VOL. LXV.3 I'HILOSOPHICAL TRANSACTIONS. 70g 



tended by Mr. William Menzies, a land surveyor in the neighbourhood, who 

 had been recommended by some of the principal gentlemen of the country, as a 

 proper person for this work, went out every day that the weather permitted, to 

 take sections of the hill, and angles between several objects, for determining its 

 figure and dimensions. The method made use of was this, which was proposed 

 by Mr. Burrow, and was well adapted to the purpose. A number of station 

 poles were set up at convenient distances all round the foot of Schehallien ; but 

 rather without its base, and chiefly on little eminencies rising from the foot of it, 

 which formed a polygon of many sides, surrounding the hill ; and when delineated 

 on paper, show very nearly the shape of its base. At each station, the angular 

 position of 2 or more of the other stations being observed with the theodolite, 

 and one side being determined by means of a measured base, all the other sides 

 will be known. From these stations, sections of the hill up to the top were 

 taken in the following manner. The theodolite, being placed at any station, 

 was pointed towards the hill ; and a labourer was sent with a number of poles, 

 which he was to plant in the ground truly upright, at regular distances and in a 

 vertical plane, according to signals which he received from the person that stood 

 at the theodolite, who also took the altitude of the foot of each pole, and the 

 horizontal angle contained between the plane of the section poles and the next 

 station pole to the right or left. The theodolite was then removed, and planted 

 directly over the centre of this station pole, which was removed for this purpose; 

 and the horizontal angle taken between a pole now planted at the first station 

 and each of the poles of the section. The horizontal distance of the 2 station 

 poles being known, the horizontal distance of each of the section poles from the 

 first station, and their respective perpendicular altitudes above it, or depth below 

 itj will be given. 



It is manifest that these operations, when connected by angles with the 2 

 stations of the observatory and the meridian line, would at the same time give 

 the shape and dimensions of the hill, and the distance of the parallels of lati- 

 tude passing through the 2 stations of the observatory, as well as their respective 

 elevations above the base of the hill. But errors being apt to accumulate in a 

 long chain of triangles ; to obviate this danger, as well as to produce a check on 

 any great mistakes, that might happen to be made in reading off, or writing 

 down, the angles, I caused a heap of stones, or cairn, as it is called by the people 

 of the country, to be raised in a circular figure 6 feet high, at the highest point 

 of the ridge of the hill, which is to the west of it, as a signal to be observed 

 from the several angles of the polygon, and as a means of connecting the 2 

 stations of the observatory by a smaller number of triangles. Another cairn 

 towards the eastern end of the ridge of the hill was afterwards set up for the like 

 purpose. I proposed to determine the distance of the 2 cairns by connecting 



