of an Arc of the Meridian. 431 
circumstanced, it would be right to depend on each base for one 
third of the distance between it and the one next at hand, and 
use the mean result, as derived from the two adjoining bases, 
for the true lengths of the several sides within the other third. 
Thus, if two bases were found at the extremities of the arc in 
question, and one in the middle, as about Brill, the compu- 
tation should be carried on, from the extreme bases, about one- 
sixth part of the meridional distance ; and, from the middle base, 
one-third of the intermediate distance on each side ; the remain- 
ing two arcs being determined from the respective base lines. 
That I may avoid prolixity, or the appearance of it, I shall 
compute the sides of the triangles northward of the two stations 
before mentioned, from the base measured on Misterton Carr 
only, and use the mean distances calculated on the above prin- 
ciple, when I find the total length of my arc. 
Length of the Base on Misterton Carr, 26342,7 Feet. 
No. of 
triangles. 
Names of stations. 
Observed 
angles. 
Diff. 
Spheri- 
cal 
excess. 
Error. 
Angles corrected 
for calculation. 
Distances. 
XII. 
Beacon Hill 
North end of Base 
South end of Base 
O t II 
20 47 19,75 
60 17 16,5 
9 8 55 2 7>5 
" 
" 
" 
0 1 11 
20 47 20 
60 17 13 
98 55 2 7 
Feet. 
180 0 3,75 
n um, r f North end of Base 
Beacon HiUfrom^ South end of Base 
64461,7 
73 3 2 it9 
XIII. 
Beacon Hill 
North end of Base 
Gringley on the Hill 
34 44 42,25 
74 46 5 6 >5 
70 28 22,25 
34 44 4 2 
74 46 5 6 
70 28 22 
00 
0 
0 
„ . . f f North end of Base 
Gringley from { Beacon HiU 
44338.2 
75068,0 
3 K 2 
