[ 2 ° ] 
It may be proper to remark, that, as in thefe 
theorems, the principal focus is fuppofed to he be- 
fore the glafs, as well as the radiant point, to adapt 
the theorem to other cafes, if the lens be of fuch a 
form, as that its principal focus lies behind the glafs,, 
F mult be taken negative : likewife, if the rays fall 
converging on the lens, or the point, to which they 
converge, lie behind the glafs, Qjnuft be taken ne- 
gative : laftly, if the firft furface be convex, R muft 
be taken negative ; and if the fecond furface be con- 
cave, r muft be taken negative ; and if, after all 
thefe circumftances are allowed for, the value of the 
theorem comes out pofitive, the aberration is of fuch 
a nature, as to make the focus of the extreme rays 
fall nearer the lens before it, than the geometrical 
focus, or farther from the lens behind it : but if the 
value of the theorem comes out negative, the aber- 
ration is of fuch a kind, as to make the focus of the 
extreme rays fall farther from the lens before it, than 
the geometrical focus. 
With refpcdt to the application of this theorem to 
Mr. Dollond’s combined objedt glaffes, it is evident, 
that if the aberrations of the convex and concave 
lenfes added together (paying due regard to the figns 
of the theorem), are made equal to nothing, the two 
lenfes will perfectly corredt one another : but as there 
are two unknown quantities unlimited in the equa- 
tion, namely, the radius of one furface of each glafs 
(for F and Q_are given, as well as m and «), there 
is room for an arbitrary affumption of one of them, 
at the difcretion of the theorift, or artift ; which 
being done, there will remain a quadratic equation, 
whence 
