14 Prof. W. G. Adams on the Forms of 



sheet under these conditions the portions of equipotential curves aud 

 lines of flow which are not near the edges of the sheet will be very 

 nearly circular. This we have seen to be the case in the experiments on 

 tinfoil (see Plate 1. fig. 1). 



"When the lines approach near the edge of the disk, or when the elec- 

 trodes are near the edge, then the form of the equip ofcential curve is 

 generally altered, because the edge of the disk will generally cut some of 

 the lines of flow of the infinite plane. We may conceive of the lines of 

 flow as distinct from one another, but as filling up the whole of the 

 disk ; if, then, we make a section of the disk along a line of flow we do 

 not alter the distribution of electricity on the disk, and so do not alter 

 the forms of the equipotential curves. But in that case, since the two 

 parts of the disk are entirely separate from one another, one of the parts 

 may be taken away without causing any change in the law of distribution 

 of the electric currents in the other. 



If, then, we cut away from an indefinite sheet a portion which is 

 bounded by lines of flow, we shall not alter the form of the equipotential 

 curves ; but, since we thereby increase the resistance of each portion, we 

 shall increase the difference of potential between the two electrodes, 

 and the distances between successive equipotential curves corresponding 

 to given differences of potential will be diminished. 



The straight line joining the battery-electrodes is a line of flow ; hence 

 when the electrodes are on one edge of a sheet which is unlimited in all 

 directions but one, the equipotential curves are still arcs of circles 

 having their centres on the straight edge of the disk; or if a portion of 

 the disk bounded by this edge and by the arc of a circle which passes 

 through the two electrodes be cut out, the forms of the equipotential 

 curves in this portion will be arcs of circles with their centres on the 

 straight edge. 



The same will apply to any portion bounded by the arcs of two circles 

 passing through the two electrodes ; so that on a circular disk with the 

 two electrodes on the circumference, the circular boundary of the disk 

 will be two lines of flow, and the equipotential curves which cut them at 

 right angles will also be circles with their centres on the straight line 

 passing through the two electrodes*. One of the electrodes will be the 



* [July 23. — This case has been worked out experimentally by M. Kirch- 

 hoff by joining the galvanometer-wires to two points of the plane sheet 

 which are at different potential, and balancing the current which would 

 flow through those wires, by introducing a thermoelectric pile into the 

 galvanometer- circuit. M. Verdet says : " M. Kirchhoff n'a etudie par 

 l'experience que le cas d'une plaque circulaire communiquant par deux 

 points de sa circonference avec les reophores d'une pile." M. Kirchhoff 

 used a copper disk, and from its being a good conductor was unable to 

 determine its resistance. M. Yerdet also adds that M. Quincke worked 

 out the case of a square disk with one battery-pole at a corner and the 

 other on a diagonal of the square. These two are the only cases con- 



