The briefcase-sized computer with dials that Mauchly is carrying around is interesting. It's an analog computer for solving scheduling and flow problems, i.e. finding the critical path. The arrows show dependencies, and you turn a knob to set how long a task takes. The computer computes the critical path and the float (slack) time. It's implemented as a corresponding network of voltages sources and diodes, where the voltage at a point indicates time. A plotter creates a time graph as output. The computer is programmed through a plugboard and cables.
This is described in patent 3250902, which is actually pretty clearly written.
This is described in patent 3250902, which is actually pretty clearly written.