In a medium bowl, cream shortening and sugar. Stir in the eggs and vanilla. Sift together the flour, baking soda, and cream of tartar, stir into the creamed mixture. Cover dough and chill for at least 1 hour.
Preheat oven to 400 degrees F (200 degrees C). In a small saucer, stir together the remaining sugar, with the cinnamon and nutmeg.
Roll dough into 1 inch balls and roll the balls in the sugar mixture. Place 2 inches apart on an unprepared cookie sheet. Bake for 8 to 10 minutes in the preheated oven, edges will be golden brown. Remove from cookie sheets to cool on wire racks.
