4 jo Mr . atwood’s Theory for the Menfuration 
refponds to about 199" in the divided arc OP : when^> is nearly 
~ i , the index being then direVed to almoft 1 8o°, it muft defcribe 
above 2 degrees to make an alteration of 1" in the obferved angle. 
The fecond term exprefles the variation in the obfervation oc- 
cafioned by an error b in adj lifting the inclination of the re- 
lieving planes to the plane of motion ; but b (art. 18.) cannot 
exceed \ of the leaf!; angle vifible in the telefcope, confe- 
quently the utmoft value of the fecond term cannot be fo great 
as that lead: angle, being at its limit when p — 1 : it is mani- 
feft when p is fmail, that the fecond term is fo much dimi- 
nifhed, as to be in a phyfical fenfe evanefcent. The fame may 
be laid of the fourth term, containing the error of the optical 
adjuftment f which befides is multiplied into s the fine 
of 1 oh The third term is occafioned by the error c, for 
which, confiderable latitude muft be allowed, fuppofe f ; 
to eftimate the effedt of this error on the obfervation, 
let a cafe be affumed : let the index be diredted to 90* 
when an obfervation is taken for determining the angle lub- 
tended between two ohjeVs : then will p =■ ; by fubfti- 
a / 2 
tuting M for p, the fine of 7 0 for/??, the fine of io' for 
2 
and iSo' 7 for c in the third term, we fliall have, by com- 
putation, the value of that term, or the error in the obfer- 
vation occafioned by this deviation of the angle of inci- 
dence from its true magnitude — ."090 not the tenth partr 
of a fecond. This is rather an unfavourable cafe, the variation 
being not much lefs than at its maximum when p = f = : if p is 
v' 2 
fmall, or nearly — 1, the * variation will be wholly infenfible. 
o n 
* The variation is a maximum when^>~ the line of 35° 1 2 ' ; and confequently 
the arc pointed to by the index ~ 70° 24'* SubHituting therefore the fine of 35 0 12' 
for 
