corundum or vitreous carbon; a field test please without fancy thermal gadgets?

Answer 1

I assume that by vitreous carbon you meant diamond.

It is very difficult to distinguish as they have close hardness (corundum 9, diamond 10) and specific gravity (cor. 4, dia 3.5).
The shape is slightly different - while corundum (trigonal crystal system) is barrel shaped/pyramidal/sometimes massive or granular, diamond (Isometric) is generally octahedral. The colour is also slightly different - while corundum shows grey, blue, red to pink, green, yellow to brown shades, diamond is generally colourless to white, rarely showing any tinge of colours.
Most important difference is perhaps in their cleavage. Corundum does not have a cleavage (only some partings), while diamond has a set of perfect cleavage.
The other difference is in their modes of occurrence.

Answer 2

A simple scratch test is in order. Corundum is 9 on Mohs Hardness Scale and it will scratch anything except a diamond. I don't know what the hardness of vitreous carbon is (in fact I don't know what vitreous carbon is), but it won't scratch corundum unless it is diamond. But then diamond has an adamantine luster, not a vitreous luster. If you don't have corundum and are just asking how tell them apart try scratching it with quartz, which has a hardness of 7. If, by chance, you have both diamond and corundum you will never be able to stratch the corundum with the diamond, unless you are superman. Corundum is just too hard to be scratched by human strength.