ancy is quite distinct, but still it is very small,
and had two objects been in the heavens at once, the actual Uranus and
the theoretical Uranus, no unaided eye could possibly have distinguished
them or detected that they were other than a single star.

[Illustration: FIG. 93.--Perturbations of Uranus.

The chance observations by Flamsteed, by Le Monnier, and others, are
plotted in this diagram, as well as the modern determinations made after
Herschel had discovered the nature of the planet. The decades are laid
off horizontally. Vertical distance represents the difference between
observed and subsequently calculated longitudes--in other words, the
principal perturbations caused by Neptune. To show the scale, a number
of standard things are represented too by lengths measured upwards from
the line of time, viz: the smallest quantity perceptible to the naked
eye,--the maximum angle of aberration, of nutation, and of stellar
parallax; though this last is too small to be properly indicated. The
perturbations are much bigger than these; but compared with what can be
seen without a telescope they are small--the distance between the
component pairs of [epsilon] Lyrae (210") (see fig. 86, page 288), which
a few keen-eyed persons can see as a simple double star, being about
twice the greatest perturbation.]

The diagram shows all the irregularities plotted in the light of our
present knowledge; and, to compare with their amounts, a few standard
things are placed on the same scale, such as the smallest interval
capable of being detected with the unaided eye, the distance of the
component stars in [epsilon] Lyrae, the constants of aberration, of
nutation, and of stellar parallax.

The errors of Uranus therefore, though small, were enormously greater
than things which had certainly been observed; there was an unmistakable
discrepancy between theory and observation. Some cause was evidently at
work on this distant planet, causing it to disagree with its motion as
calculated according to the law of gravitation. Some thought that the
exact law of gravitation did not apply to so distant a body. Others
surmised the presence of some foreign and unknown body, some comet, or
some still more distant planet perhaps, whose gravitative attraction for
Uranus was the cause of the whole difficulty--some perturbations, in
fact, which had not been taken into account because of our ignorance of
the existence of the body which caused them.

Bu