4 Mr. Nixon on the Measurement (by Trigonometry ) of the 



left of the object, the tangent screw was turned in the proper 

 direction at one uniform, somewhat rapid rate, until the wire 

 appeared to have reached the middle of the signal, when the 

 screw was abandoned as instantaneously and abruptly as pos- 

 sible. Bisections of this description are not only permanently 

 exact, but have the advantage of being completed with great 

 ceconomy of time; a consideration of great importance in vari- 

 able weather. The method, though difficult at first, requiring a 

 quick eye and considerable address in the manipulation of the 

 tangent screw, becomes with practice mechanically easy and 

 certain. If we estimate the probable angular error of bisection 

 inversely as the distance of the objects, it must be allowed, on 

 a comparison of the subjoined list with the corresponding one 

 for Wensleydale, (regard being had to the greater magnitude 

 of the triangles of the latter,) that the observations of 1829 are 

 decidedly superior to those of the year preceding it. 



List of the difference of the sum of the angles of every 



triangle, of which 



all the angles have been obser 



180°. 









-0' 2" 



-0' 53" 



+ 0' 5" 



+ 0'46" 



3 



1 2 



9 



47 



4 



1 2 



10 



58 



19 



1 7 



12 



1 5 



21 



1 10 



19 



2 3 



24 



1 14 



30 





43 



1 26 



39 





Sum of errors (disregarding signs) 17' 33", or 13" per angle. 



The loftiest of the Nine Standards and the boundary pikes 

 on Shunnor Fell and Water Crag are signals of the Ordnance 

 Survey, and form the extremities of three base-lines, sufficient 

 in number and advantageously situated for a basis to the sur- 

 vey ; but on calculating the approximate distances required to 

 obtain the corrections for the excentricity of the theodolite, it 

 was discovered that the given distance of the highest standard 

 to Water Crag must be several hundred feet in excess. On 

 this account it was considered proper to connect the triangu- 

 lation with other stations of the Ordnance Survey, which was 

 effected in the autumn following, on the occasion of the 

 measurement at Ingleborough of some angles relating to ope- 

 rations in another quarter. As the high opinion entertained 

 of the accuracy of the distances of the Trigonometrical Survey 

 has justly rendered them the foundation of county and other 

 extensive surveys, it becomes a duty to point out such as have 

 been discovered to be indisputably incorrect. 



At Water Crag the horizontal angle between Shunnor Fell 

 and the highest standard measured 52° 47' 56", or 1' 36" less 



than 



