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I have never heard of someone carrying a saddle in a bag. I think most horse saddles are too heavy and 3 dimensional to fit in a bag of this size. I wonder if the article has confused it with a saddlebag? I think the name in French would translate as something like a "dispatch bag", which sounds very much like a "saddlebag", not a bag for a saddle. --AJim (talk) 04:41, 28 July 2013 (UTC)
As the article says, when the bag was used for carrying a saddle, it was much larger than it is now. Valerie Steele says it was "originally a large a bag for holding a saddle". This seems to be quite contentious, as it was also noted at Template:Did you know nominations/Kelly bag. It turned out that there is such a thing as Saddle Carrier. For what's worth, Steele is supposed to be a highly respected expert on these things and saddle carriers are not so unheard of. Surtsicna (talk) 09:34, 28 July 2013 (UTC)
Rereading the article, I see that the Kelly bag was derived from a redesign of the original bag, so it appears that there were at least 3 steps in its evolution. The Kelly bag was apparently derived from a design called a "Sac à dépêches", which, as I noted, appears to mean something like a dispatch bag, which I think of as something more like what we commonly call a "messenger bag" these days. Perhaps the intermediate Sac à dépêches design was derived from a saddle carrier. European saddles are, after all, smaller than the Western Saddles in shown in the link above. If this story is to be credited, then I imagine that the woman the original design was created for was an avid horse rider who often carried her saddle around with her. Is there any evidence of that? Also, I still think an evolution from what we call a "saddlebag" to a "dispatch bag" (Sac à dépêches) is more plausible than an evolution from a "saddle carrier" to a "dispatch bag". --AJim (talk) 18:43, 14 August 2013 (UTC)