Heights of the principal Hills of Dent, Sfc. Yorkshire. 191 



— 11". As the observed refractions come out negative for 

 terrestrial arcs not exceeding 5', it is to be suspected that this 

 error, especially as it was determined by a method liable to 

 some objection, may have been undervalued. In the beginning 

 of the year, the graduated arcs (which had become bent from 

 improper packing) were repaired, and the divisions renewed. 

 At the same time, fine cross lines were substituted for the de- 

 licate filament extended diagonally from the original vertical 

 wire to the horizontal one ; an alteration which may account 

 in part for the refractions alluded to appearing negative ; — the 

 horizontal line being probably depressed, in order to avoid 

 the other extreme, some little below the summit of the ob- 

 served hill. 



With regard to the adjustment of the cross lines, although 

 the line of collimation should in strictness be parallel to the 

 plane of the graduated arcs, as well as to the axis of the tubes 

 of the levels, it would nevertheless require a very gross error 

 in this respect to affect elevations or depressions not exceeding 

 3°. As the sector is fitted up with two divided arcs (one on 

 each side of the tube), each furnished with a moveable index 

 carrying a spirit-level, the one used with the telescope erect, 

 and the other with it inverted, — it becomes superfluous to ren- 

 der the line of collimation strictly parallel to the cylindrical 

 rings ; for the half sum of the readings by the two indices, when 

 corrected for the error of the levels and cylindrical rings, is 

 evidently the true angle. The transverse levels were adjusted 

 by bringing their bubbles to the marks (by means of the nuts), 

 whilst the planes of the arcs appeared to be parallel to a fine 

 plumb-line suspended nearly in contact with them. 



As a preface to the regis- 

 ter of the observations it may 

 be useful to point out the re- 

 quisite corrections, and al- 

 lude to the errors and un- 

 certainties to which they are 

 liable. 



Admitting the earth to be 

 a sphere, the difference of 

 altitude or level of any two 

 points on its surface ED will 

 be equal to their difference 

 of distance fom C the centre 

 of the earth, where the ver- 

 tical of D meets that of E. 

 Through E, perpendicular 

 to its vertical EC, draw the horizontal line EH ; and per- 

 pendicular 



