New York Laws
Article 41 - Trial by a Jury
4103 - Issues Triable by a Jury Revealed at Trial; Demand and Waiver of Trial by Jury.

ยง 4103. Issues triable by a jury revealed at trial; demand and waiver
of trial by jury. When it appears in the course of a trial by the court
that the relief required, although not originally demanded by a party,
entitles the adverse party to a trial by jury of certain issues of fact,
the court shall give the adverse party an opportunity to demand a jury
trial of such issues. Failure to make such demand within the time
limited by the court shall be deemed a waiver of the right to trial by
jury. Upon such demand, the court shall order a jury trial of any issues
of fact which are required to be tried by jury.