Self-induction of Wires. 135 



the coil circuit, in a long solenoidal coil of small thickness, 

 containing a solid conducting-core, the magnetic force in the 

 core rises in the same manner as the current in the wire, 

 according to (32) ; as the boundary condition of the magnetic 

 force is of the same form as (34), q being then a function of 

 the number of windings, &c. 



There is also the water-pipe analogy, which is always turn- 

 ing up. This I made use of in the ' Electrician,' July 12,1884. 

 Water in a round pipe is started from rest and set into a state 

 of steady motion by the sudden and continued application of 

 a steady longitudinal dragging or shearing-force applied to 

 its boundary, according to the equation (32). This analogue 

 is useful because every one is familiar with the setting of 

 water in motion by friction on its boundary, transmitted 

 inward by viscosity. 



Graphically representing (32), abscissae the time, and ordi- 

 nates Y, at the centre, intermediate points, and the boundary, 

 by what we may call the arrival-curves of the current, and 

 comparing them with 



r=r (i- e - R o'/ L ), 



the linear- theory arrival-curve at all parts of the wire, we may 

 notice these characteristics. The current rises much more 

 rapidly at the boundary than according to the linear theory, 

 at first, but much more slowly in the later stages. Going- 

 inward from the boundary we find that an inflection is pro- 

 duced in the arrival-curve near its commencement ; the rapid 

 rise being delayed for an appreciable interval of time. This 

 dead period is very marked of course at the axis of the wire, 

 there being practically no current at all there until a certain 

 time has elapsed. That the central part of the wire is nearly 

 inoperative when rapid reversals are sent is easily understood 

 from this, or perhaps more easily by the use of the water-pipe 

 analogue. Some curves of (32), for two special values of q, 

 I gave in the l Electrician,' September 6, 1884. 



Let there be a simple harmonic impressed force e sin nt in 

 the circuit of wire and sheath, with no external resistance, 

 making a total circuit-resistance R. (I translate the core 

 solution into the wire solution.) The boundary condition 

 is 



e&mnt ^ dT /QKN 



ii^r =r+ ?*' (35) 



and the solution is 



r= j^ (P? + Qly* {(PoM + Q N) sin nt 



+ (P„N-Q M)cosn«} ; . (36) 



