Preheat the oven to 350°F. Grease the bottom and sides of a 1½-quart loaf pan, dust the interior with a little cornmeal, and set aside.
In a saucepan, combine the water and salt and bring to a rapid boil. Gradually add the grits, reduce the heat to moderately low, and cook, stirring frequently to prevent sticking, for 25 minutes. Add the butter, remove pan from the heat, and stir till the butter has melted. Meanwhile, combine the milk and cornmeal in a mixing bowl, stir well, and let stand 15 minutes.
Stir the grits into the cornmeal mixture, then, one by one, beat in the eggs. Scrape the batter into the prepared loaf pan and bake till the bread is golden, about 50 minutes. Serve hot with plenty of butter or, if left over, lightly toasted and buttered.