The concerted advance of mathematical astronomy during the eighteenth century was effected with the confident serenity of irresistible power. One after another the obstacles barring its path went down before repeated and skilful onslaughts, the unbroken succession of which lends a certain exultant sameness to the story of the heroic age of analysis. The _Mécanique Céleste_ attested 'victory all along the line.' There were no more worlds to conquer that Laplace knew of; the reign of gravitational law was firmly established throughout the solar dominions; menaced revolts had been appeased; anomalies removed; no extant observations any longer impaired the perfect harmony between what was and what had been foreseen. Nature for the moment submitted readily to the trammels put upon her by human thought; her intricacies had apparently ceased to defy unravelment; her modes of procedure looked straightforward and intelligible. As they were judged to be in the present, so they might be presumed to have been in the past; and the temptation was irresistible to adventure backward speculation, inferring initial conditions from the elaborated product laid open to scrutiny. It was an epoch of peremptory renewals. The formula of equality promised to regenerate society; a political panacea had been found by the creation of a republic 'one and indivisible'; and the success of the guillotine in securing its supremacy was almost outdone by the triumphs of the calculus in vindicating the unimpeded sway of gravitation. Humanity had made a fresh start; science should do likewise. The sanguine spirit of a rejuvenated world animated all forms of human endeavour. It has long since evaporated. The buoyant hopes of a century back have been crushed; the future of civilization looks dim; and its uncertainty compromises the future of knowledge. But we, at any rate, no longer delude ourselves with the idea that he who runs may read the secrets of the universe. We have learned by convincing experience how much, and how variously, 'the subtlety of nature transcends the subtlety of sense and intellect'; we are vividly aware that there is no single and simple recipe for the 'cosmification' of chaos.