Cook the turnips in boiling salted water until tender; drain, and cut out the centres, forming cups. Sprinkle the inside with oil and a few grains of salt, and, when the oil is absorbed, pour over the cups a little lemon juice or vinegar. Set aside to become cool. When ready to serve, arrange the cups on shredded lettuce and fill with cooked asparagus tips, cold and mixed with mayonnaise or French dressing, as desired. Peas, flageolets or wax beans, cut fine, may be used instead of the asparagus. Garnish with radishes.