According to Burke’s complete Cocktail & Drinking Recipes, 1934, The Bronx Cocktail is essentially a perfect martini with orange juice added. It was ranked number three in “The World’s 10 Most Famous Cocktails in 1934”
Serve straight up without ice in a cocktail glass
6 parts Gin
3 parts Sweet Red Vermouth
2 parts Dry Vermouth
3 parts Orange Juice
Pour all of the ingredients into a cocktail shaker with ice, shake well, and then strain into a chilled cocktail/martini glass.
Stuart Webster [CC BY 2.0], via Wikimedia Commons