522 The Account of a 
of the arc DR = 336980 feet, we get RE = 3288,2 feet, which 
taken from BR, as found above, leaves 44258,9 feet for the 
meridional arc, or the distance between the parallels of Beachy 
Head and Dunnose ; which is nearly the same as before. 
This method of determining the distance between the pa- 
rallels is sufficiently correct ; but the same conclusion may 
be deduced from a different principle, thus : 
Let the difference of longitude, or the angle at P, be found, 
on any hypothesis of the earth's figure, and likewise the lati- 
tudes of Beachy Head and Dunnose ; with these compute the 
latitudes of the points E and L ; then it will be found, that 
the arc R E is y£o" greater than LW ; and since of a se- 
cond on the meridian is nearly a foot, R E is 5 feet more 
than LW ; hence - 7 — 1 ~ * ,+i° 9 2 3 . ? 4 — 44257,8 feet is the dis- 
tance between the parallels, and which is very nearly the same 
as found by the other method. 
It seems therefore, that whatever be the value of the arch 
between those parallels in parts of a degree, the distance be-' 
tween them is obtained sufficiently near the truth ; therefore, 
taking 60851 fathoms for the length of a degree on the meri- 
dian, we get the arch subtended by 44258,7 feet = 7' 16", 4, 
which subtracted from the latitude of Beachy Head, namely, 
5 o° 44' 23",7i, leaves 50° 37' 7", 31 for the latitude of Dunnose. 
We have therefore, for finding the length of the degree of 
a great circle perpendicular to the meridian at Beachy Head, 
or Dunnose, the latitudes of the two stations, and the angles 
which those stations make with each other and the pole. 
Now it is proved in the Philosophical Transactions, Vol. 
LXXX. that the sum of the horizontal angles (such as PDB, 
PBD, fig. 1.) on a spheroid, is nearly the same as the sum of 
those which would be observed on a sphere, the latitudes, and 
