QUESTION: I wonder if you could help me with a concept. For the past month I’ve been trying to learn the slide rule. Haven’t touched one in almost 45 years probably, but it’s fun to relearn it all. I’ve got several rules, and am working not with a K&E 4080-3 log log trig rule using the KE manual. (I’ve become quite hooked on this, even joined the Oughtred society!) I’m on the log log scales now. This rule has LL1, 2, and 3 and LL01, LL02, LL03. I’m doing pretty well figuring it out, but one portion of the manual (I’m determined to get through it and do every problem) has me confused after staring at it for two days. The author is trying to get us to visualize the LL scales laid out end to end, with three LL scales attached, and directly opposite them the three LL0 scales strung end to end, and between them a long C scale. So far so good. Here’s a copy of the offending page. I am lost as to why the example he gives would require 4 hypothetical end-to-end C scales rather than three. Can you perhaps give me a clue as to what he’s getting at? I’m also confused about the statement relating to the 4 hypothetical C scale coverage, from.1 to 1, 1 to 10, 10 to 100, and 100 to 1000. Why? Thank you very much.
ANSWER: I will try to answer your question to the best of my ability! The main concept of LL scales is that they aren't "cyclical." (for lack of a better term). The regular scales of a slide rule are "cyclical" in that if you were to extend them, they would basically form a repetitive scale. This is one of the amazing properties of the logarithm. So you can get a lot done without multiple log scales. For example, you don't need C, C2, C3 etc. A simple C scale will do. However Log-Log scales don't have that property. As a result, you actually need a very long slide rule to have a usable Log-Log scale. And the way of making a long scale short, is to break it down into pieces. On my Pickett N3, there are four scales, and they allow calculations up to about 20,000. Also, take a look at the following link on my site: http://www.antiquark.com/sliderule/sim/sr-calcs-by-example.html#mozTocId398379 It explains how to use LL scales, and the technique needed to switch to other scales. Switching scales is based on a property of exponents. I myself have found that running through examples, gives an intuitive understanding of slide rule operations.