Vronsky's story: Two men (officers of Vronsky's regiment, whose names he's not revealing to protect their honor) were out drinking when they saw a pretty woman in a sleigh.
Drunk, the two decided to chase after the woman, who ran inside an apartment at the house where they themselves were planning to go.
She ran to the top apartment.
The men wrote a ridiculous love note and hand-delivered it to the apartment.
A maid answered the door of the apartment and held them off until a very angry man arrived to inform the two drunk men that no one lived in the apartment but his wife.
(The husband and wife are a Titular Councilor and Titular Counciloress, happily married.)
The Titular Councilor then approached the regimental commander with a complaint about these officers, who had insulted his wife.
Realizing that they have been harassing a family of some stature, the two officers have been trying to make peace with the Titular Councilor using Vronsky as a go-between.
Vronsky approaches the Titular Councilor, but as they discuss the incident, every time the official remembers the way these two young upstarts insulted his wife, he gets angry all over again.
Vronsky goes off to the French Theatre to report to his regimental commander his success (or lack thereof).
We find out that Petritsky (that guy who was using Vronsky's apartment in Petersburg when Vronsky was in Moscow) and a fellow named Prince Kedrov were the offenders. Petritsky's been getting into a lot of trouble lately, and the commander is getting fed up with him.
Vronsky tells his colonel the story of near-reconciliation, and the colonel is much amused by the official's continuing flare-ups.