208 \  -FRESNEL. 
In order that the difference of route alone may deter- 
mine whether two rays of the same origin and the same 
colour shall reinforce or destroy each other, it is neces~ 
sary that both should be traversing the same medium, 
solid, liquid, or gaseous. If it be not thus, we must then 
also take into account (as a member of the Academy* 
and similarly for successive Values of c, measured from the central 
point, involving successive multiples of 2; and if a plate of glass 
whose refraction index is y, be interposed in the path of one of the 
rays, whose thickness is ¢, the difference of retardation will be equiv- 
alent to a difference of route expressed by 
d=t(u—1) 
and this being substituted for the particular multiple of 2, which 
expresses the difference of routes in the first formula, gives for the 
displacement 
7 cot 
2 
It-may be added that the values of the wave lengths determined by 
this method from the observed widths of the stripes, or by others of 
an analogous kind, give results exactly accordant with those long ago 
assigned by Newton for the length of the “fits”? derived from his 
measures of the diameters of the coloured rings, and by which, from 
the known curvatures of the lenses, he determined the thickness of 
the films, and thence the lengths of the “ fits.”’— Translator. 
* The retardation of one of the rays, and consequent shifting of the 
stripes, is here alluded to, which was the discovery of Arago; being 
in the first instance exhibited by the total disappearance of the stripes, 
as must be the case if the plate of glass have more than almost an in- 
finitesimal thickness. The fact was first announced as a sort of par- 
adox, that as Young had found the stripes entirely disappear by inter- 
posing an opaque screen on one side only, so Arago produced the same 
effect with a perfectly transparent screen. In order to explain this 
effect, let us conceive the simple case of two rays of white light, made 
to interfere as in Fresnel’s experiment. 
The slightest consideration will show that, at the middle point of 
the mixture of light, two concurring rays, of whatever primitive col- 
our or wave length, have gone through precisely the same length of 
route; and thus the central stripe and its immediate neighbour on 
each side, are absolutely white and black, and perfectly defined; but 
in proportion as we recede from this point on either side, the differ- 
c=t(u—1) 
