measuring the comparative Intensities of Light . 6 g 
equal at the surface of the paper ; when, the distances of the 
lights from the centre of the paper being measured, the squares 
of those distances will be to each other as the real intensities 
of the lights in question at their sources. 
If, for example, the weaker light being placed at the dis- 
tance of 4 feet from the centre of the paper, it should be found 
necessary, in order that the shadows may be of the same den- 
sity, to remove the stronger light to the distance of 8 feet from 
that centre, in that case, the real intensity of the stronger 
light will be to that of the weaker as 8* to /£ ; or as 64 to 
16 ; or 4 to 1 ; and so for any other distances. 
It is well known, that any quality proceeding, from a centre 
in straight lines in all directions, like the light emitted by a 
luminous body, its intensity at any given distance from that 
centre will be as the square of that distance inversely ; and 
hence it is clear, that the intensities of the lights in question 
at their sources, must be to each other as the squares of their 
distances from that given point where their rays uniting are 
fornd to be of equal density. For putting x = the intensity of 
B ; if P represents the point where the rays from A and from 
B meeting are found to be of equal density or strength, and if 
the distance of A from P be = m, and the distance of B from 
the same point P = n ; then, as the intensity of the light of A 
at P is = ^ and the intensity of the light of B at the same 
place = A., and as it is™ == y — by the supposition, it will be 
x : y : : ml : n % . 
That the shadows being of equal density at any given point, 
the intensities of the illuminating rays must of necessity be 
equal at that point also, is evident from hence, that the total 
absence of light being perfect blackness, and the shadow cor- 
