I have continued the Sines of the Projection unto two severall revolutions, the one beginning at 77.gr. 45.m. 6.s. and ends at 90.gr. (being the last revolution of the decuplation of the former, or the hundred part of that Projection) the other beginning at 86.gr. 6.m. 48.s. and ends at 90.gr. (being the last of a ternary of decuplated revolutions, or the thousand part of that Projection) and may bee thus used. He explains the manner of using these extra graduations. Thus he claims to have attained degrees of accuracy which enabled him to do what “some one” had declared “could not bee done.” It is hardly necessary to point out that Delamain’s Grammelogia IV suggests designs of slide rules which inventors two hundred or more years later were endeavouring to produce. Which of Delamain’s designs of rules were actually made and used, he does not state explicitly. He refers to a rule 18 inches in diameter as if it had been actually constructed (pages (86), (88)). Oughtred showed no appreciation of such study in designing and ridiculed Delamain’s efforts, in his Epistle. Additional elucidations of his designs of rules, along with explanations of the relations of his work to that of Gunter and Napier, and sallies directed against Oughtred and Forster, are contained on pages (8)-(21) of his Grammelogia IV. V. INDEPENDENCE AND PRIORITY OF INVENTION The question of independence and priority of invention is discussed by Delamain more specifically on pages (89)-(113); Oughtred devotes his entire Epistle to it. It is difficult to determine definitely which publication is the later, Delamain’s Grammelogia IV or Oughtred’s Epistle. Each seems to quote from the other. Probably the explanation is that the two publications contain arguments which were previously passed from one antagonist to the other by word of mouth or by private letter. Oughtred refers in his Epistle (p. (12)) to a letter from Delamain. We believe that the Epistle came after Delamain’s Grammelogia IV. Delamain claims for himself the invention of the circular slide rule. He says in his Grammelogia IV. (p. (99)), “when I had a sight of it, which was in February, 1629 (as I specified in my Epistle) I could not conceale it longer, envying my selfe, that others did not tast of that which I found to carry with it so delightfull and pleasant a goate [taste] . . .” Delamain asserts (without proof) that Oughtred “never saw it as he now challengeth it to be his invention, untill it was so fitted to his hand, and that he made all his practise on it after the publishing of my Booke upon my Ring, and not before; so it was easie for him or some other to write some uses of it in Latin after Christmas, 1630 and not the Sommer before, as is falsely alledged by some one . . .” (p. (91)). Delamain’s accusation of theft on the part of Oughtred cannot be seriously considered. Oughtred’s reputation as a mathematician and his standing in