Resistance of Compound Conductors, 491 



the self-induction due to this was 24^°, and the resistance 

 3*8; numbers altered to 2 8 J° and 4*4 respectively by softening 

 with a spirit-flame. The effect of a bundle of thirty-five soft 

 wires of the same iron and of equal aggregate section was 

 84° of self-induction and 1*6 of resistance *. 



There is nothing surprising in the conclusion, forced upon 

 us by the observations, that the magnetic effects of iron rods 

 3*3 millirn. in diameter are seriously complicated by the 

 formation of induced internal electric currents. As I have 

 shown on a former occasion f , the principal time-constant 

 of a cylinder of radius a, specific resistance p, and per- 

 meability fju, is given by 



4:7r/jba 2 

 T ~~ (2-404) y 



This means that circumferential currents started and then 

 left to themselves would occupy a time t in sinking to e~~ Y of 

 their initial magnitude. Whether the effects of such currents 

 will be important or not depends upon the relative magnitudes 

 of r and of the period of the magnetic changes actually in 

 progress. In the present case, with 



/a = 100, /> = 9827, 2« = -33, 



the value of r is about 20V0 °^ a second, that is, about half 

 the period of the actual electrical vibration. 



The theory of an infinite conducting cylinder exposed to 

 periodic longitudinal magnetic force (I e ipt ) has been given by 

 Lamb J, who finds for the longitudinal magnetic induction 

 at any distance r from the axis 



-SSJ""'. W 



where 



f= _4tt/^ 



P 

 When the changes are infinitely slow, c reduces to /jule ipt , as 

 should evidently be the case. 



A more complete solution was worked out a little later by 



* It may be worth while to remark that in these experiments no 

 approach to a balance could be obtained when a scraping contact inter- 

 rupter was used. With the reed there wa3 complete silence, or at most 

 a slight perception of the octave. The failure of the scraping contact is 

 due, of course, to the mixed character of the vibration, and to the fact 

 that the adjustments necessary for balance vary rapidly with pitch. 



t Brit. Assoc. Report, 1882, p. 446. 



X Math. Soc. Proc. Jan. 1884, vol. xv. p. 141, 



