Beat egg whites with remaining sugar until stiff peaks form.
Place heavy cream in a deep bowl and whip until peaks are firm but not stiff.
In a separate bowl, whip the egg whites until soft peaks form.
Increase speed to high, and beat until soft peaks form.
In a large bowl whisk the egg whites until soft peaks form.
Whip the double cream until very soft peaks form when the whisk is removed.
Beat egg whites until soft peaks form, and fold in.
Beat at medium speed until peaks just begin to form.
Whip the cream with the rum until soft peaks form.
Place the egg whites in a dry, clean bowl and beat until soft peaks form.