﻿the Measurement of Light. 585 



conditions are fulfilled if the P.S. and the source are suffi- 

 ciently small, y&dw when the sum is taken over all directions 

 from the source is called the flux of light from the source ; if 

 it is taken over a limited range of directions, it is called the 

 flux emitted within the limit of those directions (F) . The 

 name that we (and everyone else) have chosen for this 

 magnitude is, of course, suggested by a theory of illumina- 

 tion ; but it is essential to notice that it can be defined 

 wholly independently of any theory. The magnitude is very 

 important, because it is closely connected with the energy 

 lost by the source and, through that energy, with the 

 magnitudes of other branches of physics. Accordingly, it 

 is often useful to invert the relations at which we have 

 arrived and to express intensity and illumination in terms of 

 flux. It is apparent that intensity is the flux per unit solid 

 angle subtended by the P.S. at the source, and illumination 

 the flux per unit area of the P.S. ; but it must always be 

 remembered that these definitions are inverted and that 

 really we know nothing about flux till we have measured 

 illumination. Again, once we have arrived at the connexion 

 between flux and illumination w r e may use this connexion to 

 measure flux when the conditions which we have hitherto 

 supposed necessary for its measurements are not fulfilled. 

 Thus, even wlien a surface is illuminated by a source or 

 sources which are not a single point obeying the inverse- 

 square law, we may say that the flux incident upon it is the 

 product of the illumination and the area. If we make this 

 purely verbal definition of flux, we then find (in virtue of 

 the law of addition of illumination) that the flux from many 

 point-sources incident on a surface is the sum of that inci- 

 dent from each of them ; when we can use a definition to 

 state a law 7 , the definition ceases to be purely verbal and 

 becomes an expression of fact ; it may be admitted to our 

 scheme on a parity with the other definitions of measurement. 

 9. One important photometric magnitude remains for 

 discussion, brightness. We have used the conception of 

 brightness before as something directly perceived, but we 

 have not framed any scheme for measuring it. The magni- 

 tudes already established enable us to measure brightness as 

 a derived magnitude. Let us take several surfaces which 

 are unequally bright, though each of them is uniformly 

 bright, and allow them in turn to illuminate a P.S., and 

 measure the illumination of that P.S. (from which we 

 deduce the intensity <I> of the light falling on it), the area S 

 of the bright surface and the angle a which the line joining 



