of the Angle fuhtended by Two Qbjetds., &c. 43 1 
32. From contemplating the value of the error = ED, 
as exp relied by the four terms juft referred to, force further oh- 
fervations arefuggefted, It appears, that betting abide the error 
of the icale exprefled by the fir ft term (the angles meafured be- 
ing here fuppofed lefs than 22' 56" 33 ") all the others become 
fmaller as the quantity p, and confequentiy tire angle meafured 
is diminifhed, p being multiplied into each of the three laft 
terms. This is a material circumftance : for the lame given error 
would afteft the men fu ration of the imaller angles in a greater- 
proportion than the larger. Moreover, it p*=i, or approxi- 
mates to that quantity, the index then pointing to an angle 
iiearlv = to 1 8o°, the firft term and the two laft terms become 
aim oft evanefcent, not only from the circumftances that have 
been conftdered, but from the quantities 1 -p\ A 1 which 
are multiplied into them. TLTiis alfo the ooferver may avail 
himfelf of : for fuppoling he fnould know, that the angle of in- 
cidence on the fixed fpeculum, and the fixed plane of reflexion, 
are, imperfectly adjufted, and even that the divided arc is incor* 
reft, he may almoft wholly avoid the errors which they would 
occasion, by fb adjufting the inclination of the reflectors 
to the plane of motion, in refpedt of the angle meafured, that 
for p in the third term, (p. 429-.) every thing elfe remaining, the s maximum of 
variation in the obferved angle on account of 3' difference in the angle of inci- 
dence on the fixed fpeculum will appear to be — ".098. 
The error of an obfervation occafioned by a variation c in the angle of inch 
deuce on the fixed fpeculum, can never exceed the tEt part of c, which is the 
maximum of error, the angle meafured being rx 22' zp> ' 33' , the index 
then pointing to 70 0 24b The error, caufed by a fmall angle at which 
the fixed plane of reflection is inclined to the primitive fecondary with which it 
fhould coincide, cannot exceed the -nnhrgr part of d, which is its maximum 
when the angle meafured js 32' 33'' 1" , the index then being dire&ed to 109 20 . 
L 1 1 2 - the 
