S8 Frauenhofer on the Refractim and Dispersive Powers 
very small ; and, with the prism with which I made these expe- 
riments, it was only 40".5 for water, I have measured, then, 
only the arcs BC, CD, DE, &c. The corrections are small, 
and consequently very exact. With the prism they amounted, 
for BC only to 2".5, for CD to 6". 5, and for DE to 8". All 
the angles in the preceding Table have received this correction. 
Calling 0 - the angle of the incident ray, g the angle of the emer- 
gent ray, 4" the angle of the prism, and n the index of refrac- 
tion, we obtain 
__ / r (sin g + cos 4^ sin g-)^ 4- (sin 4^ sin 
V L sin 4^ J 
If the angle of the incident ray is equal to the angle of the 
emergent ray, and if is the angle which the incident ray forms 
with the emergent ray, we shall have 
sin 1(^+4^) 
sm ^ 4^ 
This last expression for n will not be rigorously correct in sub- 
stances with a great dispersive power, and for an emergent ray, 
the angle of which is not equal to that of the incident ray, for the 
latter cannot be so, excepting to only one of the emergent rays, 
such as that at D, on the supposition that the prism does not 
change its place. In making use of the last Formula for calcula- 
ting the indices of refraction with great accuracy, I only measured 
the arcs BC, CD, DE, &c. when the distance of the two lines 
was the smallest. But this distance corresponds only to two 
lines of the spectrum, if a ray in the middle of them makes the 
smallest angle with the incident ray. When I measured, for 
example, the arc GH, the place of the prism was such, that a 
ray, nearly in the middle between G and H, formed the same 
angle with the prism that the incident ray did. The prism has 
this position when the angle of refraction of this mean ray is a 
minimum. By the help of the telescope, and by turning the 
plane on which the prism rests, this position may be easily found 
with the greatest exactness. With substances of a less disper- 
sive power, or with prisms of a smaller angle, the same care is 
not requisite to obtain this degree of accuracy. Calling E n the 
index of refraction for the ray E, wc have 
