This is drawing of the Transit Instruments as used by the Transit of Venus parties for determining latitude and time. The "broken-tube" design had a prism in the centre cube for reflecting the image into the eyepiece on the left and cross-hair illumination from the oil lamp on the right.
A photograph of such a telescope can be seen here (8k.jpg).
Newcomb Simon - Observations of the Transit of Venus, December 8-9, 1874 - 1880
to 1882 TOV page