of the Jingle fubt ended by Two Ohjt£is r Sc c. 
43 1 
32. From contemplating the value of the error = ED, 
as exp refled by the four terms juft referred to, fome further ob- 
fervations arefuggefted. It appears, that fetting aftde the error 
of the fcale exprefled by the firft term (the angles meafured be- 
ing here fuppofed lefs than 22' 56" 33 ") all the others become 
fmaller as the quantity p 3 and confequently the angle meafured 
is diminifhed, p being multiplied into each of the three laft 
terms. This is a material circumftance : for the fame given error 
would affect the menfuration of the fmaller angles in a greater 
proportion than the larger. Moreover, if or approxi- 
mates to that quantity, the index then pointing to an angle 
nearly =* to i 8o°, the firft term and the two laft terms become 
almoft evanefcent, not only from the circumftances that have 
been confidered, but from the quantities 1 — p z 9 s/ 1 -f*, which 
are multiplied into them. This alfo the obferver may avail 
himfelf of : for fuppofing he fhould know, that the angle of in- 
cidence on the fixed fpeculum, and the fixed plane of reflection, 
are imperfectly adjufted, and even that the divided arc is incor* 
reft, he may almoft wholly avoid the errors which they would 
occafion, by fo adjufting the inclination of the refleftors 
to the plane of motion, in refpeft of the angle meafured, that 
for p in the third term, (p. 429.) every thing elfe remaining, the maximum of 
variation in the obferved angle on account of 3' difference ill the angle of inci- 
dence on the fixed fpeculum will appear to be ~ ".098. 
The error of aft obfervation occafioned by a variation c in the angle of inci- 
dence on the fixed fpeculum, can never exceed the t P art O which is the 
maximum of error, the angle meafured being rz 22' 56'' 33"', the index 
then pointing to 70° 24'. The error, catifed by a fmali angle d, at which 
the fixed plane of -refie&ion is inclined to the primitive fecondary with which it 
fhould coincide, cannot exceed the part of d , which is its maximum 
when the angle meafured is 32' 33" 3'", the index then being directed to 109° 20'. 
L 1 1 2 the 
