Theory of Nobili's Coloured Rings. 9 



i. e. the thickness of the films of oxide is evidently in inverse 

 proportion to the diameters of the rings." 



If the thickness of the rings is inversely proportionate to 

 their diameter, it is evident that if we multiply the relative 

 thicknesses at certain spots derived from optical considerations, 

 by the distances of these spots from the central point, we must 

 obtain a constant product. Becquerel based his theory upon 

 this test as applied to two selected plates, and found as per- 

 fect an agreement of the twofold results as could be expected 

 in admeasurements of this kind. 



On account of the beautiful idea of this experiment, I regret 

 to be obliged to remark that the accordance of observation 

 with calculation found by M. Becquerel can scarcely have 

 depended upon anything more than a somewhat inexplicable 

 result of chance. 



First, it may be remarked, that in the present arrangement 

 the electricity is not propagated in straight lines. In the 

 case of the diffusion of the electric current in non-prismatic con- 

 ductors, as is well known, we have first sought for iso- electric 

 surfaces, or surfaces of equal tension. If the electrodes are 

 metallic, but the conductor, in which the diffusion of the cur- 

 rent takes place, one of Volta's second class, the tension at 

 all points in it may be regarded as the same*; consequently 

 the surface of every electrode represents the first iso-electric 

 surface. At the margins of the conductor the iso-electric sur- 

 faces are situated perpendicularly. A system of curves inter- 

 secting them at right angles, which thus lie close to the mar- 

 gins of the conductor, and are at right angles to the surfaces 

 of the electrodes, form the lines of the current, in which the 

 motion of the electricity occurs. 



If the curves of the current in the above arrangement coin- 

 cided with the lines of conduction drawn from the point to the 

 plate, the iso-electric surfaces would form spherical cups. 

 Such of these spherical cups as were in contact with the plate 

 when the projection of the point towards it was perpendicular, 

 would then possess a degree of tension common to all points of 

 the plate, and therefore all cause of further currents between 

 the latter and the former would vanish. 



It must remain for the superior analysis of those ingenious 

 philosophers who have lately engaged in the solution of so 

 many important problems in which the diffusion of the cur- 



* G. S. Ohm, The Galvanic Circuit investigated mathematically. Taylor's 

 Scientific Memoirs, vol. ii. p. 401. The procedure recommended by M. Bec- 

 querel, to conduct the current to the centre of the back of the plate, must 

 therefore have arisen from misunderstanding. It could hardly produce the 

 slightest perceptible distortion of the rings, if the current terminated at the 

 circumference of the plate instead of the spot above mentioned. 



