ON LIGHT. 279 



the interior wave will be inclined at a less angle B E p to 

 the surface than B E M, or its equal E B F, and the sines 

 of these angles to a common radius E B are evidently in 

 the proportion to each other of P B to B M, or of the velo- 

 city of light in the medium to the velocity out of it. Now, 

 as the ray is perpendicular to the wave, the inclination of 

 the latter to the surface is the same as that of the former 

 to the perpendicular, and thus these angles are respec- 

 tively identical with those of refraction and incidence. 



(62.) To such of our readers as may find a difficulty in 

 following out this reasoning, the following familiar illus- 

 tration will convey a full conception of its principle. 

 Imagine a line of soldiers in march across a tract of 

 country divided by a straight boundary line into two 

 regions, the one smooth, level, and well adapted for 

 marching, the other difficult, rough, and in which from 

 its nature the same progress cannot be made in the same 

 time. Suppose, moreover, their line of front oblique to 

 the line of demarcation between the two regions, so that 

 the men shall arrive at it in succession, and not simul- 

 taneously. Each man, then, from the moment he has 

 stepped across this line, will find himself unable to make 

 the same progress as before. He will be therefore un- 

 able to keep line with that part of the troop which is 

 still on the better ground, but must of necessity lag be- 

 hind; and that, by the greater space, the longer he 

 travels. Since each man on his reaching the line of di- 

 vision experiences the same difficulty : if they will not 

 break line and straggle, but persist in still marching in 

 line and keeping up their connexion, it will follow of 



