308 Imperial Institute of France. 
assign the situation and dimensions of the planetary orbits for 
any epoch. In a mathematical sense, the problem is resolved. 
The arbitrary constant quantities are mostly determined with a 
sufficient degree of accuracy for these researches. We are ac- 
quainted even with the quantity of matter in those planets which 
have satellites, as Uranus, Saturn, Jupiter, and the Earth; but 
Mars, Venus, and Mercury have no satellites. We have no other 
means of determining the quantity of matter in them than the 
alterations which they produce in the eccentricities and inclina- 
tions, or the equations which they give for the movements of the 
aphelions and nodes. But these variations are extremely slew. 
Good obsefvations go no further back than 60 years. There re- 
main only the periodic equations of the longitude, and these 
equations are not greater; but their periods are shorter. Half a 
period is sufficient to obtain a double effect, since it is alternately 
positive and negative. The moon is nearly in the same. situa- 
tion with Venus. Notwithstanding the assistance drawn from the 
tides, &c. we have not as yet an exact knowledge of the quantity 
of matter in our system. 
Yet unless we adopt at least a hypothetic value for these un- 
known quantities, it is impossible to have exact tables of the ap- 
parent motion of the sun. Fortunately, during the last sixty 
years we have a prodigious number of good observations. The 
estimates of the quantity of matter in these planets, which agree 
best with the average of these observations, will be, if not pre- 
cise, at least the most probable values of these doubtfu} quan- 
tities. 
In order to determine them, tle author of tlie tables of the 
sun had chosen, out of all the observations which he had calcu- 
lated, those where each of the quantities. of matter in the 
planets produced sensible effects. The results which he obtained 
did not appear.even in his qgwn 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 ob- 
servations made about 1752 and 1890, which only gave him the 
movement of 48 years, that is, a little less than one half of the 
secular motion. He presented this movement not as certain, 
“but as agreeing best with the observations calculated by himself. 
He perceived, 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 Zach pro- 
posed 
