140
Remarks on the use of
[July
a function the error is given of the difference of longitude, by changing the formula.
In the diagram (Pl. 4 fig. 3) let A D be the meridian of the first station, B C the perpendicular of any other station, then A being the pole, D C will be the parallel of latitude of C, and A D will be the co-latitude of E, and not A B, and B D will be the error or the difference of latitude between the foot of perpendicular and the parallel.
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Take A B = 90 — X
BC = 7T
A C = 90 — (X - x)
D B = x. then by right angled spherics
we have
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sin (X — x) = sin X cos v 6in X. cos x — sin x. cos X =
dividing by sin X we have cos x — sin x. cot X = cos tt
and the cos x being nearly = 1, and substituting the value of cos π
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— 2
1 — sin 07. cot X = 1—2 sin i ir
sin x. — 2 sin { v tang X and taking x" and ir 7 for the sines x 11 = J *. tang X. sin 1"
which is the formula before given,—but the angle B A C is the difference of longitude between B and C, and in the right angled triangle A B C
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Tang A = tang ir, sec X
A" = v. sec X and transposing ir" = cos X. A" • = cos X. diff. longitude
substituting this in the last formula — s
x" = 8" ».cos X- Tang X. sin 1" = i B" a. cos X. sin X. sin 1" or become cos X. sin X = 4 sin 2 X
9
x" = 1 S"' sin. 2 X. sin 1" from this formula the following table is computed x always subtractive:—
