ON THE DETERMINATION OF TRANSATLANTIC LONGITu'lS. 467 



admit of two interpretations. One of the factors depends on kbe lengtl 



of the conductor 



When this factor is very great, the quantity of - leo- 

 tricity tends towards uniformity of distribution as the time progresses, whereas the 

 current approximates towards zero. Moreover, t he formulae, in this e se.are matoffOUS 



to those which represent the propagation of sound in a narrow lube. From this Kii h- 

 hoff concludes that two electrical waves are transmitted through the comlm lor in oppo- 

 site directions, and with a velocity of 310,765 kilometres (about 195,000 mile; j>< r 

 second. If, on the other hand, the critical factor is very small, a 1 -ult i> reached which 

 shows that the propagation of electricity is analogous to that of heat. In tin cir- 

 cumstances there is no more any question about the velocity (in the common rise 

 of the word) of electricity, except that it may be pronounced greater when the con- 

 ductivity and diameter of the wire are increased. 



Almost contemporaneous with these researches of KirehhofFw ■? an investigation by 

 Sir William Thompson on the "Theory of the Electric Telegraph." He obtained a 

 complex formula for the potential at any point of the conduct inn wire (one end b in 

 connected with the battery and the other with the ground), one term of which varies 

 with the time. This term is similar to the variable term in Ohm's formula. Thomp- 

 son concludes that, though an infinitesimal effect may reach the remote end instantane 



usly, the time required for the 



stated fraction of its maximum 



f 



strength sufficient to show itself (which may be less as the galvanometer is more d< 

 cate) at the remote station will be proportional, in different lines, to the product I 

 the square of the length by the resistance, (electrostatically measured.) and by tie 



electrostatical capacity of the unit of length. Therefore 



of transmission 



We mav infer that the retardations of signals are proportional to the square. 



may 



liflerent 



of the distances, and not to the distances simply ; an 



believing they have fonnd a 'velocity of electric propagation' mav well bat* ob- 



tained widely discrepant results; and the apparent velocity would ^ ponow, 1 



the less the greater the length of wire used in the observations."' te . amp , a. 

 Professor Stokes has said, if the retardation on the submarme hue b«,,,cn «„.e „ 



•ussels (200 miles in length) is one tenth of a second, ^J* *J 

 the signal is 2,000 miles per second. If a simi.ar cable were *W 

 circumference of the earth (about 14,000 miles), the retardatton ^TT^^X 

 hundred and ninety seconds ! In this case, the average vc.octy wouM be seventy 

 times less, or only 28} miles per second. 



,.>..., c _:„ t „ Predion ( London), VII. pp. 382 - 99. 



and B 





