4 Existence and Position of [January, 
Admiring the mathematical powers and versatility, and 
the perseverant industry of Le Verrier, we must yet admit 
that Pierce was right, and that Le Verrier failed to discover 
that where he was intent on finding one planet, three made 
themselves felt. 
4. “ In 1820 we possessed forty years of regular meridian 
observations of Uranus. The planet had besides been ob- 
served nineteen times from 1690 to 1771.” Bouvard, the 
author of the first Tables of Uranus, found the discrepan- 
cies in its motion so great “ that he doubted if they resulted 
from the inaccuracy of the older observations or from some 
foreign not perceived adtion on the planet.” Le Verrier 
sees “ the only explanation of the differences between theory 
and observation ” in the existenc “ of a planet beyond 
Uranus.” 
5. Examination of all observations shows that “ the 
period between 1781 and 1820 offers no trace of great per- 
turbations ; on the other hand, it can be connected neither 
with the preceding nor with the following observations.” 
“ I said already that we satisfy well enough the move- 
ment of the planet between 1781 and 1820 without the aid 
of any extraordinary force. This remark, which seems to 
prove that the perturbing force has not exercised any per- 
ceptible influence during this period, would be sufficiently 
conforming to the adtual hypothesis of a sudden alteration 
of the motion of the planet. But the period of 1781 to 
1820 might connedt itself naturally, be it with the former, 
be it with the later series of observations, and would be in- 
compatible with only one of them. But this is not the case ; 
it may be proved that the intermediate series cannot be made 
to agree on one side with the old observations, and on the 
other with the new ones.” 
Le Verrier returns over and over again to this difficulty 
without removing it. He calls a' half the great axis of the 
orbit of the Predicted , n' the mean motion, c' the excentricity, 
w' the perihelion, e' the value of the epoch year 1800, and in' 
the mass. 
6. The first step is a guess at a'. “ I said that the planet 
required cannot be at very little distance from Uranus, and 
it is not possible to place it at a very great one ; for instance, 
at three times that of Uranus from the Sun.” Le Verrier, 
not of the disposition of Prof. Newcomb, appeals to that 
metaphysical conjedture the Bode-Titius series. “ Is it 
possible that the inequalities of Uranus are due to the 
adtion of a planet situated in the ecliptic at a mean 
distance double that of Uranus? And if so, where is this 
