4*3 $fr. atwood's Theory for the Menfuration 
and n~o, d~ i — n? + n?p % nearly, winch gives 
fill. ED — 4.sp x ^/i — m z + m z p z nearly. 
24. The cofine of the obferved angle reprefented by ED 
(fig. Zo and 14.) in, the conftruttion, being computed from the 
four given quantities p, s, m, and if either of thefe fhould 
deviate from its true value, the angle deduced will be erroneous ; 
and from the general expreffion for the cofine of ED, an efti- 
rnation of this error will be obtained In the Inveftigation, 
however, it muft be obferved, that although the fmall incre- 
ments or decrements of arcs or fines are aflumed proportional to 
the fluxions of thefe quantities, which is ftriftly true only in 
the nafcent ftate of the increments or decrements, yet when 
the given variations are in a practical fenfe very fmall, the 
eftimation of corresponding variations will be in general fuffi- 
ciently exa£l for practical purpofes. 
25. Small increments and decrements, that is, fmall varia- 
tions, being aflumed proportional to the fluxions of arcs and 
of their fines and cofines, 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 moft part inferred from the following 
proportions: as fin. : rad. :: — col. : arc; and as cof. : rad. 
fin. : arc. But thefe proportions muft be ufed under 
reftriclions very necelTary 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 feml-circie, 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 maimer, at the very extremity of the qua- 
drant, 
