414 THE ELECTRIC TELEGRAPH. 



From tine above equations the following important laws 

 are deduced : 



(1.) The charges are in the same proportion as the sines 

 of half the angles of deflection of the needle of a tangent 

 galvanometer. 



(2.) When the relations between the diameters of the wires 

 and those of the insulators are respectively equal, the charges 

 only depend upon the lengths of the lines and upon the 

 number of cells, and, according to 4), will be in direct pro- 

 portion to the products of the lengths of the cables by the 

 number of cells. 



(3.) If the proportion between the diameters of the con- 

 ductors and those of the gutta-percha coverings are the same, 

 and the electro-motive forces of the batteries are also equal, 

 while the lines are of different lengths, the charges, accord- 

 ing to formula 5), are directly proportioned to the lengths of 

 the cables. 



(4.) If the proportion between the diameters of the con- 

 ductors and those of the gutta-percha coverings is the same, 

 and the lengths of the lines are also equal, while the electro- 

 motive forces of the batteries are unequal, the charges, 

 according to formula 6), are in the same proportion as the 

 number of cells. 



(5.) The times of charge are independent of the batteries. 

 Electro-motive forces do not appear at all in the formulae 7) 

 to 10). 



(6.) When the proportion between the diameters of the 

 conductors and of the gutta-percha coverings is the same, 

 the times of charge only depend upon the lengths of the 

 lines and the diameters of the conductors, and, according to 

 8), are directly proportional to the squares of the lengths, 

 and inversely proportional to the transverse sectional areas of 

 the conductors. 



(7.) If the proportions between the diameters of the con- 

 ductors and insulators are the same, and the lengths of the 

 cables also equal, the times of charge, according to 9), 

 are in the inverse ratio of the squares of the radii of the 

 conductors. 



