166 Mr. J. Nixon on the Trigonometrical Height 



Horizontal Distances*. 



Base; Whernside to Ingleborough Tower centre, 22445ft. 



Whernside 



Ingleborough Tower centre 

 Hunt's Cross station 



Ingleborough Tower centre 

 Hunt's Cross station 

 Ingleton church tower, lop 

 north-west pinnacle 



° f .}< 90 



8 5 



Vertical Angles. 



As the levels of the sector have graduated scales, it becomes 

 superfluous to bring the bubble at every observation exactly 

 to the reversing point, (or that degree of the scale to which 

 the bubble constantly returns on inverting the telescope within 

 its Ys.). At Ingleton the reversing points, determined from 

 the average of three independent trials, were 74 0, 8 for the 

 level of the arc G, and 72°-5 for that of the arc L. In the 

 register there is given for every observation the degree of the 

 scale at which the middle of the bubble became stationary; 

 the difference between which degree and the reversing point, 

 converted into seconds, (at the rate of l"-82 per degree for the 

 level of G, and 2" per degree for that of L,) being additive 

 to, or subtractive from, elevations, according as the registered 

 degree exceeds or falls short of the reversing point. For de- 

 pressions the signs must be changed. 



Each vernier being what is termed double, two readings of 

 the fractional part of the angle are obtained, both of which are 

 given. 



At Hunt's Cross a short horizontal filament, found adhering 

 to the vertical wire, was substituted, in pointing the telescope, 

 for the cross lines made use of at the station on the base near 

 the church. In both cases the error of collimation will be 

 found in the last column but one. 



In calculating the differences of level, the angles of eleva- 

 tion, marked E, were augmented by the instrumental error of 

 20", the (angular) height of the eye, and curvature ; the re- 

 fraction, which was estimated at T ' T th of the contained arc, 

 being subtractive. For depressions, marked D, all the signs 

 were changed. 



* These distances were confirmed by using the oblique (or observed) 

 angles, and diminishing the distances thus obtained in the ratio of radius 

 to the cosine of horizontal inclination. 



