334 THE ELECTRIC TELEGRAPH. 



The mathematical expressions of the laws governing these 

 are as follows : 



First, the fundamental law of Ohm expresses the invari- 

 able relation of three of these magnitudes. 



I being intensity, E electro -motive force, and R resist- 

 ance ; of which, if any two are units, the third must also 

 be an unit. 



The second law, experimentally verified by Faraday, is 

 that the quantity, Q, of electricity conveyed by a current, 

 is in proportion to the intensity of that current, and to 

 the time, t, during which it circulates ; the equation is 



Q=It . . . . (2. 



The next law is that of mechanical effect performed by the 

 current. Whenever and wherever a current circulates, it 

 works ; it performs either mechanical effect or its equivalent. 

 Thus, if the current pass in the neighbourhood of a freely- 

 suspended magnet, it deflects it ; if it traverse in its circuit 

 a fluid conductor, it decomposes it, it separates its atoms into 

 their components, perhaps it dissolves one of the electrodes ; 

 and all this time it warms the whole circuit. And the 

 energy of this heat, of this decomposition, of this deflection, 

 if it could be directed favourably for the experiment, would 

 be found able to lift so and so many pounds weight from the 

 ground, to the height of one foot, in one second of time. 



Dr. Joule has proved that this mechanical effect is propor- 

 tional to the resistance of the circuit to the time, and to the 

 square of the intensity. Algebraically expressed, W being 

 the work 



W=FIU . . . (3. 



These three equations would, obviously, be sufficient to 

 determine the units of all the electrical magnitudes in 

 question, if one of these were chosen arbitrarily ; but this is 

 to be avoided, as the object of the system is to refer all of 



