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 are 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 are thus calculated is 2° 50' 21u'97. The observed angle difi‘ers from this by l"'38, being 2° 50' 23"'35.
In making separate estimates of the two portions of this are, 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"‘77; 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 difi'erence of 2"'60 more than appeared by observation.
A similar disagreement, it is observed, was also found by M. Mechain 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 observations themselves than to any extraneous source; since the observations of— diiferent stars give results that difi‘er more than 4" from each other.
