Thanks Malcolm. I ended up sending an email to Dr Nick Lomb at the Powerhouse Observatory and he sent back the answer. This is a portion of that reply:
The telescope shown on page 74 of my book is indeed a reflecting telescope. It is of the Gregorian type and its maker James Short was famous for making such telescopes. These telescopes consist of two concave mirrors with a hole in the centre of the primary mirror to allow observation with an eyepiece. See the Wikipedia entry for more details http://en.wikipedia.org/wiki/Gregorian_telescope.
I would enjoy owning an original example of these brass telescopes but I suspect my pockets are not deep enough.