vf the Angle fuif ended by Two ObjeBs, &e. 423 
28. Let the angle QKF = a(fig. 14.); the arc KF = <£ ; the arc 
DF = r, and the angle DFK = d ; their refpedUve increments 
being a, b, c, and d, their fines p, s, in, and n, and the co- 
temporary increments of their fines p, 's, m, and n: from the 
proportion contained in art. 24. we ihall have p = 'ax %/i -p* t 
s ~ b x v/ 1 ? ffi c X s / 1 — ni , and h — d x \/ 1 — n , which 
being fubftituted in the value of.cofi ED laft found will <nvi 
fc> 
Coi. Lu — — l 6 s 2 X if/ 1 -p z Xpaxi- 2> z p z -m z + n 2 m 2 + 
2m~p~-pri rtp" 4- 2 z m z n z p‘ 
± X * 1 ^ f X ^ 1 - n z x 3-4/ r 
i—p z 
— 16 p z x 1 - rxlix 1 — 2 s z p z — m z + n z M z + p z & -- 2f 
l f7pX 1 _ x ^ i — p z x 2 - 3? 
rr z n z -f- 2 z m np z 
4- ib z p z X ^ i-nrmc X I -n z -p z 4 2 p z n z - s z p 2 * z qq 2pn x ^ i~»“ x v i-j 2 x ^ i-/> 
__p x v' i— r x ^ r — p z x j - 2 n z 
4 1 6 s l p z m z X ^ i — n z x d x — »4 — s z p z nq 
Vi 
This quantity (art. 23.) being divided by the fine of the ob- 
ferved angle, the variation of that angle or ED will be the 
quotient. 
29. In the expreffion for cof. ED contained I11 art. 26. the 
variations^, j, m , and n , are arbitrary, as are a , c, and </, 
in the laft article. If a condition be annexed to the variation 
of any of them, two or more may become dependant on each 
other ; and their relation muft be determined by the nature of 
the cafe. Moreover, if one or more of the given arcs and 
their fines fhould be corredt, the variations correfponding and 
all the terms multiplied into them will vanilh. To give an 
example of the ufe of thefe expreffions before they are applied 
to the immediate purpofe of examining the new conftrudtions 
K k k 2 deferibed 
