It is true that in making a certain kind of rope, the velocity ratio of A and S must remain constant, in order that the strands may be equally twisted throughout; but if for another kind of rope a different degree of twist is wanted, the velocity of the pinion, E, may be altered by means of change-wheels, and thus the same machine may be used for manufacturing many different sorts.

The second combination of this kind was devised by the writer as a “tell-tale” for showing whether the engines driving a pair of twin screw-propellers were going at the same rate.  In Fig. 33, an index, P, is carried by the wheel, F:  the wheel, A, is loose upon the shaft of the train-arm, which latter is driven by the wheel, E. The wheels, F and f, are of the same size, but a is twice as large as A; if then A be driven by one engine, and E by the other, at the same rate but in the opposite direction, the index will remain stationary, whatever the absolute velocities.  But if either engine go faster than the other, the index will turn to the right or the left accordingly.  The same object may also be accomplished as shown in Fig. 34, the index being carried by the train-arm.  It makes no difference what the actual value of the ratio A/_a_ may be, but it must be equal to F/_f_:  under which condition it is evident that if A and F be driven contrary ways at equal speeds, small or great, the train-arm will remain at rest; but any inequality will cause the index to turn.

In some cases, particularly when annular wheels are used, the train-arm may become very short, so that it may be impossible to mount the planet-wheel in the manner thus far represented, upon a pin carried by a crank.  This difficulty may be surmounted as shown in Fig. 35, which illustrates an arrangement originally forming a part of Nelson’s steam steering gear.  The Internal pinions, a, f, are but little smaller than the annular wheels, A, F, and are hung upon an eccentric E formed in one solid piece with the driving shaft, D.

The action of a complete epicyclic train involves virtually and always the action of two suns and two planets; but it has already been shown that the two planets may merge into one piece, as in Fig. 10, where the planet-wheel gears externally with one sun-wheel, and internally with the other.

But the train may be reduced still further, and yet retain the essential character of completeness in the same sense, though composed actually of but two toothed wheels.  An instance of this is shown in Fig. 36, the annular planet being hung upon and carried by the pins of three cranks, c, c, c, which are all equal and parallel to the virtual train-arm, T. These cranks turning about fixed axes, communicate to f a motion of circular translation, which is the resultant of a revolution, v’, about the axis of F in one direction, and a rotation, v, at the same rate in the opposite direction about its own axis, as has been already explained.  The cranks then supply the place of a fixed sun-wheel and a planet of equal size, with an intermediate idler for reversing the, direction of the rotation of the planet; and the velocity of F is