282 Prof. J. J. Thomson. The Resistance of [Jan. 17, 



This equation (17) reduces to 



.... (18), 



a) ap 



if v = 1, that is, if Maxwell's theory is true, 



log (7*2 a) 



Now -y 2 * is the electrostatic measure of the capacity, so that if we 

 denote this by {}, 



I 



ml tan ml = 



2{}log(l/ 7 Ya) 



The form of the solution will depend upon the magnitude of 

 7/2{} log(l/7<z'a). If this is small then ml will be small, and we 

 have 



or 



since, if Maxwell's theory be true, q' = m. 



This result, however, is only true when I is not large compared 

 with <x, in this case ml tan ml will be large, and m therefore will be 

 approximately ^?r, -|TT, and so on. Thus in this case the ends of the 

 wire are nodes of the electrical vibrations, and the gravest mode of 

 vibration is that in which the wave-length is twice the length of the 

 wire ; here the wave-length, and therefore the rapidity of vibration, 

 will be independent of the capacities of the condensers at the ends. 



If v 1 is finite, since the second term on the right hand side of 

 equation (17) will in this case be large compared with the first, since 

 pa? 1 1 a is large, the equation reduces to 



am tan ml = 



op 



or since p = (l-f/3)vm, 



. 



: 



Now in the cases we are considering pTra^/ff is very large, amount- 

 ing to 10 4 or 10 5 in the C.Gr.S. sj'stem of units, so that unless {a} is 

 comparable with 1/10 of a microfarad ml will equal 7r/2, the ends of the 

 wire will again be nodes, and the wave-length of the gravest vibra- 

 tion will be twice the length of the wire. Thus in this case, except 



