78 Mr. 0. Heaviside on the 



initial values of the terminal arbitraries be taken to be zero, 

 and although it is similarly determinable when particular 

 values are given to the arbitraries, whose later values also are 

 determinable by affixing the time-factor, it does not appear 

 that this determinateness of the later values of the terminal 

 arbitraries is always of a complete character, when the sole 

 data relating to them are the form of Z and their initial values. 

 For it is possible for a terminal arrangement to have a certain 

 portion conjugate with respect to the line ; and although the 

 state of the line will not be affected by initial energy in that 

 portion, yet it will influence the later values of the other 

 terminal arbitraries. This might wholly escape notice in an 

 investigation founded upon a given form of Z with undetailed 

 connexions, owing to the disappearance from Z of terms 

 depending upon the conjugate portion. In such a case the 

 reduced form of Z cannot give us the least information con- 

 cerning the influence of the portion conjugate to the line. It 

 is as if it were non-existent. If, however, Z be made more 

 general, so as to contain terms depending upon the conjugate 

 portion, although they be capable of immediate elimination 

 from Z, it would seem that the indeterminateness must be 

 removed. 



Some JSfotes on Part IV. Looped metallic circuits. Inter- 

 ferences due to Inequalities, avd consequent limitations of appli- 

 cation. — It is scarcely necessary to remark that, in the inves- 

 tigation of Parts I. and II., the choice of a round wire or tube 

 surrounded by a concentric tube for return conductor was 

 practically necessitated in order to allow of the use of the 

 well-known J and J\ functions and their complements, 

 because it was not merely the total current in the wire with 

 which we were concerned, but also with its distribution. 

 Next, in order that it should be a question of self-induction, 

 and not one of mutual induction also, with fearful com- 

 plications, it was necessary to impose the condition that the 

 wire, tubular dielectric, and outer tube should be a self- 

 contained system, making the magnetic force zero at the 

 outer boundary. It is true that no external inductive effect 

 is observable when the double-tube circuit is of moderate 

 length. But electrostatic induction is cumulative ; and it is 

 certain that, by sufficiently lengthening the double tube, we 

 should ultimately obtain observable inductive interferences. 

 Our investigation, then, only strictly applies when the double 

 tube is surrounded on all sides, to an infinite distance, by 

 a medium of infinite elastivity and resistivity. 



[Maxwell termed 47r/c, when c is the dielectric constant, 

 the electric elasticity. I make this the elastivity : first, to 



