1 honeydew melon
So that the watermelon will sit steadily, cut a very thin slice off its least attractive side. Lay the watermelon on this cut side, then slice about 1/4 to 1/3 of the melon off the top. Set the piece aside.
With a melon baller, scoop out as much of the watermelon meat as possible. Discard as many seeds as is practical. Spoon the balls into a large bowl. Scrape out the remaining watermelon meat, and reserve it for another use. Pour all the accumulated juice into the bowl with the watermelon balls. Cut the other melons in half, scrape out their seeds, and scoop out balls of their meat as well. Add these to the watermelon in the bowl, and lightly toss everything together.
1 cup ginger ale
1/2 to 3/4 cup apricot jam or preserves
Juice of 2 limes
Fresh mint (for garnish)
Stir together the ginger ale, jam or preserves and lime juice. If the melons are not especially sweet, add the greater amount of jam to the sauce. Pour the sauce over the melon balls, mixing gently. Trim the top cut edge of the watermelon shell to a smooth finish. Or you might zigzag it or shape it decoratively. Refrigerate the melon balls and shell as long as several hours, until you are ready to serve the dessert.
Shortly before serving, spoon the melon balls into the watermelon shell, piling them attractively above the melon's rim. Garnish with mint.