Wash the tomatoes and slice a shallow wedge out of the top, stem-end of the tomato to remove the core. If they are small or average size tomatoes, cut into quarters. If they are large, cut into eighths. Add a couple cups of the chopped tomatoes at a time to a large, non-reactive (glass, enamel, and stainless steel are all good choices) stockpot over medium-low heat. Lightly break it up with a large spoon or potato masher. Continue adding tomatoes and breaking them up after each addition until all the tomatoes are in the pot. Add the carrots, celery, onion and parsley to the pot and stir to combine. Raise heat to medium high and bring to a boil, stirring frequently to prevent scorching and sticking. Lower heat and simmer for about 35 minutes, or until carrots and celery are mostly tender.
Position a strainer over a large bowl or another large, non-reactive stockpot. Ladle the vegetables and their juice into the strainer. Once everything has been strained, return the liquid you’ve collected to the (rinsed) stockpot. Juice the remaining vegetables (or process until smooth in a food processor or food mill.) Strain over the stockpot to remove seeds and peels. If using salt, stir it in now.
Heat juice to 190°F. DO NOT ALLOW TO BOIL! If you don’t have a thermometer,190°F looks like a great deal of steam coming from the surface of the juice with no bubbles breaking the surface. Hold at this temperature for 5 minutes.
Add 1 Tablespoon of bottled lemon juice to each sterile* pint jar and 2 Tablespoons of bottled lemon juice to each sterile* quart jar you will fill. Ladle the hot juice into the jars leaving 1/4? of headspace. Wipe the rims of the jars and add the lids, then tighten the rings just until resistence is met.
Fill your canner about halfway full of tepid water. Arrange the jars around the base of the canner and add water, if needed, to cover the jars by 2 inches. Cover and bring to a full, rolling boil. Start timing at that point. Process quarts for 40 minutes and pints for 35 minutes. Carefully transfer finished jars to a cooling rack or a towel on the countertop. Allow to cool overnight without disturbing the jars.
If the jars have sealed, the center of the lids will be tight when pressed gently. If the seal has failed, it will pop down and then back up when pressed. Any jars with failed seals should be stored in the fridge until used. The rest of the jars can be stored in a cool place such as a cupboard or basement for up to a year.