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XXXIII. On the Self-induction of Mm.— Part II. 

 By Oliver Heaviside*. 



XN. Part I. (p. 118) the inner conductor was solid. Let now 

 the central portion be removed, making it a hollow tube of 

 outer radius a Y and inner a . The reason for this modification 

 is that the theory of a tube is not the same when the return- 

 conductor is outside as when it is inside it ; that is to say, it 

 depends upon the position of the dielectric, the primary seat 

 of the transfer of energy. The expression for H 1? the mag- 

 netic force at distance r from the axis, will now be 



Hi={J 1 ( V )-(J,/K 1 )(w)K 1 ( v )}A 1 ; . . (49) 



instead of the former A 1 J 1 (s 1 r), of the first of equations (18); 

 if we impose the condition Hi = at the inner boundary of 

 the wire (as we may still call the inner tube). This means 

 that there is to be no current from r=0 to r = a ; we there- 

 fore ignore the minute longitudinal dielectric current in this 

 space, just as we ignored that beyond r = a 3 previously. If 

 we wish to necessitate that this shall be rigidly true, we may 

 suppose that within r = a and beyond r = a 3 we have not 

 merely k = 0, but also c = 0, thus preventing current, either 

 conducting or dielectric. In any case, with only k = 0, the 

 dielectric disturbance must be exceedingly small. On this 

 point I may mention that my brother, Mr. A. W. Heaviside, 

 experimenting with a wire and outer tube for the return, 

 using a (for telegraphic purposes) very strong current, rapidly 

 interrupted, and a sensitive telephone in circuit with a parallel 

 outer wire, could not detect the least sign of any inductive 

 action outside the tube, at least when the source of energy 

 (the battery) was kept at a distance from the telephone. In 

 explanation of the last remark, we need only consider that, 

 although the transfer of energy is from the battery along the 

 tubular space between the wire and return, yet, before getting 

 to this confined space, there is a spreading out of the disturb- 

 ances, so that in the neighbourhood of the battery the disk of 

 a telephone may be strongly influenced by the variations of 

 the magnetic field. On the other hand, the induction between 

 parallel wires whose circuits are completed through the earth, 

 is perceptible with the telephone at hundreds of miles distance, 

 or practically at any distance, if the proper means be taken 

 which theory points out. His direct experiments have, so far, 

 only gone as far as forty miles, quite recently ; but this may 

 easily be extended. 



• * Communicated by the Author. 



