of Inglehormigk above the Level of the Sea. 



255 



every successive repetition either a gradual increase or de- 

 crease*, whilst those obtained by the circle beyond the mul- 

 tiple requisite to clear the angle of the error of reading f 

 rarely oscillated out of the limits of 2" or 3'^ 



At the station S we may procure, by simple subtraction, 

 an additional measure of the angles 

 subtended by the signals AB, B C, 

 and C D, by observing ali^o those 

 formed by A C, A D, and B D. At 

 Ingleborough, out of 14- angles obtain- 

 ed by the circle (of which there were 

 on an average 4 measures), the mean 

 error was about 3", and the maximum 

 8" ; at Clougha, the mean error out of 

 13 angles (of which there averaged 3 

 measures) was 6'^ and the greatest 12", 



The mean difference between 39 (oblique) angles by the 

 theodolite and the circle equalled 11 ", the signs in all the 

 cases being disregarded J. 



Calculation of the Distances. 



Corrections. — The verniers of the circle are fixed too near, 

 and those of the theodolite too far from the centre of the 

 graduations, the former requiring a mean correction of + 2", 

 and the latter of — \" per minute. The trifling excentricity 

 of the telescope of the circle was disregarded. The correction 

 for the partial illumination of the whitewashed signals was 

 allowed for in the bisection. The reduction of the angles to 

 the centre of the signal was carefully computed from exact 

 data. Oblique angles were reduced to their horizontal value 

 by both the fornwlce of Dr. Maskelyne. The horizontal di- 

 stances were verified by those calculated with the oblique 

 angles and bases, the latter being first reduced to the same 

 plane. 



* Strictly speaking, the error of the first reading cannot be exterminated 

 in the longest series of repetitions. 



\ The verniers being too far subdivided and the lens unfixed to the in- 

 strument, the error of reading might amount to 20" or 30". 



X As a specimen of the capabihties of my repeating circle, I give the 

 two measurements at Ingleborough obtained vi^ith the highest multiple. 



Rossal Landmark and Hutton 

 Roof Moor. 

 40° 51' 7" by multiple of 5 



5 10 



8 17 



8 'Z'Z 



9 i>0 



Rossal Landmark and Farleton 



Knot. 

 47° 47' 8" by multiple of 5 

 9-5 \o 



7-5 16 



7-5 20 



