Scald milk, add shortening, sugar and salt. When lukewarm, add the yeast which has been softened; add the egg and potatoes plus the cup water to the mixture. Beat in the flour until the dough is stiff and leaves the sides of the bowl. Let rise until triple in bulk. Roll out about 1/3 - inch thick and cut with a doughnut cutter. let rise on a floured board for one hour and fry, at 400 for 2 to 3 minutes Then dip in glaze. Dip doughnuts in glaze while hot. Set on sides untill cool.