Cook potatoes in pot of boiling water until tender, and then set aside to cool.
Mix dry mustard with water and allow to stand 10 minutes.
Cook bacon in skillet until crisp, then set bacon aside and crumble for use later; reserve bacon drippings in skillet.
Cook onion in bacon drippings until soft. Add mustard paste, sugar, water & vinegar. Bring to a boil, and simmer 2 minutes.
Peel potatoes (or leave the skins on if you prefer) and slice three of them into a bowl.
Sprinkle the layer of potatoes with half of the celery, crumbled bacon, and parsley; add salt and pepper to taste. Pour a little of the vinegar dressing over this layer and then repeat procedure with remaining ingredients.
Cover and allow to stand at room temperature for 30 minutes.