216 Delermination of the Altitude of Great JJ7ienisiJe. 



depressions gave a refi'action of ^^ and ^j, the arcs being 8' 

 34" and 11' 44' respectively. The mean refraction being 

 about one-fifteenth, it is probable that the depressions were 

 alike in excess by 27". Sauntering, in June last, near a large 

 hme-kiln to the left of the road from Ingleton to Askrigg, I was 

 surprised, considering the clouded, chilly state of the atmo- 

 sphere, to observe the hills to the north-west remarkably tre- 

 mulous, whilst those in other directions were totally unaffected. 

 Placing myself on the opposite side of the huge mass of ignited 

 yet unsmoking matter within the kiln, the reverse took place ; 

 plainly indicating heat to be the cause of the ebullition observ- 

 ed in the air. On days when thermometers in the shade and 

 exposed to the sun have indicated a considerable difference, I 

 have remarked the tremor confined to a sandy road. 



Reciprocal observations of two hills having been made with 

 extreme care, and the distance correctly determined, it re- 

 mains to be demonstrated how the refraction due to each ob- 

 servation is to be ascertained. This is easily effected in the 

 course of a survey, by noting their difference of elevation as 

 deduced from the mean of a number of observations made from 

 stations nearly equidistant. The eiTors of collimation and of 

 tlie levels are consequently opposed to each other in quantities 

 nearly equal : the estimate of the refraction, whether incorrect 

 from causes confined to the locale, or from a distortion of the 

 ray in its whole extent, will but slightly affect the correct- 

 ness of the calculation. The errors arising from unequal at- 

 traction and improper pointnre will likewise be nearly annihi- 

 lated. 



The mean difference of altitude as thus determined may be 

 called tlie_^;s/ correction. An increased approximation to ac- 

 curacy may now be j^roduced, by finding the difference of al- 

 titude of each auxiliary station, and the hills themselves, by 

 the observations from the other stations, and substituting these 

 mean differences for those used in the first instance. These 

 corrections, being carried on to the third order, were found to 

 ensure to the altitudes an accuracy of less than half a foot, 

 which when the arc is not less than 4 or 5' is quite sufficient 

 for our purpose. In possession of the correct relative heights 

 and the distance, we are able to calculate the true angles, dif- 

 fering by the quantity of refraction from those observed, ex.gr. 

 — At Ingleborough tlie depressicm of Great Whernside, as 

 observed .lune 14"and 17, 1822, varied from 8' 40" to 8' 50", 

 mean 8' 45''. At Great Whernside the observed depression 

 of Ingleborough, September 1, 1821, was 3' 23", and April 15, 

 1822, 3' 17",^nean b' 20". The distance is 85,598 feet, arc 



14' 



