352 Mr KELLAND, ON THE TRANSMISSION OF LIGHT, &c. 



Similarly the retardation for the other ray is 



rj^cos*^'-!}, 



and the difference of these retardations is 

 , /I 1 



TVcosd)' i ; 



= TFcos<f>' r , '." . 

 ' V v\v -vv) 



, v" - v' 



=■ —i — !—• — -. ■ (« — C-) Sin Oxi sni Rx^ (23). 

 V v(v +v) ' 



Now (a- — c") is a small quantity, hence, if the square of such a 



quantity be omitted, 



v'v{v' + v)=2a^; 



and difference of retardation becomes 



TV 



— - cos d)' (a^ — c^) sin Oa;, sin JSt,. 

 2a' ^ 



28. In conclusion, the principal point in which the present view 

 of the subject differs from those which have gone before, is in the 

 fact of the non-existence of a normal vibratory force, or, in other 

 words, that there is no resolved part of the force perpendicular to 

 the front of the wave. The greatest utility of this view of the sub- 

 ject will appear when we shall consider the effect which takes place 

 at the confines of- two media, for it is evident that in resolving our 

 vibrations at the point of change, we shall be obliged to consider the 

 whole resolved part as lying in the plane of tlie front of the new 

 wave. The complete discussion of this point, however, involves con- 

 siderable difficulty, and I must delay it for the present, hoping shortly 

 to make it the subject of a separate communication. 



