What do "take ground" and "vested in" mean in this context?

Here is an extract from the headnote of a case [1] I am trying to understand:

The defendants, who were wharfingers, agreed with the plaintiff for a consideration to allow his vessel to discharge and load her cargo at their wharf, which abutted upon the River Thames. It was necessary in order that the vessel might be unloaded that she should be moored alongside a jetty of the defendants which ran into the river, and that she should take ground with her cargo at the ebb of the tide.

Additionally, if anyone could help illuminate this next part for me, I'd be most grateful:

The bed of the river at the point where she took ground was vested in the Conservators, and the defendants had no control over it, but it was admitted that they had taken no steps to ascertain whether it was suitable for the vessel to ground upon.

[1] “The Moorcock”, The Law Reports. Probate Division in the Courts of Probate, Divorce, and Admiralty Division, Great Britain, Volume 13, page 157 (July 1888)

Take (the) ground is equivalent to ground as a verb; sometimes barges and the like cannot be properly unloaded while they are floating. At the ebb of the tide is obviously at low tide.

Vesting is a legal term you really need to look up, but for non-technical purposes such as EL&U can help with, vested in is equivalent to owned by.