42 CALCULATIONS TO ASCERTAIN THE TRACT 20.
viz, 4 " 47 ', 9 ° 36 ', 14° 29', 19° 28', 24° 3 . 7 ', 30 ° O', 35° 41',41°48'j-, 48° 35', 56° 26'*, 66° 26'*, 90° O'.
Plate 2 contains a small plan of the principal and most cen-tral part of the ground, accurately divided in the above man-ner, for one of the observatories, namely, the Northern one,with the places of all, or most of the points, which fall withinthis part of the ground, accurately laid down, and markedwith dots, as also such of the included letters as have beenbefore mentioned in this paper.
In this plate rabcd &c, is the chain of stations, around thehill; k and n are the East and West cairns, on the extremi-ties of the ridge of the hill; o the Southern observatory, andp the Northern one. Of this kind two large plans were made,one divided for each observatory, from which were estimatedthe mean altitudes of the pillars, erected on the spaces intowhich they were divided.
These altitudes are easily estimated, when several of thepoints fall near and in the small spaces or bases, especiallywhen they are near the middle of them; but, numerous as thepoints are, there were many bases in which none at all werecontained, nor even near them. This circumstance at firstgave much trouble and dissatisfaction, till I fell upon the fol-lowing method, by which the defect was in a great measuresupplied, and by which I was enabled to proceed in the esti-mation of the altitudes, both with much expedition, and aconsiderable degree of accuracy. This method was, the con-necting together, by a faint line, all the points which were ofthe same relative altitude: by so doing, I obtained a greatnumber of irregular polygons, lying within, and at some dis-tance from, one another, and bearing a considerable degreeof resemblance to each other: these polygons were the figuresof so many level or horizontal sections of the hills, the rela-tive altitudes of all the parts of them being known ; and asevery base, or little space, had several of them passing throughit, I was thus able to determine the altitude belonging to eachspace with much ease and accuracy. In this estimation, Icould generally be pretty sure of the altitude to within 10