Electrical Signals on Land Lines, 413 



distance x from the origin of the cable, ^ is the specific con- 

 ducting-power of the wire, and 7 a purely hypothetical quantity, 

 the existence of which Ohm cannot prove, but which he regards 

 as a specific capacity for electricity analogous to the specific 

 capacity of a body for heat, proportional, therefore, to its length 

 and section. Professor AVilliam Thomson's expression is 



, dv _ d 2 v 



where v is the u of Ohm's expression, and k and c have the 



meanings given above. Thus, if we write - = hc } the two expres- 



/C 

 sions become identical. The difference between Ohm's statement 

 and that of Thomson is simply, that whereas the former assumed 

 a certain quantity for which he can give no value, and of the 

 existence of which he can give no proof, the latter uses a quan- 

 tity, c, of which he can not only prove the existence, but calcu- 

 late the amount from independent data. Ohm was wrong in 

 supposing the capacity for electricity analogous to that for heat, 

 and proportional to the section of the wire ; and therefore no value 

 applicable to all wires even of one metal could be found by ex- 

 periment for his constants. M. Guillemin starts with Ohm's 

 expression, uses his phraseology, and apparently still believes 

 7 to be a specific capacity proportional to the section of the line 

 and the material employed. He is well aware of the existence 

 of the statical charge, but does not appear to have understood 

 its connexion with the phenomena he observed. 



The results, however, of M. Guillemin's experiments are, as 

 was to be expected, in accordance with the completed theory, 

 and allow the constants required for its application to land lines 

 to be calculated with some accuracy. 



The direct measurement of the retardation of a single signal 

 in the manner which has been practised for submarine cables 

 would be exceedingly difficult, if not impossible; for not only is 

 the retardation on a long line so trifling as to be measured by 

 a few hundredths of a second, but during that exceedingly short 

 interval it would be necessary, if accurate information were 

 wanted, to measure the gradual increase of the electrical current 

 from nothing to a maximum. The direct measurement of the 

 statical charge, from which the retardation could be readily 

 calculated, could hardly be made on land lines as usually insu- 

 lated, owing to the loss of electricity by the posts ; the experi- 

 ment would be further vitiated by the so-called polarization at 

 the moist surfaces of the insulators, tending to send a reverse 

 current to that employed to charge the cable. Some indirect 



