196 Mr. Nixon on the Measurement by Trigonometry of the 



(CAi on -v 



— y |-SAcv)SB), and g 



the reciprocal of ( — - h TA cv> TB) : then if //' repre- 

 sent the difference of altitude calculated from the observations 

 at S and T, the correct value may be considered as equal to 



•* 8 . The heights of two or more hills having been simi- 

 larly determined, it may be useful, in the event of being sta- 

 tioned on one of them, to observe the elevation or depression 

 of the others, with a view to learn the actual refraction. On 

 such occasions it is requisite to have given the instrumental 

 and adjustment errors. Adopting this method, the following 

 refractions were obtained : Arc Re p, 



Gt.Whernside as observed from Pen-y-gent . 8' 50" + 4"*5 



DodFell .. 10 24 +25 



Noughtberry 13 34? +28 



Pendle Hill Noughtberry 24. 42 + 1 -30 



The refractions deduced from the reciprocal observations 

 are given below: Arc Refll 



Between Whaw Fell and Noughtberry .... 1' 14"+ 6" 



Dod Fell and Noughtberry 3 10+ 9 



Whaw Fell and Whernside 3 21 — 18 



Ingleborough and Whernside .... 3 41 — 9 

 Noughtberry and Whernside .... 4 6 + 2 

 Ingleborough and Pen-y-gent .... 5 16 — 6 



Dod Fell and Whernside 5 45 + 4 



Pen-y-gent and Whernside 6 54 + 1 1 



Noughtberry and Ingleborough ...714+ 3*5 



Dod Fell and Ingleborough 7 31 — 7*5 



Noughtberry and Pen-y-gent .... 7 53 + 16*5 

 Mean arc 5'"6: Mean refr. + 1". 



As the refraction resulting from observations made some 

 years ago by the same instrument ^on numerous arcs, several 

 of which were "of considerable extent, appeared to be about 

 1-1 8th of the arc, the refraction adopted in the calculations, 

 when not determinable from reciprocal observations, has been 

 1-1 8th minus the constant quantity 18". In addition to the 

 elevations being observed in defect after the substitution of 

 the cross lines for the filament, two other causes may be as- 

 signed for the smallness of the refraction ; — the ray, as the hills 

 were lofty and differed little in elevation, would be confined 

 to a stratum of rare air; and the observations were made (a 

 little too early in the year) about the warmest part of the day, 



when 



