Surcingle longe lines, requires the use of a surcingle to thread the longe lines through the rings. Compared to a saddle, a surcingle allows more precise adjustment of side reins due to the placement of additional rings. While a saddle only provides one height to attach the rings (the girth buckles), and can be uneven or at the wrong position, a training surcingle places rings at more appropriate locations for ground work. Many surcingle designs allow the side reins to be attached at several different heights along the sides of the horse. When used without a saddle, a surcingle sits just
Girth (geometry) width, with the same width "w". All curves of constant width have the same perimeter, the same value "w" as the circumference of a circle with that width (this is Barbier's theorem). Therefore, every surface of constant width is also a surface of constant girth: its girth in all directions is the same number "w". Hermann Minkowski proved, conversely, that every convex surface of constant girth is also a surface of constant width. For a prism or cylinder, its projection in the direction parallel to its axis is the same as its cross section, so in these cases the girth