420 Astronomical and Nautical Collections. 



rectilinear distance in a tangent plane with the two meri- 

 dians ; for if the tangent of the difference of the two azimuths 

 thus measured, be divided by the sine of the true latitude 

 at the point of contact, where the lines are horizontal, the 

 result will be accurately the tangent of the difference of 

 longitude, whatever the form of the solid of revolution 

 may be. 



This proposition will be readily admitted on considering 

 that the axis of the solid is the intersection of the two meri- 

 dians, and that the distances of the points of the axis in the 

 plane of the given horizon and in the plane of a parallel 

 circle, either from the tangent point or from the perpendicu- 

 lar falling from the remoter station on the meridian, are in 

 the ratio of the radius to the sine of the latitude, and that 

 this perpendicular is the tangent of each of the angles to be 

 compared, with respect to these two distances considered as 

 radii of the respective angles. 



In the practice of surveying there can be no possible dif- 

 ficulty in taking stations near enough to employ this method 

 with the utmost accuracy, and in ascertaining separately 

 the true latitude of each station, with moderate care, as 

 subservient to the computation of the difference of longi- 

 tudes. 



The observed difference of latitude between the two 

 oblique stations, compared with the difference of longitude 

 and the azimuth, will give the relation of the two radii of 

 curvature, and consequently the eccentricity of the spheroid, 

 without any linear measurement whatever; unless there 

 should be any error in these hasty remarks. 



T. Y. 



