324 



Mr. T. C. Porter. 



[May 14, 



ally between n and the varying breadth of the white sector under five 

 different illuminations (in sense (1)); these illuminations, being to one 

 another as the numbers 1, 2, 4, 8, 16, consequently, by what has gone 

 before, since the logs of these numbers are in A.P., the distances 

 between points on these five curves, corresponding to the same width of the 

 white sector, should lie, as they do, at equal distances measured parallel 

 to the axis of X. The meaning to be attached to the fact that a point 

 • — say P in the figure on the curve marked 2 — lies on this continuous 

 lined curve is that, under an illumination called here " 2 " (actually 

 that given by a 17*8 candle-power Ediswan lamp at a distance from the 

 rotating disc of 3037 mm.), a disc of 110° white sector and 250° black 

 must be rotated very approximately 32*3 times a second for flicker to 

 vanish. 



The dotted curves in the same figure are all derived from the general 

 expression n — a + b log w (360 - w), by attributing to b values which 

 depend on the logs of the different illuminations (in sense (1)) to which 

 the disc was exposed in the five experiments by which the experi- 

 mental curves were obtained. To make it clear how these curves are 

 drawn, take the last curve on the right for example. The successive 

 products of the numbers expressing the angular magnitudes of corre- 

 sponding white and black sectors, e.g., 10 and 350, 20 and 340, 30 and 

 330, &c, are calculated, and their logs taken ; each logarithm is multi- 

 plied by a factor, b, which is constant for each curve, and which is 

 itself of the form c + d log I, where c and d are constants, and I is the 

 illumination in sense (1). The series- of numbers thus obtained is 

 multiplied by 100, and each number laid off' in the paper-scale 

 divisions as units from an origin which lies 132 paper-scale divisions to 

 the left of the point B, corresponding to 20 rotations of the disc per 

 second, and therefore lies 76*5 of the same divisions to the left of the 

 origin of the continuous (experimental) curves, and these successive 

 distances are the abscissae of the points which have for ordinates 

 lengths corresponding to the distances marked 10°, 20°, 30°, &c, on the 

 axis of Y, being proportional to the angular magnitudes of the white 

 sector in the successive products. 



n stands for the number of rotations the disc makes per second when 

 the flicker just vanishes, and it will be found that, one division of the 

 paper corresponds to 0*3588 of a rotation per second. Hence, if x is 

 the abscissa of a point P on the experimental curve, reckoned in paper 

 divisions, n = x x 0*3588 or x = ?i/0'3588. If X is the abscissa, also 

 in the divisions of the paper, for the same point P on the theoretical 

 (dotted curves), we have 



x = X - 76 • 5, and therefore X = x + 76 • 5 = njO ■ 3588 + 76 • 5. 



But x = 100 b log w (360 - w), therefore the equation connecting 

 n and w is ?*/0*3588 = - 76*5 + 100 x b x log w (360 - w). 



