though unknowingly), and then had
been destroyed, there would have been no means of tracing its previous
existence. In past ages it had no doubt been perturbing the orbit of
Uranus, and had effected large changes in it; but if it had then been
suddenly destroyed, we should have had no means of identifying these
changes. There might have been instead of Neptune another planet, such as
that supposed by Adams and Le Verrier; and its action in all past time
would have been very different from that of Neptune, as is properly
represented in the mathematical expressions which Professor Peirce
considered. In consequence the orbit of Uranus in 1690 would have been
very different from the orbit as it was actually found; but in either case
the mathematicians Adams and Le Verrier would have had to take it as they
found it; and the disturbing action which they considered in their
calculations was the comparatively small disturbance which began in 1690
and ended in 1846. During this limited number of years the disturbance of
the planet they imagined, although not precisely the same as that of
Neptune, was sufficiently like it to give them the approximate place of
the planet.

Still it is somewhat bewildering to look at the mathematical expressions
for the disturbances as used by Adams and Le Verrier, when we can now
compare with them the actual expressions to which they ought to
correspond; and one may say frankly that there seems to be no sort of
resemblance. Recently a memorial of Adams' work has been published by the
Royal Astronomical Society; they have reproduced in their Memoirs a
facsimile of Adams' MS. containing the "first solution," which he made in
1843 in the Long Vacation after he had taken his degree, and which would
have given the place of Neptune at that time with an error of 15 deg.. In an
introduction describing the whole of the MSS., written by Professor R. A.
Sampson of Durham, it is shown how different the actual expressions for
Neptune's influence are from those used by Adams, and it is one of the
curiosities of this remarkable piece of history that some of them seem to
be actually _in the wrong direction_; and others are so little alike that
it is only by fixing our attention resolutely on the considerations above
mentioned that we can realise that the analytical work did indeed lead to
the discovery of the planet.

[Sidenote: Suggested elementary method for finding Neptune illusory.]

A second curiosity is t