Wash fish in cold water, and pick in very small pieces, or cut, using scissors. Wash, pare, and soak potatoes, cutting in pieces of uniform size before measuring. Cook fish and potatoes in boiling water to cover until potatoes are soft. Drain through strainer, return to kettle in which they were cooked, mash thoroughly (being sure there are no lumps left in potato), add butter, egg well beaten, and pepper. Beat with a fork two minutes. Add salt if necessary. Take up by spoonfuls, put in frying-basket, and fry one minute in deep fat, allowing six fish balls for each frying; drain on brown paper. Reheat the fat after each frying.