[ 1 77 ] 
C B : C H :: D F : D G, or i :\J i — -z % :: s : DG = 
5 1 — ; and C B : BH :: CF : GI, or i : z :: c : 
GI = cz. But (by Hypoth.) DI:BH :: m : n ; 
that is D G d- G I, or 5 \J i—z" -V* cz i z :: m \n\ 
which gives \j i — z z : z, or CH : BH, or i : tang. 
n s 
ACB :: m — nc : ns\ that is, tang. ACB~- . 
In words — multiply the fine of the given difference 
by the lead term of the given ratio for a dividend : 
from the greater term fubtradt the product of the co- 
line of the difference and the leffer term for a divifor ; 
and the quotient fhall be the tangent of the leffer an- 
gle ACB. 
Or, if you prefer a geometrical conftrudlion ; In 
the femidiameter C B produced take CM to C B as 
D I to BH; and in the tangent to the circle at B, 
make BL to BC, as DF to FM, and BCL fhall 
be the leffer angle fought. 
Or you need only join D M and draw the femidia- 
meter C A parallel to it. 
8. But before we apply this folution, it may be 
proper to give a table of the refra&ive powers of glafs, 
water and fpirit of wine, whether contiguous to the 
air, or perhaps the fluids contiguous to glafs : thefe 
being the fubffances in which experiments may be 
moft conveniently made : and it is alfo neceffary to 
know the limitations that arife from thofe feveral 
powers. 
Vol. LIII. 
Bb 
I. When 
