DIFFERENCES OF ROUTE. 207 
we operate with white light 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 the 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 millimétre.* 
* 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 ata very 
small angle 26. Then the crossings of the waves will give rise to a 
set of bright and dark points at +-, 0, &c., according as like or unlike 
portions meet. Let c be the interval between two successive bright 
points and 2 the wave lengths. Then we have obviously the rela- 
tion — 
a 
c =3 cot @ 
26 
