of Electricity in a uniform plane conducting Surface, 471 



from A' and B r , whereby we get 



_ 1 . AG.BF.A'F.B'G ,_._, 



R= ws * log — p *.A'Q.m ' {19b) 



The equipotential circles with the centres C and D being com- 

 mon to the system due to the source at A and sink at A', and 

 also to that due to the sink at B and source at B', and having 

 equal but opposite potentials when taken as belonging to either of 

 these systems separately, will, in the system due to the four poles, 

 form the two branches of the line of zero potential. The other 

 equipotential lines of the system due to the four poles con- 

 sist also each of them of two branches, both of which never 

 lie within the same one of the two circles in question. From 

 this it follows that each circle divides the sheet into two equi- 

 resisting portions ; and consequently the resistance of each of 

 them is i a q gp a'F B'G 



41. Since half the lines of flow due to each pole lie within the 

 circle drawn through them all, the resistance of the portion of 

 the sheet bounded by this circle is (§ 25) twice the resistance of 

 the unlimited sheet ; consequently it is equal to B/ or to li" 

 according to the arrangement of the poles. 



42. It was pointed out in § 39 that the resistance of the part 

 of the sheet outside the circular flow-line with centre C, to the 

 flow from the source A' to the sink B', is the same as the resist- 

 ance of the part inside this circle to the flow from A to B. 

 Accordingly the value of equation (20) remains unaltered when 

 A' and B' are put for A and B, and vice versa, and at the same 



time /> 2 (or p A p B ) is replaced by p A ,p B ,= p A p B ( -^g-J . The 



circles round the two sources then coincide approximately with 

 the two branches of a single equipotential line ; and the same is 

 true for those surrounding the sinks. 



Similar remarks are applicable to equation (22). 



Experimental verifications of some of the conclusions here 

 arrived at will be given in Part II. of this communication. 



* It may be noted that by adding together the values of R' and R" we 

 1 , /AG.BF\2 . ... 



^ ~ } TTK.d ' & I o* — ) ' wn i cn > wr itten m the simpler form 



2 \ AB 

 -—.log , 



7TKO p 



is the resistance of a circular disk on whose edge the poles A and B are 

 placed (see equation 13). 



Errata in No. 326. 

 Page 395, line 3, for in read on. 

 — 398, line 17, for from line read from one line. 



