Add-O-Matic Adding Machine circa 1937
Made by Allied MFG. Co. Chicago
The Add-O-Matic Adding Machine is a large chain adder with an automatic tens carry and a unique setting entry mechanism. A slider is moved to the number desired, then the brass button is depressed -- which engages the chain running beneath -- and dragged downward to add the number to the result.
Here's a blurry video of the Add-O-Matic in action (note: audio lags video by several seconds)