146 Captain Sabine on the 



three degrees, extending from Dunnose, in the Isle of Wight, to 

 Clifton, was measured by General Mudge, and it has since been 

 extended as far as Unst, one of the Shetland islands. Various 

 other arcs have been measured at different times, as, at the Cape 

 of Good Hope, by La Caille ; in Pennsylvania, by Mason and 

 Dixon ; in Italy, by Boscovich ; in Hungary, by Liesganig ; and 

 in India, by Lambton. If many of the contiguous partial arcs 

 show an elongation, still all, when compared with others at a con- 

 siderable distance, to the north or south, show a flattening towards 

 the Poles : but, although this may be considered as fully esta- 

 blished, there yet remains very considerable doubt as to the value 

 of the fraction that expresses the relation between the Polar and 

 Equatorial diameters of the generating ellipsis ; the results, ob- 

 tained by comparing the different measurements with each other, 

 varying so greatly as scarcely to have narrowed the question 

 within the limits in which it had been reduced by the hypotheses 

 of Newton and Huygens, and the demonstrations of Clairault. 



This variation, particularly where recent measures are con- 

 cerned, is not attributable to a deficiency either in the observers, 

 the instruments, or the methods of observation and calculation. 

 It appears to be occasioned principally, if not entirely, by the de- 

 flection which the plumb-line undergoes, from the unequal density 

 of the materials near the surface of the earth, and which affects 

 the celestial determination of the latitude at the extremities of 

 the measured arc : no means are as yet known by which the 

 errors thus occasioned may be avoided, or their amount ascer- 

 tained and allowed for. It is to their influence that we must 

 ascribe the fact, that by combining together the French and 

 British surveys, whereby an arc of nearly a fourth of the quad- 

 rant of the meridian is obtained, the ellipticity deduced is much 

 greater than would appear, from a comparison of the separate 

 degrees of this very arc with those measured near the Equator. 

 If a precise determination of the figure of the earth can ever be 

 hoped for by the measurement of portions of the meridian, it can 

 only be by the comparison of arcs of very considerable extent, 

 certainly of not less than five degrees, accomplished at parts of 

 the meridian extremely distant from each other. 



Other methods, however, exist, that are liable to less uncer- 

 tainty. The accumulation of matter in the Equatorial regions 

 modifies the action of the earth upon the moon, insomuch that 

 the motion of the latter is affected by two irregularities — one in 

 latitude, and the other in longitude. The maximum effect of 

 these equations may be determined by observation ; and hence 

 the extent of the cause may be investigated. The calculation 

 has actually been made by Bouvard, Burg, and Burkhardt, at the 

 instance of La Place, and gives an ellipticity of -^fa. This me- 



