Nothing beats a good mechanical computer. Gets interesting at 1:46.

via Mechanical Computer (All Parts) – Basic Mechanisms In Fire Control Computers – YouTube. via .http://www.evilmadscientist.com/2013/analogmech/

Mechanical multiplier (explained in above video @ 35:50)

Disk Type Integrator… looks complex but check out the above video @ 30:55 for a simple explanation.

I love those analog computing methods. So beautiful and direct. Despite the complexity of the gearing and the true tragedy was that they were all victims of ‘backlash‘ which can corrupt the final output’s precision. Although in these examples we’re talking about old school military computers used for calculating artillery trajectory – and a few millimetres either way… it still goes boom.

Lots more info here as well: Mechanical Computers