of the Angle fubt ended by Two ObjeBy , &c. 
42.9 
pointed to by the index ; b = the error of the inclination of the 
reflectors to the plane of motion ; c — the error in the angle of inci- 
dence on the fixed fpeculum ; and d~- the inclination of the fixed 
plane of reflection to the primitive fecondary with which it 
fihould coincide. Referring to the general value of cof. ED, 
(art. 28.) and making n — o we fhall have 
Col. EDzr- 16x1/ 1- 
,2 . 2 
P pi 
CXI- 
n r> 
-2 i p - 
~rn~ + wf iP—lbfPsl'X.'d i—P 
XI- 
A 
D S 
~rn+n z 
P 
-f 1 bP/'cm x v' 1 -- m' x 1 — f -7= 1 bm z p z Pd x C 1 — s z x v' 1 — />% 
and hecaufe s being very Imall, the fine of ED (art 23.) ap- 
proximates to 4 sp x %/ 1 — ni -f y '/.7 ' , the error of the obferva- 
tion it.felf, or ED 
4 «.f X 
v' 
■/>“ X 1 -- 2 p~S — m~ + 2 pm" 
v' I — nr + p'rtp 
. 4 pbx 
2,2 
• s~ X 1 — 2 p~$~— & + m p 
fi -m z +p z m z 
4-spmc >< V' 1 — nP x I —p 2 
V i~ m 1 -\-p z m z 
^ _ 4 m z p z sdx 1 — fi x v' 1 — p l * 
1 — w 2 -4 -p~?rf 
The firft term of this expreffion gives the relation be- 
tween any fmall variation in the arc pointed to by the index, 
and the correfponding alteration in the angle ohferved ; if 
therefore the variation on the divided arc be any fmall angle 
rt 2 a, 4- or — the firftterm will exprefs the variation by which 
the obferved angle is increafed or diminifhed. According to the 
magnitude of m and s album ed for this confiruciion m being the 
fine of 7 0 , and j = the fine of 10', it appears, that at the very 
beginning of the fcale one fecond of a degree in the angle ob- 
ferved correfppnds to fomewhat lefs than three minutes on the 
divided arc OP; that is, when za — about 173", 
• • • 
c , bj and d^ not being here confidered. When^^f, the in- 
dex then pointing to 6o° ? one fecond in the obferved angle cor- 
Vol, LXXh L 1 1 refpondg 
