of Bonrdeaux, for tJie Year \S05. 123 



practicable : it cannot be done when the latitude and de- 

 clination are of a contrary denomination; neither can it 

 about the equinoxes, because the sun passes the prmie ver- 

 tical then in the horizon, or very near it. 



The time when the second altitude is taken, which the 

 author of the memoir leaves to the observer's pleasure, has 

 not appeared indifferejit to the commissioners with regard to 

 the greater accuracy of the result : they have engaged to 

 turn their attention to the examination of the most favoura- 

 ble time for taking the second altitude *•. 



When circumstances will permit the proposed method to 

 be practised, it vi'ill be preferable to that of Douves, which, 

 according to the formula given in the report, for an error at 

 all considerable in the latitude by account, gives a result 

 strongly erroneous. 



M. Leupold has been occupied in a memoir, which he 

 read to the society, 7ipnn the generation of surfaces of the 

 second order. All of them may result from one common 

 o-encration, which is executed by a curve of the second kuid, 

 variable in its dimensions, moved in such a manner that its 

 plane may always remain parallel to itself. The equations 

 which point out this circumstance give the law of the mo- 

 tion of the generatrix. This curve will be an ellipsis for 

 surfaces having a centre, and a parabola for surfaces having 

 no centre. In the case where each of the points of the ge- 

 neratino- curve has a right line for its direction, the surface 

 may be engendered by a straight line moved in space. The 

 analytical condition for this to happen indicates the hy- 

 perbolcjid with only one 7iappe, the hyperbolic paraboloid, 

 and the parabolic cylinder. The common generatrix to all 

 these surfaces may become a circle, except with regard to 

 the hyperbolic paraboloid and the parabolic cylinder, for 

 which the analysis used in this n)emoir shows that the ge- 

 neratrix can never be a circular curve. 



This memoir is tcrminatid by some general considera- 

 tions upon the relation between elimination and the genera- 



* In a note M. Ducom establishes, that the most favourable time to take 

 llie bccoml altitude is when the Fvm is near the meridian : iic is occupied in 

 ■ dctcrniining the minimum of the interval between the two obsei vations. 



tion 



