CHAP, iv.] ELECTRICITY AND MAGNETISM. 233 



electricity to the potential V, the work done is V ergs. 

 This assumes, however, that the total potential V is not 

 thereby raised, and on this assumption the work done 

 in bringing up Q units would be QV. If, however, the 

 potential is nothing to begin with and is raised to V by 

 the charge Q, the average potential during the operation 

 is only JV ; hence the total work done in bringing up 

 the charge Q from zero potential to potential V is JQV 

 ergs. Now, according to the principle of the con- 

 servation of energy, the work done in charging a jar 

 or condenser with electricity is equal to the work which 

 could be done by that quantity of electricity when the 

 jar is discharged. Hence a ^QV represents also the 

 energy of the discharge, where V stands for the dif- 

 ference of potential between the two coatings. 



Since Q = VC, it follows that we may write JQV in 

 the form J^. That is to say, if a condenser of capacity 

 C is charged by having a quantity Q of electricity 

 imparted to it, the energy of the charge is proportional 

 directly to the square of the quantity, and inversely to 

 the capacity of the condenser. 



If two equal Leyden jars are charged to the same 

 potential, and then their inside and outside coatings are 

 respectively joined, their united charge will be the same 

 as that of a jar of equal thickness, but having twice the 

 amount of surface. 



If a charged Leyden jar is placed similarly in com- 

 munication with an uncharged jar of equal capacity, the 

 charge will be shared equally between the two jars, and 

 the passage of electricity from one to the other will be 

 evidenced by the production of a spark when the 

 respective coatings are put into communication. Here, 

 however, half the energy of the charge is lost in the 

 operation of sharing the charge, for each jar will have 

 only ^Q for its charge and |V for its potential ; hence 

 the energy of the charge of each being half the product 

 of charge and potential will only be one quarter of the 



