E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
The committee was at a loss to know whom next to throw the handkerchief to (The Times). The meaning is that the committee did not know whom they were to ask next to make a speech for them; and the allusion is to the game called in Norfolk Stir up the dumplings, and by girls Kiss in the ring.