Manchester Mevioirs, Voi. xHv. {i^gg), No. \. 3 



symmetry it is also evident that the triangle ACB maybe 

 transformed into the triangle A'C'B\ and two contiguous 

 points on opposite sides of AC transform into two 

 contiguous jjoints on opposite side of A'C\ i.e. the quadri- 

 lateral ABCD in the rj plane transforms into the square 

 A'B'C'D' in the rj' plane. 



If/ is the thickness of the square and () the resistivity 

 of the medium, the quotient of the difference of potential 

 between A'D' and B'C by the current from one to the 

 other = p//. 



Hence the resistance of the quadrilateral ABCD from 

 the side AD to the side BC is equal to p//, where / is the 

 thickness and p the resistivity of the material of the 

 quadrilateral. 



fig- 3- 



Fig. 3 shows approximately the equipotential lines 

 when the angles at B and D are right angles, and that at 

 ^=45.^ They have been drawn by making use of the 

 fact that in the neighbourhood of each angular point the 

 transforming equation may be written s' = Ad^. The 

 closeness of the approximation will therefore be least near 

 the centre of the quadrilateral. 



