Astronomical and Nautical Collections^ 111 



light passes to the extraordinary image; and the same eifects 

 are repeated in the other quadrants. It is obvious that 

 these consequences of the formula agree with the observa- 

 tions. In order that it should be considered as fully demon- 

 strated, it would be necessary that it should be directly 

 verified with intermediate values of t : but it has been sub- 

 jected, in such cases, to several indirect criterions, which, 

 without being perfectly decisive, very greatly increase the 

 probability of its accuracy ; besides that we are encouraged 

 by analogy and by mechanical considerations to conclude 

 that it is rigorously correct. 



In examining the fundamental principles of the theory of 

 undulation, we have found that the intensity of the light must 

 be supposed proportional to the living force or energy of 

 each undulation, or simply, for the same medium, to the sum 

 of the squares of the forces of the different points of the 

 undulation, and must consequently be proportional to the 

 square of the common coefficient of these velocities : conse- 

 quently if cos H is the intensity of the light of the ordinary 

 image, cos i is the common coefficient of the velocities of 

 oscillation in this image, and represents their magnitude ; 

 and in the same manner, sin^e being the intensity of the liglit 

 of the extraordinary image, sin i represents the velocity of 

 the oscillations in the system of undulations which has under- 

 gone the extraordinary refraction. We see then that the 

 decomposition of the velocities of oscillation of the primitive 

 polarised pencil, which is resolved into two others at its 

 entrance into the crystal, are proj^ortioned exactly in the 

 same manner as if the oscillatory motions, instead of being in 

 the direction of the rays, were in a transverse direction, and 

 either parallel or perpendicular to the plane of polarisation ; 

 for in this case the two velocities conceived to have been 

 united, and to be separated, would be proportional to sin i 

 and cos i, according to the principle of the composition and 

 resolution of the small motions of a fluid, which must be con- 

 formable to the laws of statics. The formula of Malus 

 appears, therefore, to imply, that the oscillatory motions of 

 the ethereal particles are performed in directions perpendi- 

 cular to the rays : and this hypothesis is rendered still morq 



JULY— SEPT. 1828. N 



