C 9«i ) 
ftrcatfe the Beams are parallel, as coming ff am an In- 
finite diftance, (which is fappofed in the caft of Te!e- 
fcopes ) then will d be fuppofed infinite, and in the 
Theorem the Term pr p vanifhes, a„ 
dr fyd p >—p r p r r ' s 
being finite, which is no part of the other infinite terms 
and dividing the remainder by the infinite part d, the 
Theorem will ftand thus £i-T =,f, or in Gafs 
rt$p J » 
In cafe the £m were Piano-Convex expofed to diverg- 
ing Beams, inftead of ^ . r being infinity 
D dr^d^—pr^ . 
it will be 5- = /. or f ° ^ - = /, if the ZW 
d—p% J d^-x § J 
be Glafe. 
If the Z>/*5 be Double-Convex, and r be equal to ^ 
as being formed of Segments of equal Spheres, then will 
^ / ft be reduced to = /5 and 
drfy dg — /> r ^ z a — p r 
in cafe ^ be infinite, then it will yet be farther ccn- 
traded to \p r, and /> being = — the focal di- 
fiance in Glafi will be = r, in Water 1 * butinDia- 
mmt i >. 
lamftnfible that thefe Examples are too much for 
the corapleat Ahalyft, though I fear too little for the 
lefs Skilful, it being very hard, if pcfiible, in fuch mat- 
ters, fo to write as to give (atisfa&ion to both ; or to 
pleafe the one, and inftru<5t the other. But this may 
fuffice to {hew the extent of our Theorem, and how 
eafy a Reduction adapts any one cafe to all the reft. 
M m m Nor 
