Tarragon Lemonade

In a medium saucepan, combine 4 cups of water with the sugar and bring to a boil, stirring to dissolve the sugar. Simmer over moderately high heat until reduced to 3 1/4 cups, about 25 minutes. Remove from the heat and add 5 of the tarragon sprigs. Let stand, stirring often, until cooled to room temperature, about 30 minutes. Discard the tarragon sprigs. In a large glass pitcher, combine the remaining 6 cups of water with the tarragon syrup and fresh lemon juice. Add a pinch of salt, stirring until it dissolves. Serve the tarragon lemonade over ice, garnished with the lemon slices and the remaining 12 tarragon sprigs.