The act or operation of allowing a cord, cable, or rope to be pulled or drawn out; specifically, the operation of passing or running out a submarine cable from a ship which is laying it.(noun)
The Century Dictionary (Public Domain)
Use "paying-out" in a sentence
"I am naturally in good spirits, but keep very quiet, for misfortunes may arise at any instant; moreover tomorrow my paying-out apparatus will be wanted should all go well, and that will be another nervous operation."
"There was a grooved pulley used for the paying-out machinery with a spindle wheel, which might suit me."
"I have made my calculations and find the new paying-out gear cannot possibly answer at this depth, some portion would give way."