188 On the Arcs perpendicular to the Meridian, 



mean of the six partial results ; differences which, in respect 

 to the ultimate employment of the number itself in the deduc- 

 tion of the EUipticity, may be regarded as altogether incon- 

 siderable. 



Applying, then, the value of the degree so deduced to the 

 several equations of condition formed from the subdivisions of 

 the total arc, the probable error assigned by the calculation 

 to each of those determinations is shown as follows : 



Marennes and Saint Preuil . . correction + 0",351 



Saint Preuil and Sauvagnac 

 Sauvagnac and Isson 

 Isson and Geneva 

 Geneva and Milan . 

 Milan and Padua 



- ,336 

 ■- ,390 

 + ,608 

 + ,047 



- ,407 



These corrections, assigned on the system of the least 

 probable errors, must be regarded in each case as applicable 

 to the sum of the errors arising from three sources ; namely, 

 in the comparison of the clocks with sidereal time at the two 

 extremities of the arc, and in their comparison with each 

 other by means of the intermediate signals : the average cor- 

 rection to each arc is 0,35". 



For the deduction of the EUipticity from the combined 

 values of a degree of the parallel and a degree of the meri- 

 dian, MM. Brousseaud and Nicollet have employed the formula 

 given by M. Puissant, in the memoir to which we have already 

 referred. 



i (B - A cos H ) 



a :rr 



^ { i ■<- ; — — I + i A cos H sin2 H 



wherein A is the mean degree of the meridian betAveen the 

 latitudes X and x" ; B the mean degree of the parallel in the 

 latitude H ; tt the circumference of a circle of which the 

 radius is unity ; and a the ellipticity. Combining then 

 77865,75 m^t. as the mean value of the degree of the parallel 

 in the latitude of 45° 43' 12", with 111140,51 met., the mean de- 

 gree of the meridian between the latitudes of Dunkirk 51° 02' 

 09",2, and Mont-Jouy 41° 21' 46",58, (which is the measured 

 arc of the meridian passing through France,) the ellipticity is 



obtained r^;— ^. Substituting, in the combination, the ^rc of 



