358 



Mr. H. E. Ives on the 



curves are those for deep red ('650 //,) and for blue (*480 /*). 

 The red curve maintains its direction. The blue curve 

 changes from a diagonal to a horizontal line ; that is, the 

 critical frequency becomes a constant, independent of illumi- 

 nation. The behaviour of the other colours is intermediate. 



Fig. 4. 



Critical Frequency-Illumination Relations for Different Colours. 



A simple relationship therefore exists between the 

 luminosity curves at different illumination s, as given by 

 i his method. In the region above the change of direction 

 we have, if S\ is the slit-width at X, F the critical frequency, 

 F = Kx log Sx + Px, where Kx is a constant involving the 

 relation between critical frequency and intensity of radiation 

 for the individual eye for the colour in question and for the 

 size of the photometric field, and where PX is a constant 

 involving the quantity of energy emitted by the source 

 and the dispersion and dimensions of the instrument of 

 observation, as well as the relative sensibility of the observer's 

 eye to flicker at different colours at a given speed. In short, 

 the law found by Porter holds for different colours if the 

 values of the constants are changed in the equation expressing 

 the law. Upon determining the inverse luminosity curve 

 or slit-width curve for any chosen critical frequency, 

 knowledge of the constants Kx enables one at once to 

 construct the corresponding curves for any other critical 

 frequency. This may be done graphically, by determining 



