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of the crystal prism, so that the faces $CB,\ DE$ of the crystal and glass, may be nearly parallel. The two prisms are to be joined together, by heating them, and melting between them a few grains of very pure gum-mastic, which on being pressed, will spread into a very thin transparent layer. This, when cooled, will be quite sufficient to make the prisms cohere together very strongly, and to let the rays pass from one into the other.

The double prism is to be placed on the pillar $Hh,$ as in the Figure, and the observer is to look through it at the vertical scale $AZ.$ This scale will appear double, the ordinary and extraordinary image being, in the simple case here considered, in the same vertical line. Now whatever be the law of the two refractions, the corresponding lines of the two scales seen, are never equally separated in all places, so that if in one part the separation amounts to half a degree of the scale, a little further on it will be a whole degree, in another place a degree and a half, two degrees, and so on. If, for instance. No. 451, of the extraordinary division, which we will represent by 451_e, coincides with No. 450, of the ordinary (450₀), so that here the separation of the images is of one degree, it will perhaps be found that 502_e falls on 500₀. This shows that the extraordinary rays coming from 502, enter the eye together with the ordinary from 500, and since the glass prism can produce no effect beyond simple refraction on these rays, it is certain that the rays from 500₀ and 502_e, must coincide at their emergence from the crystal. This condition furnishes a very accurate method to verify the law followed by the extraordinary rays in the crystal. In fact, the directions of incidence of the two pencils may be determined, since one of them $EI,$ proceeds from the point $E$ of the scale, of which the place is known from the graduation, and arrives at the point of incidence $I,$ the position of which is also determined by the known height of the pillar $Hh,$ and its position on the horizontal scale. There are similar data for the other $Oi,$ which undergoes only the ordinary refraction, whether its point of incidence be supposed the same as that for $EI,$ or whether the small distance of those points be estimated by calculation, taking into account the thickness of the crystal prism, as will be hereafter mentioned.

Now if the ordinary refracted pencil $OI$ be followed through the crystal, which may be done by the common law of refraction, it

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