And having regard to some other observations and phenomena of which I shall speak afterwards, I put N at 156,962 parts, of which the semi-diameter CG is found to contain 98,779, making this ratio 8 to 5-1/29.

Now this proportion, which there is between the line N and CG, may be called the Proportion of the Refraction; similarly as in glass that of 3 to 2, as will be manifest when I shall have explained a short process in the preceding way to find the irregular refractions.
31.

Supposing then, in the next figure, as previously, the surface of the crystal _g_G, the Ellipse GP_g_, and the line N; and CM the refraction of the perpendicular ray FC, from which it diverges by 6 degrees 40 minutes.

Now let there be some other ray RC, the refraction of which must be found.
About the centre C, with semi-diameter CG, let the circumference _g_RG be described, cutting the ray RC at R; and let RV be the perpendicular on CG.

Then as the line N is to CG let CV be to CD, and let DI be drawn parallel to CM, cutting the Ellipse _g_MG at I; then joining CI, this will be the required refraction of the ray RC.