Core and coarsely chop tomatoes. Transfer tomatoes to a large colander set in sink; drain. Measure 19 cups coarsely chopped tomatoes.
In an 8- to 10-quart stainless-steel, enamel, or nonstick heavy pot combine the 19 cups chopped tomatoes, celery, and onion. Bring to boiling, stirring frequently; reduce heat. Simmer, covered, about 15 minutes or until tomatoes are soft, stirring frequently to prevent sticking.
Press tomato mixture through a food mill or sieve set over an extra-large bowl to extract the juice. Discard seeds and skins. Measure 12 cups juice; return to pot. Bring to boiling, stirring frequently; reduce heat. Simmer, uncovered, for 20 minutes, stirring frequently. Remove from heat. Measure 9 1/2 to 10 cups juice and return to pot. Stir in lemon juice, sugar, Worcestershire sauce, horseradish, salt, and hot pepper sauce. Return to boiling; reduce heat. Simmer, uncovered, for 10 minutes more.
Ladle hot juice into hot sterilized pint canning jars, leaving a 1/2-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner for 35 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks. Makes 4 pints.