1. Wash raw rice. Soak overnight in water to cover. Then drain well.
2. Blanch walnuts. Grind walnuts and rice to a fine powder, either by hand (with a mortar and pestle) or in a food mill.
3. Gradually stir the powder to a smooth paste with the second quantity of water; then stir in the third quantity.
4. Strain mixture through a double thickness of cheesecloth into the top of a double boiler. Gather together corners of the cheesecloth and squeeze every possible drop of liquid into the pan. Add sugar and the fourth quantity of water.
5. Bring remaining water to a boil in the lower half of the double boiler; then reduce heat to medium. Cook walnut-rice mixture over it, stirring constantly until it thickens (7 to 10 minutes).