Cabochon: An unfaceted cut stone of domed or convex form, or the style of cutting itself. 
The top is unfaceted and smoothly polished; the back or base, usually flat, 
or slightly convex and unpolished.
The height of the domed top is varied to accomplish various desired effects.
With convex top and flat base it is called a simple or single cabochon; 
with convex top and base a double cabochon 
All asterias, cats-eyes, and girasols, most moonstones, opals and turquoise, 
are cut cabochon (or spherical),
as well as many translucent or semitransparent jades and other gem minerals.
Less desirable specimens of various gem varieties are also sometimes cut cabochon. 
The girdle outline may be oval, round, square or any other shape. 
The backs of almost all transparent or semi-transparent cabochons are polished.

Process:
Dopping- The process of attaching a rough gem to a stick or metal rod with 
"dopping wax" for
the purpose of holding and manipulating the stone, against a grinding wheel, sander,
or polishing wheel.

	I recommend buying the Cabochon and gem cutting book set, 
by Jack R Cox and Dr. H.C. Drake
Valuable for both novices and experts, this three-book set shows how to produce cabochons, 
faceted gems , gem spheres and cameos. 
Available from  Rio Grande 
in their tools catalog, order #550-388 for $11.25 
They also have a multitude of other how to books on jewelry at reasonable prices.
As well as "dop wax" order #206-054 for $7.00/lb, enough to last a long long time. 
And many other tools and accessories in their Lapidary section.

Cutting a Cabochon: The standard method.
Starting with a slab cut to the right thickness with a diamond saw, you 
would use a template to lay out your cabs and mark them with an aluminum
scribe. Then cut as close as you can with a diamond trim saw.
Sand amd polish the flat back side and on a medium grinding wheel, carefully grind to within
1/32 of the aluminum outline. chamfer the bottom edge at 45 degrees to prevent chipping.
Next grind the edge at a 10 degree angle so when you set the stone your 
bezel will hold it in. Then cut an arc end to end to get the right shape for the top.
After that cut an arc across the stone for the silhouette of the cross section. 
Starting at the height you want the bezel to cover on a fine stone work the rest of the 
stone into a smooth curve.
Ok, once your satisfied you have nice and even curves without ridge lines, you shift to 
the sander. 
	On sanding you want to use figure 8 motions to even out any ridges or flat spots,
and get rid of the grinder scratches.  As soon as the scratches are gone from one grit
shift to the next.
I start with 220 grit and work down to 400 grit, you can go on down to 600 if you wish.
The harder the stone the finer I would try to get it with the sander.
	Polishing, you want the wheel to have some give to it so it fits to the curve
of the stone slightly, I use a leather pad.  Linde A, an aluminum oxide, is a 
synthetic corundum and is well graded for unifomity, which helps in eliminating
scratch carry over. There are many other good polishing compounds that are cheaper.
A canvas belt on a belt sander also works well for polishing as it conforms to the 
shape of the stone.
THE BENCH TOOL METHOD
	A slight modification on a cheap ($49.00)Harbor freight bench belt sander, 
with a variety of belts, will do the entire job.
The modification is to duct tape a gallon plastic baggie, over the motor and switch so
the rock dust and oil or water don't short them out.
Then I use vegetable oil and just dip my dop stick and stone in the oil every now and then
to lubricate and cool the stone.
 All the grits and belts are available at a discount autoparts store that caters to 
body and fender shops. You may have to hunt for a canvas one to put polish on.
You can also use the side wheel with peel off adhesive, sanding and polishing disks.
Practice on cheaper gem rough before you start on your best material.
One other thing You need diamond grits for working on Ruby or Sapphire.
They are harder than your grinding wheels and will eat them up fast.
Diamond adhesive sanding disks are available.
Scrub your stones and dopstick with dishsoap and a toothbrush before switching to
finer grits, emeralds in particular carry grit over in fine fracture lines.