the 'Trigonometrical Operation * 
N° of 
triangles. 
Names oi the Nations. 
Obferved 
angles. 
Spheri- 
cal 
excels. 
DifF, or 
error. 
Angles cor- 
rected for 
calculation. 
Diftances. 
r 
f 
* 
AUington Knoll , 
Ruckinge 
Kigh Nook 
0 / // 
9 r 2 7 20 
54 >9 1 7 
34 13 21 
n 
// 
0 / n 
91 27 i 9 . 5 
54 19 18.5 
34 13 22 
Feet. 
XXIV. J 
1 
*79 59 5 8 
0.09 
— 2.09 
1 
Aliington Knoll, from 
f High Nook 
1 Ruckinge 
• • 0 « 
_.•••• 
23184.93 
16052.44 
Hence, in the quadrilateral formed by High Nook , Ruckinge , 
Lydd , and AUington Knoll , making ufe of the two obtufe an- 
gles, as contained within their now refpedive known fides 
we have for the mean diftance of the points of the acute an- 
gles, at Lydd and AUington Knoll, reprefented by a dotted 
line in the plan of the triangles, 47849,27 feet. This dis- 
tance agrees accurately with the length of the fame fide in the 
XXth triangle, as given by the bafe meafured on Hounflow 
Heath. Here however it is to be remarked, that, in order to 
produce this agreement, the angle at Hoilingborn Hill, be- 
tween Aliington Knoll and Fairlight Down, has been made 
48° 56' 28" inftead of 48° 56' 31"!, being a difference of 
3 // t+.9 which, according to obfervation, it fhould have been. 
Had not this redudion been made, the diftance between Al- 
iington Knoll and Fairlight Down, being one of the fides of 
the XXIId triangle, would have been 106924 feet, that is to 
£ ay, if foot longer. Now, fince this fide, compared with 
the bafe of verification, bears nearly the proportion of four to 
one, it follows, that the real difference between the meafured 
length of that bafe, and its computed length deduced from 
that on Hounflow Heath, feventy miles to the weft ward, or of 
Vol, LXXX. A a either 
