4'i$ Mr. Atwood's Theory for the Menfuratlon 
and n~ o, d~ i — m q- mf 2, nearly, which gives 
fm. ED — 4.sp x 1 — m z -±- rn f nearly. 
24. The cofinc of the obferved angle reprefented by ED 
(fig. 2. and 14.) in the eonffruffion, being computed from the 
four given quantities p, s, and n, if either of thefe fhould 
deviate from its true value, the angle deduced will be erroneous t 
and from the general expreffion for the cofine of ED, an efti- 
ination of this error will be obtained. In the Inveffigation, 
however, it muff be obferved, that although the fmall incre- 
ments or decrements of arcs or fines are affumed proportional t© 
the fluxions of thefe quantities, which is ffriclly true only in 
the nafcent ffate of the increments or decrements, yet when 
the given variations are in a praffical fenfe very fmall, the 
eftimation of correfponding variations -will be in general fuffi- 
ciently exact for practical purpofes. 
25. Small increments and decrements, that is, fmall varia- 
tions, being affumed proportional to the fluxions of arcs and 
M their fines and coflnes, if the variation of the fine or co- 
fine of any given arc be known, the cotemporary variation 
•of the arc will be for the moil part inferred from the following 
“ * 
proportions as fin. •: rad. :: — col. : arc; and as cof. : rad. :: 
* _ » 
fin. : arc. But thefe proportions muff be ufed under 
reffdtlions very neceffary to be inferted in this place, be- 
ing true when applied to the intermediate parts of the 
quadrant only and failing at the extremities ; for -example, 
at the very beginning of the quadrant, or at the very end 
of the femi-circle, the variation of the cofine is the verfed fine 
of the arcs increment or decrement, which gives the proportion 
as fin. : 2 x rad. :: —cof. : arc, being wholly different from the 
former : in like manner, at the very extremity of the qua- 
drant, 
r j - ' \ ! 
