Flow of Electricity in a uniform plane conducting Surface, 453 



very rapid succession. On this account we cannot expect the 

 band-spectrum even with apparently very thick sparks, as, even 

 when the quantity of electricity passing in the spark was rising, 

 I constantly obtained only the unshaded continuous spectrum in 

 addition to the line-spectrum or developed out of it. 



After the foregoing, it is unnecessary at present to go into 

 M. Goldstein's further experiments, some of them very inter- 

 esting ; closer consideration shows that not one of them contains 

 any contradiction of my explanation of spectra. I reserve to 

 myself a more detailed examination of them when I have oppor- 

 tunity to finish and communicate the above-mentioned ex- 

 periments on the forms of the discharges in spaces filled with 

 rarefied gases. 



LIII. On the Flow of Electricity in a uniform plane conducting 

 Surface. — Part I. By G. Carey Foster, F.R.S., and Oliver 

 J. Lodge. 



[Concluded from p. 400.] 



[With a Plate.] 



22. T}ESISTANCE.—The resistance, in the direction of the 

 flow, of the part of the sheet extending between two 

 given equipotential circles follows directly from equation (4) (in 

 § 19). Thus for the potentials of the circles characterized by the 

 ratios r l : r\ and r 2 : ^ 2 respectively, where r x and r 2 are distances 

 from the source, and r\ and r' 2 the corresponding distances from 

 the sink, we have 



u ' = aSs los n and u * = *Ss l0S 7*' 



whence 



Consequently the resistance of the part of the sheet between 

 these circles is 



Bi -^-sa.-*& • • • ^ 



If pj is the radius of the circle which has the greater absolute 

 potential, or the one nearest the source, and p 2 is the radius of 

 the circle nearest the sink, the similarity of the triangles A P C 

 and B P C in fig. 2, Plate IX., gives 



a-\-d Y r' a + d 2 r 1 ^ 



