of the "Paralogisms" of his more formidable antagonist in the first five lessons, he ended with a lesson on "Manners" to the two professors together, and set himself gravely at the close to show that he too could be abusive. In this particular part of his task, it must be allowed, he succeeded very well; his criticism of Wallis's works, especially the great treatise _Arithmetica infinitorum_ (1655), only showed how little able he was to enter into the meaning of the modern analysis. Wallis, on his side, was not less ready to keep up the game in English than he had been to begin it in Latin. Swift as before to strike, in three months' time he had deftly turned his own word against the would-be master by administering _Due Correction for Mr Hobbes, or School Discipline for not saying his Lessons right_, in a piece that differed from the _Elenchus_ only in being more biting and unrestrained. Having an easy task in defending himself against Hobbes's trivial criticism, he seized the opportunity given him by the English translation of the _De corpore_ to track Hobbes again step by step over the whole course, and now to confront him with his incredible inconsistencies multiplied by every new utterance. But it was no longer a fight over mathematical questions only. Wallis having been betrayed originally by his fatal cleverness into the pettiest carping at words, Hobbes had retorted in kind, and then it became a high duty in the other to defend his Latin with great parade of learning and give fresh provocation. One of Wallis's rough sallies in this kind suggested to Hobbes the title of the next rejoinder with which, in 1657, he sought to close the unseemly wrangle. Arguing in the _Lessons_ that a mathematical point must have quantity, though this were not reckoned, he had explained the Greek word [Greek: stigme], used for a point, to mean a visible mark made with a hot iron; whereupon he was charged by Wallis with gross ignorance for confounding [Greek: stigme] and [Greek: stigma]. Hence the title of his new piece: [Greek: Stigmai ageometrias, agroikias, antipoliteias, amatheias], or _Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity_ (_E.W._ vii. 357-400). He now attacked more in detail but not more happily than before Wallis's great work, while hardly attempting any further defence of his own positions; also he repelled with some force and dignity the insults that had been heaped upon him, and fought the verbal points, but could not leave the field without making political insinuations against his adversary, quite irrelevant in themselves and only noteworthy as evidence of his own resignation to Cromwell's rule. The thrusts were easily and nimbly parried by Wallis in a reply (_Hobbiani puncti dispunctio_, 1657) occupied mainly with the verbal questions.