DIFFERENCES OF ROUTE. 



207 



we operate with white hght in phenomena of colora- 

 tion. In the course of such singular results we may, 

 perhaps, be curious to find the numerical value of these 

 differences of route, so often mentioned, and which place 

 two rays in (he conditions either of accordance or com- 

 plete destruction. I will mention, then, that for red light 

 we pass from the one of these conditions to the other 

 when we make the difference of route amount to three 

 ten thousandths of a millimetre.* 



* The numerical values of the differences of route, as Arago ex- 

 presses it, or the connection of the wave lengths for different rays 

 with the intervals between the stripes is easily investigated; and the 

 latter being readily susceptible of accurate micrometrical measure- 

 ment, the former may be deduced. Let two rays be inclined at a very 

 small angle 2 6. Then the crossings of the waves will give rise to a 

 set of bright and dark points at +, o, &c., according as like or unlike 

 portions meet. Let c be the interval between two successive bright 

 points and X the wave lengths. Then we have obviously the rela- 

 tion — 



C = r- cot d 



