Cut the butter into thirds and bring it to room temperature.
In the top of a double boiler, combine egg yolks, water, lime juice, and salt. Add a piece of the butter. Place over boiling water (upper pan should not touch water). Cook, stirring rapidly with a whisk, until butter melts and sauce begins to thicken. Add the remaining butter, a piece at a time, stirring constantly until melted. Continue to cook and stir about 2 minutes more or until sauce thickens. Immediately remove from heat. If sauce is too thick or curdles, immediately whisk in 1 to 2 tablespoons hot water. Serve with poached eggs. Makes 3/4 cup sauce (six, 2 tablespoon servings).