of the Angle fuhtended by Two Objects, &c. 433 
The divarication of the images while they traverfe the field 
of the telefcope during the time of an observation, and the 
errors of the obferved angle in confequence of any change in 
the quantities m * and n (p. 429 ) fiaould they appear to be of 
fenfible magnitude, may be diminifhed until they are in 
phyfical fenfe evanefcent, by altering the values of s and m 
(art. 31.) : for this purpofe it will be requifite to ufe two fie- 
parate conftruciions ; the one for obferving very fmall angles, 
thofe, for example, which do not exceed A : and the other,, 
for meafuring fuoh angles as are fubtended by the fun and moon. 
In the former of thefe s may be alTumed = the fine of 30'", 
m =- fin. 7 0 , and n — o. From thefe data tab. in. is calcu- 
lated. In the other conftrudlion, becaufe very fmall refieftinp' 
furfaces are neceflary to obferve the fun by two reflections (art. 
17.) m may be affumed — fin. 1%. s being = fin. io', and 
n = o : from which conditions the fourth table is calculated. 
Thefe tables may be eafily extended, by calculating from the 
value of cof. ED or fin. iED 2 contained in art. 21. or 22. 
* Let the telefcope with the entire confix udlion be headily fixed : then if the 
objects obferved be in contact while the touching points occupy the center of the 
held, the angle of incidence on the fixed fpeculum will be of its true magnitude ; 
that is, its fine or m will = fin. 7 0 in tables I. II. and III. ; and m. ~ fin. i° in 
table IV. The fixed plane of reflection alfo will be coincident with the primitive 
fecondary in all the conftrudtions correfponding to tables I. II, III. and IV. The 
telefcope continuing unmoved, the diurnal motion of the heavens will caufe the 
points in contact to leave the center of the held; this willoccahon no alteration in 
the quantities s and p, but will affedt m and n only : therefore, s an dp zr o. To 
eftimate the effects of this, change in the values of m and n, let mzzc xV ' 1 — 
and nzidx^i—n 2 , as in art. ^8. andfuppofe aline to be drawn through the centre 
of the held in a plane, perpendicular to the plane of motion : this line will be in the 
hxed plane of reflection ; and any deviation of the points in contact through a 
fmall angular fpace r, from the center of the held will caufe an equal variation c in. 
the. 
