P.T. Barnum's American Museum

In 1861, Barnum had two white whales captured for him at the mouth of the St. Lawrence, and conveyed them alive to his museum at New York, where they were exhibited in large tanks constructed for the purpose. Other tanks were shortly afterwards constructed by him, in which sharks, porpoises, "angel" fish &c., were shown. These animals were kept alive by a stream of salt water from high tide. This was the first rude attempt at aquaria in America.

What happened to it?
P.T. Barnum had in fact been keeping marine life in the basement of his American Museum since 1856 (after he went to London and was inspired by the Regent's Park Aquarium), and this might be considered to be the first public aquarium in the United States. It was part of the great showman's collection of curiosities and freaks.
Conditions were not good in the basement. Ventilation was poor and saltwater was made artificially by adding salt to freshwater. In 1861 more tanks were constructed on the second floor, and real sea water was pumped in by a steam engine. Barnum bought the Boston Aquarial Garden (founded 1859), and transferred most of its exhibits to New York for his new tanks.
The white (beluga) whales were brought from Canada to New York with much publicity. Thousands of people came to see them, but they died within a week. Two more were caught and housed in a new larger tank, but again they died, and then two more. Barnum soon came up with a new occupant for the whale tank - the first hippopotamus ever seen in America, which was again heavily publicized and highly popular.

Aquariums and Public Aquariums in Mid-Victorian Times, by Howard ...