of the Angle fub tended by Two Objects, &c. 423 
128. Let the angle QKF = a (fig. 1 4,) ; the arc KF == b ; the arc 
DF = £, and the angle DFK = ^/; their refpe&ive increments 
being a, b , c, and d, their fines p , s, vi , and n , and the co- 
temporary increments of their fines p, s, m, and n : from the 
proportion contained in art. 24. we fhall have p =■ a x s/ 1 ~p z ^ 
• • ~~ * • • O " 
5 = b x V 1 - j% m ~ c x v 1 — m\ and n = dxs/i~n z , which 
being fubftituted in the value of col'. ED lafF found will give 
Col. tu=z- 1 6s-X^i-p z xp-axi - 2?p z -nF+ rdm + znff-qnfuY + 2 /wV/ 
V; 
1)fn h x ^ 1 — fix o' 1 — 7/ x 3 — 4 /r 
T 1 -p z 
1 6/ x Vi - f x j £ x 1 - 2// - w 2 + » 2 /« 2 + - 2/wV + 2 ?m 2 n z p z 
rri 
' npx F I — « 2 X C I — /> 2 X 2 
. o c 
Fi-/ 
4- i6fF X F \-rnmc x \-n-f + %p L rf- z p z n'^'ipn x ^i-a 1 x F i_p x V 
- J>xF I-Zx^I-f XI-2r* 
■+ 1 (jCf'rn X F 1— n z x dX — H-f 2 p z n — f/> 2 « : 
Fi-n 
This quantity (art. 23.) being divided by the fine of the ob- 
served angle, the variation of that angle or ED will be the 
quotient. 
29. In the expreffion for cof. ED contained in art. 26. the 
variations />, s , w, and are arbitrary, as are b, c, and d , 
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 muffc be determined by the nature of 
the cafe. Moreover, if one or more of the given arcs and 
their fines fhould be correct, the variations correfponding and 
all the terms multiplied into them will vanilh. To give an 
example of the ufe of thefe expreffion s before they are applied 
to the immediate purpofe of examining the new conflrufUons 
K k k 2 defcribed 
