294 Messrs. H. E. Ives and E. F. Kingsbury on the 



the ordinary critical frequency relation. The sensibility of 

 the flicker photometer is measured by the width of the 

 no-flicker region, as already noted. This is extremely small 

 — a matter of a few per cent. — for low speeds, even for the 

 largest value of 8. The figure clearly shows the desirability 

 of using as low a speed as possible, which means the careful 

 elimination of all mechanical flicker. It is obvious why the 

 sensibility of the flicker photometer decreases with increasing 

 colour difference, since this necessitates a higher speed and 

 consequent wider zone of possible setting. 



The case just considered was not studied by us experi- 

 mentally, as our arrangement of apparatus did not make 

 this convenient. AVe have, however, obtained data for the 

 common case where one illumination is maintained constant 

 while the other varies. The calculation of this case is like 

 that of the preceding, except that it becomes necessary to 

 introduce a changing value of the diffusdvity (and possibly 

 of the Fechner fraction) as the mean illumination changes. 

 In accordance with the results of the previous paper we have 

 assumed the diffusivity to vary according to the relation 



7c = X 2 (rtlogI A + b), (5) 



where I A is the average value of the illumination, the con- 

 stants being derived from experimental critical frequency 

 relations and the formulae previously developed. 



Fig. 2 shows the calculated curves for various values of S, 

 and a set of experimental points. (The apparatus used is 

 described under a later section.) 



It is to be noted, first of all, that both theoretical and 

 experimental curves show a lack of symmetry, the median 

 lying for low speeds toward the fixed light, at high speeds 

 toward the movable one. This is a point of very great 

 practical importance. The obvious moral is that the photo- 

 metric arrangement should be such that the mean illu- 

 mination remains constant, that is, as the illumination on 

 one side is increased that on the other should be decreased, 

 as was done in the first case considered and shown in fig. 1. 

 The effect of this lack of symmetry is, at the speeds which 

 would ordinarily be used, to displace the setting toward the 

 fixed illumination, which is therefore under-rated. In most 

 practical cases, with a good design of flicker photometer, the 

 effect of this lack of symmetry would be largely eliminated 

 where a strict substitution method is employed. If, however, 

 colours are measured which call for greatly different speeds, 

 the displacement will be different for each. This difference 

 could amount to as much as two per cent., judging from 



