5*5 . 
Trigonometrical Survey. 
is about 62 fathoms, and hence the angle N B M, or N D M, 
will be found between 2 and 3". The value of the arc be- 
tween the stations is about 55' 30", and its length 339401 
feet ; hence the versed sine of half the arc will be 685 feet 
nearly; now, suppose the versed sines to form an angle of 3", 
the greatest distance of the vertical planes on the earth's sur- 
face between the stations, will be but about t X q of an inch. 
It may also be remarked, that the inclination here deter- 
mined, is the angle in which the vertical plane at one station 
cuts the vertical at the other; and therefore no sensible varia- 
tion can arise in the horizontal angles, on account of the dif- 
ferent heights of the stations. 
If the figure of the earth be that of an ellipsoid, (fig. 5.) then 
B R, which is perpendicular to the surface at the point B, is 
the radius of curvature of the great circle, perpendicular to the 
meridian at that point ; therefore the length of a degree of lon- 
gitude is obtained by the proportion of the radius to the cosine 
of the latitude. Thus at Beachy Head, where the length of the 
degree of a great circle is 61183 fathoms nearly, we have this 
proportion ; rad. : cosine 50° 44' 24" : : 61183 : 38718 fathoms, 
for the length of the degree of longitude. And at Dunnose, as 
rad. : cosine 50° 37' 7" : : 61182 : 38818 fathoms for the length 
of the degree of longitude, being about 100 different from the 
former. But nearly the same conclusions may be otherwise de- 
duced ; for the chords.of the parallels may be found from the 
small triangles B W L and D E R, (fig. 3.) and these, when aug- 
mented by the differences between them and the arcs, give the 
length of the degree of longitude at Beachy Head 38719 fa- 
thoms, and Dunnose 38819 fathoms. 
by 
MDCCXCV. 
