72 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 13, No. 5 
into “‘light’’ there is no real disadvantage in passing over to entirely 
different units at the same time. 
Derived Quantities —lf we may then start with this half-imaginary 
quantity which we cali “‘light’’ and which is simply energy with the 
proper kind of tag on it, all the other things with which one has to 
deal in photometry and illumination follow logically. In nearly all 
illumination problems we are concerned with the rate at which light 
is supplied. Letting Q be the amount of light, then S = luminous 
flux (F), that is, the rate of flow of light. In order to deal with this 
flow mathematically it is frequently necessary to consider three 
ds 
either from, to, or through a given surface, (2) divergence of flow or 
: " : ; dF 
derived quantities, (1) density of flow or flux per unit area | —@ }, 
dF 
flux per unit solid angle (=), and (3) a combination of these, flux per 
2 
dSdweose 
latter quantities are, of course, applicable in all kinds of problems, 
such as that of calculating the flow of light through a projector or 
other optical system, but more commonly they are used in restricted 
senses for which special names have been given. The flux per unit 
area on a surface is its illumination (E), the flux per unit solid angle 
from a source is its intensity or candlepower (J), the flux per unit solid 
angle per unit of projected area of a light source is its candlepower 
per unit of projected area, or brightness. The source concerned need 
not be a self-luminous one, since the same reasoning will apply to 
light diffusely reflected or transmitted. Volume sources, such as 
flames or the sky, have to be considered as virtual surfaces, but this 
introduces no serious difficulties and is in effect what the eye itself does.. 
Units—We have so far talked about these quantities without 
attempting to tie them up to any definite magnitudes. When we 
come to the matter of units and actual measurements difficulties arise 
in following out the logical scheme outlined. It is agreed that the 
ultimate basis of measurement is to be the effect on the eye, but all 
that the eye can do quantitatively is to equate brightness. We must 
somewhere make an arbitrary start in order to establish a system of 
units. As a matter of history you all know that this has been done 
by adopting a certain value for the candlepower of some kind of light 
source, so that historically the candle is the basic unit. From this 
unit solid angle per unit of projected area ( ) These three 
