INDUCTION IN TELEGRAPH CABLES. 531 



during the variable state, we have disregarded the effects of in- 

 duction, which are due to changes in the strength of the current. 

 From this there arises a fresh cause of delay in establishing and 

 in suppressing the principal current, and this retardation can no 

 longer be calculated as we have done before (535), since the 

 duration of the propagation is very considerable as compared with 

 the duration of the phenomena of induction ; it is not possible to 

 assume then that the strength of the current has the same value 

 at every instant in the whole extent of the circuit. 



If there are a series of alternate charges and discharges in 

 the wire, as is the case with telegraphic signals, we may consider 

 the phenomenon as being due to a variable electromotive force, 

 and effects will be produced analogous to those which have been 

 mentioned above. 



The cable may, moreover, be considered as near other ones, 

 which react on the first either by their mere presence, or by the 

 variations in their own currents which traverse them. The resul- 

 tant effects are very manifest in air wires resting on insulators. 



Finally, when several conductors are enclosed in the same 

 dielectric sheath, as is the case with subterranean, or submarine 

 cables, the potential at each point of one of the wires depends on 

 the charge of the adjacent wires. From this follows a new kind 

 of influence or induction, purely electrostatic in character, and 

 which Sir W. Thomson called peristaltic, to distinguish it from 

 that of Faraday. This phenomenon is completely analogous with 

 the reciprocal influence of elastic tubes connected lengthwise, which 

 are filled and surrounded by the same liquid, when the liquid is 

 made to circulate in one or more of the tubes, while the ends of 

 the others are opened or closed, or in any other special condition ; 

 a closed tube would correspond to an insulated conducting wire, 

 and an open tube to an uninsulated wire. 



From these suggestions it will be seen how complex is the pro- 

 blem of the propagation of electricity, if we take into account all the 

 circumstances which may have an influence on the phenomenon. 



552. CALCULATION OF THE COEFFICIENTS OF INDUCTION. 

 SOLENOIDS. The preceding examples show the importance of the 

 part which the coefficients M and L play in the calculation of the 

 phenomena of induction. We shall examine a few simple cases, 

 in which these coefficients may be easily estimated. 



Let us, in the first case, consider a cylindrical solenoid so long 

 that for a considerable portion of its length we may disregard the 

 action of the ends. 



M M 2 



