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] Lyræ (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] Lyræ, 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. But 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.