It’s not generally known, but there were mechanical computers long before there were electronic computers.  The Babbage engine is well known, even though Charles Babbage never completed a difference engine in his life.  The Babbage engine was not an isolated machine.  There were many other machines built to do a multitude of different jobs.

Here’s the wiki on the difference engine.

http://en.wikipedia.org/wiki/Difference_engine

The page form the computer museum, which has one of the two competed machines.

http://www.computerhistory.org/babbage/

A video.

Here are two tide predictors the NOAA used in the 19th and early 20th Centuries.

http://tidesandcurrents.noaa.gov/predma1.html

http://tidesandcurrents.noaa.gov/predma2.html

Engineer Guy explaining a mechanical computer.

How a fire control computer on a US Navy Battleship.

A mechanical calculator.

It’s amazing what can be done with gears, pulleys and levers.