In a 2 quart saucepan, cook the rice with the salt, 1 tablespoon butter and the water until it is tender and the water is all absorbed. Stir and fluff the rice in the pan, then add the 4 tablespoons of butter, walnuts, sugar, orange rind and cinnamon. Put the eggs and milk in a small bowl and beat them together. Add them to the rice mixture, mix well and put in greased baking dish. Cover and bake at 325 degrees for about 1 1/4 to 1 1/2 hours, or until a skewer stuck in the center comes out reasonably clean. Serve warm or cold-preferably warm with whipped cream.