440 Mr. Wheeler on the Application of Photometry 



difficulties in the calculation of the results, which I am obliged 

 to confess I cannot bring into accordance with those of Mr. 

 Potter. My object, then, in the present communication will 

 be to state the results I have arrived at, such as they are, in 

 the hope that they will receive a candid examination. And in 

 order to afford all facilities for tracing out the cause of error 

 wherever it may lie concealed, and disentangling the subject 

 from its perplexities, I will first lay down the simple elementary 

 principles by which I have been guided in my calculations, 

 and which appear to me to involve the correct principles of 

 this branch of optical science. 



The fundamental principle on which all photometrical com- 

 parisons must proceed is easily seen to be, the equalization 

 of the illuminating effects as estimated by the eye, and the 

 comparison of ,the distances of the luminous bodies necessary 

 to produce that equalization. 



Now the illuminating effect is due jointly to the absolute 

 brightness of the luminous points, and the number of them ; or, 

 in jither words, the product of the intensity and the quantity 

 of fight. 



For the same light at different distances (d), the intensity 

 (z) owing to the diffusion of the rays is inversely as d 2 , but 

 at the same time the apparent area into which the rays are 

 condensed diminishes, or the condensation increases, in the 

 same ratio ; hence on both considerations the intensity is con- 

 stant for all distances. 



For different lights, the absolute intensity of each being thus 

 constant for all distances, the quantity of light varies with the 

 absolute area {a) directly, and the apparent visual area in- 

 versely ; thus, for the illuminating effect (I), we shall have 



T * a 



If we are examining the light reflected from a given sur- 

 face inclined to the direction of vision, it will be easily seen 

 that the inclination is the complement of the angle of reflection 

 ($), and that instead of the absolute area (a) we must take 

 for the effective area a . cos <J>, or the illuminating effect will 



be 



I = 



i . a . cos $ 



d 2 



And in comparing two lights, we shall have as a general formu- 

 la, to be modified to suit the particular cases which may arise, 

 (accenting the letters for the second light,) 



I i . a. cos $ d ,% 

 T '' i. a 1 , cos $' d* ' 



