In its report on the donation of the Customs House clock to the Newcastle Museum following the 1989 earthquake, the abc advises that

Customs administration was first established in 1828 and was housed at various locations until the current building was built and occupied in 1877.

You can see the time-ball on top of the tower of the building, which dropped everyday at 1pm enabling sailing ship captains to synchronize their ships chronometers.

The leaning tower is due to the camera lens I was using when I took the picture.