Otto Wolff/Arthur H. Thomas Co. Variable Resistor
This is a variable resistor, also known as a "resistance box" or "potentiometer," and is used as a standard-value resistor for teaching, circuit prototyping, or lab work. By inserting the brass pegs into the holes separating the brass blocks, one can change the resistance between the input screw (on the back) and one of the outputs (labelled "I" and "II") on the front.
Interestingly, this resistance box functions very differently from the standard design. Normally, a resistance box is made up of a single line of brass blocks, each connected to the next by a precise resistor. By inserting a low-resistance brass peg between two blocks, one allows the current to flow to the next block through the peg rather than the resistor, decreasing the overall resistance of the circuit. However, in this resistance box, rather than decreasing resistance, inserting pegs merely decides which resistor the current flows through. This greatly limits the variety of resistance values which can be achieved, and it is unknown why this resistance box was designed in this way.
This instrument was made by Otto Wolff, a German manufacturer specializing in standard resistors. It was imported into the US by the Arthur H. Thomas Company, the scientific instrument manufacturer which would go on to become the lab equipment giant Thomas Scientific.