434 Astronomical and Nautical Collections. 



nation ; bat with some reflection it will be found that nothing 

 can be simpler than the principles on]which they are founded, 

 and their application will soon become familiar to the imagi- 

 nation. 



In order to complete the bases of the general theory of 

 diffraction, it remains for us to consider the principle of 

 Huygens, which appears to be a rigorous consequence of the 

 system of undulations. 



The principle may be thus expressed : The vibrations of a 

 luminous undulation^ in each of its points, may he regarded 

 as the result of the elementary motions which would be trans- 

 mitted to that point, at the same instant, from all the points 

 of the undulation, considered separately, as they existed in 

 any one of its earlier situations. 



It is a consequence of the principle of the co-existence of 

 small motions, that the vibrations, produced at any point of 

 an elastic fluid, by several agitations, are represented by the 

 result of all the velocities belonging to that point at the same 

 instant, as derived from the difi'erent centres of the undula- 

 tions, combined according to the laws of motion, whatever 

 may be the number and situation of the centres, and what- 

 ever the periods and nature of the undulations. This general 

 principle is applicable to every particular case. We may 

 suppose the agitations infinite in number, of the same kind, 

 simultaneous, and taking place in contiguous points of a 

 plane or a spherical surface : it will also be convenient to sup- 

 pose the motions of the particles to take place in the same 

 direction, perpendicular to the surface, their velocity being 

 proportional to the condensation of the medium, and none of 

 them retrograde in their direction. In this manner a deriva- 

 tive undulation will be produced by the union of these agi- 

 tations, and the principle of Huygens may be truly applied 

 to such a propagation. [This may be called a rigorous 

 consequence of the system, but it can scarcely be considered 

 as a proposition mathematically demonstrated : and the fun- 

 damental law of Huygens must perhaps be assumed as an 

 axioni or a phenomenon. Tr.] 



The intensity of the primitive undulation being uniform 

 throughout the surface, it results from this *' theoretical" 



