More Fun with Slide Rules

published 2025-10-06

by Christopher Howard

I have continued my exploration of the slide rule with my Pickett N-16-ES. Having worked out basic multiplication and division, I then explored main

powers, using the Log Log scales
trigonometry problems using the T scale

The fundamental ideal behind the Log Log, or LL, scales is

x^y = x^y

log(x^y) = log(x^y)

y log x = log(x^y)

log(y log x) = LL(x^y)

log y + LL x = LL(x^y)

Also, the different LL scales (LL1, LL2, LL3) are each a factor of 10 apart, so that you can multiple or divide by ten, just by moving up and down the scales. This is often useful when a problem does not fit inside a scale. E.g., 2^12 can be re-written as (2^1.2)^10, which means you can solve 2^1.2 with LL2 and the C scale, them move that answer up to the LL3 scale.

In regards to trigonometry, something that threw me off is that the T scale is inverted on the N-16-ES compared to the traditional T scale. The T scale, compared to the C scale, will give you tan(θ). But on the N-16-ES, you have to think of it as

T = 1 / tan(θ)

The effect of this, in solving right angle problems, is to reverse some actions. E.g.

tan(θ) = opp / adj

becomes

T(θ) = adj / opp

I thought it ways interesting to see, on the Internet, that some slide rules had common conversion factors marked out on a scale, e.g., inches to centimeters, lbs to kilograms, and so forth. Something that sounds useful would be a small, compact circular slide rule, with just log scales, and a bunch of conversion factors marked out on one of the scales.

Copyright

CC BY-SA 4.0 Deed