258 THE ELECTRIC TELEGRAPH. 



to n elements connected in series, by increasing their surfaces 

 n times. 



The remaining relation expressed by Ohm's law that of 

 current and resistance is proved experimentally by obtaining 

 a deflection 0!, with a certain inserted resistance, p, and electro- 

 motive force, E, and then doubling the length of the wire, p, 

 diminishing the size of the plates to half, and doubling their 

 distance from each other, by which the total resistance of the 

 circuit is doubled, while the electro-motive force remains the 

 same, and the needle is deflected a smaller angle, ^j . 

 Expressed algebraically the first observation gives 



and the second, 



2) . . . i,- *(*)__ ;|i 



from which it follows that 



F (0) = 2 F (0,0) 

 1 = 21, 



which will be verified by reducing the deflections to degrees 

 of force. 



A law upon which the truth of both these results depends 

 has still to be proved. It is that the resistance is reciprocal, 

 and the intensity thereof directly proportional to the surface 

 of the plates and to the section of the conductor. If the 

 plates be first immersed a known fraction of their surface in 

 the solution, and afterwards other fractions, and completely, 

 and at the same time the sectional area of the conductor be 

 similarly increased by taking thicker wire, or two or more 

 wires of the same length and diameter parallel to each other, 

 the intensity, as indicated by the functions of the galvano- 

 meter, will be found to increase, other things being equal, as 

 the section of the conductor and surface of the exciting plates 

 increases. 



The application of Ohm's law in the solution of different 

 problems which the electrician finds it necessary to answer is 

 very extended. It forms, in fact, the basis upon which all 



