Final answer:
The police were looking for individuals engaged in same-sex interactions at the Danglars' party, surveilling to catch anyone being themselves in a period when such behavior was illegal.
Step-by-step explanation:
At the Danglars' party, the police were not looking for any individual in particular, but rather were surveying the crowd for any signs of same-sex interactions that were considered illegal at the time.
They were observing to see if a man was touching another man’s hand under the table or if a woman's knee was pressed against another woman's.
If caught, those individuals would be taken to jail. The patrons at the party were aware of the police intention and used a signaling system to switch back to opposite-sex dancing partners to avoid arrest, thereby winning the game against the police at least for that night.
The police were looking for people engaging in same-sex relationships when they arrived at the Danglars' party.