(239) It is thus easy to see that with the bobbin leading it should gradually diminish in speed, and it is consequently the practice to run it at a much higher speed at the beginning than at the termination of winding. For instance, an empty spool 1 inch diameter takes up per revolution 3·1416 inches of roving, while one 3 inches diameter would take up 9·42 inches. It thus becomes imperative to reduce the speed of the bobbin wheels, and these being constantly geared with their driving wheels, it is necessary to reduce the velocity of the bobbin shafts. These are driven, as described hereafter, by a train of gearing from the main shaft, and special means are adopted to compass the reduction. The spindles are running at a constant speed, and it follows, in consequence, that the bobbin must run at the same rate, plus the number of revolutions necessary to take up the length of yarn delivered in any given time. If, for instance, the spindles made 100 revolutions while 10 inches of yarn was being delivered, the bobbin must revolve 100 times plus the number necessary to take up the 10 inches of yarn.
(240) When the flyer leads, the application of this principle is not quite so clearly seen at first sight, but a little reflection will make it understood. In this case the winding is effected by the excess of the speed of the flyer over that of the bobbin. This is exactly the reverse of the practice when the bobbin leads, but the essential condition is, as before, the preservation of the relative surface speeds of the bobbin and roller. Suppose that, in starting, the diameter of these two are the same, then the bobbin must lag behind the flyer to the extent of one revolution for each revolution of the roller. But as the bobbin increases in diameter, it requires more yarn to cover its surface, and a less difference in speed is needed, as, if the bobbin continues to lag one revolution, the difference between the speed of delivery and that of winding become so great as to stretch and break the roving. Instead of wrapping it round, for instance, a circumference of three inches it has eventually to be wound on one of six inches, and it is obvious that if the speed of the bobbin remains constant the roving will be drawn and broken. It is, therefore, necessary to gradually increase the speed of the bobbin so that for every inch of yarn delivered, an inch of the circumference will be covered by it. The difference between this and the former case consists in the fact that the roving is wrapped on a concentric surface, revolving in the same direction at a slower speed, while, with the bobbin leading, the surface on which the roving is wound, moving in excess of the speed of the flyer, draws the roving through the flyer eye at a rate equal to that of its delivery. In other words, it is in one case _wrapped_ on by the excess of the flyer speed or the drag of the bobbin, while, in the other, it is _drawn_ on by the excess of speed of the bobbin. The conclusion is thus arrived at that when the flyer leads, the bobbins must start at their slowest speed, and gradually increase; while, when the bobbin leads, it must begin at its highest speed and gradually diminish.