This fact allows volume elements to be defined as a kind of measure on a manifold.

Here we will find the volume element on the surface that defines area in the usual sense.

The fluid in volume elements approach plug flow as they move though the tubes of the reactor.

A representative disk is a three-dimensional volume element of a solid of revolution.

- The volume element is invariant under the bar conjugation.

We can split the fluid into a large number of cuboid volume elements.

Finally, the weight of the volume element causes a force downwards.

In these coordinates, the metric volume element then has the following expansion at p:

Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized.

The proper volume element is then just the product of and :