488 Flow of Eectricity in a uniform plane conducting Surface. 



where both the electrodes were on the edge of the disk. The 

 differences between the results of these experiments and those 

 with other arrangements of the electrodes are in the direction 

 which would be caused by the actual departure from the theore- 

 tical conditions. 



The discrepancy is greatest in Case 5, where both the elec- 

 trodes touch the edge of the disk. In this case the additional 

 poles A' and B ; , required in an imaginary unlimited continuation 

 of the conducting sheet in order to make the circumference of 

 the disk a line of flow, would be points outside the circum- 

 ference, but very near to it and to A and B respectively. If, for 

 an instant, we regard the electrodes as mere points whose dis- 

 tance from the circumference of the disk is very small compared 

 with its radius or with their distance from each other, the equi- 

 potential lines for a short distance from A and B will be very 

 nearly indeed a system of lemniscates (see Part I. § 36, at the 

 beginning) — the node of the self-cutting curve, or lemniscate 

 proper, being sensibly on the circumference. The circle of 

 contact formed by each electrode may be regarded as approxi- 

 mately representing one branch of such a lemniscate, if, instead 

 of taking its centre for the actual pole (A or B), we take a point 

 nearer the centre of the disk by (<\/2 — l)/o, where p is the radius 

 of the electrode. A recalculation of the experiments of Case 5 in 

 this way reduces the mean value of 2C from 3*245 to 3*11 ; and 

 a similar correction applied to Case 4 gives 2C = 3*10 instead 

 of 3*20. Thus corrected, the results of these experiments agree 

 fairly with those of Case 1. 



54. Taking the mean value of 2C obtained with electrodes on 



TT 



the edge of the disk and multiplying it by r ™ we get 



4011, 



which ought to be the resistance of a square centimetre of the 

 tinfoil used. For comparison with the value so found, the same 

 quantity was determined by measuring the resistance of an ob- 

 long strip of tinfoil, the electrodes being flat pieces of brass, 

 firmly clamped down on the ends of the strip, and making con- 

 tact with its entire width. Five measurements, made with dif- 

 ferent lengths of a strip 3 centims. broad, gave as the resistance 

 of a square centimetre 



4-032, 



the unit being, as before (see § 52), 0*00155 ohm ; and five 

 measurements, with a strip 1*5 centim. broad, gave 



4*029. 



