What is the name of the measurement along a 4th dimensional axis? Given that measurement along the X, Y and Z axes correspond to the terms "width", "height", and "depth", is there an accepted term for spatial measurement along the W axis when dealing in four dimensions?  For that matter, are there such terms for additional dimensional axes?

I'm not sure about "measurement," per se, but Henry More used the term "spissitude" to describe a point's position along the W axis.  The following is an excerpt from this article on Wikipedia...

Comparatively, 4-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w. To describe the two additional cardinal directions, Charles Howard Hinton coined the terms ana and kata, from the Greek words meaning "up toward" and "down from", respectively. A position along the w axis can be called spissitude, as coined by Henry More.

Considering the nature of tensors and linear algebra, you could make a solid case for using it as a term for measurement along the W axis.  Hope this helps!
