When children are tired of swinging, or think it is time for the swinger to give way to another, the phrase is “let the old cat die.” After this has been said, it is unlucky to quicken the motion of the swing again.
General.

When children are tired of swinging, or think it is time for the swinger to give way to another, the phrase is “let the old cat die.” After this has been said, it is unlucky to quicken the motion of the swing again.
Source: Current Superstitions (1896), entry 93.
Fanny D. Bergen, editor.