Preheat the oven to 325°F (160°C).
In a large bowl, stir together the cake flour, 1 1/4 cups sugar, baking powder, and salt.
In another bowl with a stand mixer fitted with the whisk attachment on high speed, beat the egg yolks, water, oil, lemon zest, and vanilla until smooth, about 1 minute. Stir this into the flour mixture and keep stirring until the batter is smooth.
In a third bowl with the stand mixer on medium speed and with clean beaters, beat the egg whites and cream of tartar until soft peaks form, 2 1/2 to 5 minutes.
Gradually add the remaining 1/4 cup sugar, switch to high speed, and beat until stiff but not dry peaks form, about 5 minutes.
Using a rubber spatula, gently fold 1/4 of the beaten egg whites into the batter to lighten it. Then gently fold in the remaining whites. Carefully scrape the batter into an unbuttered 10-inch tube pan with a removable bottom and use the spatula to smooth the surface. Bake the cake until the top springs back when lightly pressed and a cake tester, toothpick, or strand of spaghetti inserted in the center comes out clean, 60 to 75 minutes. Turn the pan with the cake upside down, propping the tube of the pan on a long slender bottle or resting the pan on four short glasses. Let the cake cool in the pan for 1 1/2 hours.
To unmold the cake, slide a thin, long-bladed knife around the cake to detach it from the sides and center tube of the pan, pressing the knife against the pan to avoid tearing the cake. Then gently pull the tube upward. The cake should release from the sides of the pan. Slide the knife under the cake to gently detach it from the bottom. Place a wire cooling rack or a plate over the top of the cake pan, turn the cake pan and rack or plate upside down, and place the cake on the rack or plate. Turn the cake right side up and place it on a rack to cool completely.
Slice, sever, and sigh in bliss. Originally published April 21, 1997.