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Rh a makeshift for the proper transition required in the system from questions of Body Natural to questions of Body Politic. Hobbes had in fact spent himself in his earlier constructive efforts, and at the age of seventy, having nothing to add to his doctrine of Man as it was already in one form or another before the world, was content with anything that might stand for the fulfilment of his philosophical purpose. But he had still in him more than twenty years of vigorous vitality, and, not conscious to himself of any shortcoming, looked forward, now his hands were free, to doing battle for his doctrines. Rather than remain quiet, on finding no notice taken of his latest production, he would himself force on a new conflict with the enemy. Wallis having meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of mathematical analysis and reasserting his own earlier positions. Accordingly, by the spring of 1660, he had managed to put his criticism and assertions into five dialogues under the title Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii, with a sixth dialogue so called, consisting almost entirely of seventy or more propositions on the circle and cycloid. Wallis, however, would not take the bait. Hobbes then tried another tack. Next year, having solved, as he thought, another ancient crux, the duplication of the cube, he had his solution brought out anonymously at Paris in French, so as to put Wallis and other critics off the scent and extort a judgment that might be withheld from a work of his. The artifice was successful, and no sooner had Wallis publicly refuted the solution than Hobbes claimed the credit of it, and went more wonderfully than ever astray in its defence. He presently republished it (in modified form), with his remarks, at the end of a new Latin dialogue which he had meanwhile written in defence of another part of his philosophical doctrine. This was the Dialogus physicus, sive De natura aëris (L.W. iv. 233–296), fulminated in 1661 against Boyle and other friends of Wallis who, as he fancied, under the influence of that malevolent spirit, were now in London, after the Restoration, forming themselves into a society (incorporated as the Royal Society in 1662) for experimental research, to the exclusion of himself personally, and in direct contravention of the method of physical inquiry enjoined in the De corpore. All the laborious manipulation recorded in Boyle’s New Experiments touching the Spring of the Air (1660), which Hobbes chose, without the least warrant, to take as the manifesto of the new “academicians,” seemed to him only to confirm the conclusions he had reasoned out years before from speculative principles, and he warned them that if they were not content to begin where he had left off their work would come to nought. To as much of this diatribe as concerned himself Boyle quickly replied with force and dignity, but it was from Hobbes’s old enemy that retribution came, in the scathing satire Hobbius heauton-timorumenos (1662). Wallis, who had deftly steered his course amid all the political changes of the previous years, managing ever to be on the side of the ruling power, was now apparently stung to fury by a wanton allusion in Hobbes’s latest dialogue to a passage of his former life (his deciphering for the parliament the king’s papers taken at Naseby), whereof he had once boasted but after the Restoration could not speak or hear too little. The revenge he took was crushing. Professing to be roused by the attack on his friend Boyle, when he had scorned to lift a finger in defence of himself against the earlier dialogues, he tore them all to shreds with an art of which no general description can give an idea. He got, however, upon more dangerous ground when, passing wholly by the political insinuation against himself, he roundly charged Hobbes with having written Leviathan in support of Oliver’s title, and deserted his royal master in distress. Hobbes seems to have been fairly bewildered by the rush and whirl of sarcasm with which Wallis drove him anew from every mathematical position he had ever taken up, and did not venture forth into the field of scientific controversy again for some years, when he had once followed up the physical dialogue of 1661 by seven shorter ones, with the inevitable appendix, entitled Problemata physica, una cum magnitudine circuli (L.W. iv. 297–384), in 1662. But all the more eagerly did he take advantage of Wallis’s loose calumny to strike where he felt himself safe. His answer to the personal charges took the form of a letter about himself in the third person addressed to Wallis in 1662, under the title of Considerations upon the Reputation, Loyalty,	 Manners and Religion of Thomas Hobbes (E.W. iv. 409–440). In this piece, which is of great biographical value, he told his own and Wallis’s “little stories during the time of the late rebellion” with such effect that Wallis, like a wise man, attempted no further reply. Thus ended the second bout.

After a time Hobbes took heart again and began a third period of controversial activity, which did not end, on his side, till his ninetieth year. Little need be added to the simple catalogue of the untiring old man’s labours in this last stage of his life. The first piece, published in 1666, De principiis et ratiocinatione geometrarum (L.W. iv. 385–484), was designed, as the sub-title declared, to lower the pride of geometrical professors by showing that there was no less uncertainty and error in their works than in those of physical or ethical writers. Wallis replied shortly in the Philosophical Transactions (August 1666). Three years later he brought his three great achievements together in compendious form, Quadratura circuli, Cubatio sphaerae, Duplicatio cubi, and as soon as they were once more refuted by Wallis, reprinted them with an answer to the objections, in compliment to the grand-duke of Tuscany, who paid him attentions on a visit to England in 1669 (L.W. iv. 485-522). Wallis, who had promised to leave him alone henceforward, refuted him again before the year was out. In 1671 he worked up his propositions over again in Rosetum geometricum (L.W. v. 1–50), as a fragrant offering to the geometrical reader, appending a criticism (Censura brevis, pp. 50-88) on the first part of Wallis’s treatise De motu, published in 1669; also he sent Three Papers to the Royal Society on selected points treated very briefly, and when Wallis, still not weary of confuting, shortly replied, published them separately with triumphant Considerations on Dr Wallis’s Answer to them (E.W. vii. 429-448). Next year (1672), having now, as he believed, established himself with the Royal Society, he proceeded to complete the discomfiture of Wallis by a public address to the Society on all the points at issue between them from the beginning, Lux Mathematica excussa collisionibus Johannis Wallisii et Thomae Hobbesii (L.W. v. 89-150), the light, as the author R. R. (Roseti Repertor) added, being here “increased by many very brilliant rays.” Wallis replied in the Transactions, and then finally held his hand. Hobbes’s energy was not yet exhausted. In 1674, at the age of eighty-six, he published his Principia et problemata aliquot geometrica, ante desperata nunc breviter explicata et demonstrata (L.W. v. 150-214), containing in the chapters dealing with questions of principle not a few striking observations, which ought not to be overlooked in the study of his philosophy. His last piece of all, Decameron physiologicum (E.W. vii. 69-180), in 1678, was a new set of dialogues on physical questions, most of which he had treated in a similar fashion before; but now, in dealing with gravitation, he was able to fire a parting shot at Wallis; and one more demonstration of the equality of a straight line to the arc of a circle, thrown in at the end, appropriately closed the strangest warfare in which perverse thinker ever engaged.

We must now turn back to trace the fortunes of Hobbes and his other doings in the last twenty years of his life. All these controversial writings on mathematics and physics represent but one half of his activity after the age of seventy; though, as regards the other half, it is not

possible, for a reason that will be seen, to say as definitely in what order the works belonging to the period were produced. From the time of the Restoration he acquired a new prominence in the public eye. No year had passed since the appearance of Leviathan without some indignant protest against the influence which its trenchant doctrine was calculated to produce upon minds longing above everything for civil repose; but after the Restoration “Hobbism” became a fashionable creed, which it was the duty of every lover of true morality and religion to denounce. Two or three days after Charles’s arrival in London, Hobbes drew in the street the notice of his former pupil, and was at once received into favour. The young king, if he had ever himself resented the apparent disloyalty of the “Conclusion” of Leviathan, had not retained the feeling long, and could appreciate the principles of the great book when the application of them happened, as now, to be turned in his own favour. He had, besides, a relish for Hobbes’s wit (as he used to say, “Here comes the bear to be baited”), and did not like the old man the less because his presence at court scandalized the bishops or the prim virtue of Chancellor Hyde. He even went the length of bestowing on Hobbes (but not always paying) a pension of £100, and had his portrait hung up in the royal