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Bill Houghton, Sebastopol, CA
>Most speed reducers are some form of jackshaft, in which you have an intermediate shaft, running on bearings (pillow blocks, which are bearings in castings that can be bolted to a surface, are commonest), between the lathe and the motor, with appropriate pulleys to reduce the speed (or increase it, but that wasn't your question).
For instance, imagine transferring the pulley on the motor to an intermediate shaft, then putting a 4" pulley on the intermediate shaft, in line with a 2" pulley on the motor. You'd drop all your lathe spindle speeds by, if I recall the math correctly, 50%. Most often, you want a pulley set that allows you to match your existing speeds and have at least one lower range.
Have a look at the article below. Then go to your local library and look through the machinery-related books (machinist's books probably best) until you find more detail on the principles of power transmission. A more visual way to understand it is to go to Sears and look at their 12- and 16-speed drill presses - they use an intermediate shaft, although they fudge and use one pulley in the middle, meaning you have to juggle belts around above and below each other to get your speeds. The principle's the same, though.
Then, if you're a little intimidated by the principles or the hardware requirements, try to find a smart guy (male or female) in a good hardware or industrial supply store, explain what you're trying to do, and ask for some help in putting together the hardware.