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Mr. Hook's Answer to Monsieur Auzout's Considerations, in a Letter to the Publisher of these Transactions.
SIR,
Together with my most hearty thanks for the favour you were pleased to do me, in sending me an Epitome of what had been by the ingenious Monsieur Auzout animadverted on a description, I had made of an Engine for grinding spherical Glasses, I thought my self obliged, both for your satisfaction, and my own Vindication, to return you my present thoughts upon those Objections. The chief of which seems to be against the very Proposition it self: For it appears, that the Objector is somewhat unsatisfied, that I should propound a thing in Theory, without having first tried the Practicableness of it. But first, I could wish that this worthy Person had rectified my mistakes, not by speculation, but by experiments. Next, I have this to answer, that (though I did not tell the Reader so much, to the end that he might have the more freedom to examine and judg of the contrivance, yet) it was not meer Theory I propounded, but somewhat of History and matter of Fact: For, I had made trials, as many as my leisure would permit, not without some good success; but not having time and opportunity enough to prosecute them, I thought it would not be unacceptable to such, as enjoyed both, to have a description of a way altogether New, and Geometrically true, and seemingly, not unpracticable, whereof they might make use, or not, as they should see reason. But nothing surprised me so much, as, that he is pleased (after he had declared it a fault, to write this Theory, without having reduced it to practice) to lay it, as he seems to do, in one place of his book, p. 22 upon the Royal Society. Truly, Sir, I should think my self most injurious to that Noble Company, had I not endeavoured, even in the beginning of my Book, to prevent such a misconstruction. And therefore I cannot but make this interpretation of what Monsieur Auzout saith in this particular, that either he had not so
