508 Proceedings of Philosophical Societies. [ApRlt, 



and probably likewise in the value of the quantity of matter in the 

 planets. 



M. Biirc'khardt finds 3-8" to be added to the motion for 49 

 years, which gives 7'7" for the secular motion. This motion ii 

 the mean between that of Zach and that which La Caille had 

 pubhshed about 56 years ago. Mayer, who had attempted to cor- 

 rect this motion, had considerably increased the small error in it, 

 Lalande had diminished Mayer's motion 20", and had given a 

 quantity 8" greater than that now given by Burckhardt. 



We see at least that in these osciliations the error is always dimi- 

 nishing, and that if vve have not yet obtained the true quantity, we 

 have made a sensil)lc approach to it. The mean length of the 

 year, according to M. Burckhardt, is 365 days, 5 hours, 48' 49 7"-- 

 The author of the tables made it 5 1*5". But in the second volume 

 of his astronomy, which was published aljout a year ago, we shall 

 find that he inclines to 50", and was therefore himself approaching 

 to the new determination. The diH'erence is now only 5 3" a quan- 

 tity respecting which it will l)e always difficult to decide. 



The author of the tables had found for the lunar equation 7'5"; 

 La Caille supposed 7.03", Maskelyne 7-1", M. Burckhardt 6-8'\ 

 Tlie mean will be O'lS". So that the uncertainty is reduced to a 

 ^mall fraction of a second, 



M. Burkhardt finds that the quantity of matter in Mars pre- 

 viously determined must be diminislied ^'-. Now as the equation 

 itself is very small, this correction, very uncertain on many ac- 

 counts, does not deserve any attention. 



The most considerable correction is that for Venus } and as the 

 equation is much more sensible, the uncertainty ought to be much 

 less. M. Burkhardt diminishes its quantity of matter^, wliich 

 will produce a diminution of about 1" in the greatest equation. 



The quantity of matter was sujjposed by Laplace .... 1 -0000 



The author of the tables made it 1 "0743 



M. Burkhardt reduces it to 0-9549 



M. Lindenau has lately found it 1'0797 



and 1-1131 



The mean of these four results is 1*0555, and differs only -r^j 

 from that supjwsed in the tables. 



It was by the movements of Mercury that M. Lindenau endea- 

 voured to determine the quantity of matter in Venus. He has 

 united the results which he obtained front the motions of the aphe- 

 lion and the nodes. His mean is 1-0961, so that he augments the 

 equation of the tables as much as we should diminish them, if we 

 were to make choice of the above mean. Between these opposite 

 testimonies, the author of the tables may adhere to his own num- 

 ber. But he puts no greater confidence in his determination than 

 in iny other. He will even agree that the result obtained by M. 



