Trigonometrical Survey. 63 7 



In making computations on a given hypothesis of the earth's 

 figure, the truth of the conclusions, as well as the ease with 

 which they are found, materially depends on the distances of the 

 objects from their respective fixed meridians. 



If the difference of longitude approaches nearly to, or exceeds 

 3 , to compute that longitude, and also the latitude, it is necessary 

 the precise figure should be understood ; because the analogy 

 does not hold good, in that case, between the equality of the 

 sums of the angles of spherical and spheroidical triangles on 

 the earth's surface. With regard to latitudes, more particularly 

 when the distances are diminished by means of frequent new 

 directions of meridians, a knowledge of the exact length of a 

 degree of a great circle is not necessary ; because the determi- 

 nation of those latitudes, by means of spherical computation, 

 being true as to sense, the cosines of those small arcs will remain 

 the same. 



As there cannot be a doubt justly entertained of the latitude 

 of Greenwich being very accurately determined, as particularly 

 set forth by the Astronomer Royal in his reply to M. Cassini, 

 it is reasonable to suppose, that if any errors do exist in the 

 latitudes of those stations, they can only have arisen from the 

 computations being made with erroneous lengths of degrees on 

 the meridian. 



In our former Papers on this subject, we have taken it for 

 granted, that the length of a degree of the meridian at the 

 middle point between Greenwich and Paris, (50 10',) is 60842 

 fathoms, (which supposition maybe considered just, provided 

 the latitude of Paris, 48 50' 14", be as near the truth as 51 28' 

 40" is to that of Greenwich,) and afterwards added 9 fathoms, 



MDCCC 4 N 



