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III. On the Latitudes and Difference of Longitude of Bcacky 

 Head and Dunnose in the Isle of PVight, as laid down in the 

 Trigonometrical Survey of England; and the Length of a 

 Degree perpendicular to the Meridian at the Latitude of 

 Beachy Head. By J. Ivory, Esq. M.A. F.RS* 



r I ^HE investigation of the figure of the earth by measure- 

 ■*- ments of the meridian, has given rise to a question of great 

 moment. Although the entire arcs agree very exactly with the 

 elliptical figure, yet on comparing the parts into which the same 

 arc is subdivided, the greatest irregularity is found to prevail. 

 This is so much the case in the arc measured between Dun- 

 nose and Clifton, in England, that the length of a degree is 

 found to decrease in advancing from south to north, instead 

 of increasing as the theory requires. To what cause can so 

 great an anomaly be ascribed ? In attempting to throw some 

 light on the irregularities of the English arc, I have been led 

 to examine the operations at Beachy Head and Dunnose; 

 and, reserving the discussion of the original question to a fu- 

 ture occasion, my present intention is to communicate the 

 observations I have made respecting the operations alluded to, 

 as they materially affect a capital part of the Survey. 



If a geodetical line be drawn through the station at Beachy 

 Head, perpendicular to the meridian of Greenwich, the meri- 

 dional distance of the line from Greenwich is, according to the 

 Survey, 44888 fathoms : and if a plane parallel to the equator 

 be drawn through the same station, this plane will meet the 

 meridian 17 fathoms more to the south fj so that the me- 

 ridional distance between Greenwich and the parallel of la- 

 titude passing through Beachy Head, is 44905 f fathoms. In 

 order to find the difference of latitude between the two places, 

 the terrestrial arc must be converted into degrees of a great 

 circle of the heavens. In the Survey 60851 fathoms is al- 

 lowed to a degree, which undoubtedly is too much. For if 

 we divide the terrestrial arc measured by Col. Mudge, by its 

 amplitude, we shall get 60826 fathoms for a degree at the la- 

 titude 52° 2' ; and even this length must exceed a degree at 

 the more southern point in the middle between Greenwich 

 and Beachy Head. The latitudes of the two places being 

 known nearly, I have employed the formula (C), p. 433, Phil. 



* Communicated by the Author. f Survey, vol. i. p. 294. 



X This length should be multiplied by 1 '00007, in order to bring it to a 

 general standard for the purpose of comparison with other measurements. 

 (Phil. Trans. 1821, p. 93). The same observation applies to all the other 

 lengths that occur. I have omitted to make the correction, which how- 

 ever does not sensibly affect any of the conclusions. 



Mag. 



