OS OUTLINES OF NATURAL PHILOSOPHY. 



measured, the length of a degree becomes known. 

 It is not necessary that AD should be accurately 

 at right angles to either of the meridians AP, DP : 

 If it is nearly so, it* length can easily be reduced 

 to that of the perpendicular. 



This method of finding the amplitude of an arch per- 

 pendicular to the meridian, is only applicable in 

 high latitudes, where the convergency of the meri- 

 dians is considerable. Near the equator, where the 

 meridians became almost parallel, a small error in 

 determining the azimuths will produce a very great 

 one in the amplitude of the arch, so that this me- 

 thod cannot be safely employed. The manner of 

 finding the amplitude of the perpendicular arch ac- 

 curately in such cases, depends on the methods of 

 finding the difference of longitude, which are to 

 be explained in the next section. 



It appears from the preceding investigations, that the 

 earth is an oblate spheroid, generated by the revo- 

 lution of an ellipsis about its shorter axis, that 

 axis being to the longer axis as .9968 to 1. All 

 the arches, however, that have been measured, do 

 not agree equally in bringing out this result. In 

 general, though the conclusions from arches, which 

 are large, and at a considerable distance, are con- 

 sistent with one another, the contrary holds where 

 arches very near to one another, and more especi- 

 ally, contiguous portions of the same arch, are com- 

 pared together. It has been shewn, that, according 

 to the elliptic hypothesis, the differences of the 



contiguous 



