CURRENT IN A WIRE OF FINITE LENGTH. 



227 



The curve I (Fig. 59) represents the values of the expression 



i/W a \ n 

 -( - ) ( 2--I W-7, 



4V/ V ' / 



which is proportional to the current. 



o,3 



\ 



Fig- 59- 



236. WIRE OF FINITE LENGTH. To pass, to the case of a wire 

 OE (Fig. 60) of finite length /, the end of which is in connection 

 with the earth, let us consider an unlimited wire X'X, and imagine 



x- o,. 



0' 



o" 



0'" X 



Fig. 60. 



on this wire two series of sources O^ O 2 . . . , O', O", O"' . . at 

 successive distances each equal to 2/5 the first O v O 2 , . . . are 

 identical with the given sources which exists at the point O, and 

 the others O', O", O'" , ... are of the same numerical value but of 

 opposite signs. 



All these sources, O and O', Oj and O", . . . being symmetrical 

 in pairs in reference to the point E, and of opposite signs, the 

 potential at E will always be zero. In like manner, all the 

 sources added, O l and O', O 2 and O" . . . are symmetrical in pairs 

 in reference to the point O and of contrary signs: the potential 



Q 2 



