186 On the Area perpendicular to the Meridian^ 



has been made to determine the difference of longitude between 

 the extreme stations on a line of such considerable extent, by 

 the method of instantaneous signals; and, second, because the 

 value of the ultimate deduction, as to the figure of the earth, is 

 in fact chiefly dependent on the degree of exactitude which 

 has been practically attained in the determination of the celes- 

 tial arc, inasmuch as errors in that determination of such small 

 amount as it would seem almost impossible altogether to avoid, 

 far outweigh, in their consequences, the utmost error, which, in 

 the present advanced state of geodesical measurement, could 

 be possibly apprehended as likely to arise from that source. 

 In the parallel of 45° a single second of time is equivalent to 

 about 324 metres ; and, of course, in an arc of 13°, which rather 

 exceeds that comprised between Marennes and Padua, an error 

 of 1" in the celestial arc (could such an error be supposed to 

 exist as the sum of all the errors of the separate determinations 

 into which the arc has been divided) will equal 25 metres in the 

 length of the mean degree of the parallel; the influence of 

 which on the fraction expressing the ellipticity, deduced from 

 the comparison of the degree of the parallel with the degree 

 of the meridian, will amount to between 22 and 23 in the 

 denominator of the fraction. We have therefore considered 

 it the preferable course to enable our readers, as far as it is in 

 our power, to form their own estimate of the measure of accu- 

 racy which has been attained. 



We recapitulate, in order to present in one view, the ampli- 

 tudes of the several portions forming the total arc between 

 Marennes and Padua : — 



1st Arc . . Marennes and St. Preuil . . 3' 48",990 



2d Arc . . St. Preuil and Sauvagnac . 6' 23",094 



3d Arc . . Sauvagnac and Isson . . 6' 5l",391 



4th Arc . . Isson and Geneva . . 11' 57",820 



5th Arc . . Geneva and Milan . . 12' 09 ',5 70 



6th Arc . . Milan and Padua . .10' 45,383 



Total . Marennes and Padua . .51' 56",248 



The following are the geodesical measures, expressed in 

 metres, comprised on the parallel of 45° 43' 12" between the 

 meridians of the stations which form the limits of the several 



