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XL Proceedbigs of Learned Societies, 



FRENCH NATIONAL INSTITUTE. 



Analysis of the Lnlours of the Clasi of Mathematical and 

 physical Sciences of the French Institute, for the Year 1807. 



• [Continued from vol. xxxiii. p. 501.] 



iV-1.. BuBCKHARDT proposes another new method for deter- 

 mining the moon's node. This inquiry is delicate ; for 

 six seconds of error in the meridian altitude may produce a 

 minute of difference in the place of the node. It is true that 

 it is not necessary to be known with any precision except 

 for the calculation of the latitude, and that a minute of error 

 in the node only produces reciprocally six seconds in 

 the moon's latitude. This element has therefore nearly 

 the same precision in the tables as the very observations 

 which serve to determine it. But these observations, when 

 the moon is very iow, are subject to the irregularities of re- 

 fraction ; they were in the same way affected with imcer- 

 tainty, as to the parallax and the semi-diameter, when these 

 two quantities were not yet so well determined as they arc 

 now. It is, therefore, the refractions which he endeavours 

 to avoid by making choice of a method over which they 

 have no influence. We do not allude to the errors in 

 the division of the mural circle; for we might, as M. Burck- 

 hardt himself has pmved, observe the altitudes of the moon 

 by the repeating circle, or determine with the same instru- 

 ment the errors of the mural circle. The occultations of stars 

 would furnish a method, if their latitudes were certain; but 

 these latitudes may be subject to uncertainties similar to that 

 of the meridian altitude of the moon, when these stars are 

 south ; and in order to be proper for the determination of the 

 node, they must be close to the ecliptic. All these con- 

 siderations singularly limit the choice which we may make; 

 and there is scarcely any other but Rcgulus and the Virgin's 

 Spike which will satisfy all the requisite conditions. \Vc must 

 confine ourselves to these two stars, and they will be sufli- 

 cient. We shall choose the eclipses observed successively 

 when the moon was in the vicinity of its ascending and de- 

 scending node. Wc may suppose the latitude of the star to 



be 



