[ 121 ] 
diftance, found as above in the firft obfervation be- 
tween the firft objedt and any other objedt feen by 
reflexion, will give the true angular diftance between 
them reduced to the centre of the index-glafs. 
But if you fhould happen to be in a place where 
you cannot command a convenient diftant object, the 
following method may be ufed. 
The back-horizon-glafs being adjufted, find the 
inftrumental angular diftance between the objedtsj 
this is to be corrected by means of the following 
operations. Set up a mark at any convenient 
diftance oppofite or nearly fo to the object which 
has been taken as the direct objedt; and looking at 
the diredt objedt move the index of the quadrant, 
and bring the image of the mark to coincide with 
the diredt objedt, and read off the degrees and 
minutes ftanding on the arch of the quadrant, which 
fubtradt from 180 degrees, if (o) of the index falls 
upon the quadrantal arch ; but add to 1 80 degrees, if 
it falls upon the arch of excefs j and you will have the 
inftrumental angular diftance of the objedt and mark. 
Invert the plane of the quadrant, taking care at the 
fame time not to change the place of its centre, and 
looking at the fame diredt objedt as before, move the 
index of the quadrant, and bring the image of the 
mark to coincide again with the diredt objedt, and 
read off the degrees and minutes ftanding on the arch, 
and thence alfo find the inftrumental angular diftance 
of the objedt and mark. Take the fum of this and the 
former inftrumental angular diftance ; half of its differ- 
ence from 360° will be the corredtion, which added 
to the inftrumental angular diftance firft found be- 
tween the fame diredt objedt and the other objedt feen 
Vol. LXII. R by 
