52 4 The Account of a 
have been obtained correctly, the difference of longitude be- 
tween Beachy Head and Dunnose, as thus found, must be very 
nearly true ; since the difference between the sums of the 
angles which would be observed on a spheroid and those on a 
sphere, having the latitudes and the difference of longitude 
the same on both figures as those places, is so small as scarcely 
to be computed : and it is easy to perceive, that the distance 
between the parallels is obtained sufficiently correct, since an 
error of 15 or 20 feet in that meridional arc, will vary the 
length of the degree of the great circle but a very small quan- 
tity. 
It may possibly be imagined, that because the vertical planes 
at Dunnose and Beachy Head do not coincide, but intersect 
each other in the right line joining these stations, neither of 
the two included arcs is the proper distance between them, 
and that the nearest distance on the surface must fall between 
these arcs ; but it is easy to show, that in the present case, 
the difference must be almost insensible. 
In fig. 4, let B be Beachy Head, and E B P its meridian, 
and N and M, the points where the verticals from Beachy 
Head and Dunnose respectively meet the axis P P. 
Now it is known, that if the| planes of two circles cut each 
other, the angle of inclination is that formed by their diame- 
ters drawn through the middle of the chord, which is the line 
of intersection. Therefore, if we draw B M, and also con- 
ceive D to be Dunnose, and E P its meridian, and join D N ; 
it is evident, that either of the angles N B M, N D M will be 
the inclination of the planes very nearly, because of the short 
distance between the stations, and their small difference in 
latitude. In the ellipsoid we have adopted, the distance M N 
i 
