of an Arc of the Meridian. 
439 
Distance between the Parallels of Latitude of Greenwich and 
Dunnose. 
In the Phil. Trans, for 1795, the station on Beachy Head is 
shown to be 269328 feet from the perpendicular at Greenwich, 
and 58548 from its meridian. In Plate XVI. Fig. 2, of this 
account, let DPB be a great spheroidical triangle on the earth’s 
surface, P the pole, and DB the two stations at Dunnose and 
Beachy Head. Let also PGM be the meridian of Greenwich, 
rGJ and M the point where the parallel of Beachy Head to 
the perpendicular at G cuts that meridian. Then, from the 
above values of GM and BM, it will be found, that the latitude 
of B is i",03 less than the latitude of M, and that too on any 
hypothesis of the earth’s figure. Therefore, the distance in feet, 
between the parallels of B and G, is 269328 -f 103 — 269431. 
Now it has been shown, in the volume above referred to, (see 
page 522,) that the meridional distance between D and B is 
the mean of the two numbers 44258,6 and 44258,9 feet; and it 
must be remembered that, in deducing those conclusions, re- 
course was not had to matters of assumption, but to matters of 
fact, which were, the observed directions of the two meridians 
PD, PB, and the distance DB. Therefore, if 44.259 feet be 
taken for the meridional distance between D and B, we shall 
have 269431 -f 44259 == 313690 feet, for the space between 
the parallels of latitude of Greenwich and Dunnose.* 
* In the Phil. Trans, for 1800, (see note to page 641,) in finding the value of the 
oblique arc between Black Down, in Dorsetshire, and Dunnose, I have used the 
expression — — — d ; where d is the length of the required degree, p that of 
p + m — s . 
the great circle perpendicular to the meridian, m that of the degree of the meridian 
itself, and s the sine of the angle constituted by the oblique arc and the meridian. 
3L 2 
