of the Light emitted by Luminous Bodies. 5 



weaker as 8 2 to 4 2 , or as 64 to 16, or 4 to i ; and so 

 for any other distances. 



It is well known that, if any quality do proceed 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 must necessarily be 

 as the square of that distance inversely ; and hence it 

 is evident 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 the light A, and y = the 

 intensity of B : if P represent 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 is = -~, and as it is ^ = ^ by the sup- 

 position, it will be x : y : : m 2 : n 2 . 



That the shadows being of equal density at any 

 given point, the intensities of the illuminating rays 

 must also of necessity be equal at that point is evident 

 from hence ; that the total absence of light being per- 

 fect blackness, and the shadow corresponding to one of 

 the lights in question being deeper or fainter, accord- 

 ing as it is more or less enlightened by the other, when 

 the shadows are equal the intensities of the illuminat- 

 ing rays must be equal likewise. 



In removing the lights, in order to bring the shad- 

 ows to be of the same density, care must be taken to 

 recede from or advance towards the centre of the 

 paper in a straight line, so that the one light may 



