278 ON LIGHT. 



any point in the surface is struck by the wave it will be 

 set in undulatory motion and propagate from it a move- 

 ment which wdll run out spherically from that point in 

 all directions with such (uniform) velocity as belongs 

 to the luminous undulation in the medium. When, there- 

 fore, the wave has reached the position e e, e will just 

 have begun to move ; the internal wave propagated from 

 D will have travelled during one second, from c two, 

 from B three seconds, and the motion, in virtue of 

 these, respectively, will have extended to the surfaces ot 

 spheres about those points as centres, having radii in 

 the proportions i, 2, 3, so that a plane passing through 

 E, which touches one of them, will toucli tliem all, and 

 the same is true for all points intermediate between 

 these. Such a plane will define the limit up to which the 

 vwvcnient has reached wdthin the medium w-hen the ex- 

 terior w^ave has the position e e, and will, therefore, be 

 the fi'ont of a plane 7vave advancing within it. If the 

 velocity of the undulation wdthin the medium be the 

 same as w'ithout, do, c n, b m, the radii of our spheres 

 will be equal to e h, e g, e f, the spaces run over in 

 one, two, three seconds outside, and the touching plane 

 e o N M will evidently be a continuation of the exterior 

 plane w-ave e e. In this case, then, there is no 7-efrac- 

 tion, the direction of the interior ray b m being the same 

 as A B, perpendicular to the exterior wave. But suppose 

 the velocity within the medium less than that without. 

 In that case the radii of our spheres d r, c q, b p, \\\\\ 

 be less than d o, c n, b m, and in a constant proportion. 

 The plane e p touching them all then, or the front of 



