“From a very exact centre a circle was described on the ring c, about 4⁄10 inch within where the bottom of the teeth would come. This circle was divided with the greatest exactness I was capable of, first into five parts, and each of these into three. These parts were then bisected four times; that is to say, supposing the whole circumference of the wheel to contain 2160 teeth, this being divided into five parts, and these again divided into three parts, each third part would contain 144, and this space, bisected four times, would give 72, 36, 18, 9; therefore, each of the last divisions would contain 9 teeth. But, as I was apprehensive some error might arise from quinquesection and trisection, in order to examine the accuracy of the divisions, I described another circle on the ring c, [Fig. 1378], 1⁄10 inch within the first, and divided it by continual bisection, as 2160, 1080, 540, 270, 135, 671⁄2, 333⁄4, and, as the fixed wire (to be described presently) crossed both the circles, I could examine their agreement at every 135 revolutions (after ratching could examine it at every 333⁄4); but not finding any sensible difference between the two sets of divisions, I, for ratching, made choice of the former, and, as the coincidence of the fixed wire with an intersection could be more exactly determined with a dot or division, I therefore made use of intersections on both sides, before described.
“The arms of the frame l, [Fig. 1381], were connected by a thin piece of brass, 3⁄4 inch broad, having a hole in the middle 4⁄10 inch in diameter; across this hole a silver wire was fixed, exactly in a line to the centre of the wheel; the coincidence of this wire with the intersections was examined by a lens of 1⁄10 inch focus, fixed in a tube which was attached to one of the arms l. Now (a handle or winch being fixed on the end of the screw) the division marked 10 on the circle f was set to its index, and, by means of a clamp and adjusting-screw for that purpose, the intersection marked i on the circle c′ was set exactly to coincide with the fixed wire. The screw was then carefully pressed against the circumference of the wheel by turning the finger-screw h; then, removing the clamp, I turned the screw by its handle nine revolutions, till the intersection marked 240 came nearly to the wire. Then, turning the finger-screw h, I released the screw from the wheel, and turned the wheel back till the intersection marked 2 exactly coincided with the wire, and by means of the clamp before mentioned, the division 10 on the circle being set to its index, the screw was pressed against the edges of the wheel by the finger-screw h, the clamps were removed, and the screw turned nine revolutions, till the intersection marked i nearly coincided with the fixed wire; the screw was released from the wheel by turning finger-screw h as before, the wheel was turned back till intersection marked 3 coincided with the fixed wire; the division 10 in the circle being set to its index, the screw was pressed against the wheel as before, and the screw turned nine revolutions, till intersection 2 was nearly coincident with the fixed wire, and the screw released, and I proceeded in this manner till the teeth were marked round the whole circumference of the wheel. This was repeated three times round to make the impressions deeper. I then ratched the wheel round continuously in the same direction, without ever disengaging the screw, and, in ratching the wheel about 300 times round, the teeth were finished.
“Now, it is evident that if the circumference of the wheel was even one tooth, or ten minutes, greater than the screw would require, this error would, in the first instance, be reduced by 1⁄240 part of a revolution, or two seconds and a half, and these errors or inequalities of the teeth were equally distributed round the wheel at the distance of nine teeth from each other. Now, as the screw in ratching had continual hold of several teeth at the same time and thus constantly changing, the above-mentioned irregularities soon corrected themselves, and the teeth were reduced to a perfect equality. The piece of brass which carried the wire was now taken away, and the cutting-screw was also removed, and a plain one put in its place. At one end of the screw arbor, or mandrel was a small brass circle f, having its edge divided into 60 parts, numbered at every sixth division, as before mentioned. On the other end of the screw is a ratchet-wheel v (x, [Fig. 1380]) having 60 teeth, covered by the hollow circle (v, [Fig. 1380]), which carries two clicks that catch upon opposite sides of the ratchet-wheel. When the screw is to be moved forward, the cylinder w turns on a strong steel arbor e′′, which passes through the piece x′; this piece, for greater firmness, is attached to the screw-frame by the braces w. A spiral groove or thread is cut upon the outside of the cylinder w, which serves both for holding the string and also giving motion to the lever i on its centre, by means of a steel tooth v, that works between the threads of the spiral. To the lever is attached a strong steel pin m, on which a brass socket turns; this socket passes through a slit in the piece u, and may be tightened in any part of the slit by the finger-nut y. This piece serves to regulate the number of revolutions of the screw for each tread of the treadle b′.”
Fig. 1382.
Fig. 1383.
[Figs. 1382], [1383], and [1384] represent a method adopted to divide a circle by the Pratt and Whitney Company. The principle of the device is to enable the wheel to be marked, to be moved through a part of a revolution equal to the length of a division, and to test the accuracy of the divisions by the coincidence of the line first marked with that marked last when the wheel has been moved as many times as it is to contain divisions. By this means any error in the division multiplies, so that the last division marked will exhibit it multiplied by as many times as there are divisions in the whole wheel. The accuracy of this method, so long as variations of temperature are avoided, both in the marking and the drilling of the wheel, appears to be beyond question. In the figures, w represents a segment of the wheel to be divided, and c what may be termed a dividing chuck. The wheel is mounted on an arbor in a gear-cutting machine. On the hub of the wheel (which has been turned up for the purpose) there is fitted, to a close working fit, a bore at the end of an arm, the other end of the arm being denoted by a in the figures. The dividing chuck is fitted to the slide s of the gear-cutting machine, and is of the following construction.