He died on 24 December 1893, aged 86, and is buried at the West Terrace Cemetery.
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In 1864 the South Australian government, desiring to open up the Northern Territory, organized a survey party under Finniss, appointing him Government Representative and giving him instructions to examine the Adelaide River and the coastline to the west and east of it.
In 1864 the South Australian government charged B. T. Finniss with finding a suitable site by the Adelaide River for the capital of the Northern Territory.