476 Messrs. G. C. Foster and 0. J. Lodge on the Flow of 



Moreover 3 if an equal similar area be taken in a limited conducting 

 sheet, whose conductivity and thickness outside this area vary 

 in any manner, the electrical state within the area will still be 

 the same as in the previous case, if only the conditions at the 

 boundaries remain unchanged ; for evidently the electrical flow 

 within the area will depend on the actual electrical state of the 

 boundaries, and not upon the way in which this state has been 

 produced. Consequently the truth or falsehood of conclusions 

 arrived at, like those given in Part I. of this communication, on 

 the assumption of an unlimited uniform conducting surface, may 

 be tested by experiments on a conducting sheet of finite size, if 

 we can ensure that, at the edges, the electrical conditions are the 

 same as they would be at the boundaries of a portion of the same 

 size and shape taken in an infinite sheet in which there is a 

 known distribution of sources and sinks. 



44. In order to carry out such experiments, it is needful that 

 the boundaries of the part of the conducting sheet examined should 

 be formed either wholly by equipotential lines, or partly by equi- 

 potential lines and partly by lines of flow. It is evident that an 

 area within which there is a flow of electricity (unless the circuit 

 is complete within this area, as in a conducting plate moving in 

 a magnetic field) cannot be bounded entirely by lines of flow ; 

 for in that case no electricity could enter or leave the area. 



Any line in a conducting sheet can be practically made to be 

 an equipotential line by laying along it, and in close contact with 

 the sheet, a conductor whose resistance in directions parallel to 

 the sheet is insensible — for instance, a thick band of copper. 

 And any line along which the sheet is bounded by non-conduc- 

 tors (e. g. the free edges of the sheet) is necessarily a line of flow, 

 since no electricity can pass across such a boundary in either di- 

 rection. The experimental conditions can thus be chosen so that 

 • a conducting area may be bounded either by equipotential lines 

 wholly, or partly by equipotential lines and partly by lines of 

 flow, placed so as to correspond to any given system of poles. 



45. Methods of testing experimentally the conclusions deduced 

 from theory, founded on the general principles above indicated, 

 have been employed by various investigators. Thus Kirchhoff, 

 in his paper of 1845 (Pogg. Ann. vol. Ixiv.), traced the form and 

 distribution of the equipotential lines on thin sheets of metal 

 bounded by four circular arcs, two of which, being free edges, 

 were lines of flow and belonged to the same circle ; while the 

 others, of much smaller extent than the first two, were equipo- 

 tential lines determined by the contact of small cylindrical elec- 

 trodes (conducting wires) with the margin of the sheet. He 

 traced the course of the equipotential lines by fixing a wire con- 

 nected with one terminal of a galvanometer in succession at 



