Then DS will be 62,163.

But CL is also determined, and contains 99,324 parts, as has been said in Articles 34 and 40.

Then the ratio of PD to DS will be as 99,324 to 62,163.

And thus one knows the elevation of the point at the bottom I by the refraction of this section; and it appears that this elevation is greater than that by the refraction of the preceding section, since the ratio of PD to DS was there as 99,324 to 70,283.
[Illustration] But by the regular refraction of the crystal, of which we have above said that the proportion is 5 to 3, the elevation of the point I, or P, from the bottom, will be 2/5 of the height DP; as appears by this figure, where the point P being viewed by the rays PCR, P_cr_, refracted equally at the surface C_c_, this point must needs appear to be at S, in the perpendicular PD where the lines RC, _rc_, meet when prolonged: and one knows that the line PC is to CS as 5 to 3, since they are to one another as the sine of the angle CSP or DSC is to the sine of the angle SPC.

And because the ratio of PD to DS is deemed the same as that of PC to CS, the two eyes Rr being supposed very far above the crystal, the elevation PS will thus be 2/5 of PD.
[Illustration] 42.