C *88 J 
whatever be the refracting power of the medium 
PN», provided that, in a given medium, the quan- 
tities m, n, &c. of the lemma, which reprefent the 
fines of refraction of the feveral forts of rays, to a 
common fine of incidence, continue to be in con- 
flan t ratios to one another. 
Converfely, if, from experiments fuch as that 
which Sir Ifaac Newton made, it follows that, what- 
ever be the refractive powers of the media, and the an- 
gle of incidence of the light, the pencils SO, so, may 
be made to reciprocate with each other, while all 
the forts of rays, in paffing or repaffing through the 
prifm P N n, become parallel 5 if, I fay, this is con- 
firmed by experiments, it is a proof that, for any 
given medium, the ratios of thofe quantities m, n , &c. 
are invariable. 
III. 
And hence Sir Ifaac deduces the two theorems fub- 
joined to his 8th experiment ; by the firft of which 
he contrives to make the ratios of the fines of refrac- 
tion belonging to the feveral forts of rays, to a com- 
mon fine of incidence, when they pafs from glals in- 
to air, to ferve for finding the like ratios for the rays 
patting from water into air, without the trouble of 
new experiments. 
His firft theorem may be deduced in this manner : 
Let all the forts of rays, whether united in a pen- 
cil of light, or leparated parallelwife by refraction, 
have the fame angle of incidence whofe fine is I, 
when they pafs from a denfer into a rarer medium ; 
and let V and R Hand for the fines of refraction of 
„ the 
