Theory of the Flicker Photometer. 301 



where 



I g = transmitted impression. 

 I = intensity o£ stimulus. 



= fraction of cycle during which stimulus is acting. 

 £ = time. 

 co = frequency. 



X = distance from surface of medium. 

 K = difFusivity. 



Were we in possession of extensive tables of values of 

 this expression for a wide range of values of <fi, X, co, and K, 

 it would be possible to pick out those values of co which, for 

 any chosen combination of the other variables, would make 

 the fractional range of fluctuation whatever Ave chose. 

 Such tables are not, however, available, and this is a pro- 

 blem in heat conduction which has not apparently been 

 investigated experimentally. No simple method of solving 

 for the range of fluctuation or for co has been found by us,, 

 and, as a consequence, we have had to be content with a 

 rough and approximate solution. 



In default of the complete solution we have worked with 

 the simplified expression furnished by the first two terms 

 only. 



The range is given by the difference between the maximum 

 and minimum values of the cosine term, or 



4 _x-v/^- 

 E = - le 2K s i n tt^ . . . . (10) 



the fractional range is this divided by the mean value, and 

 this we assume, for the condition of no flicker, to be a 

 certain small quantity which we have called &, or 



^ 4 -XV^ 



° = —~L e - K sin.7rcf) (11) 



Taking logarithms, 



4 

 log 



9 



og — I- log sin Trcfi — log cj> — log 



■"=,.. (12> 



loo- e — i X 



-Jfi. . (12 



© 



If, now, for the difFusivity we introduce the value derived 

 in the former paper (equation (7) of that paper), substituting 

 the mean illumination for the illumination there used, and 

 also using the actual values of the constants, in place of the 



