42 z Mr . atwood’s Theory for tie Mcnfuraiwn 
Co i. LU — — 1 6 s 2 pp X i — 2 — tf/ 2 4- n„L + 
i m~ p — a u. n" p 4~ 2 & z# vy 
m nt>. x v i — x ^ i -- i 2 x 3 — 4// 
— 16 ^ 2 i j X I — 2 J 2 y — Zft 2 + zz' zzr -j- p 2 n 2 — 2 p~ nr n 4 - 2 / ’ m x n z r 
z/, rip xv i-« x V 1 — y> x 2 — 
+ 
1 6 s z p z mnX 1 - w 2 -// 2 + 2 />V-j7>Vh= 2/);.X ^i-zrx ^i-rX ^ 1 -^ 
+ 1 6 j 2 /> 2 /w z « X — w + 2 ^ 2 n — f/> 2 zz : 
a/ i — r x ^ 1 — z/ 2 
/, X p X 1 — 2h 
V T _ 
I — 
27. This value of col. ED is expreffed in terms of the va- 
riation of the fines of the given quantities : if it be neceflary 
to exprefs col. ED in terms of the variation of the arcs them- 
ielves, it muft firft be confidered to what part of the quadrant 
they belong : for example, if s be a line of an arc b not very 
near the extremity of the quadrant, and the variation be r, the 
cotemporary variation of the arc b will be py -~— 2 > but if the 
variable arc be nearly = 90°, and becomes exaftly equal to it 
ultimately having varied by a fmall arc b of which the verfed 
fine - - v ; then will - s = the verfed line of b and - b — v/ 2 v. 
Laftly, if the variable angle approximates to 90% but is not 
equal to it, and the variation of its line fhould be = s, the co- 
temporary variation of the arc muft be obtained from the 
general theorem in art 25. When either of the two lat- 
ter cafes happen, the variation of the arc muft be 
determined for each particular cafe ; but it will be neceflary 
to give a general expreflion for cof. ED in terms of the varia- 
tions of the given arcs, of which p y r, //;, ri, are the refpe&ive 
fines when thefe arcs are at feme diftance from 90°; this is 
contained in the next article* 
7 
28. Let 
