Why L? -- the log scale explained
Вставка
- Опубліковано 20 вер 2024
- The L scale is often discounted by modern users who don't see much need to find common logarithms. In this video I show how base-10 logs can be used to simplify otherwise intractable calculations.
Slide Rule Playlist (starts with basic videos):
Playlist: • All Slide Rule Videos
I remember the 6 foot slide rule our teachers had attached to the walls at John A O'Connell vocational/technical high school in 1960 San Francisco. Still have my slide rule.
3:00 I was playing around with my Teledyne Post 44BA-470 last night. It has a reversed logarithm scale like this one (and is indeed the direct successor made by Hemmi for Teledyne). Of interest is that if you flip the slide so that the S and T scales are oriented with the A and D scales, that reversed log scale can be used in the NEGATIVE to find the logarithms (log-base-ten) of decimal numbers between 0.1 and 1.0, thus 2 on D --> 0.699 on L; read as log (0.2) = - 0.699
The advantage of this is that all other positive numbers less than 1 can have their logs (base ten) determined by the usual trick of subtracting 1 from the log for every division by ten, i.e. every zero between the decimal point and the first non-zero figure. This comes in handy when you're trying to take the nth root of a number 0 < x < 1.0 and you want to directly convert that pesky negative mantissa rather than pulling the old log-tables trick of keeping the mantissa positive but putting a bar over the characteristic (very, very messy).
Naturally if you have a slide rule with a proper, left-to-right oriented L scale and a CI or DI scale on the same side as the rule, this trick is also possible at a glance without losing your B and C scales, and I have a Hemmi with a Reitz scale set which does just that.
Slightly OT, but since you did mention DMS: It's bizarre that some of the last slide rules ever made continued the DMS angle scales right to the end, when almost everyone else had long since gone over to deci-trig. Perhaps there was a perceived market for this model among sailors and other navigators for whom it was still more pertinent, if only just. This was, after all, the era when there were still three people in most airliner cockpits; air navigators would have had to learn the basics in training before being let loose on the fancy new systems, and a light, cheap slide rule would be an asset here.
Great insight! Because of the reversal it's essentially like using L with CI/DI. I don't mention it, but you can also read the L of this rule when it's on the reverse side at the indicator against the CI scale at the index of D.
I've made a new video with a technique I've been using for some time now when dealing with negative logarithms. I find it's easiest to simply interpret the log scale backwards instead of changing the solution technique in this situation: ua-cam.com/video/DRZin_OkDh0/v-deo.html
Nice video, it helped me a lot, thank you :-)
I'm glad it was useful, Gustaf. Let me know if you have any suggestions for future videos.
I have some ideas. First is M scale used for solving triangles, but I'm afraid that this scale is specific to communist bloc as I saw only on one slide rule (polish Skala SLPP) and manual says that this method was patented by polish engineer in 1957. My other ideas are slide rules with addiators or maintenance and restoration of slide rules.
Thanks! I'm curious about the M scale. I'll look into that when I get back from vacation. I don't have any slide rules with one. Maybe it's related to the P scale.
By the way I hope you have a nice vacation ;-)
Intriguing! In physical format it looks a little like the differential trig. scales on some Thornton rules except shorter.
Am I correct Professor that the Pickett N4 is the only rule to use log log scales to base 10 ?
The N4's predecessors the Model 2 and the Model 3 (Not the N3) also use base 10, but they're the only ones I've ever seen.
so annoying, in Asia I cannot find any cheap "used" or new slide rules
americanswan What part of Asia are you?
I dont know where americanswan is, but Im in the Philippines and I have the same trouble. Took me two years to find a Ricoh 550...
Ebay, y'all. It's worldwide. And if you have something that you really really want but they won't ship it international I don't mind forwarding it along to you. Hmu.