Heights of the principal Hills of Wensleydale, Yorkshire. 433 



subtractive according as the half-sum exceeds or falls short of 

 the reversing point. For angles of depression the correction 

 is to be applied with the contrary signs. The value of one 

 division (of forty to the inch) of the right-index level is 1"*91 ; 

 that of the left-index level 2"-12. 



On calculating the cylindrical error of the sector from mea- 

 surements by the scales, substituted for those previously ob- 

 tained by the divided arcs, its amount was determined to be 

 20", instead of 11" as last stated; the discrepancy arising 

 principally from a gross error existing in the formula*. 



The ground about the station at Penhill being an almost 

 impassable bog destitute of rocks, the tripod of the theodolite, 

 having a firm board screwed to it, was fixed on the turf-mound 

 already described. From the elastic nature of the materials of 

 the mound, the slightest change in the position of the observer 

 displaced the bubble of the level several minutes, and threat- 

 ened to render the accurate measurement of the angles utterly 

 impracticable. Fortunately, after abandoning various plan^ 

 of overcoming the difficulty, the following method of conduct- 

 ing the observations was tried and found to succeed extremely 

 well. An approximate measurement being effected, the weight 

 of the body was thrown for a moment on one foot, and a light 

 stone, placed on the board, moved gradually in the proper 

 direction until the line of coUimation pointed exactly at the 

 base of the signal. Averting the head as slightly as possible, 

 the position of the bubble was then read off at one rapid 

 glance, and the eye replaced as instantaneously at the telescope, 

 to ascertain that its direction remained unvaried. Tedious 

 and difficult as was the method in execution, it was gratifying 

 to find that the results equalled in accuracy the measurements 

 effected in the usual way at Settronside with the sector placed 

 on a wall, or supported, as at the other stations, on firm piles 

 of stones surmounted by a heavy flag. 



The observed refractions, with their deviations from the 

 mean value, about 1-1 7th, are stated below: 



Arc. Refr. Deviat. 



Shunnor Fell and Bakestone Edge 4' 19" —17" —32" 



Bear's Head and Whaw Fell 



Bakestone Edge and Bear's Head 



Penhill and Settronside 



Bear's Head and Shunnor Fell 



Settronside and Bear's Head 



Shunnor Fell and Knoutberry Hill 



♦ Soniu lime in the course of the present year I hope to be able to fur- 

 nish 3oiir readers with a complete treatise " On the constant Krror of Col- 

 limution of a 'J'cicscopic Level." 



N.S. Vol. 5. No. 30. June 1829. 3 K Dod 



