his process of limitation was faulty and actually misleading. Let
us compare what is said about it by Professor Peirce a little later.

"Guided by this principle, well established, and legitimate, if
confined within proper limits, M. Le Verrier narrowed with consummate
skill the field of research, and arrived at two fundamental
propositions, namely:--

"1st. That the mean distance of the planet cannot be less than 35 or
more than 37.9. The corresponding limits of the time of sidereal
revolution are about 207 and 233 years.

"2nd. 'That there is only one region in which the disturbing planet
can be placed in order to account for the motions of Uranus; that the
mean longitude of this planet must have been, on January 1, 1800,
between 243 deg. and 252 deg..'

"'Neither of these propositions is of itself necessarily opposed to
the observations which have been made upon Neptune, but the two
combined are decidedly inconsistent with observation. It is
impossible to find an orbit, which, satisfying the observed distance
and motion, is subject to them. If, for instance, a mean longitude
and time of revolution are adopted according with the first, the
corresponding mean longitude in 1800 must have been at least 40 deg.
distant from the limits of the second proposition. And again, if the
planet is assumed to have had in 1800 a mean longitude near the
limits of the second proposition, the corresponding time of
revolution with which its motions satisfy the present observations
cannot exceed 170 years, and must therefore be about 40 years less
than the limits of the first proposition.'

"Neptune cannot, then, be the planet of M. Le Verrier's theory, and
cannot account for the observed perturbations of Uranus under the
form of the inequalities involved in his analysis"--(_Proc. Amer.
Acad. I._, 1846-1848, _p._ 66).

[Sidenote: Newcomb's criticism.]

At the time when Professor Peirce wrote, the orbit of Neptune was not
sufficiently well determined to decide whether one of the two limitations
might not be correct, though he could see that they could not both be
right, and we now know that they are _both wrong_. The mean distance of
Neptune is 30, which does _not_ lie between 35 and 37.9; and the longitude
in 1800 was 225 deg., which does _not_ lie between 243 deg. and 252 deg.. The
ingenious