Page:Optics.djvu/194

 may be traced to its emergence from the second surface $$CD$$. Thus it will only remain to calculate the position of the extraordinary pencil, which should enter the crystal by the same surface, accompanying the exterior ray $$I''\ I';$$ and following back this pencil through the prism, to the first surface by an assumed law, for the extraordinary refraction, it will be seen whether it coincides, as it ought, with the incident pencil $$EI.$$ It is not irrelevant to remark that this condition, and indeed every part of the observation, is quite independent of the greater or less refracting power of the glass prism $$CDEF,$$ which serves merely to receive the rays refracted into the crystal, and make their emergence possible.

In the above instance, I have supposed the crystal to be cut so that the extraordinary refraction took place in the vertical plane, like the ordinary: that is the simplest case; but when there is a lateral deviation, I place perpendicularly to the vertical division, a divided ruler $$RR,$$ (Fig. 219,) which is fixed at the point from which the refracted rays proceed. Then there are observed certain lateral coincidences on the scale of $$RR,$$ on each of the vertical rods, if the direction of the point or line of incidence be marked on the first surface of the crystal, by a small line drawn on it, or by means of a little strip of paper stuck to it, to limit the incidence of the rays of which the common incidence is observed.

Similar means are used to fix the heights of the points of incidence on the crystal, when the coincidences are observed on the vertical scale, but then the edge of the strip of paper must be put horizontal.

One may even observe the coincidences on the horizontal scale $$AX,$$ on which the pillar stands. Then the places of incidence on the crystal must be limited as before.

One of the data of the calculation must be the ordinary refracting power of the crystal. This may be measured by observing on what line of the horizontal, or vertical scale another line falls, which is observed by ordinary refraction through the double prism, or through a crystal prism of a smaller angle, without a glass one. One may even see whether the ordinary refraction follows, in all cases, the law of the proportionality of the sines.