426 Mr. atwood’s Theory for the Menfuratlon 
30. To examine in what degree an obfervation taken by tire 
new conftruclion deferibed in art. 15. is affeefted by known 
errors in the given quantities, let the refledors B and C deviate 
by excels from their true angle of inclination to the plane of mo- 
tion by a fmall angle y b: let the angle of incidence on the 
fixed fpecuium be too great by the increment c: let the fixed 
plane of reflection deviate from the fecondary KO with which 
it fhould coincide by a fmall angle d ; and laftly, let the error 
o 
of the arc pointed to by the index be = 2 a; then thefe variations 
are arbitrary, no condition being annexed. Moreover, by the 
conftruclion m — and » = o, which values being fub- 
v 2 
ftituted in the general expreftion contained in art. 28. we 
flhall have. 
Cof.EDrr -4 ap x/ 1 - /- 4 /ix I-/ + 4 /fX ^ \-p z % 
and becaufe the fine of the angle meafured — 2px\/i~p\ 
the error of the obfervation required, or 
coincide (fig. 7.) let the inclination of the telefcope to the plane of motion with 
which it fhould coincide, be meafured by the fmall arc D d ; then the correfponding 
variation of the angle DOK will be ~DOd. Let D^rr^, and its verfed fine rr v 1 
fince the fine of DOr ?n, and the fine of DOKrr 1 ~n by the problem, n — the 
verfed fine of DO d; but DO d— — , and the verfed fine of DOi rr 
m 
2 m 
v 
rn 
— v 
wherefore n ~ — ~. This being premifed, it appears from art. 26. whenp, and s, 
m 
are rr o, that cof. ED rr -f 1 6 s p m n X -n + 2p n-i p n , 
V 1— j 2 Xy^ 1— p z XfX 1—2 ; 
+ ibs z p z mmXi-n z -p z +2p z n z -s z p z n z 2y 2 pnx^i-nX\di -dx%/i-p z 
— v 
in which quantity, fubftituting 1 for r, 1 for n , and for », we fhall have 
cofTEDzr + i 6 p z v X x -p z , which being divided by the fine of the obferved 
angle rr ^px^i -/ X i-y ,the quotient will be the variation of that angle or ED rr 
— 4 vp x 1 / x — p z 
