The Time Machine

Just finished H.G. Wells' "The Time Machine" for the third time in my life.  I love this story.  Such a provocative consideration of how social distinctions may drive the future differentiation of our species from the view of an educated man living in the late 1800's C.E.  I think a reading of "The Time Machine" is probably obligatory for anyone interested in ideas of time travel.  Though very dated, and lacking in scientific explanation for the underpinnings of the actual machine itself, "The Time Machine" shows how a rational thinker could view time before the beginnings of modern physics and without all of the inundation of temporal travel we see in modern sci-fi media.  I won't take up too much space here appraising the value of this fantastic read, but I will quote one line from the story that I found very interesting:

"There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it."

I thought this line was interesting for two reasons.  1) Wells' wrote this story in 1895, yet he is thinking fully in the realm of space-time, with time only serving as another dimension of space as we perceive it and possibly just as physically tangible of a dimension as the others, and 2) Wells wrote that our consciousness moves along in time, but implies that our consciousness does not necessarily move along in space.  I found this second bit to be really intriguing.  Was Wells implying that our consciousness is just that part of us that moves in time (the way our body moves in three-dimensional space), or was Wells stating something deeper about his take on what consciousness is?  I'm not sure what Wells meant to say with this, but I do have to wonder.  Any thoughts?