or 



Equipotential Curves and Surfaces, fyc. 25 



In the case when p = 2, 



I = 3-2\/2andl, 

 a 



the distances being measured in opposite directions. 



To find the change in the value of - when /x has a slightly different 



value. Let > ^ = 2 +— suppose ; 



= 3-2 V2+^--^ = 3-2V2--002 nearly, 



= 1+1/^2 + 1^ .1=1- ^""^ l — 227 nearly. 

 30 V V 30; 30 30 



Hence if fi be increased by -— , the curve cuts the axis at a distance of 



nearly one fourth of the radius from the singular point. 



If fj, is less than 2, the curve does not cut the axis on the negative 

 side of the origin. 



We may find where it cuts the edge of the disk by making -=1. 



then fl-2+^-co^} -^/(1-^+cos e) (8-i+o* •} 



and 1 — — + cos0 = O; 



so that is very nearly 15°. 



Hence a very small variation in the value of ft produces very great 

 •changes in those parts of the curve which are not near to the centre of 

 the disk. 



This is a point of very great importance in connexion with the tracing 

 of equipotential curves on tinfoil or copper disks ; and the uncertainty in 

 the experimental determination of points in the neighbourhood of the 

 singular point (see Case 6, p. 6) is entirely explained. 



Supposing that one of the galvanometer-electrodes is placed on the 

 straight line joining the two battery-electrodes at the point L in Plate 2. 

 fig. 6. "When the pin or electrode is 1 millim. in diameter the equipo- 

 tential curve corresponding to one extremity of the diameter of the pin 

 cuts the edge of the circular disk at a point 22° distant from the sin- 

 gular point, whilst the equipotential curve through the other extremity 



