This section is from the book "Preserving And Pickling", by Mary M. Wright. Also available from Amazon: Preserving and Pickling: Two Hundred Recipes for Preserves, Jellies, Jams, Marmalades, Pickles, Relishes and Other Good Things.
Pickled carrots are something new, and many people like them prepared in this way who do not relish the fresh vegetable. To make, choose an equal number of deep yellow and light yellow carrots; peel and out into strips. Boil in slightly salted water until tender. Drain, then cover with spiced vinegar, using a quart of vinegar and one cupful of water to a gallon of carrots. Add to the vinegar and water one pound of sugar, two ounces of mixed spices tied in a thin muslin bag, and bring to a boil. Then add the carrots, and boil a few minutes longer, after which put them in jars.