Nobody seems to know the origin of the Paloma (Spanish for "dove"). The recipe was first mentioned in a pamphlet by Evan Harrison entitled "Popular Cocktails of the Rio Grande." Many authorities claim it is the most popular tequila-based cocktail in Mexico, and it is easy to see why.
If desired, rim a highball glass with the lime wedge and dust the outside of the rim with coarse salt. Do not get any salt inside the rim, as that could compromise the quality of the cocktail within.
Fill your highball glass with ice and squeeze, then drop, your lime wedge into it. Add the tequila, grapefruit juice, simple syrup and club soda. Stir twice. Note: If you are using bottled soda, simply add the tequila and top the glass off with the soda, then stir twice.