1902.] 



Contributions to the Study of Flicker. 



325 



The value to be attributed to b must be of the form c -f d log I, where 

 I is the illumination of the disc for the particular experiment in sense 

 (1), because this has been already established by the results of the 

 experiments expressed in fig. 3 ; and since the illuminations used to 

 obtain the five curves were I, 21, 41, 81, and 161 respectively, and I itself 

 was the illumination of the disc by an incandescent lamp of measured 

 brightness 17*8 (in terms of the standard candle before mentioned) at 

 a distance of 3037 mm. from the disc, it will be found that I = 30*9 

 units (the unit being the illumination given by the same candle at a 

 distance from the disc of 4000 mm.) : c + d log I can therefore be 

 written c + d log I + md log 2, where in the curves from I to XVI on 

 the fig., m has the successive values 0, 1, 2, 3, and 4. Log I = 1*49 

 approx.; c = 0*2560085; d = 0*0662837, and the corresponding values 

 of b become — 



0*3547722 

 0-3747256 

 0-3946791 

 0-4146325 

 0-4345875 



The equation to the curve I is w/0'3588 = - 76 -5 + 100 x 

 0*3547722 x log w (360 - w), with similar equations for the other 

 four curves. 



Inspection of fig. 4 is sufficient to show how closely the theoretical 

 and experimental curves coincide, but it may be well to take an 

 example or two showing the same thing. We have seen that experi- 

 ment shows that for flicker to vanish on a disc with a white sector of 

 110° under an illumination 2 x 30*9 units, it must be rotated very 

 approximate!}^ 32*3 times per second (vide the point P, fig. 4). Now n 

 can be calculated from the equation ?i/0*3588 = - 76*5 + 100 x 

 0*3747256 x log w(360 - w) by putting w = 110, when we find n = 

 33*23. The experimental value of n = 32*3 approx. Similarly the 

 position of the point Q on the curve marked VIII shows that experi- 

 ment proved that for a disc with a white sector of 130°, under an 

 illumination 1 = 8 x 30*9 units, a rotation of approximately 39'4 

 times a second is necessary ; and the result as found from the dotted 

 curve whose equation is ?i/0"3588 = - 76*5 + 100 x 0*4146325 x log 

 w (360 - w) by putting w = 130 will be found to be 39*13. 



Experiments have proved that each of the experimental curves is 

 symmetrical with respect to the horizontal line passing through the 

 point on the axis of Y marked 180°, but only the lower half of the 

 experimental curves has been drawn. (This is also true of fig. 4.) The 

 chief result attained by these experiments is the knowledge of the exact 

 relation between the variation in the illumination of a disc, having a variable 

 white sector, and the number of rotations per second necessary in order that 



For the curve 



marked 



I 



5) 



II 



5 5 



IV 



55 



VIII 



55 



XVI 



