Simmer celery in stock in a covered saucepan 15 minutes.
Place celery and stock in a food processor or blender; add 1 cup of flaked crab meat, the milk solids, water, milk, salt, and mace.
Puree mixture; pour back into saucepan.
Heat crab mixture to simmering.
Mix arrowroot with a little cold water; stir into crab mixture.
Simmer, stirring constantly, until mixture has thickened.
Stir in sherry and remaining crab meat.
Garnish with celery slices.