490 INVESTIGATIONS EELATIVE TO ILLUMINATING MATERIALS. 



the two lights are equal, or when from their respective distances they 

 throw equal amounts of light on the two faces of the screen. 



In order that both sides may be seen at the same moment without 

 moving the head on one edge of the screen, two mirrors, making with 

 each other an angle of 90°, are placed so that the screen itself will 

 bisect the angle. 



For dividing the scale into parts related to each other as the square 

 of their distances from a center, the following formula and table will 

 furnish the means. Let a be the length of the scale, and x the distance 

 from the candle end to the movable screen; then a — x is the distance 

 between the lamp end and the end of the screen. Denote the degree of 

 illumiuiuation on the candle and lamp sides of the screen by L and L' 

 respectively. Let the intensity of the candle end equal one candle, 

 while that of the lamj) is n candles. Then, since the illumination of the 

 screen varies directly as the iutensity and inversely as the square of the 

 distance, we have the following proportion : 



L:L' 



1 



n 



{a—xfi 



a7= 



l+^/, 



its form into x=^a 



and when L=L' we have {a—xf =wa^ whence 

 For convenience of using this formula it is best to change 



n-1 



The following table has been computed by calling the length of the 

 scale 100 and assigning successive integral values to n, from 1 to 100 

 The column A shows the value of x for each assumed value of w: 



