404 SCIENCE PROGRESS 



air. He deduced some results about the parabolic orbits. The 

 whole business is an interesting instance of how an incorrect 

 theory may nevertheless lead to the discovery of a new effect. 

 The interpretation of the law of refraction on the wave 

 theory by Huygens' principle is well known, and leads to the 

 result that the velocity of light is less in the more dense medium, 

 and that the index of refraction gives the ratio of the velocity 

 of light in air to its velocity in the medium in question. All 

 the different forms of the wave theory lead to the law of 

 refraction ; it must hold if there are to be boundary conditions 

 at all, quite apart from the particular form of these boundary 

 conditions. But it is not generally known how extensive is 

 the application of the law of refraction. It and the whole 

 theory of reflection and refraction for transparent media apply 

 to metals, if the index of refraction is made complex ; for 

 mercury, for example, the index of refraction has the value 



1*73 + i 4'96 where t is -y/ — i. If cos — [/ — ~| represents 



the hght-wave, where r is the period, /j, the index of refraction, 

 and V the velocity of hght in vacuo, the cosine can be written 

 as 



real part oi e ''^ "' 

 Now, suppose that /x is made complex and = y — itc. Then 



iVlii — ^^ ~ *'^^^ \ 



real part oi e W v ) 



= real part e "tu ^ * t V v) 



— e Tw cos 



T 



a wave which is being absorbed as it progresses. It is rather 

 curious that we can use the complex quantities in this way, 

 and it is, of course, a great simplification ; they were used thus 

 first by Fresnel in connection with total reflection. He showed 

 that in this case the cosine of the angle of refraction has still 

 a meaning when the sine becomes greater than unity. 



Is the law of refraction absolutely true, or is it only the 

 approximate form of a more exact law, which we shall discover 

 in the future, when our observations become more refined ? 

 Of course, when we attempt to verify the law in a particular 

 instance we may find a discrepancy, owing perhaps to the 

 temperature of the glass having altered, or to the glass itself 

 not being sufficiently homogeneous. But we can allow for such 

 sources of error. The question arises as to whether, after we 



