4 ?o Mr. Atwood’s Theory for the Menfuratlon 
refponds to about 1 99" in the divided arc OP : when/> is nearly 
— 1 5 the index being then diredied to almoft 1 80% it muft defcribe- 
above 2 degrees to make an alteration of 1" in the obferved angle. 
The fecond term exp relies the variation in the obfervation oc- 
eafioned by an error h in adj lifting the inclination of the re- 
Meeting planes to the plane of motion ; but b (art. 18.), cannot 
exceed \ of the leaft angle viftble in the telefcope, eonfe- 
quently the utmoft value of the fecond term, cannot be fo great 
as that leaft angle,, being at its limit when p = 1 : it is mani- 
fieft when p is fmall, that the fecond term is fo much dimi- 
nifhed, as to. be in a phyfical fenfe evanefeent.. The fame may 
be laid of the fourth term, containing the error of the optical 
adjuftment a\ which befides is multiplied into t the fine 
of 1 oh The third term is occafoned 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 aflumed : let the index he diredted to 90° 
when an obfervation is taken for determining the angle fub- 
by fubfti- 
tended between two objects : then will p 
V. 
tilting -i= for p r the fine of 7 0 for m, the fine of ro' for /, 
y 2 
and 180" for c in the third term* we fhall have, by com- 
putation, the value of that term, or the error in the obfer- 
vation occafoned by this deviation of the angle of inci- 
dence from its true magnitude = T090 not the tenth part 
of a fecond. This is rather an unfavourable cafe, the variation, 
being not much lefs than at its maximum when p ~ f = : ^ 
fmall, or nearly =- 1 , the * variation will be wholly rnfenfi ble. 
3 2a 
* The variation is a maximum whenj!>“ the line of 35 0 12 ' ; and confequently 
the, arc pointed to by the index = 70° *4'.. Subftituting therefore the fine of 35° 12 1 
fo s. 
