Heights of the 'principal Hills of Swale dale, Yorkshire. 123 



Stations. 



Great Pinch Yate and Water Crag 

 Keasdon and Shunnor Fell 



Bakestone Edge. 



Great Whernside and Settronside 

 Pickington Ridge & BakestoneEdge 



Shunnor Fell 



Pickington Ridge & G c Pinch Yate 

 Shunnor Fell and Nine Standards 

 Water Crag and Shunnor Fell... 



Pickington Ridge 



Bakestone Edge 



Shunnor Fell and Pinch Yate .... 



Pickington Ridge 



"Great Whernside and Dod Fell 

 Shunnor Fell and Wherjiside ... 

 Gt. Whernside and BakestoneEdge 

 Shunnor Fell and Pen-y-gent ... 



• Ingleborough... 



G c Whernside and Ingleborough... 



Whernside . 



Shunnor Fell . . . 



Rumbles Moor 



Arcs. 



2 



3 



3 



3 



3 



4 



4 



4 



5 



6 



6 



7 



7 



10 



10 



11 



12 



13 



14 



14 



15 



16 



26 



3 



6 



26 



46 



20 



31 



54 



52 



25 



48 



9 



58 



21 



23 



56 



54 



30 



1 



44 



2 



36 



Refrac- 

 tions. 



-20-5 



- 1-5 

 -11'5 



- 2- 



- 8* 



- 1-5 



- 4-5 



o- 



+ 8- 



- 5- 

 + 0-5 

 + 23 

 + 12-5 

 + 33* 

 + 27" 

 + 37*5 

 + 39-5 

 + 45- 

 + 46- 

 + 58- 

 + 55' 

 + 65* 



Error of 

 Formula. 



+ 



+ 



+ 



6-5 



9-5 



1- 



6-5 



1-5 



- 25 



- 0-5 



- 0-5 



- 3-5 

 + 12-5 

 + 9- 

 -11-5 

 + 3-5 



- 4- 



1-5 



0- 



3-5 



1- 



3- 



5* 



0-5 



Sum of arcs 10991"; 

 Sum of refractions ( + 450" + -54\5 = )+396". 



Mean refraction — ^ = ~^- positive. 



The indiscriminate adoption, throughout the calculations, of 

 a positive refraction in one constant ratio of the arc, although 

 nearly one-half of the observations indicate its negative qua- 

 lity, would evidently lead to irreconcileable discordances in 

 the results. As the negative quantities diminish, and the af- 

 firmative ones increase with the contained arc, it is possible 

 that the refraction may have been always positive, and nearly 

 in the same proportion to the arc, but diminished by some 

 unvarying quantity arising from local refraction or imperfec- 

 tion of the instrument. If we denote by ?'(= — cc) the 



observed refraction of the arc a, affected by the unknown 

 quantity x, and represent by t' f— — xj the correspond- 

 ing quantity for the greater arc C, then will the true refraction 

 S of an arc b, equal to their difference (= c— a) be equal to 



R2 t'-rU 



