A sidesaddle is specially designed for ladies, with both of the rider's legs positioned on the same side of the horse. A set of curved posts on the left side of the saddle hold the rider's legs in position while the upper torso is turned slightly to a fairly normal riding pose. Properly adjusted, a sidesaddle is secure enough that it can be ridden at a gallop and even be used for jumping low obstacles.
In the photo above, the young woman at left is mounted on her side saddle, with her skirt demurely covering her legs and the devices that hold her legs in place. Those projections from the saddle can be glimpsed behind the raised arm of the woman at the right in the picture.
Photo above by Solomon D. Butcher, 1907. Courtesy of Nebraska State Historical Society, [Digital ID nbhips 13494]
At right, Mrs. Arthur Aldis rides sidesaddle on the horse Parson as they hurdle a low stone wall in a field at Onwentsia Country Club in Lake Forest, Illinois. Photograph taken by a Chicago Daily News photographer in 1905. Courtesy of the Library of Congress.