and Refraction of Solitary Plane Waves. 189 



believe, irrefragable proof that in light polarized by reflexion 

 the vibrations are perpendicular to the plane of the incident 

 and reflected rays, and therefore, that it is for vibrations in 

 this plane that Fresnel's tangent-law is fulfilled. 



§ 16. Of our present results, it is (35) of §14 which is really 

 important ; inasmuch as it shows that Fresnel's tangent-law 

 is fulfilled for vibrations in the plane of the rays, with the 

 rotational law of force, as I had found it in 1888 * with the 

 elastic-solid-law of force, provided only that the propagational 

 velocities of condensational w T aves are small in comparison 

 with those of the waves of transverse vibration which 

 constitute light. 



§17. By (28) we see that when a~ l , the velocity of the 

 wave-trace on the interface of the two mediums, is greater 

 than the greatest of the wave-velocities, each of b, b n c, Cj is 

 essentially real. A case of this character is represented by 

 fig. 2, in which the velocities of the condensational waves 

 in both mediums are much smaller than the velocity of the 

 refracted distortion al wave, and this is less than that of the 

 incident wave which is distortional. When one or more of 

 b, b /y c, Cy is imaginary, our solution (26) (28) remains valid, 

 but is not applicable to /regarded as an arbitrary function ; 

 because although f(t) may be arbitrarily given for every real 

 value of t, we cannot from that determine the real values of 



f(t +l g)+f(t- lq ) (37), 



»{/(* + «?)-/(«-«?)} .... (38). 



The primary object of the present communication was to 

 treat this case in a manner suitable for a single incident soli- 

 tary wave whether condensational or distortional ; instead of 

 in the manner initiated by Green and adopted by all subsequent 

 writers, in which the realized results are immediately applicable 

 only to cases in which the incident wave-motion consists of 

 an endless train of simple harmonic waves. Instead, therefore, 

 of making / an exponential function as Green made it, I 

 take 



to-thz < 39 )' 



where r denotes an interval of time, small or large, taking the 

 place of the " transit-time " (§7 above), which we had for the 

 case of a solitary wave-motion starting from rest, and coming 

 to rest again for any one point of the medium after an interval 

 of time which we denoted by t. 



* See footnote §14. 



