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Terra sigillata is a very smooth, lustrous coating of clay which resembles a glaze and is virtually waterproof. The name means "sealed earth" and has been used to refer to the Classical Greek Attic black-figure and red-figure painted pottery.
These days, the name terra sigillata is used to refer to an especially fine coating of clay applied to a ceramic piece.
For centuries the secret of making terra sigillata was lost and only in the middle of this century was the true nature of this material, the technique of its creation and use rediscovered.
The silkiness and shine of terra sigilatta is due to the plate like shape of the clay particles and the use of only the smallest particles. Polishing this surface with your hand or a soft cloth lines up all the clay 'plates' and gives the surface its shine.
Most terra-sigillatas are made by a process of levigation in water which allows the larger particles to settle to the bottom, leaving the very finest, sub micron sized particles in suspension. These very fine particles are siphoned off and become the terra-sigillata.
There are many ways to make terra-sigillata. This is a simple method that works for me.
Add dry or moist clay to a lot of water. The proportions by weight  are usually 1 part clay to 2 parts water. This can be as high as 1 part clay to 4 parts water for a REALLY plastic clay, like a ball clay .
Mix the clay and water very thoroughly to break down any lumps. Let the mix sit for a day and mix again. I do this over several days mixing for about 15 minutes a day. 
Mix thoroughly one more time and pour the mix into the largest, tallest, transparent containers you can find 
Add 7 grams of liquid sodium silicate  per litre and mix thoroughly in the containers
Leave this undisturbed for about 24 hours and it should settle into 2 or 3 visible layers . The layer you want should look like VERY thin milk.
Siphon off the VERY thin, milky layer into another container.
Congratulations, you now have terra-sigillata!
You want to start with the most "naturally" plastic clays that you can. The amount of terra-sig that you get in the end will depend on the amount of very fine particles in the clay. Generally the more naturally plastic a clay is, the more terra-sig it will yield. I use the term "naturally" plastic because many claybodys are only workable because they have had plastisizers, like bentonite, added. These clays probably won't yield enough fine particles to make your work worth the effort.
In general, Porcelains will yield less terra-sig than "natural" earthenware clays.
For White or "Colorable" Terra-sigillata, use a very plastic, white burning ball clay. Avoid low fire, white clays. Many of these contain "plastisizers". White terra-sigs can be colored using Mason stains or coloring oxides like cobalt. The stains or oxides should be as finely ground as possible otherwise the relatively large size of the oxide particles can interrupt the shine of the sub-micron size terra-sigillata clay particles.
"Natural", low fire earthenware clays like Red Art from Ceder Heights make great TS. Most earthenware clays, through the natural process of their making are very plastic, have LOTS of extremely small particles and yield a lot of terra-sig. They also lend their own natural "earth" colors colors; reds, browns, oranges, yellows, etc. Color depends on the final burning color of the clay.
Some people treat the surface of the clay before applying the terra-sig by either lightly sanding the surface with a very fine sandpaper  or burnishing it with the back of a spoon or a smooth stone. I never did any of this.
Most people I know, brush or spray the terra-sig onto bone dry clay , applying several thin coats, letting it dry again between coats. If you're lucky, you can apply the terra-sig to bisque. This allows the additional option of dipping and will eliminate losses due to handling fragile bone dry clay. It will take some testing to see if this is possible. If the terra-sig flakes off after firing, go back to applying to bone dry.
How successfully the terra-sig hides the body underneath is important to many people. However, cover isn't everything. Sometimes it's nice to have some of the body color coming through.
If it's a good terra-sig, just the act of brushing it on should raise a sheen. I usually leave it at this. However some people want more of a shine and there are probably as many ways of doing this as there are artists working in terra-sigillata. I find that lightly rubbing the dry surface of the terra-sig with my bare hand will raise a mild shine. A "Baggies" type plastic bag over my hand will raise quite a bit more shine. This is about the limit for my tastes. If I do want to raise a really shiny surface, I lightly brush my finger tips over a block of lard then rub my finger tips against my palm  to distribute the lard some more. Then I start by lightly brushing my finger tips over the surface of the terra-sig, gradually making more and more contact with the surface. You'll find that this can raise quite a shine. For other methods of burnishing the terra-sig look to the work of Vince Pitelka, Michael Wisner, etc.
Terra-sigillata can be fired to what ever temperature you like. As long as it's above the sintering temperature of the clay used to make the terra-sig. Sintering of the clay is required to join the coating to itself and to the body it's covering.
In general, the lower the temperature, the more shine will remain. The higher you go, the more shine, you'll lose. However, some people fire their terra-sigs quite high. The ball clay that I use for my white terra-sig is a high fire ball clay and still retains a pretty good shine up to about 1200c / 2185f / ^5.
Also, I think that the higher you go, the better the terra-sig bonds with the claybody underneath.
Of course, the clay you use to make the terra-sig, the claybody underneath, the thickness and method of the application, the firing temperature, etc, as well as your own ideas of "success" will determine if the terra-sig is "successful". Your mileage will vary.
My recommendation is to test making terra-sig out several different clays. If you're working with students, this can  be part of the exploration.
Test each one to see:
How much terra-sig does the clay yield?
How it can be applied:
Does it prefer bone dry or can it be applied to bisque
does it prefer to be brushed on, sprayed or dipped?
How many coats does it take to hide the body underneath?
Does it like a thick application of many coats or only a few coats
Can it be burnished easily ?
Do you like the burnished surface that it gives?
Does it stay on after firing or does it flake off?
How thick a coat will stay on without flaking off?
How high can the terra-sig go without losing it's shine
 Weighing these out in metric is easier because 1 litre of water weighs 1 kilogram.
 It's better for the process of levigation to have too much water than too little. If you have too little water, the clay doesn't settle out properly. Either the clay will appear to have not settled out at all or it will have settled out into only two layers with the top layer totally clear.
Also see end note  below.
 Don't worry about exact measurements here, it's not rocket science.
 The object is to break the clay up into the smallest particles possible by the soaking action of the water and the agitation of the mixing. If you're making a lot at a time the best way to do this is with a "Jiffy Mixer" in a powerful drill. If you're only making a little or doing tests, use a blender. Since the blender does a pretty good job of pulverising the clay, you probably only need to mix it once.
 I use 2 litre pickle jars
 The reason for this will be obvious in a minute.
 Also known as "water glass" or "egg keep".
 See end note  ;-)
 None of the layers should be TOTALY clear, if so, most likely you don't have enough water or, less likely, not enough sodium silicate.
 A NEW gasoline siphon with a hand pump works really well for this and is really cheap.
 This is dusty so wear an OSHA approved mask.
 Use a humid sponge to remove any remaining clay dust before applying the terra-sig
 If spraying, wear a mask
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 This looks like you're trying to scratch the palm of your hand with fingers of the same hand.
 All of these methods, including the one with the lard are all a bit tricky. If you want to keep it simple, stick to the "Baggie".
 Some clays end up too powdery for burnishing and just brush off the pot onto your hand. A little bit of this is ok but if it does it a lot, try another clay.