Bloody Caesar

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3 tablespoons plus 1/2 teaspoon celery salt, divided

1 lime, quartered

3 tablespoons freshly squeezed lime juice

24 ounces canned clamato juice

2 teaspoons Worcestershire sauce

1 teaspoon hot pepper sauce

1/2 teaspoon freshly ground black pepper

1 teaspoon freshly grated, or bottled horseradish (optional)

6 ounces vodka