Trigonometrical Survey. 491 
trigonometry, if the angles formed by the chords could be de- 
termined pretty exact. We have endeavoured to adopt this 
method in computing the sides of the principal triangles, in 
order to avoid an arbitrary correction of the observed angles, 
as well as that of reducing the whole extent of the triangles to 
a flat, which evidently would introduce erroneous results, and 
these in proportion as the series of triangles extended. 
The length of a degree on the meridian in these latitudes 
being about 60874 fathoms, and that of a degree perpendicu- 
lar to the meridian, about 61183; it follows, that the values 
of all the oblique arcs are between these extremes : now hav- 
ing obtained the sides of the triangles within a few feet by a 
rough computation, we take their values in parts of a degree, 
nearly as their inclinations to the meridian ; this proportion, 
though not found on an ellipsoid, is sufficiently true for find- 
ing the values of the sides of the triangles ; for in this case 
great accuracy is not necessary. With the sides thus deter- 
mined, we compute the three angles of each triangle by sphe- 
rical trigonometry ; and taking twice the natural sines of half 
the arcs, we get, by plane trigonometry, the angles formed by 
the chords ; then, from the differences of these angles we in- 
fer the corrections to be applied to the observed angles, to re- 
duce them for computation : an example, however, will make 
this matter much plainer ; for which purpose we shall take 
the very oblique triangle formed by the stations Beachy Head, 
Chanctonbury Ring, and Rook's Hill. 
^ rc f Rook's Hill and B. Head 39' 7" 'i 113785156 
hPtwPPn I Ch - Rin g and B - Head 47 chords l 75000501 
l Rook's Hill and Ch. Ring 140 J 4072432© 
Hence the angles by spherical trigonometry will be 
