C i8 9 ] 
the extreme (or any two forts of) rays. Then feeing 
by the experiments, the ratio of V to I is given, as 
alfo that of R to I ; the ratio of V — I to I, as alfo 
(invert.) that of I to R — I, and (ex^quo) that of 
V — I to R — I, are given : for this laft write the ratio 
of i to p. 
In like manner, let the refractive power of the 
medium from which the rays emerge into the fame 
medium as before, be increafed or diminifhed, as alfo 
the common angle of incidence ; and we need only 
write other marks <v and r for the fines, and i for 
the common fine of incidence j for we fhall have as 
before v — i to r — i in a given ratio ; which call 
that of i to q. And, from thefe two, we have 
V— I R- 
-I q 
- x 
p 
But p is always nearly equal to y; 
in the refractions from glafs, and from water into air, 
their difference is lefs than part of either ; we 
V I 
may therefore put the ratio -• equal 
is the firfi: theorem. 
And thence, if one difference R--I becomes equal 
to r — /, the other differences V— I, &c. will be re- 
fpeftively equal to v— i, See. and the fame fet of dif- 
ferences may be made to ferve for feveral media, pro- 
vided the fines of incidence are taken in their due 
proportion. 
Thus when red rays pafs from glafs into the air, 
we have I : R :: 50 : 77 and R— I : I :: 27 : 50, and. 
when they pafs from water into air i : r~i :: 3 : i, 
and therefore, as we are to make R— I every where 
equal to r— /, we get, ex aequo, / : I :: 8 1 : 50, as 
Sir Ifaac Newton finds it. 
IV. But 
