1. This is a most unusual,  indeed unique, rule. Whilst it has basic slide rule scales (A, B, C and D) its main feature is the use of scales for dimensional analysis. The uses of the rule are:

• Checking equations dimensionally
• As an aid to recalling formulae
• As an aid in deriving formulae
• For performing numerical calculations.

2. The rule uses four basic dimensions: Length, Mass, Time and Electric charge. It is based on the MKSC (metre, kilogram, second, coulomb) system of units.
3. The basic method is to move the rule as if you were "multiplying" or "dividing" dimensions and then reading the result. For example to check that:

   resistance * charge / inductance = current

Push the hairline to R (resistance)
Draw L (inductance) on the U scale under the hairline (as if you were dividing)
Push the hairline to Q (charge) on the U scale (as if you were multiplying)
Under the hairline read I on the V scale.

4. The rule has the dimensional equivalents of inverse and squared scales for units which are raised the equivalent exponents (-1 and 2 respectively).

5. The rule was introduced toward the end of the slide rule era so whether it would have become popular or not we will never know. In fact less than 1000 were actually put into circulation. My personal feeling (and I have never handled an Analon) is that the rule is an ingenious device and for someone used to using a slide rule it could demonstrate the way different units can be combined.  On the other hand the arrangement of the marks for the dimensions is artificial and would not help the understanding of many students.

My thanks to John Mosand for the providing scans of the rule.

Thanks to Michael P S O'Leary who uploaded the files.