of the Angle Jubtended by Two GbjeSls , &c. 42 p 
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 iecondary with which it' 
fhould coincide. Referring to the general Value of cof. ED, 
(art. 28.) and making n — 0 we fh all have 
Col. ED— -1 Cx/ i~p 2 ps 2 . Xi-3f&> 2 -^ 2 4- 2 m z p 2 - 1 6p z sl x ^ 1 x 1 - 2 pr s'; -tn 4- n. y 
+ 1 6s 2 /) 2 cm x 
^ I — /x 
I ~?n X I — p~ -P 1 6^7> 3 
and becaufe s being very fmall, the flue of ED (art 23.) ap- 
proximates to 4 sp x %/ 1 
tion itfelf, or ED — 4 x 
in the error of the obferva- 
x v' I 
rxi — 2z/ 
+ 2 p 2 m l 
“h 
V 
I — ni +p 2 n? 
4 -pb xv' 1 — s 1 
xi - 2 p 2 s z — >t? -f n?p 2 
V 
’ i-m 2 yp 2 rn 
4 spmcY^ v' 1 ~ 
nr x I - / 
V 1 — rn 
+ p*m z 
Apm 2 p 2 $dx */ 1 
1 ' 
c- I 
1 ^ 
A 
1 
V' 1 — 
-p 2 ?ri 
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 obferved ; if 
therefore the variation on the divided arc be any fmall angle 
2#, 4- or — the firft term will exprefs the variation by which 
the obferved angle is increafed or diminifhed. According to the 
magnitude of in and s affumed for this conftruction m being the 
fine of 7 0 , and s ~ the fine of io\ it appears, that at the very 
beginning of the fcale one fecond of a degree in the angle ob- 
ferved correfponds to fomewhat lefs than three minutes on the 
divided arc OP; that is, when 2a ~ about 173", ED= f 7 , 
c, b , and d, not being here confidered. When^>=§, the in- 
dex then pointing to 6o°, one fecond in the obferved angle cor- 
Vol, LXXL L 1 1 refponds 
