1902.] 



Contributions to the Study of Flicker. 



321 



Calling the illumination for which the direction of the straight line 

 seems to change, the critical illumination, the equation to the upper 

 part may be written clnjcl log I = cot 39° (approx.) for the scale of the 

 diagram, whilst below the critical illumination it is dn/d log I = cot 

 82° 30' (approx.). It may be noticed that the angle made with the 

 axis of X by the lower part, i.e., 82° 30', is a little more than twice 

 the similar angle made by the upper part, i.e., 39°. Remembering 

 that the scale of the logs (to base 10) is that of one-tenth, that of the 

 numbers expressing the rotations per second, the two equations may be 

 written — 



n = 12-4 log I + 10, 



and 



n = 1-56 log I + 17 -75, 



where n is the number of rotations of the disc per second when nicker 

 just vanishes, and I is the illumination of the disc. 



The actual " last " (undiminished) of the impression on the retina is 

 obtained for any illumination as the fraction of a second by dividing 

 unity by twice n. Thus, for the feeblest illumination experimented 

 with, that of the standard candle at 4 metres, it is about l/35th, 

 whilst for the brightest illumination, that of the arc light at 50 cm., 

 it is 1/1 47th. It is also to be noted that the illumination caused by 

 the 25 candle-power lamp at 4 metres is less bright than that of the 

 single candle at half a metre, and also that that of the arc light at 

 4 metres is as bright as that of the 25 candle-power lamp at half a 

 metre, so that the illuminations given by the moderately bright source 

 of light overlap, as it were, those given by the most feeble and the 

 most intense, and the fact that the values of n obtained were equal 

 when the photometric results showed that they should be so, is a proof 

 that the ^errors made in estimating the quantitative values of the 

 illuminants were not seriously in error. Direct photometric com- 

 parisons were made between the different illuminants both before and 

 after each set of experiments, and it was thus proved that their 

 illuminating powers had not sensibly changed. The lowest degree of 

 illumination was one in which, in popular language, it was not easy 

 to see, whilst the brightest was so bright as to make the disc uncom- 

 fortable to look at, even when the room in which the experiments 

 were performed was flooded with the diffused light of a bright 

 summer day. 



Although the primary object of this research is to throw light upon 

 the process of vision, there are some practical issues to the lines of fig. 3. 

 We can easily determine by its means the number of pictures which 

 must be projected on a screen per second in order that there may be 

 no trace of flicker; the illumination of the brightest part of the 

 brightest view, and that of the darkest part of the darkest view being 



vol. lxx. z 



