DETERMINATION OF TRANSATLANTIC LONGITUDES. 473 



microfarads for the shorter branch in less than two seconds. 



As the whole 



time over both cables amounted to less than one second, it is evident that th 



1 



I 



remotest from the battery must have begun to discharge when the cabl, was imper 

 fectly charged. This might be expected when it is considered that a part of ft. 

 electricity which constitutes the charge is free to move. As the transmission ti.m * 

 for different cables are proportional to the products of the total electrostatics! 

 ties multiplied by the total resistance, the transmission time between Duxburv sad St 

 Pierre would be about one fourth (more exactly }§) of the transmission time beiw, n 

 St. Pierre and Brest. Of the whole transmission time between Duxhury and Ureal* 

 four fifths (or .639 of a second) would belong to the larger branch, and one fifth (oi 

 .177 of a second) to the shorter branch. The former was traversed at an aura^e 

 rate of about 4,000 nautical miles per second, the latter at an average rate of 4.230 

 nautical miles per second, the whole distance having been passed over at the average 

 rate of 4,080 nautical miles per second. 



The transmission time obtained by Dr. B. A. Gould in 1866, for the passage of signsJt- 

 between Valencia and Newfoundland, was about three tenths of one seemd. If \v< 

 apply Thompson's formula, viz. that the time which elapses before the current reaches 

 a stated fraction of its maximum strength is proportional to kcP (or the total flee- 

 trostatical capacity (el), multiplied by the total resistance (kl),), we have the ratio of 

 the times for signals to pass between Valencia and Newfoundland, and between Hrest 



and St. Pierre, expressed by the fraction [^ * til x .429 = H nearly ' WhC " 

 the transmission time observed between Brest and St. Pierre (viz. .639 of one second) 

 is multiplied by this ratio (|J), the product is .36 of a second. Hence there appears 

 to be a satisfactory agreement between the velocities of transmission, as deduced from 

 the longitude campaign of 1866 upon the Anglo-American cable, and the longitude 

 campaign of 1869-70 upon the French cable, when the two are reduced to tin same 

 standard of length, conductivity, and electrostatical capacity. 



Mr. Varley » made experiments with a battery, varying from twelve to thii y-six of 

 Daniell's cells, upon a cable coiled in a mass, and upon lengths of 150. 300, and 450 

 miles, and found the transmission times independent of the force of the battery, but 

 proportional to the squares of the lengths of cable introduced into the cireuit He 

 also experimented upon 270 and 540 miles of submerged cable between Dunw.ch and 

 Zandvoort, and found the time on the shorter length to be only one quarter of what it 

 was with the double length. Jenkins* has described some observations wh.ch be 



it> ,. * , • t a YTIS11 " Proceedings of the Royal Society, Londoo, Xll. 188. 



Proceedings of the Koyal Society, London, X1L 211. 



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