ON THE DETERMINATION OP TRANSATLANTIC LONGITUDES. 47 



air ; or, if it was a cable wire, coated with gutta-percha, that it suffered no Ion of 

 electricity from the surrounding water; in other words, that, in both caw*, the m ,ln 

 tion was perfect, so that there was no leakage to the electrical eunv.it. The inilu nee 

 of this leakage, at least so far as the naked wires are concerned, has been carefully 

 studied by Gaugain, 1 and the deductions from Ohm's theory have been tested by ni 

 experiments, and with one curious result. Gaugain designates the time n |iii <1 by 

 the current to reach its highest limit of tension at any point as the absolute (Jurat m f 

 the propagation, and he calls the time which elapses before the current attains a defr 

 nite percentage of this maximum the relative duration of the propagation. Now, w hen 

 the disturbing effect of the air is taken into account, in consequence of its imj.orft •■•t 

 insulation, Ohm's theory indicates that the absolute duration of the propagation would 



t 



increase fas ter than in proportion to the square of the length of the conducting wire, 

 and that the relative velocity of propagation would increase more slowly than the 

 square of the length. The absolute duration of the propagation is of no practical im- 

 portance as it is indefinitely long in any case ; and there can be no question as to its 

 comparative values. But the law in regard to the relative duration of propagation 

 was tested experimentally as follows. Two threads of cotton were taken, each 1" in 

 length. When tried separately, the transmission time was on the average eleven sec- 

 onds. If they were placed end to end, so as to double the length, the transmission 

 time was four times larger, or forty-four seconds. In these experiments the 

 the air was comparatively insignificant. Gaugain tried, next, two threads of silk. • -,h 

 four metres in length, so that the loss by the air might be sensible, compare*! with 

 their own imperfect conducting power. The transmission time with the united 

 lengths (eight metres) was only three times as great as when either was tried alone. 

 He obtained the same result with two threads of cotton, each only one metre in 

 length, when the current was diverted laterally by mean* of three p.- ees of silk 

 edging symmetrically placed. The battery used in all the experiments consisted of 630 

 elements, of which 140 were those known as the couronne de tmses, and 4!i0 v re 

 those of Pulvermacher.* These results accord with Ohm's more general expressmn 

 for the tension, in which the influence of the air is not neglected, viz. : 



%T 



(l + x) -*»«**« 





The formula , conned - it H holds g ood -J ^^^ J* 

 turbing influence of the air is uniform throughout the whole est 



LX. 



Pbywque, 3 S., LXIII. 201 



