2i 8 Gen. Roy’s Account of a 
and the laft 125 0 f ; thus we (hall have two fpherical tri- 
angles to compute, in each of which two Tides, and the con- 
tained angle, are known, and one fide, viz. the co-latitude, is 
common to both. Now, from thefe data, making ufe of the 
half fum and half difference of the Tides, we fhall have 
the angles in thefe two triangles as * underneath, and the 
angle of longitude between Bottle-hill and the Brunemherg , 
equal to that at the pole, will be found to be 1 0 5 f 5 6 X/ . 1 . 
If from this angle w r e deduct about 30" or 35", for the fpace 
that the Bottle-hill feems to be to the wefcward of the meridian 
of Greenwich, there will then remain i° 55'' 2i /x for the eaft 
longitude of the Brunemherg , being very nearly that exprehed 
in the map of the triangles which accompanies this paper. 
* Bottle-hill. 
Brunemberg. 
O 
/ 
// 
O / // 
Half difference — 
5 1 
25 
14.05 
Half difference — 
26 44 12.2 
Half fum — 
5 2 
32 
25.07 
Half fum — 
27 32 57-3 
Angle at Bottle-hill 
10 3 
57 
39.12 
Angle at Brunemberg 
54 17 9-5 
Angle at the pole — 
i 
7 
1 1.02 
Angle at the pole - 
48 45.1 
Contained angle — 
75 
10 
0. 
Contained angle - 
12 5 5 °* 
Sum of the three angles 
180 
14 50.14 
Sum of the three angles 
180 10 54.6 
Angle of convergence 
52 
N> 
O 
bo 
00 
Angle of convergence 
- 37 5°«5 
Excefs above 1 8o° 
14 50.14 
Excels above 180° — 
10 54.6 
Angle of longitude — 
1 
7 
I 1.02 
Angle of longitude 
48 45.1 
Sum of the two longitudes i° 55' 56". 12. 
It is to be obferved, that the meridians, which are all parallel to each other at 
the equator, on their departure from thence converge more and more as they 
approach towards the pole, where the angle of convergence becomes equal to the 
angle of longitude. It may alfo be remarked, that the angle of convergence, 
augmented by the excefs of the three angles of the fpherical triangle above 180°, 
is always equal to the angle of longitude, or that at the pole. And as this holds 
univerfally in all latitudes, it affords a ready means of proving that the compu- 
tations are juft. 
3 As 
