Judge Bykovsky has quite a tolerant view of this particular vice. Although he understands why the governess is so concerned at catching Seryozha smoking, he nonetheless finds it rather amusing to imagine his seven-year-old son wreathed in thick clouds of cigar smoke.
Bykovksy's tolerant attitude is further influenced by memories of his childhood, when it was common for children to be mercilessly flogged or expelled from school if they were caught smoking. Nevertheless, he's still acutely aware that as a father and a judge, he must make Seryozha see the error of his ways.
At first, he tries to do this by giving his son a mild ticking off. This involves a little lecture on the importance of respecting other people's property—in this case, Judge Bykovsky's cigars. When that doesn't seem to work, Bykovksy spins a scary story about an emperor's son who died of tuberculosis at the age of twenty as a result of smoking. It appears to have done the trick, as a chastened Seryozha promises not to smoke again.