The window pattern as seen from the outside of the Carnegie building -- three long windows on one side and four short on the other -- confirms what Barrett wrote (and using Google satellite view to look from above, the skylight position also matches). 

And Barrett should be considered the expert on this, as his photos seem to be the only interior photos of the building available anywhere online, other than some recent pictures of the rotunda and a few historic photos of the children’s section on Minnesota Reflections. 

As he noted, however, his photo showing a part of the ceiling is likely of a different room. The orientation of the windows line up with the southeast corner and I believe his photo looks into the southwest room. 

According to Zenith City Press, the southwest corner was in fact the location of the reading room, but it had a large carved sandstone fireplace. This room is likely not the reading room, but another room mentioned in the same article – the newspaper room, as suggested by the large number of people reading newspapers and the newspaper racks at the back of the wall.



You can see hundreds of people in the space of the room in this picture but the room itself does not yet exist. 

For a definite answer, someone would need to go down to the building and break open the wall directly below the stone being placed in the construction photo. According to David Ouse at Vintage Duluth, it contains a time capsule in the form of a sealed copper box with information about the library inside.