2 C. A. Chant — Variation of Potential along the 



axis ; while in the electro-magnetic case the radiation is from 

 without inwards, being limited by the surface of the wire, and 

 on account of the transversality of the vibrations there is no 

 radiation along the axis. Moreover, in the air-vibrations there 

 is a displacement of the entire system of nodes and loops 

 towards the open end, while, with the electrical oscillations, to 

 a first approximation, there is no such displacement. On a 

 closer examination, however, there is found to be a displace- 

 ment of this kind, variable with the frequency. The phase of 

 the advancing waves alters in a discontinuous manner, some- 

 what as in the vibrations of a plucked string.* 



When two wires are used, as in Lecher's arrangement, the 

 radiation in the direction of the axis does not vanish, and the 

 analogy to the open pipe is more marked. There is then a 

 decided displacement of the nodes and loops, well exhibited in 

 an investigation by de Forest. f 



The best acoustical analogy to a wire connected at one end 

 to earth or to a large capacity and free at the other seems to 

 be a closed pipe, gas-pressure in the pipe corresponding to 

 potential or charge in the case of the wire. Here there is a 

 displacement of the nodes and loops, but it is very small, and 

 only the odd harmonics are present in the two cases. Of 

 course a rod clamped at one end is similar to the closed pipe. 



Birkeland and Sarasin,;}; in their investigation of the field 

 about a free-ending wire, explored with a circular resonator, 

 and found the first node distant from the end by one-half the 

 circumference of the resonator (a result similar to that obtained 

 by Sarasin and de la Rive in their investigation on two parallel 

 wires, and ascribed by them to the geometrical form of the 

 resonator), and other nodes regularly spaced along the wire at 

 intervals equal to twice the diameter of the resonator. The 

 form of the nodal surfaces in the space about the wire obtained 

 by them agrees with that deduced by Abraham.. 



Slaby's theoretical treatment§ of the problem is much sim- 

 pler than Abraham's, and from his results he was led to his 

 method of syntonic telegraphy. He takes the so-called " tele- 

 graphic equation," 



hi T 6 2 i 1 bH 



*bt + 'bf~a l bx~ ii 



where i is the current strength at any time at a place x on the 



*Helmholtz, Sensations of Tone, p. 54; Rayleigh, Theory of Sound, art. 

 146. 



| L. de Forest, this Journal, viii, p. 58, 1899. 



^K. Birkeland and E. Sarasin, Comptes Rendus, cxvii, p. 618, 1893. 



§A. Slaby, Lond. Electrician, vol. xlvi, Jan. 18, 1901; also vol. xlix, 

 April 25, 1902. 



