any slack rope by the engine.

For flat ropes the drum or bobbin consists of a solid disk, of the width
of the rope fixed upon the shaft, with numerous parallel pairs of arms
or horns, arranged radially on both sides, the space between being just
sufficient to allow the rope to enter and coil regularly upon the
preceding lap. This method has the advantage of equalizing the work of
the engine throughout the journey, for when the load is greatest, with
the full cage at the bottom and the whole length of rope out, the duty
required in the first revolution of the engine is measured by the length
of the smallest circumference; while the assistance derived from
gravitating action of the descending cage in the same period is equal to
the weight of the falling mass through a height corresponding to the
length of the largest lap, and so on, the speed being increased as the
weight diminishes, and vice versa. The same thing can be effected in a
more perfect manner by the use of spiral or scroll drums, in which the
rope is made to coil in a spiral groove upon the surface of the drum,
which is formed by the frusta of two obtuse cones placed with their
smaller diameters outwards. This plan, though mechanically a very good
one, has certain defects, especially in the possibility of danger
resulting from the rope slipping sideways, if the grooves in the bed are
not perfectly true. The great size and weight of such drums are also
disadvantages, as giving rather unmanageable dimensions in a very deep
pit. In some cases, therefore, a combined form is adopted, the body of
the drum being cylindrical, and a width equal to three or four laps
conical on either side.

Counterbalance chains for the winding engines are used in the collieries
of the Midland districts of England. In this method a third drum is used
to receive a heavy flat link chain, shorter than the main drawing-ropes,
the end of which hangs down a special or balance pit. At starting, when
the full load is to be lifted, the balance chain uncoils, and continues
to do so until the desired equilibrium between the working loads is
attained, when it is coiled up again in the reverse direction, to be
again given out on the return trip.

In Koepe's method the drum is replaced by a disk with a grooved rim for
the rope, which passes from the top of one cage over the guide pulley,
round the disk, and back over the second guide to the second cage, and a
tail rope, passing round a pulley at