420 THE ELECTRIC TELEGRAPH. 



squares of the length. 2. If the lengths are the same, and 



the cables different, then 



P 

 r.'log., 



or the speeds are related directly as the transverse sections 

 of the conductors, and as the logarithms of the proportion 

 between the diameters of gutta-percha and copper. 

 With aid of the formula 



S = r 2 log.- 

 r 



the diameter 2 R, of the gutta-percha being given, the thick- 

 ness of conductor which would give the greatest speed is 

 found by the ordinary method of maxima and minima, 

 by the differential calculus. The value of r which, set 

 in the above formula, gives the greatest possible value of S 

 is 



R R 



~ v/T* 1-649 .... 



When the conductor is a solid or a sectional wire, the value 



-o 



is best deduced from the weights of the conductor and 



core. The weight w of a knot of the copper conductor, and 

 that of a knot of finished core, W, being known, the weight 

 of the insulating coat (W w) will, be also known. Knowing 



the specific gravity s of the insulating material, and that of 



p 



the conductor p, we can find the value of from the 



r 



equations 



1) . . . W w = (R'- 

 and 



2) . . . w = r* I TT ff 

 which, divided by each other, give 



W 8 

 e= 2-7183 . . . . etc., the base of the Naperean system of logarithms. 



