Have ready two quarts of boiling water. Cut up three or four potatoes, well pared, a thick slice or two of bread, six or eight leeks, well peeled and cut, as far as the white extends, into slices. Turn the whole into the water, which must be boiling at the time, cover, and let it come to a brisk boil after the ingredients are added, then throw in a teacupful (not a breakfast-cup*) of rice, a spoonful of salt, and half that of pepper. Boil slowly for an hour, or till all the ingredients amalgamate.† Serve. This is a savory and cheap soup, very common in France and Germany. Cabbage soup is made in the same way, omitting the potatoes, and substituting bread.
*A breakfast cup (approximately the size of our coffee cup) was larger than a tea cup.
Recipe from "Civil War Recipes: Receipts from the Pages of Godey's Lady's Book" by Lily May Spaulding and John Spaulding
Potato Soup Modern Version