Theory of the Flicker Photometer. 303 



given by this equation under various conditions of illu- 

 mination. These are all worked out for a value of 8 of '001. 



Curves a and b show the speeds called for at two illumina- 

 tions for white sectors from zero to 360 degrees. It will 

 be seen that the maximum near 180 degrees, and the drop 

 toward zero for both large and small angles, are predicted, 

 in general agreement with the findings of Porter. Unlike 

 the curves given by Porter's equation these are somewhat 

 unsymmetrical. 



Curve c shows a very interesting consequence of our 

 theory. The experimental results obtained by the senior 

 author on blue light at low intensities, are interpreted on 

 the present theory as indicating that the diffusivit}- of the 

 transmitting medium is a constant for those conditions. 

 2sow, if the diffusivity becomes constant there is nothing to 

 bring the critical speed back to zero when the opening 

 becomes small. Consequently the speed should continually 

 increase with decreasing angle. The actual shape of the 

 curve for illuminations below which the critical speed is 

 independent of the illumination is obtained by making the 

 term within brackets in the above equation constant, choosing 

 an experimental 180-degree value. No relationship of this 

 character between critical speed and angular opening has been 

 observed before, so that its existence or non-existence forms 

 a severe test of the new theory. 



The straight lines d are the critical frequency-log I lines 

 as predicted for various openings. It will be noted that 

 thev are of different slopes, the slope varying continuouslv 

 with the angle. As a consequence, the curves showing the 

 relationship between angular opening and speed are unsym- 

 metrical to different degrees at different illuminations, as 

 shown also by curves a and b. 



The experimental study of these points is described in the 

 next section. 



(b) Experimental. 



The apparatus used in all the experimental work described 

 in this paper is shown diagrammatically in fig. 5. L : and 

 L 2 are point source " 100 candle-power " carbon lamps, L T 

 being fixed and L 2 movnble along a photometer track T. 

 F is a white surface of magnesium oxide on which falls the 

 light from the lamp L^. D is a sector disk of the form 

 shown in the separate sketch at the side whose purpose is to 

 interrupt the view of the surface F when the apparatus is 

 used for critical frequency studies, and to receive the light 

 from the lamp L 2 when the apparatus is used as a flicker 



