first.

It is necessary for practical purposes that the cop of yarn should be
built up of a conical shape in the upper part, as shown in the
illustration. Now it must be obvious to the least technical of the
readers of this story, that to wind a given portion of yarn upon the
thin apex of a cone, will require a greater number of revolutions than
would be necessary to wind the same length of yarn upon the base of the
same cop. All the way between the apex and the base of the cone are also
other varying diameters, and during each return movement of the mule
carriage the thread is wound upon all the varying diameters of the cone
in succession.

This implies the necessity for the revolutions of the spindles to a
varying quantity all the time of the return or inward movement of the
spindle carriage.

The quadrant gives this varying speed in a manner which is all but
mathematically correct, any slight deviation from any such mathematical
correctness being easily compensated for in other ways.

For the specific manner in which this quadrant works, the reader is
referred to any of the recent text-books on cotton spinning.

The third primary and important operation, which takes place during each
return movement of the carriage, is the guiding of the thread upon the
spindles in a correct manner. This operation is closely associated,
however, with the action of the quadrant.

That portion of a "self-actor mule" which guides the faller wires is
termed the "shaper" or "copping motion." It consists of an inclined iron
rail upon the upper smooth surface of which slides the "copping bowl,"
this being a portion of the mechanism which connects the rail with the
faller wires. The rail rests upon suitable inclines termed "copping
plates," whose duty it is to regulate the movement of the rail so as to
allow for the ever-increasing dimensions of the cop during the building
process. When the carriage again reaches its initial position, suitable
mechanism causes all the parts to return in the position required for
spinning.

Such is the complete cycle of movements of the "mule," each succeeding
cycle being simply a repetition of the preceding. It will probably take
such a mule as the one described about six hours to make a "set of
cops," _i.e._, one on each spindle, each cop being 1-1/4 inches in
diameter and 7-1/2 inches long. Every fifteen seconds, while the mule is
making a cycle of its movements, may be divided up approximately a