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Read my article Fitting An English Saddle to learn how to ensure your saddle is appropriate for you and your horse.
The panel is the portion of the English saddle that has contact with the horse's back; it is a leather "bag" of sorts cushioned with a shock absorbing material such as wool, foam, etc. While panels do help lend some comfort to the horse during riding, there is only so much a panel can do when the saddle's tree isn't a proper fit. Sometimes a panel can be further stuffed or manipulated to help accommodate a better fit with a horse, but it's best to avoid this necessity in the first place. In addition it's important to keep in mind foam panels cannot be further stuffed or enhanced – what you see is what you get. The upside to foam is they are more durable and thus maintain their shape and protection longer.
The girth is the equivalent of a western saddle's cinch; it wraps underneath the horse's belly and latches to the opposite side of the saddle. While the girth should be tight enough to prevent the saddle from slipping to the left or right while riding, it should not be taken to an extreme where actual discomfort is caused to the horse.
Although leather is still the most popular material of choice for both English and Western saddles, synthetics are quickly becoming popular due to their lightness and ease of maintenance and use. It took me a while to finally try out a synthetic saddle, but once I did it quickly became a favorite for training and general riding purposes. My synthetic was a Western (my English saddles are leather) style, so it was pretty darn convenient being able to rest the saddle easily on an outstretched arm… a difficult feat with my heavy leather Western saddles!
The stirrups consist of two parts: the stirrup irons where the rider's feet are inserted and the stirrup leathers, which connect the irons to the saddle. The leathers have notches punched into them, making their length adjustable such that they suit the rider's needs. Depending on the saddle and rider, you may need to punch a few of your own holes in the stirrup leathers before your first ride to ensure the fit is perfect.
One significant difference between Western and English saddles is that unlike a Western, many English saddles are not sold as a complete set. The girth, stirrup irons and stirrup leathers are generally purchased separately, and while this is not a real problem, it's something to keep in mind when putting an order in for a brand new English saddle.
Finally, although at first glance all English saddles look just about the same, it's important to keep in mind there are distinct types of English saddles, each suited to a specific purpose. Read our article Different Styles Of English Saddles to learn more about the various English saddles.