360 PHILOSOPHICAL TRANSACTIONS. [aNNO 1794. 



able stands, in a darkened room ; let a sheet of clean white paper be equally 

 spread out, and fastened on the wainscot or side of the room, at the same height 

 from the floor with the lights, and let the lights be placed over against this sheet 

 of paper, at the distance of 6 or 8 feet from it, and 6 or 8 feet from each other, 

 in such a manner, that a line drawn from the centre of the paper, perpendicular 

 to its surface, shall bisect the angle formed by lines drawn from the lights to that 

 centre; in which case, considering the sheet of paper as a plane speculum, the 

 one light will be precisely in the line of reflection of the other. This may be 

 easily performed, by actually placing a piece of a looking-glass, 6 or 8 inches 

 square, flat on the paper, in the middle of it, and observing by means of it the 

 real lines of reflection of the lights from that plane, removing it afterwards as 

 soon as the lights are properly arranged. 



When this is done, a small cylinder of wood, about -i- of an inch in diameter, 

 and 6 inches long, must be held in a vertical position about 2 or 3 inches before 

 the centre of the sheet of paper, and in such a manner, that the 2 shadows of 

 the cylinder corresponding to the 2 lights may be distinctly seen on the paper. 

 If these shadows should be found to be of unequal densities, which will almost 

 always be the case, then that light whose corresponding shadow is the densest, 

 must be removed farther off", or the other must be brought nearer to the paper, 

 till the densities of the shadows appear to be exactly equal; or in other words, 

 till the densities of the rays from the 2 lights are equal at the surface of the 

 paper; when, the distances of the lights from the centre of the paper being mea- 

 sured, 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 be- 

 ing placed at the distance of 4 feet from the centre of the paper, it should be 

 found necessary, in order that the shadows may be of the same density, 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 4% or as 64 

 to l6, 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 found to be of equal density. For putting x = the 

 intensity of b; if p represent tlie point where the rays from a and from b meet- 

 ing 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 inten- 

 sity of the light of a at p is = -^. and the intensity of the light of b at the same 



])lace = -\, and as it is ^- = ^ by the supposition, it will hex: y :: m'- : rr. 



