ON LIGHT. 373 



the distances i (^C i) from O P, or in the direction O/ 

 parallel to c a. In virtue of both movements, then, it 

 will be found at x, the extremity of the diagonal of the 

 square O x at that moment. And similarly at the end 

 of the 2d, 3d, &c., interval, it will be found at the ex- 

 tremities of the diagonals of the squares next in succes- 

 sion, and as these all lie in one line, o E, 45 inclined 

 both to O P and O /, it appears that in this case the 

 resultant vibration will be rectilinear, and will be per- 

 formed along the diagonal E G of the square E F G H ; 

 and thus it appears that the superposition of two rays of 

 equal intensity, polarized in opposite (i.e., rectangular) 

 planes, results in the production of a ray polarized in a 

 plane 45 inclined to each of the former. Moreover, 

 the square of the diagonal being double that of either 

 side of a square, and the intensity of a ray being mea- 

 sured by the square of the vibrational excursion of its 

 ethereal molecules, the intensity of the compound ray 

 will be double that of the components, or, equal to their 

 sum. And, vice versa, any polarized ray may be con- 

 sidered as equivalent to two rays, each of half its in- 

 tensity, polarized in planes 45 inclined on one side, 

 and on the other of its plane of polarization. It need 

 hardly be observed that if the molecule in starting from 

 O be moving in the direction C A, in virtue of the one 

 vibration, and of c b in virtue of the other, that is, if 

 it be commencing its first semi-vibration in the one 

 direction, and its second in the other, or again in other 

 words, if the vibrations differ in phase by an exact semi- 

 undulation ; all the same reasoning will apply, with this 



