325 FIGURE OF THE EARTH. 



his Memoir, what were the formulae wl.ich lie employed in the 

 computations of the meridian ; but one >-:ees, by the arrange- 

 ment of his mater'als, that he made use of the method of the 

 perpendiculars without regard to the convergence of the meri- 

 dians j and although this method is not rigorously exact, it can 

 make but a very few fathoms more in the total arc, and will 

 if erroneous, have very little effect on the nsagnitude of each degree. It 

 bly"so%rom ^' is therefore a more probable supposition, that, if any errors 

 the celestial exist, they have occurred in the astrououucal observations. But 

 obseivations. j^ j^ scarcely possible to determine the amount of the errors, or 

 in what part of the arc they may have occurred, excepting by 

 direct and rigorous computation of the geodetiral measure- 

 ment. I have therefore been obliged to have recourse to calcu- 

 lations, v/hich I have conducted according to fhe method and 

 formulae invented and published by M. Delambre. 

 The usual The means generally employed for finding the extent of a 



method of degree of the meridian, con^iists in dividing the length of the 

 finding the j^j^j ^^^ -^^ fathoms, by the number of degrees and parts -of a 

 dividing the degree deduced from observations of the stars ; but if these 

 \°'h ^h^ '" observations are affected by any error, arising from unsteadi- 

 measureindeg. "ess of the instrument, from partial attractions, or from any 



and parts, will other accidental causes, then the degrees of the meridian will 

 not detect the , ^ , . , ., .,. ,- ,. . , 



errorsofobser- "° directed. Without a possibility of discovering such an error 



vation, in this mode of operating. It is consequently necessary, in 



such a case, to employ some other method, which may serve 

 as a means of verifying the observations themselves, of detect- 

 ing their errors, if there be any, or at least of shewing their 

 probable limits. 

 "Calculations by My object therefore is to communicate the result of calcu- 

 ' lations that I have made, from the data published by Lieut. 

 Col. Mudge in the Philosophical Transactions : and I hope to 

 make it appear, that the magnitude of a degree ot the meridian, 

 corresponding to the mean latitude of the arc measured by 

 this skilful observer, corresponds very exactly with the results 

 of those other measurements that have been above noticed, 

 by means of ^^ M. Delambrc's method nothing is wanting but the sphe- 

 the spherical rical angles, that is to say, the horizontal angles observed, 

 Debmbre's corrected for spherical error. Moreover, for our purpose, we 

 method. have no occasion for the numerical value of the sides of the 



series of triangles, but only for their logarithms. Thus the 



logarithm 



