288 Prof. S. P. Thompson on the 



able n times as many conductors to be employed ; and the 

 thickness of the selenium film may be reduced to - of what it 

 was reckoned above. This will reduce the total normal re- 

 sistance of the cell to — , of what it was reckoned above, and 

 n 1 ' 



would therefore make it ri 2 times as sensitive were its resist- 

 ance the only one in the circuit. 



Combining this result with the former, we obtain the result 

 that the change of electric resistance exhibited by the cell of 

 linear dimensions n, under the influence of a given quantity 

 of light distributed uniformly over its surface, will be n % 

 times as great as that exhibited by a cell of linear dimensions 

 1, provided that the absolute thickness of the films and con- 

 ductors remain the same (the resistance of the brass conductors 

 themselves being reckoned small). 



(4) The practical inference from this is, that the selenium - 

 cells should be made as large as possible, and that the beam 

 of light received by the mirror from the distant station should 

 be so constructed as not to concentrate the light on one point 

 of the selenium, but to distribute it uniformly over the sen- 

 sitive surface. 



Now the supposed advantage of the parabolic mirrors 

 hitherto employed is that they collect parallel rays to one 

 focus. If this be no longer necessary or advisable, then some 

 other form of mirror than that of the paraboloid of revolution 

 ought to be employed. 



(5) A short cone, polished on the interior surface, appears 

 therefore to offer certain advantages over the paraboloid in 

 respect of its distribution of light, besides being far cheaper to 

 construct. It only remains to calculate the appropriate angle 

 of aperture that shall, with a cylindrical selenium-cell of given 

 length, give the greatest available linear aperture and reflect 

 into the cell the greatest number of effective rays. 



(6) Theorem III. A hollow cone along whose axis lies a 

 cylindrical selenium-cell of given length will reflect onto that 

 cylindrical surface the greatest number of rays (that traverse 

 space parallel to the axis) if its angular semi-aperture be 

 45°. 



The calculation amounts to finding the angle that will, with 

 a given length of cell, give the greatest possible linear aper- 

 ture. 



In the figure 1, let POM represent the angle of half-aper- 

 ture, which we will call 6. Let OQ ( = be the length of 

 cylinder, which may be supposed to be thin. Let the ray 



