hat a mistaken idea should have been held by at
least one eminent man (Sir J. Herschel), to the effect that it would have
been possible to find the place of the planet by a much simpler
mathematical calculation than that actually employed by Adams or Le
Verrier. In his famous "Outlines of Astronomy" Sir John Herschel describes
a simple graphical method, which he declares would have indicated the
place of the planet without much trouble. Concerning it I will here merely
quote Professor Sampson's words:--

"The conclusion is drawn that _Uranus_ arrived at a conjunction with
the disturbing planet about 1822; and this was the case. Plausible as
this argument may seem, it is entirely baseless. For the maximum of
perturbations depending on the eccentricities has no relation to
conjunction, and the others which depend upon the differences of the
mean motions alone are of the nature of forced oscillations, and
conjunction is not their maximum or stationary position, but their
position of most rapid change."

Professor Sampson goes on to show that a more elaborate discussion seems
quite as unpromising; and he concludes that the refinements employed were
not superfluous, although it seems _now_ clear that a different mode of
procedure might have led more certainly to the required conclusion.

[Sidenote: The evil influence of Bode's Law.]

For the third curious point is that both calculators should have adhered
so closely to Bode's Law. If they had not had this guiding principle it
seems almost certain that they would have made a better approximation to
the place of the planet, for instead of helping them it really led them
astray. We have already remarked that if two planets are at different
distances from the sun, however slight, and if they are started in their
revolution together, they must inevitably separate in course of time, and
the amount of separation will ultimately become serious. Thus by assuming
a distance for the planet which was in error, however slight, the
calculators immediately rendered it impossible for themselves to obtain a
place for the planet which should be correct for more than a very brief
period. Professor Sampson has given the following interesting lists of the
dates at which Adams' six solutions gave the true place of the planet and
the intervals during which the error was within 5 deg. either way.

I. II. III. IV. V. VI.