686 INDUSTRIAL APPLICATIONS. 



The maximum useful work, lastly, corresponding to a yield of 

 50 per cent, is 



2 - 



It will be observed that the useful work 



is equivalent to that which would be absorbed either by an elec- 



E' 



tromotive force E x = E' + IR', or by a resistance x = R' + , and 



that the efficiency may be written 



x 



E R + x 



For an efficiency of 50 per cent, the useful resistance x should 

 be equal to the useless resistance R, or the useful electromotive 

 force E! equal to half that of the battery. 



Equations 



_U_i^ * 



_ 

 W E R + x' 



contain several quantities which give rise to a great number of 

 problems, when there are only three unknown quantities, and when 

 any relations are established between them, provided these relations 

 are compatible with the physical phenomenon. 



We may add that the same considerations apply to an electro- 

 motor of any nature whatever, chemical or mechanical, which is 

 characterised by a constant electromotive force E, and a constant 

 resistance R . 



1244. CHOICE OF CONDUCTORS. If S is the section of a 

 conductor, o- its specific resistance, the resistance for unit length is 



