Remove outer leaves and any undesirable portions from firm mature heads of cabbage; wash and drain. Cut into halves or quarters; remove core. Use a shredder or sharp knife to cut cabbage into thin shreds about the thickness of a dime.
In a large bowl, thoroughly mix 3 tablespoons salt with 5 lbs. shredded cabbage. Let salted cabbage stand for several minutes to wilt slightly; this allows packing without excessive breaking or bruising of the shreds.
Pack salted cabbage firmly and evenly into a large, clean pickling container. Using a wooden spoon, tapper or hands, press down firmly until the juice comes to the surface.
Repeat shredding, salting and packing of cabbage until the container is filled to within 3 to 4 inches of the top. If juice does not cover cabbage, add brine: 1 1/2 tablespoons salt to 1 quart water; bring brine to a boil; cool.
Cover cabbage with muslin or cheesecloth and tuck edges down against the inside of the container. Weight down cabbage under brine. Formation of gas bubbles indicates fermentation is taking place. Remove and discard scum formation each day. A room temperature of 70 degrees to 75 degrees F is best for fermenting cabbage. Fermentation is usually complete in 3 to 6 weeks.
TO CAN: Bring sauerkraut to a simmer (185 to 210degrees F). Do not boil. Pack hot cabbage into hot jars, leaving 1/2 inch headspace. Remove air bubbles. Adjust caps. Process pints 15 minutes, quarts 20 minutes, in a boiling water canner.