t though such an idea was mentioned among astronomers, it was not
regarded with any special favour, and was considered merely as one among
a number of hypotheses which could be suggested as fairly probable.

It is perfectly right not to attach much importance to unelaborated
guesses. Not until the consequences of an hypothesis have been
laboriously worked out--not until it can be shown capable of producing
the effect quantitatively as well as qualitatively--does its statement
rise above the level of a guess, and attain the dignity of a theory. A
later stage still occurs when the theory has been actually and
completely verified by agreement with observation.

Now the errors in the motion of Uranus, _i.e._ the discrepancy
between its observed and calculated longitudes--all known
disturbing causes, such as Jupiter and Saturn, being allowed
for--are as follows (as quoted by Dr. Haughton) in seconds of
arc:--

ANCIENT OBSERVATIONS (casually made, as of a star).

Flamsteed 1690 +61.2
" 1712 +92.7
" 1715 +73.8
Le Monnier 1750 -47.6
Bradley 1753 -39.5
Mayer 1756 -45.7
Le Monnier 1764 -34.9
" 1769 -19.3
" 1771 -2.3

MODERN OBSERVATIONS.

1780 +3.46
1783 +8.45
1786 +12.36
1789 +19.02
1801 +22.21
1810 +23.16
1822 +20.97
1825 +18.16
1828 +10.82
1831 -3.98
1834 -20.80
1837 -42.66
1840 -66.64

These are the numbers plotted in the above diagram (Fig. 92), where
H marks the discovery of the planet and the beginning of its
regular observation.

Something was evidently the matter with the planet. If the law of
gravitation held exactly at so great a distance from the sun, there must
be some perturbing force acting on it besides all those known ones which
had been fully taken into account. Could it be an outer planet? The
question occurred to several, and one or two tried if they could solve
the problem, but were soon stopped by the tremendous difficulties of
calculation.

The ordinary problem of perturbation is difficult enough: Given a
disturbing planet in such and such a position, to find the perturba