The postcard is by Photochrom. It is not
dated and has not been sent through the post. However, Douglas Beath
(Tasmania, formerly of Edinburgh) has helped to
date the photo.
Apparently, the central poles
in Princes Street had light brackets east-west as on the photo
below (though with a later lamp housing)
Reproduced by courtesy Lothian Buses plc
About 1950 (and certainly before 1952) these were
replaced by high and long north-south brackets giving better spread of
light and avoiding large shadows from passing trams. It is these newer
poles that appear in the postcard above.
fact, the nearest pole on the postcard has no new brackets and those
behind seem recently painted. Perhaps the photo was taken at the very
time of conversion.
Douglas, for the observation above