1858.] Geodetic Operations of (he Ordnance Survey, 519 



each triangle : and, secondly, the proof arismg from a comparison 

 of the computed length of one base, as derived from the angular 

 measurements, and the actual length from the linear measurements. 

 The difference between the computed length of the Lough 

 Foyle base, through the triangles extending from it to Salisbury 

 Plain, a distance of 360 miles, and the actual measured length, was 

 live inches. 



But as this error could not be attributed to one base rather than 

 the other, a mean base was established by a correction to each in 

 the proportion of the square roots of their lengths, so that com- 

 puting from the mean base, the measured bases have apparent 

 differences of -f- or — 2^ inches. 



Three other bases were measured with Ramsden's 100 feet steel 

 chains, one on Hounslow Heath, another at Misterton Car, near 

 Doncaster, and the third at Belhelvie, near Aberdeen; and the 

 measured lengths of these bases, differed in no instance 3 inches 

 from the lengths as computed from the mean base. 



' The observed angles have also been so corrected as to render the 

 triangulation consistent in every part ; and the result is, that taking 

 any side of any triangle as a base, and computing in any way 

 through the triangulation, the same length will be reproduced. The 

 triangulation may, therefore, be said to be perfect in every respect. 



The latitudes of 32 of the principal stations were observed with 

 Ramsden's great zenith sector, which was afterwards burnt in the 

 great fire at the Tower, and with Airy's zenith sector, which was 

 made expressly for the survey. 



If the figure of the earth be first supposed to be a sphere, it is 

 obvious that the length of every degree of latitude would be equal, 

 and that when the length of a certain number of degrees of latitude 

 is accurately known, we have all that is required to compute the 

 length of the 360 degrees of a great circle of the earth, and of the 

 length of its diameter ; but if the figure of the earth is not a sphere, 

 but a spheroid compressed at the poles, then the length of each 

 degree, as measured towards the poles, will be unequal and con- 

 tinually increasing, and this is found from observation to be the 

 actual fact. Thus, for example, the length of a degree in the 

 parallel of Edinburgh is 100 yards longer than a degree at South- 

 ampton ; and in the Shetland Islands, it is 200 yards longer ; and 

 from a knowledge of the length of the several portions of arcs of 

 meridians measured in this and other countries, the true figure and 

 dimensions of the earth are known. 



The elements of the spheroid which most nearly represent all 

 the distances and latitudes, are 



Polar diameter = 7899 ' 5 miles. 

 Equatorial . = 7926*5 miles. 



EUipticity • • = 294 



