. . . you may make use of the Projection of the Circles of the Ring upon a Plaine, having the feet of a paire of compasses (but so that they be flat) to move on the Center of that Plaine, and those feet to open and shut as a paire of Compasses . . . now if the feet bee opened to any two termes or numbers in that Projection, then may you move the first foot to the third number, and the other foot shall give the Answer; . . . it hath pleased some to make use of this way. But in this there is a double labour in respect to that of the Ring, the one in fitting those feet unto the numbers assigned, and the other by moving them about, in which a man can hardly accommodate the Instrument with one hand, and expresse the Proportionals in writing with the other. By the Ring you need not but bring one number to another, and right against any other number is the Answer without any such motion. . . . upon that [the Ring] I write, shewing some uses of those Circles amongst themselves, and conjoyned with others . . . in Astronomy, Horolographie, in plaine Triangles applyed to Dimensions, Navigation, Fortification, etc. . . . But before I come to Construction, I have thought it convenient by way introduction, to examine the truth of the graduation of those Circles . . . These are the words of a practical man, interested in the mechanical development of his instrument. He considers not only questions of convenience but also of accuracy. The instrument has, or may have now, also lines of sines and tangents. To test the accuracy of the circles of Numbers, “bring any number in the moveable to halfe of that number in the fixed: so any number or part in the fixed shall give his double in the moveable, and so may you trie of the thirds, fourths &c. of numbers, vel contra,” (p. 54). On page 55 are given two small drawings, labelled, “A Type of the Ringe and Scheme of this Logarithmicall projection, the use followeth. These Instruments are made in Silver or Brasse by John Allen neare the Sauoy in the Strand.” IV. CONTROVERSY BETWEEN OUGHTRED AND DELAMAIN ON THE INVENTION OF THE CIRCULAR SLIDE RULE Delamain’s publication of 1630 on the ‘Mathematicall Ring’ does not appear at that time to have caused a rupture between him and Oughtred. When in 1631 Delamain brought out his Horizontall Quadrant, the invention of which Delamain was afterwards charged to have stolen from Oughtred, Delamain was still in close touch with Oughtred and was sending Oughtred in the Arundell House, London, the sheets as they were printed. Oughtred’s reference to this in his Epistle (p. 20) written after the friendship was broken, is as follows: