42 OUTLINES OF NATURAL PHILOSOPHY. 



angles of each exceed two right angles, by a quan- 

 tity called the Spherical Excess ; which is to four 

 right angles, as the area of the triangle to half the 

 superficies of the globe. By knowing the spherical 

 excess, the errors in the measures of the angles are 

 discovered ; and it is also known, that if from each 

 of the angles of any of the triangles, be subtracted 

 one-third of the spherical excess, the sines of the 

 angles so corrected are proportional to the lengths 

 of the sides ; so that all the triangles, though strict- 

 ly speaking spherical, may be resolved by the rules 

 of plane trigonometry. 



IQ this way, the distance of the two points at first as- 

 sumed is computed, as also their distance reduced 

 to the meridian of either of them. 



, 55. When, by such accurate observations, the 

 lengths of degrees were determined in different 

 latitudes, they were found to increase gradual- 

 ly from the Equator to the Pole. 



The radius of curvature of the meridian, therefore, 

 increases as we go toward the Pole, and the curva- 

 ture itself diminishes. The earth, therefore, is not 

 a sphere, but is flattened at the Poles, so that the 

 axis from Pole to Pole is less than the diameter of 

 the Equator. Though it is only by experiment 

 that the true figure of the meridian can be disco- 

 vered, it has been found necessary to assume hypo- 

 thetically, for its figure, the curve which is next in 



simplicity 



