On the Self-induction of Wires. 419 



moment of inertia, and k the known change of moment of 



inertia ' K= k J-., 



Now a small error in the determination of either t or t' pro- 

 duces a comparatively large error in the value of K ; and it is 

 therefore of considerable importance here that there should be 

 no approach to the previously mentioned synchronisms. It 

 is important also here to notice the fourth source of error 

 which has been mentioned ; for it is very difficult to change 

 the moment of inertia without imparting some shock to the wire. 



L. On the Self-induction of Wives. — Part IV. 

 By Oliver Heaviside*. 



AS mentioned at the close of Part III., it would appear 

 that the only practicable way of making a workable 

 system, which will allow us to introduce the terminal con- 

 ditions that always occur in practice, in the form of linear 

 differential equations connecting and V, the current and 

 potential difference at the terminals, is to abolish the very 

 small radial component of current in the conductors. This 

 does not involve the abolition of the radial dielectric current 

 which produces the electric displacement, or alter the equation 

 of continuity to which the total current in the wires is subject. 

 The dielectric current, which is SV per unit length of line, 

 and which must be physically continuous with the radial cur- 

 rent in the conductors at their boundaries, may, when the 

 latter is abolished, be imagined to be joined on to that part of 

 the longitudinal current in the conductors that goes out of 

 existence by some secret method with which we are not con- 

 cerned. 



We assume, therefore, that the propagation of magnetic 

 induction and electric current into the conductors takes place, 

 at any part of the line, as if it were taking place in the same 

 manner at the same moment at all parts (as when the dielec- 

 tric displacement is ignored, making it only a question of 

 inertia and resistance), instead of its being in different stages 

 of progress at the same moment in different parts of the line. 

 This requires that a small fraction of its length, along which 

 the change in C is insensible, shall be a large multiple of the 

 radius of the wire. The current may be widely different in 

 strength at places distant, say, a mile, and yet the variation in 

 a few yards be so small that this section, so far as the propa- 



* Communicated by the Author. 



