310 Imperial Institute of France. 
M. Burckhardt finds that the quantity of matter in Mars pre- 
viously determined must be dimished 34,. 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. Burckhardt diminishes its quantity of matter 1, which 
will produce a diminution of about 1” in the greatest equation. 
The quantity of matter was supposed by Laplace.... 1-0000 
The author of the tables made it........eeee00++ 10743 
M. Burckhardt reduces it to .. 1... cceccceeccese's 09549 
M. Lindenau has lately found it..........2.....- 1:0797 
SAUL IB alg. 'a ned eiaigs Utne \s al'as aoe ee ETE 
The mean of these four results is 1:0555, and differs only =!; 
from that supposed in the tables. : 
It was by the movements of Mercury that M. Lindenau en- 
deavoured to determine the quantity of matter in Venus. He 
has united the results which he obtained from the motions of the 
aphelion and the nodes. His mean is 1:0964, so that he aug- 
ments 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 number. But he puts no greater confidence in his 
determination than in any other. He.even admits that the re- 
sult obtained by M. Burckhardt, founded upon a greater number 
of observations, and upon newer researches, offers in consequence 
a greater degree of probability. A reason of great weight adds 
strength to the necessity of diminishing the mass of matter of 
Venus, and this reason long excited distrust in the author of the 
tables. In whatever manner he combined the observations of 
Lacaille, Mayer, Bradley, Le Gentil, Maskelyne, Piazzi, and 
his own, he could never obtain more than 48” for the secular 
variation of the obliquity of the ecliptic. The mean obliquity 
which he found in 1800 has been since confirmed by all the sol- 
stices observed at Paris. That which results for 1750, from so 
many observations agreeing remarkably well with each other, 
cannot be wrong further than 1”. Hence he concludes that the 
secular diminution cannot be greater than 50”. He has never 
believed that it amounted to 52’. We may therefore ascribe to 
Venus a quantity of matter which weuld give 48” or 50” for the 
secular diminution, and give to the equation of Venus in the 
solar tables the value which will result from this supposition. 
M. Burckhardt proposes a diminution of 1” for the greatest 
equation of the centre. If we collect together all these corrections, 
it will follow, that the sun’s place, calculated at a id 
1850, 
