not amount to four feet; a small quantity in a side of three-andtwenty miles. I shall, however, use 120557,7, because I think it the most accurate determination.

No. of

triangles. Names of stations.

XXXV11. Broadway Beacon
Epwell
Corley

XXXV111. Brill

Epwell
Arbury Hill

XXXIX. Arbury Hill

Epwell
Corley

XL. Bow Brickhill

Arbury Hill
Brill

Observed
angles.

Diff.

Corley from Broadway Beacon

2,5

89 57 4,5-1,14

54 45 18.75-0,57
35 17 36,75 -0,57

180

Spheri-
cal Error.

excess.

"

1,58 -1,58

Arbury Hill from

68 22 56,75 -1,21

43 16 55,5

-0,99 7,75 -1,22

68 20

2,46 -0,04

Epwell
Brill

Angles corrected

for calculation. Distances.

3,43 -3,43

2,29 -2,291

Corley from {Arbury Hill
{Epwell

Bow Brickhill from{

1

56 32 44,75

95 34 24,75
27 52 50,5

34 23 57,5
85 O 17,5
60 35 57,5

By the triangle Broadway Beacon, Epwell, Corley, (see the above) the distance from Corley to Broadway Beacon is the only distance computed; and this has been obtained through the means of two observed angles only. When the observations were made at Broadway Beacon, it was not imagined Corley could be seen; and the contrary was not known till the party arrived at the latter place. In so large a triangle, it would certainly be right to observe all the angles: but I have given the angles as they now stand, because the distance from Epwell to Corley comes out 143831 feet, which determination differs only three feet from the same distance found by the last triangle.

Arbury Hill

89 57 5.5
54 45 18,25
35 17 36,25

68 22 59 43-16 54,5 68 20 6,5

Feet.

171568

83098,4 146530

117463 143827,8

146481 108058,9

It will now be expedient to compute the distance from Bow Brickhill to Brill, by means of another set of triangles. And it was for the express purpose of verifying this distance found by the last triangle, that Scutchamfly Barrow, in Berkshire, and the station above Wendover, were chosen. The base on which these triangles are to rest, is the distance between Nuffield and White Horse Hill, viz. 120557,7 feet.

XLVI. Kinsworth

Bow Brickhill
Brill

XLVII Wendover

Quainton
Brill

{

1,58 -0,07

{

Wendover
Brill

Quainton from {

According to the first determination, the distance from Bow Brickhill to Brill is 108058,9 feet, and by the last, 108855 feet. There is, therefore, a difference of 4 feet nearly; a quantity which must be deemed inconsiderable; hence, 108056,9 feet may be taken for the true distance.

Wendover
Shotover Hill

Angles corrected

for calculation. Distances.

0,55 -2,55

"

23 23 57,25 48 30 40,5 108 5 22,25

Brill
Wendover

80 II

8,5

57 25 0,75
42 23 50,75

Brill

Bow Brickhill

62 55 38,5

88 41 59,25

28 22 22,25

Feet.

33 26 49

94 58 38
51 34 33

73940,3 39200,2

192400,7 108055

121322,5 57668

40908 58146,4

XLIX. Bow Brickhill

Kinsworth

Quainton

L.

Angles observed.

•

38
38 51 40,75
46 44 29,5
94 23 50,25

180 O

1,251

Quainton from {

85 952,75

52 17 56,75

Diff.

42 10 36,75

82 50 30,5

54 38 53

"

180 O

Spheri

cal

excess.

0,25

་

Error.

In the above triangle, I have computed the distances of Wendover and Bow Brickhill from Quainton with 92400,7 feet, the side Wendover and Bow Brickhill, as determined in a former triangle.

0,83 +0,42

Angles corrected
for calculation.

Wendover
Bow Brickhill

0

"

"1

38 51 40,75
46 44 29,25
94 23 50

Lillyhoe from {

Quainton from

Therefore, 67490 may be considered as nearly the true distance, in feet, between Quainton and Bow Brickhill.

Distances.

Kinsworth
Bow Brickhill

Feet.

58146,9 67491,3

84997 167490,3

47278,7 69867

As the stations Lidlington, Trusler Hill, together with Crouch Hill, Cumner Hill, and Whiteham Hill, have been used for purposes of greater importance than secondary ones have been generally applied to, I shall insert the triangles formed by their intersections in this article.