refractive and dispersive Poxvers. 367 
Let A, Fig. 1, Plate XIV. be a square or rectangular prism, 
to which any substance is applied at b, and let any ray of light 
parallel to cb be refracted through the prism, in the direction 
bde. 
Then, if ef and ed be taken proportional to the sines that 
represent the refractive powers of the prism and of air ,fg, which 
is intercepted between f and the perpendicular eg, will be the 
corresponding sine to represent the refractive power of the 
medium b. For, since edg (opposite to ef) is the angle of re- 
fraction, efg (opposite to ed) must be equal to the angle of 
incidence bdh; and ef :fg : : bd : dh : : sine of cbi : sine of 
hbd. 
All therefore that is requisite for determining the refractive 
power of h, is to find means of measuring the line fg. On this 
principle, the instrument in the annexed sketch (Fig. 2.) is con- 
structed. On a board a b is fixed a piece of flat deal cd , to which, 
by a hinge at d, is jointed a second piece de, 1 o inches long, car- 
rying two plane sights at its extremities. At e is a second hinge, 
connecting ef, 15,83 inches long; and a third at the other extre- 
mity of ef by which fg is connected with it. At i also is a hinge, 
uniting the radius ig to the middle of ef; and then, since g 
moves in a semicircle egf, a line joining e and g would be per- 
pendicular to fg. 
The piece cd has a cavity in the middle of it, so that, when 
any substance is applied to the middle of the prism P, it may 
continue to rest horizontally on its extremities. When ed has 
been so elevated that the yellow rays in the fringe of colours 
(observable where perfect reflection terminates) are seen through 
the sights, the point g, by means of a vernier which it carries, 
shows by inspection the length of the sine of refraction sought. 
3 B 2 
