MAR. 4, 1923 CRITTENDEN: MEASUREMENT OF LIGHT 81 
relative subjective brightness of two different colored surfaces may 
vary considerably according to the part of the retina the light falls on, 
for most parts of it the relative brightness depends more or less on 
the absolute brightness, and in general it is different for different 
people. 
As a convenient illustration of these variations a piece of blue 
paper on a red background may look brighter than the red at low 
illuminations, become equally bright at somewhat higher illumination 
and decidedly darker at a still higher level. The transition point 
depends on the size of the samples used, and different persons will 
place it at. quite different illuminations. Moreover, when the illumi- 
nation is fairly high and the color of the surfaces distinctly different, 
most persons find it almost impossible to judge when equal brightness 
is attained. 
The question is then how shall we determine when colored lights 
are equally bright, or how otherwise shall we meet the need of de- 
scribing these lights in definite terms. To begin with, it should be 
recognized that the thing we want to define and measure has no real 
and definite existence, but must be more or less arbitrarily established. 
The problem is not merely one of finding a value for a quantity which 
varies with other conditions. If one unit of radiant energy gives rise 
to a certain sensation, we must remember not merely that ten times 
as much energy does not produce ten times the original sensation, 
but that the multiplying factor may vary appreciably with conditions. 
An analogy may make the troubles more evident. It is sometimes 
necessary to compare a length standard of brass with one of platinum. 
In order to have a definite ratio they must, of course, both be kept 
_ at specified temperatures. Now let us imagine three kinds of diffi- 
culties to arise; first, when the meter of brass has been carefully 
adjusted to equal the meter of platinum, a measurement by centi- 
meters indicates that one bar is longer than the other; second, if -we 
change the size of the microscope field used for observations one bar 
expands and the other contracts; third, each individual observer 
when he looks through the microscopes causes a temporary differential 
shrinkage or expansion of the two bars, the amount of this differential 
being more or less characteristic of the individual, but varying some- 
what from day to day. Now if all these troubles really arose I think 
we would be inclined to say that comparing brass meters with plati- 
num was a useless undertaking. Yet when we make such a measure- 
ment as the direct comparison of a normal tungsten filament lamp 
with a carbon lamp there are systematic difficulties closely analogous 
