368 Sir Isaac Newton’s Book III.

the tangent of the angle under NFS. Thus much being premi-fed, the fenfeof theforementioned propofition is this. Let therebe two refrading fubftances(infig. 13 y) A BCD , and EFGH.Take a point, as I, in the furface AB, and to the center Iwith any femidiameter defcribe the circle KLM. In likemanner on the furface EF take fome point N, as a center,and defcribe with the lame femidiameter the circle OPQ,.Let the angle under BIR be the leaft which the refractedlight can make with the furface A B, and the angle underFNS the leaft which the refraded light can make withthe furface EF. Then if LT be drawn perpendicular toAB, and P V perpendicular to EF; the whole power, where-with the fubftance A B C D ads on the light, will bear tothe whole power wherewith the fubftance E F G H ads on,the light, a proportion, which is duplicate of the proporti-on, which LT bears to PV.

10 . Upon comparing according to this rule the refra-dive powers of a great many bodies it is found, that undu-ous bodies which abound moft with fulphureous partsrefrad the light two or three times more in proportion totheir denfity than others : but that thofe bodies, which feemto receive in their compofition like proportions of fulphu-reous parts, have their refradive powers proportional to theirdenfities; as appears beyond contradidion by comparingthe refradive power of fo rare a fubftance as the air withthat of common glafs or rock cryftal, though thefe fub-ftances are 2000 times denfer than air; nay the fame pro-portion