426 Mr . atwood’s ‘ Theory for the Menfuration 
30. To examine in what degree an obfervation taken by the 
new conftrudiion defcribed in art. 15. is affefted by known 
errors in the given quantities, let the refieftors B and C deviate 
by excels from their true angle of inclination to the plane of mo- 
tion by a fmall angle -f b : let the angle of incidence on the 
fixed fpeculum be too gi*eat by the increment c : let the fixed 
plane of refleflion deviate from the fecondary KO with which 
it fhould coincide by a fmall angle d\ and laltly, let the error 
of the arc pointed to by the index be = 2 a\ then thefe variations 
are arbitrary, no condition being annexed. Moreover, by the 
conftruflion m~s = -d=, and n = o 9 which values being fub- 
v 2 
ftituted in the general expreffion contained in art. 28. we 
fhall have. 
Cof.EDzz -4 ap xV 1-/ + 4/4-X 1 -p z l 
and becaufe the fine of the angle meafured = 2p x v/ 1 - />% 
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 T)d; then the correfponding 
variation of the angle DOK will be DOd. Let Dd~e , and its verfed fine — v 1 
fince the fine of DOzw, and the fine of DOK — i zzn by the problem, n — the 
e e z v 
verfed fine of DOi; but DO d — — , and the verfed fine of T>Od ~ — 5=1-5 : 
m 2 m m 
• — v , • • 
wherefore nz=.—r. This being premifed, it appears from art. 26 . when and s , 
rn 
are=o, that cof.’ED = + 16 ?fri?n X -n + 2fn-i L p L n^ l ~^ y ^ l - trWAl - z 
V'l-rT 
4. 16 s T p z mm x 1 — rf — p 2 + 2p z rf — s z p z n z ~i-2 pn x ^ 1 n X/i •* xyT p 
— v 
in which quantity, fubftituting 1 for s, 1 for », and yr for w, we fliall have 
coffED = + 1 6p z v X 1 -p z 9 which being divided by the fine of the obferved 
angle “ 
4 px^ 1 — p z x i-p ,the quotient will be the variation of that angle or ED — 
— 4 vp x/ 1 — p z 
