So, if you see somebody riding side saddle, you'll realize something. If legs are used to control the horse, what do you do when you only have one on one side?
The answer is a ladies' whip. It is longer than a normal riding crop and more like a dressage whip, and is used to replace the leg cues on the right side. Ladies' whips normally have a flapper like crops, rather than a short lash like dressage whips. It is never used to hit or discipline the horse. Victorian ladies' whips were often fashion accessories as well.
A lady jumping side saddle, you can clearly see the whip in her right hand. Image source: Wikimedia commons.