Heights of the principal Hills of Swaledale, Yorkshire. 125 



on Keasdon in lieu of the base of the signal, of which it would 

 interrupt the view, — a mistake that would tend to give a re- 

 fraction proportionately too great. At Water Crag the de- 

 pression of Pickington Ridge is noted in the field-book as an 

 uncertain observation ; the signal, owing to the heat and hazi- 

 ness, being tremulous and dim. From the same causes it was 

 never once possible to bisect, even with the telescope of the 

 theodolite, the signal on West Stonesfield Moor, at that time 

 undestroyed. The difference of 11"*5 in the observed and 

 computed refraction between Pinch Yate and Shunnor Fell 

 will not appear extraordinary, when we take into consideration 

 that the elevation of the latter must be in a great degree vi- 

 tiated by the rare deviation of 12"*5 in the error of collima- 

 tion from its mean value. Lastly: were the refraction be- 

 tween Bakestone Edge and Water Crag founded exclusively 

 on the data of last year, it would accord within 6" of its as- 

 signed value. 



The formula of refraction for the survey of the Dent Hills, 

 deduced chiefly from small arcs, was confessedly inapplicable 

 to those of considerable extent. 



The formula of the Swaledale survey may however be 

 substituted with singular success, and will be found to satisfy 

 the observations on arcs of both descriptions. On the other 

 hand, it is remarkable that the latter formula should differ 

 materially from the equally correct one made use of in com- 

 puting the altitudes of the Wensleydale Fells. The three sur- 

 veys were nevertheless carried on all about the same time of 

 the year, and the observations took place nearly at the same 

 hours of the day. In fact, the only circumstances peculiar to 

 the Wensleydale survey which could possibly account for the 

 difference in its refractions, were the almost total absence of 

 frost, and the excessive humidity of the atmosphere. 



If we may not ascribe the constant error of 27" to the in- 

 fluence of local refraction, it is quite certain that it cannot just- 

 ly be attributed to a false estimate of the cylindrical error of 

 the sector. Not only do the most recent experiments indicate 

 the quantity already assigned to be too great, but every com- 

 parison of the measurements by the sector with the corre- 

 sponding ones by the great theodolite of Ramsden confirms 

 the exaggeration. A few of the zenith distances observed 

 at Ingleborough by the two instruments, corrected for their 

 respective constant errors, and reduced to the level of the 

 ground, are cited in the next table. 



By 



