In a large saucepan over medium heat, combine the sugar, corn syrup and water and bring to a boil. Continue to boil, undisturbed, until the mixture reaches the hard-ball stage, 265 degrees F on a candy thermometer. Remove from the heat.
In a standing electric mixer, whip the egg whites and salt until stiff peaks form. Working very slowly, add the sugar syrup in a thin, steady stream, and continue beating on high speed until the candy begins to lose its shine - this can take as long as 10 or 15 minutes, depending on your mixer. (When adding the hot sugar syrup to the egg whites, make sure to stop occasionally to scrape down the bowl if any syrup has collected on the sides. When the beaters are lifted out of the candy mixture, it should fall in a smooth thick ribbon that mounds on itself.
Working quickly, fold in the vanilla and drop by tablespoonfuls onto waxed paper. Cool completely before serving. The candies will firm up as they cool. Store in an airtight container.
Cook's Note: this is best made on a low-humidity day or in a dry location; damp conditions will prevent divinity from firming up.
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