436 



are known by other measurements, and thence infers what ought to 

 have been the angles ascertained by Col. Mudge's astronomical ob- 

 servations. 



Col. Mudge's base in fathoms is first converted into toises, of which 

 the logarithm is taken as the logarithm of an arc. The radius of that 

 arc being assumed from the supposed figure of the earth, its angular 

 extent, its logarithmic sine, and chord, are inferred by the method of 

 Delambre. The horizontal angles measured are then corrected for 

 spherical error, so as to convert the triangles into spherical triangles, 

 the sides of which are found first as logarithmic sines, and thence the 

 logarithmic arcs are deduced. The azimuths of these being also known, 

 the portions of the meridian to which they each correspond are com- 

 puted both in angular and linear measure : the results are given by 

 the author in two tables, one of which is deduced from the eastern 

 series of triangles, and the other from the western series. 



The angular extent of the whole arc thus calculated is 2 50' 21 w< 97. 

 The observed angle differs from this by 1"'38, being 2 50' 23"'35. 



In making separate estimates of the two portions of this arc, 

 that are to the north and south of the central station at Arbury Hill, 

 he finds that the former exceeds its calculated amount by 4"' 7 7 ; 

 while in the latter the calculated extent is greater than that deduced 

 from astronomical observations by 3"'39. He therefore infers that 

 the astronomical observations at Arbury Hill must be erroneous nearly 

 to the amount of 5", notwithstanding the goodness of the instruments 

 and the skill and care of the observer. 



By a mode of calculation similar to the foregoing, made upon the 

 measurement in Lapland, Don Joseph Rodriguez arrives at a result 

 which differs only 0"'6 from that of M. Svanberg ; and by the same 

 method, with respect to the measurement in Bengal by Major Lamb- 

 ton, the difference between observation and calculation is only 0"*53. 



A portion of the French measurement between Dunkirk and Paris, 

 similarly estimated, is not found to accord so well with the author's 

 calculations, which make a difference of 2"' 60 more than appeared 

 by observation. 



A similar disagreement, it is observed, was also found by M. Me- 

 chain in the very short distance between Montjui and Barcelona, the 

 latitudes of which, as determined by a very long series of zenith 

 distances, do not agree with the results of measurement by as much 

 as 3"-24. 



Local attractions were supposed to be the cause of this irregularity ; 

 and Col. Mudge also was of opinion, that the irregularities which 

 occur in his measurements are to be ascribed to deviations of the 

 plumb-line from local attractions. But the author of the present 

 communication thinks they should rather be ascribed to the observa- 

 tions themselves than to any extraneous source ; since the observa- 

 tions of different stars give results that differ more than 4" from 

 each other. 



