[ 60 ] 



XII. Ohservutions on the Measurement of an Arc of the Meri- 

 dian. By T. FiRMiNGER, LL.D.* 

 i.HE measured meridional arcs, in different degrees of latitudcj 

 have not. been found to give a ratio of the earth's axis at all con- 

 sistent either uitn the tiieory of a homogeneous ellipsoid of re- 

 volution, or with themselves, as deduced l)y trials of measured arcs 

 in different latitudes : for while some give a ratio nearly the same 

 as Newton has assigned it from theory, others, on the contrary, 

 make the polar axis the longest, or the earth flattened at the 

 equator. Many causes have been assigned as the probable rea- 

 son of the discrepancy in the results. Colonel Mudge and Cap- 

 tain Kater have attributed the want of agreement to the effect of 

 local attraction : but they differ in toto as to the effect of its in- 

 fluence ; or rather, as to the situation of the attracting mass. 

 Colonel Mudge believes the principal effect to take place at Clif- 

 ton, and Captain Kater at Dunnose. Others again have doubted 

 whether the amplitude of the celestial arc has been correctly ob- 

 tained ; and have supposed, either that the zenith sector with 

 which Colonel Mudge made his observations, might not have been 

 exactly placed in the plane of the meridian, or that some error 

 has been committed in the use of it. Mr. Fisher, in a paper just 

 published in the Quarterly Journal of Science and the Arts, en- 

 deavours to account for and to rectify these discrepancies, by a 

 supposition "that measured arcs of the meridian are not legiti- 

 mate measures of the radii of curvature " at the middle point of 

 curvature of those arcs. Mr. Fisher seems to have been led into 

 this idea from the consideration of the position of a plumb-line 

 upon a sphere having the same rotation as the earth urged by a 

 centrifugal force : and having calculated the deflections from the 

 centre, at each degree of latitude, he found that the difference, in 

 the deflections, upon the whole arc measured by Colonel Mudge, 

 amounted to exactly that quantity which would reduce the arc to 

 agree with an excentricity of 229 to 230 ; from which he con- 

 cluded that measured arcs are not legitimate measures of the radii 

 of curvature, and " that so long as these measured arcs are con- 

 sidered arcs of circles, this correction for deflection will obtain. 

 Mr. Fisher was no doubt led into this mistake from finding that 

 his differences rectified the arcs in those instances in which he 

 applied them ; an J too hastily adopted his conclusion, without 

 taking time to exaniine and consider the problem : for although 

 the arc of a circle and ellipse of the same number of degrees, 

 and of the same radius of curvature, will differ in length ; yet 

 this difference is too small (as Dr. Hutton observes, in the account 

 of the formula alluded to by Mr. Fisher,) to sensibly affect the 

 result. There is a circumstance however which has not, that I 

 * Communicated l)y the Author. 



know 



