Line a large baking sheet with foil; grease foil and set aside.
In a large saucepan stir together sugar, tapioca, ginger, and nutmeg. Stir in rhubarb and apples until coated. Let stand about 15 minutes or until a syrup begins to form, stirring occasionally. Cover and cook over medium heat for 15 minutes or just until fruit is softened, stirring occasionally. Remove from heat. Let cool for 30 minutes.
Meanwhile, preheat oven to 375 degrees F. In a large mixing bowl combine flour and salt. Using a pastry blender, cut in shortening until pieces are pea-size. Sprinkle 1 tablespoon of water over part of the mixture; gently toss with a fork. Push moistened mixture to side of bowl. Repeat, using 1 tablespoon of water at a time, until all the dough is moistened. Divide dough in half. On a lightly floured surface roll out each portion of pastry to a 12-inch square. Cut each portion into four 6-inch squares.
Spoon about 1/4 cup of the cooked rhubarb mixture onto half of one pastry square, leaving a 1-inch border around edge of pastry. Brush edges of square with water. Fold pastry over filling, forming a rectangle. Press edges gently to seal. Brush edges lightly with water again. Fold edges up and over about 1/4 inch. Press edges with tines of a fork to seal again.
Place tart on prepared baking sheet. Repeat with remaining squares of pastry and rhubarb filling. Prick tips 2 or 3 times with the tines of a fork for escape of steam. Pat down top to get rid of excess air around filling. Brush tops with milk and sprinkle with coarse sugar. Bake for 30 to 35 minutes or until golden brown. Cool on wire rack about 30 minutes; serve warm. Makes 8 servings.