9 u 

 Jt 



= when t = 0, 

 — Cwhen t = 0, 

 when t = 0, 



and < x < x , 

 and x Q < x < x + a, 

 and x + a < x < /, 



it can easily be shown that the envelope depends only on the constants a 

 and C and not at all upon x . A second standard method of observation 

 was therefore made use of, and it proved to be more powerful, although 

 much less accurate, than the first. The point of a fine needle was 

 broken off and fastened to the wire with shellac, 14 and a microscope slide 



14 The added weight was that of about half a millimeter of wire. 



