How archaic and fun!
I whipped out some Google-fu and found the following for you:
Tincture of Capsicum
You can actually buy this on Amazon: Cayenne Capsicum Tincture 2 Ounces. It's available other places, but I saw prices as high as 2x this. (9 ml ~ 0.3 oz)
Essence of Ginger
This is from a late 19th century Jamaican cookbook (Classic Jamaican Cooking: Traditional Recipes and Herbal Remedies).
- Three ounces of freshly grated ginger
- Two ounces of thinly cut lemon-peel
- Two pints of brandy or proof spirit (white rum)
Just combine and let sit for 10 days, shaking well.
Essence of Lemon
This can also be purchased. You can likely find some lemon extract in your grocery store, if not here is some on Amazon: Flavorganics Organic Lemon Extract, 2-Ounce Glass Bottles (Pack of 3) - note that it's 3 bottles.
Solution of Burnt Sugar
This isn't just typical caramelized sugar, it's burnt sugar. Sugar that has been heated to the dark caramel stage of 370 F to 400 F (188 C to 204 C). The sugar at this point has lost most of it's sweetness, smells burnt, and tastes kind of bitter. It's commonly called caramel color these days. This is what is gives Cola's their dark color. In the small amount of 25ml and in the presence of 2.5 lbs of sugar (wow!) you won't taste it.
My amazon-fu fails here, but have found it available on this site: http://www.spiceplace.com/mccormick_caramel_color.php
It might be simpler to buy this than attempt making your own. Caramel coloring can be a little hazardous to make, it's easy to go too far and burn your sugar, and dumping any quantity of water into 400 F sugar is a sketchy experience. Here is a how-to if you desire though:
http://www.ehow.com/how_5673239_make-caramel-food-coloring.html
Tartaric Acid
This too can be purchased - Tartaric Acid 2 oz. (56 gr.)
Please note that tartaric acid is not the same as cream of tartar. Cream of tartar is an acid-salt in which the tartaric acid is partially neutralized. This site suggests you can use a 2:1 substitution ratio of cream of tartar to tartaric acid. I'm not sure if this will make a difference in your drink because I've never used cream of tartar in such a way or quantity before.
There is also the possibility that a recipe of this age simply used the term tartaric acid to refer to cream of tartar. Who knows?
This is not yogurt per definition, you are making a fresh cheese. You can actually use other types of milk for such a cheese, but the mouthfeel and taste will be very different and won't be as similar to yogurt.
There is a large class of acid-curdled cheeses, including paneer, tvorog, quark and many others. I don't know if yours has a specific name. I know that there are people who for some reason can't tell the difference in taste betwen quark and yogurt. But it is still cheese, even if it tastes similar to yogurt.
Best Answer
Soda-like drinks have traditionally been made in the same way as beer, but with less fermentation to keep the alcohol content low. Without alcohol, (and with a bunch of protein and fat around from the yogurt) you run the risk of growing some botulism in your soda. Some traditional fermentation techniques carry risk of botulism, and any 'new' technique should undertaken very carefully. That being said, your soda should be quite acidic and probably safe. Get some pH paper and use it!
There are a few things I would change in this plan:
Yogurt is made at fairly high temperatures to encourage lactobacillus growth while inhibiting others. Find out the best temperature for your culture, and make sure you can maintain it during fermentation.
Try get the culture growing independent of any yogurt: grow it in your sugar/lemon solution for a few generations without pressure and with a bit of oxygen. If it's still alive and still tastes good, you're probably OK. Otherwise, if the culture dies halfway through fermentation, something else is likely to grow in its place :-(
Lemon juice is quite acidic, and will clean metals quite nicely. So don't put your soda in any metal container unless your really like the taste of iron. (Even beer is acidic enough to cause this problem, fermentation is always in glass, plastic or stainless steel). Used plastic soda bottles work well when clean.
The other major problem with a pressure cooker is getting the soda out: if the cooker did hold pressure from a fermentation (actually it will probably leak CO2 faster than it is made) you shouldn't be able to open it until the pressure is removed. Again, soda bottles are a good choice here.
Last - your water should not be chlorinated, the flavor of your soda could be ruined by chlorine.