﻿584 Dr. N. Campbell and Mr. B. P. Budding on 



source (to be discovered by trial and error) while all n o£ 

 them acting at the same time make the illumination of A 

 equal to unit illumination. And so on for the values rn/n, 

 and the completion of the standard series. 



We now illuminate B by some point source which can be 

 moved along a straight line passing through B. When the 

 distance of Y from B is r, we find what member of the 

 standard series gives the same illumination on A as Y on B. 

 We then multiply r 2 by the value assigned to this member, 

 and find, after a large number of trials, that there is some 

 value of this product such that we cannot find any law to 

 predict whether any value of it resulting from single obser- 

 vation will be greater than or less than this value. We have 

 then proved the numerical law. 



7. This numerical law, like almost any other, enables us 

 to define a derived magnitude, namely; the constant product. 

 Ir 2 . Experiment shows that this constant is indeed a 

 magnitude, an ordered property of the system under con- 

 sideration, determined by and in general variable with 

 (1) the nature of the point source, (2) the constant imper- 

 fectly transparent medium (if any) intervening between it 

 and the P.S., (3) the direction of the line joining the source 

 to the P.S. relative to lines characteristic of the source, 

 (4) the angle 6 which that line makes with the normal to the 

 P.S. We shall suppose that (2) is not important because all 

 the medium is perfectly transparent. Experiment shows 

 that Ir 2 is approximately proportional to cos 0. We might 

 therefore define a new derived magnitude Ir 2 sec 6, which 

 would depend only on the source and on the direction of the 

 P.S. relative to it ; we might term it the intensity of the light 

 emitted by the source in the direction of the P.S. and denote 

 it by <I>. But since the cos 6 law is not accurately true, <I> 

 would not be truly a magnitude ; it is better to define <E> as 

 the value of Ir 2 when cos = 1 ; it is then totally indepen- 

 dent of the cos 6 law, and the limitation to one value of 6 is 

 not practically troublesome. 



8. <3> is a function, not only of the nature of the source, 

 but also of the direction of the P.S. relative to it. . We can 

 eliminate the direction and obtain a magnitude depending 

 only on the nature of the source, if we can form the sum 

 §*&dw, where co is the solid angle subtended at the source by 

 the P.S. in any direction. The formation of this sum will 

 be legitimate if the inverse-square law is obeyed whatever 

 the direction, so that there is a <E> in every direction, and if 

 <J> is independent of to, the direction being the same; these 



