On the Measurement of an Arc of the Meridian. 6 1 



know of, been noticed by any mathematician, and which will ope- 

 rate, if it amounts to any quantity, as a correction to the ob- 

 served meridional arc. In an ellipse no two points have the same 

 radius of curvature in the same quadrant : taking, therefore, any 

 part of a meridional line upon the earth's surface (as for instance 

 from Dunnose to Clifton), and cojiceiving this as an arc of an el- 

 lipse, the radii of curvature, at each extremity of the arc, will not 

 have the same centre; and, therefore, the difference of the zenith 

 distances of any star, taken at the two extremities, will not be a 

 correct measure of the elliptic arc, or rather of an arc of a circle 

 of curvature, which the formula requires. 



Let ABD be a semi-ellipse, PQ an arc ; let PT, QS be two 



lines drawn perpendicular at P and Q, and let TP be a radius 

 of curvature at P, and let TQw be drawn: m and o are the 

 zenith points at P and Q, supposing PQ to be an arc of the me- 

 ridian upon the earth's surface; but nin is the measure of PQ, 

 which the problem requires; and therefore an arc in the heavens, 

 measrred bv zenith distances, is not a correct measure of a cor- 

 responding arc of curvature on the earth's surface. In the arc 

 measured by Colonel Mudge's sector l)ctween Dunnose and Clif- 

 ton, the angle ?iQo, I believe, will be about eight seconds of a 

 degree. If therefore all the stations of Colonel Mndge should be 

 verified by independent observations, it will not show the result 

 deduced by him to be correct, as the meridional difference of ze- 

 nith distances of any two places upon the earth's surface, is ac- 

 curately the difference of latitude of those places. If the angle 

 «Qo should, upon accurate computation, amount to S' upon 

 the whole arc measured between Dunnose and Clitton, the arc 

 between Dunnose and Arbiny Hill will recjuire a correction of 

 about [Wit, leaving the results' deduced by Colonel Mudgc as in- 

 conclusive as before, as to the elliptical figure of the meridian. 

 Would it not, therefore, be useful to determine the latitude of 



tlic 



