This is a Comptometer Model E mechanical calculator, made between 1913 and 1914. Comptometers were made starting around 1900 and were a direct competitor to the 1908 Burroughs adding machine I featured earlier.
The Comptometer had a superior design. Pressing a key immediately updated the register, no need to pull a lever (the lever here clears the register). This design was so effective it stayed essentially the same (with minor improvements on error prevention) through the `50s.
You can perform many calculations surprisingly quickly and w/ one-hand. A well-trained Comptometer user was probably as fast as you'd get until electromechanical calculators. Here I'm calculating 1024 x 768, which just requires pressing 768 a few times and shifting left.
Subtraction was weird. You'd subtract w/ addition by the complements method, but would first subtract one from the number, then press down that number using the small digits on each key. You also slide the correct metal tab at the bottom to stop the carry. Here's 9 - 2.
Division was possible via repeated subtraction starting from the left and shifting to the right. There were no underflow bells, you'd just have to know when to stop subtracting a row. This is hard to do one-handed so I didn't film a video of that.
Experts would only use the bottom rows so their hand was stationary. To enter larger numbers they'd enter two smaller numbers so to enter an 8 they'd enter 4 two times. This and later models had features to catch "fat finger" errors and partially-depressed rows.
To close out this thread, here is correspondence between Felt himself (the inventor of the Comptometer) and Zenith Pub. Co.
Even though I have more "advanced" mechanical calculators like my Monroes, the more I use this Comptometer the more impressed I am at the design. It's actually faster to use than my Monroes, at least for addition and multiplication.