Scales (Slide Rule): Difference between revisions

The LL scales are unique in that they do not wrap around on themselves, and instead have a set decimal place present directly on the scale. They are most commonly seen on Duplex style rules, with one notable exception being Darmstadt system rules, which also uniquely have LL scales on the slide rather than the base of the rule.  LL scales usually come in groups of either three (LL 1,2,3 and their inverses) or in groups of four (LL 0,1,2,3).  In both cases, LL3 is considered the "base" scale, with its lower index showing the base of the logarithmic relationship it has -- usually e, though in rare cases 10.  The LL scales are set up in such a way that exponents can be easily found for any number. This is because any arbitrary exponent x^y = alog( y log(x) ), which just becomes a multiplication read from the LL scales.  A good example here is as follows: