7. OUR great author teaches in the next place how from the refraction of the most refrangible and least refrangible rays to find the refraction of all the intermediate ones[315]. The method is this: if the sine of incidence be to the sine of refraction in the least refrangible rays as A to B C, (in fig. 133) and to the sine of refraction in the most refrangible as A to B D; if C E be taken equal to C D, and then E D be so divided in F, G, H, I, K, L, that E D, E F, E G, E H, E I, E K, E L, E C, shall be proportional to the eight lengths of musical chords, which found the notes in an octave, E D being the length of the key, E F the length of the tone above that key, E G the length of the lesser third, E H of the fourth, E I of the fifth, E K of the greater sixth, E L of the seventh, and E C of the octave above that key; that is if the lines E D, E F, E G, E H, E I, E K, E L, and E C bear the same proportion as the numbers, 1, 9/8, 5/6, ¾, ⅓, ¾, 9/61, ½, respectively then shall B D, B F, be the two limits of the sines of refraction of the violet-making rays, that is the violet-making rays shall not all of them have precisely the same sine of refraction, but none of them shall have a greater sine than B D, nor a less than B F, though there are violet-making rays which answer to any sine of refraction that can be taken between these two. In the same manner B F and B G are the limits of the sines of refraction of the indigo-making rays; B G, B H are the limits belonging to the blue-making rays; B H, B I the limits pertaining to the green-making rays, B I, B K the limits for the yellow-making rays; B K, B L the limits for the orange-making rays; and lastly, B L and B C the extreme limits of the sines of refraction belonging to the red-making rays. These are the proportions by which the heterogeneous rays of light are separated from each other in refraction.