three Degrees of the Meridian. 25 



he employed in the computations of the meridian; hut one 

 sees, by the arrangement of his materials, that he made use 

 of the method of the perpendiculars without regard to the 

 convergence t)f the meridians ; and althovigh this method 

 is not rigorously exact, it can make but a very few fathoms 

 more in ihe total arc, and will have very little eftect on the 

 magnitude of each degree. It is therefore a more probable 

 supposition, that, if anv errors exist, they have occurred in 

 the astronomical observations. But it is scarcely possible 

 to determine the ainount of the errors, or in what part of" 

 the arc ihey may have occurred, excepting by direct and 

 rigorous computation of the geodetical measurement. 1 

 have therefore been obliged to have recourse to calculations, 

 which I have conducted according to the method and for- 

 mulae invented and published by M. Dflambre. 



The means ii;enerallv eniployed for finding the extent of 

 a degree of the meridian, consi>ts in dividing the length of 

 the total arc in fathoms, by the number of degrees and 

 parts of a degree deduced from ribservaiions of the stars: 



- hut if these observations are affected by any error, arising 

 from unsteadiness of the instrument, from partial attrac- 

 tions, or from any other accidental causes, then the degrees 

 of the meridian will be affected, without a possibility of 

 discovering such an error in this mode of operating. It is 

 consequaitiv necessary, in such a case, to employ some 

 other method, v/hich may serve as a means of verifying the 

 observations themselves, of detecting their errors, if there 

 be anv, or at least of showing; their probable limits. 



My object therefore is to communicate ihe result of cal- 

 culations that i have made, from the data published by 

 Lieut. Col. Mudge in the Philosophical 'iVansactions ; and 



. I hope to make it appear, that the magnuude of a degree 

 of the meridian, corresponding to the mean latitude of ihe 

 iirc measured by this skilful observer, corresponds very ex- 

 actly with the results of those other measuren)euls that 

 have been above noticed. 



In M. JJelambre's n)ethod nothing is wanting but the 

 spherical angles, that is to say, the horizontal angles ob- 

 served, corrected for spherical error. Moreover, for our 

 purpose, we liave no occasion for the numerical value of the 

 sides of tlie series of tiianirles, but only for their logarithms. 

 Thus the logarithm of the base measured at Clifton, as an 

 arc, gives us that of its sine in feet or in fathoms, so that 

 by means of this latter logarithm, and the spherical angles 

 ai the scries of triangles, we obtain at once, and as easily iis 



Id 



