Lots of laughs

Yesterday I watched an old British WW1 movie. Two officers were disscussing how to tell thier superior officers of an unusual plan. One officer's comment was "When they hear this they'll be "laughing up thier sleeves". Where did this come from?

Why were the Germans called "Jerries " ?

If you cover your mouth with your hand to try to conceal your laughter, it may appear that you are laughing up your sleeve.