180 Mr KELLAND, ON THE DISPERSION OF LIGHT, 



Now, from the symmetry of the medium, we have 



2-r— A=2.f— -A: 



.•. v' = -^^ . 2 — 7-2- sin = V ', 



and v^ = — Y- 2 — — -. sm^ ^-- = ^ 2 5— sm' — — 



€^ r X fc- i X 



But by reference to the preceding part of the investigation it will be 

 found, that the forces have been considered positive when they acted 

 in the direction in which the disturbing particle lay, and vice versa; 

 that is, they have been considered attractive. It appears, then, that 

 such a supposition makes v and v" possible and equal, but v' impos- 

 sible, and of a different magnitude. 



If, on the other hand, we had considered the forces repulsive, the 

 factor A would have been negative, we should also have had v' pos- 

 sible, whilst V and v" would have been impossible. Hence attractive 

 forces give rise to transversal vibrations only, repulsive to direct vibra- 

 tions only. The latter corresponds, both as to forces and vibrations, to 

 the particles of air, the former then may be reasonably supposed true 

 for light ; and hence it follows, that from a comparison of our formula 

 with observed facts, the forces are found to be attractive. I must, 

 however, observe, that the equations deduced as I have obtained . them 

 will but very imperfectly apply to sound ; there seems, however, a great 

 probability that the general form will be an analogous one; and should 

 it be found to be the same, then since all the waves of sound of dif- 

 ferent lengths travel with an equal velocity, the conclusions which we 

 have deduced as to the forces varying inversely as the square of the 

 distance might hold equally in air, a conclusion to which I hope shortly 



