On the Construction of the Photophone. 287 



For let it be supposed (as in the proviso of the theorem, 

 introduced so as not to complicate the electrical conditions) 

 that the enlargement should be to the scale n : 1 in all respects, 

 save only in the depth of the selenium film, the brass con- 

 ductors being the same in number as before, but of n times 

 their former size, touching selenium along edges n times as 

 long as before, the intervening selenium films being n times 

 as broad as before. Such an enlargement will leave the 

 normal electric resistance where it was before, provided the 

 depth of the selenium films be not increased — though, as the 

 photo-electric action is almost entirely a surface action, a 

 slight increase in the depth of the film would probably pro- 

 duce no great change in its electric sensitiveness. 



Suppose the light to be caused, by appropriate optic means. 

 to fall upon the whole enlarged surface uniformly. The linear 

 dimensions being increased in the ratio n : 1, the area will 

 be increased as n 2 : 1. The average intensity of the illumi- 



nation will now be — of what it was. Each portion of surface 



. . n . 1 



equal to the original surface will receive but — part of the 



whole light. n 



But by Adams's law the change of electric resistance is pro- 

 portional to the square root of the illumination. Hence the 

 electric effect over each portion of surface equal to the original 



surface will be - of the original electric effect : and, since the 

 n c 



effect is proportional also to the amount of surface which is 



under illumination, this quantity - multiplied into the ratio 



of the enlarged surface to the former surface (V 2 : 1). gives 

 for the total electric sensitiveness of the enlarged cell a value 

 n times as great as that of the original cell. Thus the propo- 

 sition is proved. 



(3) Theorem II. — With a given maximum of incident light 

 the change of electric resistance will vary in proportion to the 

 third power of the linear dimensions of the cell, if, while its linear 

 dimensions are increased, the absolute thicknesses of the brass 

 conductors and of the selenium ji 1ms remain the same as before, 

 and their number be proportionately increased. 



It was supposed above that the surface was increased n times 

 by an enlargement in length and breadth, which left the total 

 normal resistance where it was before. But since the breadth 

 of the films is dictated solely by practical considerations of 

 construction, the increase of linear width to n times will en- 



