What about Rifleman the TV show, wasn't the guns a little to modern for that suppose time it was taken.
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Living in Texas have visited the Alamo a time or two. On one such visit, I saw what was alleged to be the rifle that Crockett used at the Alamo. It was about 4-41/2 feet long percussion not flintlock. Plus, it appeared to be .32 caliber. A kids' rifle, in other words. Nothing Crockett would have been carrying at the time. I managed to upset the guide by pointing this out. I managed to further anger said guide by pointing out that a short 'artillery' sword labeled as having been carried by Mexican troops, was actually a 'wasp waist' Roman gladius. I was told that if I wasn't happy with the exhibits that I really didn't need to comment on then.
Not trying to be ugly here, but...
1. Actually, many smaller-caliber guns WERE carried at that time, as the more finely-refined powder allowed equal ballistics with smaller projectiles.
2. I am not familiar with which of his guns Crockett carried in the final defense of the Alamo, but he DID have what is believed to be a percussion rifle presented to him in Phiadelphiia as they had been around for about three decades by that point. This one was NOT with him in defending the Alamo but another one being in DC's possession or usage might not be out-of-line, given his status (much of which came about after his death, it appears) and resources.
3. Starting with the Napoleonic Wars, French artillery non-com's swords very commonly were patterned on old Roman designs. (My best friend in college in 1976 had one exactly like the one you describe that was picked up off the battlefield at Waterloo in 1815...)
Since the French had the rep throughout the first 60-70 years of the 19th century for having the best weapons, everyone, Mexico, U.S., etc.,copied them, all the way up into the WBTS. DGW used to carry the American artilleryman's sword of similar design. I have seen Confederate naval cutlasses also modelled on Graeco Roman patterns.
You might be glad the ranger DIDN'T "know. their stuff..."