On Areal Induction. 125 



where <f> (r) is the maximum value of the function on the circle in 

 question. When /> is integral, this approximation becomes 



log <fr (/') 



logr 



A number of theorems are given relating to the order of functions 

 combined from functions of given order. 



It is shown that a function is of the same order as its derivative, 

 and that from the knowledge of the zeros of a function we may derive 

 an approximation to the large zeros of its derivative. 



If a function is of " genre " p, its derivative can at most have only 

 j) zeros beyond those given by the extension of Rolle's theorem. 



The memoir closes by suggesting other applications of the theory. 



" On Areal Induction." By GEORGE J. BURCH, M.A., F.R.S., 

 Reading College, Reading. Received September 10, 1901. 



In my paper " On the Relation of Artificial Colour-blindness to 

 Successive Contrast,"* I described a modification of some experiments 

 by Sigmund Exner. 



A disc, half black and half white, with a very narrow slit at the 

 junction of the two halves, revolves in front of an incandescent lamp. 

 Another lamp throws a light upon the face of the disc. While it is 

 rotating slowly, the incandescent filament of the lamp, seen through 

 the slit as it passes across, looks bright against the white card, but 

 when a certain velocity is reached it appears as a black thread against 

 a brighter background. 



I suggested as the explanation of this phenomenon that the intense 

 light of the filament induced an amount of fatigue out of all proportion 

 to the sensation excited by it, so that the less fatiguing illumination of 

 the white card produced a greater effect on the senses than the sum of 

 the sensations due to the filament and the subsequent light. 



In a recent paper,! however, Dr. Shelf ord Bidwell has described an 

 experiment having an important bearing on the subject. 



By a suitable arrangement a disc of green light is projected on a 

 screen ; this is followed by a somewhat larger disc of white light, and 

 the cycle is completed by an interval of darkness. The novelty of 

 the experiment consists in the addition of a black spot in the centre of 

 the white disc, so that when the apparatus is worked the site of this 

 spot is illuminated five or six times a second by green light only, 



* ' Eoy. Soc. Proc.,' vol. 66, p. 212. 

 t 'Koy. Sec. Proc.,' vol. 68, p. 277. 



