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I am probably off the mark here but in my mind the projection of the original 1955 map sheet is a non issue since you are (if I understand correctly) georeferencing 1955 to a 2011 dataset/projection and thus stretching the old to match new. Best of luck regardless.
Without the projection parameter values, it's going to be difficult to figure out what might be in use. Is it US data? You could try the local state plane zone (based on NAD27 which uses Clarke 1866). You'll still need to identify points on the map for which you have coordinate values. You may have to georeference it directly to lat/lon.
Thanks for the replies.
This is a tricky one because I have both the projection and the ellipsoid but not the datum. Ideally I would have liked to accurately georeference the map using the grid however, without the datum there would be no point. As a solution I decided to use the cities on the map as reference points which worked fine for this purpose.
Why not getting some points with known coordinates in both systems and calculate your own parameters? If the area is not that big, a 2D transformation will do just fine.