56 OUTLINES OF NATURAL PHILOSOPHY. 



that point, the centre of curvature of this sec* 

 tion, at the point where it cuts the meridian, is 

 the point in which the direction of gravity, or of 

 the plumb-line, intersects the axis of the earth. 



. The direction of gravity, if the earth be a solid of 

 revolution, passes always through the axis of the 

 earth. If, therefore, we conceive the plumb-line 

 to be carried over an indefinitely small arch of the 

 perpendicular to the meridian, either to the east or 

 west, its direction will intersect the axis at the 

 same point where it intersected it before, which 

 point, therefore, is the centre of curvature of the 

 arch, or the same with K (fig. 3.). EK is great- 

 er than EH, and the degree of the perpendicular 

 arch is greater than the degree of the meridian in 

 the same ratio. 



b. The radius of curvature of the arch perpendicular 

 to the meridian, is therefore the normal of the 

 meridian, relatively to its shorter axis, or it is 



V a* cos* A + * sin* 

 p. 14. 



Edin. Trans, vol. v. 



63. If D be the degree of the meridian, at a 

 point of which the latitude is X, and A the de- 

 gree of the curve perpendicular to the meridian 

 at the same point, 



c = 



