1814.] Imperial Institute of France. 307 



motion of the sun. Fortunately during the last sixty years we have 

 a prodigious number of good observations. The values of the 

 quantity of matter in these planets, which agree best with the 

 totality of these observations, will be, if not certain, at least the 

 most probable values of these doubtful quantities. 



In order to determine them, the author of the tables of the sun 

 had chosen, out of all the observations which he had calculated, 

 all those where each of the quantities of matter in the planets pro- 

 duced sensible effects. The results at which he arrived did not 

 appear even in his own eyes so certain, that they might not be 

 somewhat changed either from other observations or from the same 

 observations differently combined, especially if different elements 

 be used in reducing them, such as the right ascensions of the 

 stars. 



It is the same with the mean secular motion of the sun. He 

 had determined it by the comparison of a great number of obser- 

 vations made about 1752 and ISOO, which only gave him the 

 movement of '18 years, that is a little less than one half of the 

 secular motion. He presented this movement not as certain, but 

 as agreeing best witli the observations that he had calculated. He 

 perceived, himself, that the slightest change in the position of the 

 stars at the two extreme epochs would introduce an equal change 

 in the movement obtained. He did not venture to affirm that this 

 movement was preferable to that which M. de Zacli proposed 

 about the same time; and which was the same with that upon 

 which he himself had fixed in his first researches. He remarked 

 in his preface that time alone would decide upon a point so delicate. 



But what will certainly be obtained in a long interval of time, 

 and by more numerous and more precise observations, may likewise 

 be obtained at least in a certain degree by redoubling the care, 

 multiplying the calculations, and employing more correct data. 

 This is what M. Burkhardt has attempted, and he has neglected 

 nothing to obtain a successful result. 



He began by calculating 36 years of observations from 1774 to 

 1810: in order to be aWe to neglect without inconvenience the 

 small equation of tlie latitude of the sun, which ought to pass 

 several times over all the values of which it is susceptible, in this 

 double revolution of tiie nodes of the moon. He employed be- 

 sides 310 observations of Bradley in 175'_'. By this means ho 

 gained already 8 years, which have elapsed since the construction 

 of the last tables. To calculate these ol)servations he took a mean 

 between the corrected right ascensions of .Maskelyne and those of 

 Al. Bessel. The author of the tables had employed the right as- 

 ccn>-ions of Maskelyne corrected by his own observations in 1800. 

 And for 1 752 he had taken the right ascensions of Bradley, newly 

 corrected by Hornsliy the editor of Bradley. From these changes, 

 which the researches and observations made of late years rendered 

 [)ossible, there ought to result a difference in (he mean motion, 



