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