SCIENCE AND PRACTICE. 419 



K = K' ~ 

 m 



in the other. 



Of the cables submitted for experiment with this apparatus, 

 all those insulated with gutta-percha give nearly the same 

 value when K is reduced for dimensions, and this value 

 is entirely independent of the insulating capacity of the 

 specimens examined. 



107. Hate of Working. The comparative rates of speaking 

 through two submarine cables of the same materials, and 

 of known dimensions, may be calculated by means of the 

 formula, 



B '''''* 7 



O 9791 ' L 



r>V lg.e 

 whence 



R, 



S, = 8 



in which S and S, are the speeds attainable, r and r,, 

 the radii of the copper conductors, R and R, the radii 

 of the gutta-percha covering (therefore R r, th e 



-p T> 



thickness of the covering), log. e and log. e - 1 , the 



Naperean or natural logarithms of the ratios of the 

 diameters of the gutta-percha to the copper, and / and l lt 

 the lengths. 



Certain conditions of equality in the dimensions of the 

 two cables simplify the above formula. 1. For instance, 

 if two lengths I and /, of the same cable be taken, the 

 remaining dimensions are equal, and 



B,= 



or the speeds, in this case, are to each other severally as the 



