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The way the centers and sockets are designed can be seen in Figures 12 and 13. Figure 13 shows them in an end-view perspective, while Figure 12 shows a side-view perspective. Number 1 is the roller original: "Rowler"; a cylindrical component used to rotate or move parts of the instrument of the upper tube, and 2 is the roller of the lower tube. 3 3 are the screws used to fasten them in the holes. 4 4 is the enclosing or socket-screw that presses tightly against the cylinder. 5 and 6 indicate the smooth cylindrical socket that guides the cylindrical screw, ensuring its axis passes exactly over the center of the roller 2 2. By using a ring (7) on the screw, the pointed end (8) is held against the support original: "portance"; a bearing or supporting part (9). It is not difficult to understand how to make a dividing plate and its hand or pointer original: "Index"; a pointer on a scientific instrument, nor how it can be turned from the center of the two tubes by a long rod, as shown in Figure 8. Once it is determined through observation how many rotations (and what fraction of a rotation) correspond to five whole degrees, it will be easy to calculate a table of subtenses original: "Subtenses"; linear measurements used to determine the size of an angle; effectively a table of chords. This table will show exactly what fraction of a turn is needed to measure every minute and second of that angle.
3. In 1665, I achieved the same result using a roller that rolled along the edge original: "limb"; the graduated arc or outer edge of an astronomical instrument of the quadrant. This was done with the help of two wires coiled around those rollers, with their ends fastened to the edge of the quadrant. By using a large pointer on the end of this roller, I was able to move the arm of the instrument to any five-second interval on the quadrant with great ease and certainty.
At the same time, I also built another frame with a straight screw that opened only to five degrees. This used rollers original: "Tumbrels"; here used to describe small cylinders or wheels within the mechanism similar to a pair of dividing compasses (using the same method I just described for measuring diameters or distances up to five degrees). I used very precise original: "curious"; in this period, the word meant highly detailed, expert, or intricately made lines drawn on a smooth glass plate and points very precisely marked at every five degrees on the edge of the quadrant (or whatever instrument it was attached to). With the help of a very thick plano-convex lens (with its flat side facing down toward the plate and the curved side toward the eye), this frame could be moved five degrees at a time across the entire edge of the quadrant. Using this instrument, I could easily and accurately divide an angle into five-second increments.