In the C18th women are armed with fans as men with swords, and sometimes do more execution with them. To the end therefore that ladies may be entire mistresses of the weapon which they bear, I have erected an academy for the training up of young women in the Exercise of the Fan, according to the most fashionable airs and motions that are now practiced at court. The 'fan kiss' was a way of inviting a kiss. In order to send an invite a woman would press her fan as in the anticipation of a kiss. Even the pressure of the fan on the mouth had a meaning; the harder the pressure the increased level of sincerity and passion involved.
This "Fan Language" was used as a marketing tool by Fans Sellers in the C19th. It was especially used by the Duvelleroy branch in London, who gave booklets with this secret code to their customers.
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Reference: Blakemore Colin, Jennett Sheila, Kiss The Oxford Companion to the Body.