( 1 5° ) 
Refiedion?, through an Arch of that Circle, equal to 
twice the Inclination of the Specula, as is before faid. 
But Objeds at a Diftance from that Circle will appear 
removed thro’ the fimilar Arch of a Parallel : There- 
fore the Change of their apparent Place will be mea- 
fured by an Arch of a great Circle, whofe Chord is 
to the Chord of the Arch equal to double the Incli- 
nation of the Specula, as the Sines Complements of 
their refpeQrive Diftances from that Circle are to the 
Radius: And if thofe Diftances are very final!, the 
Difference between the apparent Tranflation of any one 
of thefe Objeds, and the Tranflation of thofe which 
are in the Circumference of the great Circle aforefaid,, 
will be to an Arch equal to the verfed Sine of the 
Diftance of this Object from that Circle, nearly as 
double the Sine of the Angle of Inclination of the 
Specula, is to the Sine Complement of the fa tic. 
F i g. II. The Inftrument conlifts of an Oftant 
ABC, having on its Limb BC an Arch of 45 Degrees, 
divided into 90 Parts or half Degrees j each of which 
anfvvers to a whole Degree in the Obfervation. It has 
an Index M L moveable round the Center,, to mark 
the Divifions: And upon this, near the Center, is fix’d 
a plane Speculum E F perpendicular to the Plane of 
the Inftrument, and making fuch an Angle with a Line 
drawn along the middle of the Index, as will be moft 
convenient for the particular Ufes the Inftrument is 
defigned for:, (for an Inftrument made according to 
Fig. 2. the Angle LMF may be of about 6y Degrees.) 
IKGH is another fmaller plane Speculum, fix’d on 
fuch Part of the Odant as will likewife be determin’d 
by its particular Ufe, and having its Surface in fuch 
Diredion, that when the Index is brought to mark 
