The Account of a 
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art. ir. Of the Selection of the Angles constituting the prin- 
cipal Triangles , and the Manner of reducing them for Com- 
putation. 
The angles of the several triangles, constituting the gene- 
ral series, are, with a very few exceptions, those arising from 
using the means of the several observations given in the fore- 
going part of this work ; for although the rejecting of such as 
might apparently suit the purpose, would give the sums of the 
three angles of many of the triangles, nearer to 180 degrees 
plus the computed excess ; yet as all the observations have 
been made with equal care, and are for the most part to be 
considered as of equal accuracy, it has been thought proper to 
select those means, as being the fairest mode of proceeding. 
If the observations had been made on a sphere of known 
magnitude, and the angles accurately taken, the most natural 
method of computing the sides of the triangles from the mea- 
sured bases, would be by spherical trigonometry; but if the 
magnitude was such, that the length of a degree of a great 
circle was equal to a degree of the meridian in these lati- 
tudes nearly, in order to obtain the sides true to a foot from 
such computation, with any facility, a table of the logarith- 
mic sines of small arcs computed to every of a second of 
a degree, would be necessary, because the length of a second of 
a degree on the meridian is about 100 feet. As the lengths of 
small arcs and their chords are nearly the same (the difference 
in these between Beachy Head and Dunnose being less than 4, 
feet) it is evident this business might be performed sufficiently 
near the truth in any extent of a series of triangles, by plane 
