Up until the end of the eighteenth century, the sleeve of most women's dresses ended near the elbow. From beneath the dress sleeve, the ruffled white sleeve of the cotton undergarment was revealed. The exposed ruffles or bits of lace were called engageantes. Engageantes could be a single layer of ruffle or several tiers of frilly lace gathered around a woman's lower arm. Often the lace on the engageantes matched the lace used on the woman's cap and the tuft of lace she often tucked into her bodice near the bustline of her dress. Engageantes continued Europeans' love affair with lace until the end of the eighteenth century, when dress sleeves were shortened to small shoulder caps.
Contini, Mila. Fashion: From Ancient Egypt to the Present Day. Edited by James Laver. New York: Odyssey Press, 1965.
Cosgrave, Bronwyn. The Complete History of Costume and Fashion: From Ancient Egypt to the Present Day. New York: Checkmark Books, 2000.