Wash six medium sized potatoes, and cook in boiling salted water until soft. Cool, remove skins, and cut in very thin slices. Cover bottom of baking-dish with potatoes, season with salt and pepper, sprinkle with finely chopped celery, then with finely chopped parsley. Mix two tablespoons each tarragon and cider vinegar and four tablespoons olive oil, and add one slice lemon cut one third inch thick. Bring to boiling-point, pour over potatoes, cover, and let stand in oven until thoroughly warmed.