The gun might actually be a Model 1908 chambered in .380, rather than the Model 1903 chambered in .32 ACP, but the latter is the original design and seems a bit more likely.
Seeing this photo, reminded me of Mark Twain’s comments on handguns in Roughing It (1872):
[Travelling West from St. Louis to Nevada:]
I was armed to the teeth with a pitiful little Smith & Wessonâ€™s seven-shooter, which carried a ball like a homoeopathic pill, and it took the whole seven to make a dose for an adult. But I thought it was grand. It appeared to me to be a dangerous weapon. It only had one faultâ€”you could not hit anything with it. One of our â€œconductorsâ€ practiced awhile on a cow with it, and as long as she stood still and behaved herself she was safe; but as soon as she went to moving about, and he got to shooting at other things, she came to grief. The Secretary had a small-sized Coltâ€™s revolver strapped around him for protection against the Indians, and to guard against accidents he carried it uncapped. Mr. George Bemis was dismally formidable. George Bemis was our fellow-traveler.
We had never seen him before. He wore in his belt an old original â€œAllenâ€ revolver, such as irreverent people called a â€œpepper-box.â€ Simply drawing the trigger back, cocked and fired the pistol. As the trigger came back, the hammer would begin to rise and the barrel to turn over, and presently down would drop the hammer, and away would speed the ball. To aim along the turning barrel and hit the thing aimed at was a feat which was probably never done with an â€œAllenâ€ in the world. But Georgeâ€™s was a reliable weapon, nevertheless, because, as one of the stage-drivers afterward said, â€œIf she didnâ€™t get what she went after, she would fetch something else.â€ And so she did. She went after a deuce of spades nailed against a tree, once, and fetched a mule standing about thirty yards to the left of it. Bemis did not want the mule; but the owner came out with a double-barreled shotgun and persuaded him to buy it, anyhow. It was a cheerful weaponâ€”the â€œAllen.â€ Sometimes all its six barrels would go off at once, and then there was no safe place in all the region round about, but behind it.
Mark Twain (1835-1910) lived, of course, through the percussion era when obsolete and inaccurate Allen & Thurber pepperboxes were still carried by the ill-advised, right down to the modern world of semiauto pocket pistols of John Browning’s design.