﻿tlte Measurement of Light* 583 



numerical law concerning it :--The illumination on a surface 

 A from a source X is inversely proportional to the square 

 of the distance of: X from A, so long as (1) X and A are 

 " points " ; (2) the angles between the line XA and any 

 linos characteristic of X and A remain the same ; (3) the 

 medium between X and A (or rather the variable part of it) 

 is perfectly uniform and transparent ; (4) that the bodies sur- 

 rounding X and A are perfectly black. Of course, as usual, 

 these four conditions are really in part definitions of points, 

 perfectly transparent media and perfectly black bodies, the 

 significant proposition being that there are conditions in 

 which the numerical law is true and that they are indicated 

 by the crude meaning. attributed to the terms used. 



Though the principles involved in the fundamental mea- 

 surement of illumination by means of the definitions of 

 equality and addition are the same as those involved in any 

 other fundamental measurement, it may be well to describe 

 in some detail one form of experiment by which the inverse- 

 square law might be proved. 



Two plane P.S. A and B are taken. A is viewed along 

 its normal, and any sources X (all of which must be points) 

 illuminating it are disposed in fixed positions on the surface 

 of a circular cone of any apical angle with this normal as 

 axis. B is viewed at any convenient angle, and the sources Y 

 illuminating it are placed in any convenient positions with 

 regard to it. Some one constant source Y is chosen arbi- 

 trarily and placed arbitrarily in some constant position 

 relative to B. The illumination of J> by Y is arbitrarily 

 chosen as unit. ^Ve proceed, then, to find two sources, X x 

 and Xj' such that either of them, acting alone, makes the 

 illumination of A equal to that of B. Each of these sources 

 then gives unit illumination on A. Xj and X/ are then made 

 to illuminate A together; Y is extinguished and some other 

 source Y 2 is found which, placed in a certain position, makes 

 the illumination of B equal to that of A. X x and X/ are 

 now extinguished, and a source X 2 found which, in some 

 position on the cone, makes the illumination of A equal to 

 that of B. The illumination of A by X 2 is then 2. And so 

 on for the other positive integral values of the illumination 

 of A. Experiment shows that it is impossible to find sources 

 which give negative values for the illumination. But frac- 

 tional illumination can be obtained. In order to make the 

 members of the standard series of illumination the value of 

 which is ljiij we have to find n sources placed on the cone 

 such that any one of them illuminating A makes the illumi- 

 nation of A equal to that of B when illuminated by some 



