440 Mr. 0. Heaviside on the 



the case of an iron wire. The nature of the dielectric wave 

 is far more simply studied graphically than by means of 

 Fourier series, on the assumption of infinite conductivity, 

 which allows us to represent things by means of two oppo- 

 sitely travelling waves. To this I may return in the next Part. 



I will conclude the present Part with a brief outline of the 

 reasoning which guided me six months ago, when my brother's 

 experiments on induction between distant circuits (mentioned 

 in Part IP) in the north of England commenced, to the con- 

 clusion that long-distance signalling (i. e. hundreds of miles) 

 was possible by induction, a conclusion which has been some- 

 what supported by results, so far as the experiments have yet 

 gone. Recognizing the great complexity of the problem, and 

 the difficulty of hitting the exact conditions, I made no special 

 calculations but preferred to be guided by general considera- 

 tions ; for, in the endeavour to be precise when the data are 

 uncertain and very variable, one is in great danger of swallow- 

 ing the camel. 



One may be fairly well acquainted with electromagnetism, 

 and also with the capabilities of the telephone, and yet receive 

 the idea of signalling by induction long distances with utter 

 incredulity, or at least in the same way as one might accept 

 the truth of the statement, that when one stamps one's foot 

 the universe is shaken to its foundations. Quite true, but 

 insensible a few yards away. The incredulity will probably 

 be based upon the notion of rapid decrease with distance of 

 inductive effects. This, however, leaves out of consideration 

 an important element, namely the size of the circuits. 



The coefficients of electromagnetic induction of linear cir- 

 cuits are proportional to their linear dimensions. If, then, we 

 increase the size of two circuits n times, and also their distance 

 apart n times, the mutual inductance M is increased n times. 

 Let Ei and R 2 De the resistances of primary and secondary. 

 The induced current (integral) in the secondary due to start- 

 ing or stopping a current Q x in the primary is MC^/I^, or 

 M£ 1 /R 1 R 2 , if «i be the impressed force in the primary. Now 

 increasing the linear dimensions, and the distance, in the 

 ratio n (with the same kind of wire) increases M, R,, and R 2 

 all n times. So only e,i remains to be increased n times to get 

 the same secondary-current impulse. We can therefore en- 

 sure success in long-distance experiments on the basis of the 

 success of short-distance experiments, with elements of uncer- 

 tainty arising from new conditions coming into operation at 

 the long distances. 



But practically the result must be far more favourable to 



