Page:Proceedings of the Royal Society of London Vol 69.djvu/133

Rh

where  (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.

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,

t 'Roy. Sec. Proc.,' vol. 68, p. 277.
 * ' Roy. Soc. Proc.,' vol. 66, p. 212.