448 Prof. Maxwell and Mr. P. Jenkin on the Elementary 



may be made to take place in very different times ; or, in other 

 words, currents of very different magnitudes are produced, and 

 very different amounts of work are done in the unit of time. 

 The quality of the conductor in virtue of which it prevents the 

 performance of more than a certain amount of work in a given 

 time by a given electromotive force is called its electrical resistance. 

 The resistance of a conductor is therefore inversely proportional 

 to the work done in it when a given electromotive force is main- 

 tained between its two ends ; and hence, by equation (5), it is 

 inversely proportional to the currents which will then be pro- 

 duced in the respective conductors. But it is found by experi- 

 ment that the current produced in any case in any one conductor 

 is simply proportional to the electromotive force between its ends; 



hence the ratio ^ will be a constant quantity, to which the re- 

 sistance as above defined must be proportional, and may with 

 convenience be made equal ; thus 



, R=g> (6) 



an equation expressing Ohm's law. In order to carry on the 

 parallel with the pipes of water, the resistance overcome by the 

 water must be of such nature that twice the quantity of water 

 will flow through any one pipe when twice the head is applied. 

 This would not be the result of a constant mechanical resistance, 

 but of a resistance which increased in direct proportion to the 

 speed of the current ; thus the electrical resistance must not be 

 looked on as analogous to a simple mechanical resistance, but 

 rather to a coefficient by which the speed of the current must be 

 multiplied to obtain the whole mechanical resistance. Thus if 

 the electrical resistance of a conductor be called R, the work W 

 is not equal to CRi, but C x CR x t, or 



W=C«R/*, (7) 



where C may be looked on as analogous to a quantity moving at 

 a certain speed, and CR as analogous to the mechanical resist- 

 ance which it meets with in its progress, and which increases in 

 direct proportion to the quantity conveyed in the unit of time. 



18. Measurement of Electric Currents by their Action on a 

 Magnetic Needle. — In 1820, Oersted discovered the action of an 

 electric current upon a magnet at a distance ; and one method of 

 measurement may be based on this action. Let us suppose the 

 current to be in the circumference of a vertical circle, so that in 

 the upper part it runs from left to right. Then a magnet sus- 



E , 

 * By equation (5) we have W=CE* ; but by equation (6) R= ^ ; hence 



W = C 2 R*.— Q.E.D. 



