I have always found Vernier scales fascinating. It’s a bit of a challenge to use them these days with older eyes, but I do keep a proper Vernier caliper in my shop.
A few weeks back I purchased a new rotary table for a project I’m working on and was surprised to find that the dial has a Vernier scale to allow you to rotate a part as little as 10 seconds of arc.
When I started messing around with it, I was amazed that even a minute of arc appeared to not move a thing–after a bit of calculation it was clear why: 6" table * pi / 360 is just over .050" per degree, so dividing that by 60 minutes results in less than .001" per minute at the edge. I’m not even going to bother using the Vernier seconds scale.
Yes. The prof was trying to get across to the first generation of calculator/home computer kiddies that just because a computer can tell you the answer to 8 digits does not mean the answer is meaningful. A slide rule jockey might be more aware of how many significant digits (s)he’s working with and what they mean, but people used to plunking numbers into a box and copying the 8-digit answer may be less attuned to this detail - even if they wrote the program themselves.
Except in this case, even though eccentricity can’t be negative, the “negative eccentricity” case was actually meaningful: That is to say, you can smoothly change the real-world situation in such a way as to decrease the eccentricity, and you can continue that that smooth case until the eccentricity reaches zero, and then you can continue smoothly changing the situation in the same direction, further than that. In the process, you pass through a coordinate singularity, but it’s not a true singularity.
The real lesson to take away here is that you always need to understand what your numbers actually mean, and not just blindly apply any sort of statistical technique.
I still have the vernier caliper that I bought when in grad school. It’s in my desk drawer, and I still use it constantly. The fake leather case, though, is falling apart.
My primary Vernier is a Craftsman from 1973. It still has acceptable accuracy. I got one when my father passed away and it is from 1944. He got it when he was servicing PBYs during WWII. It is slightly less accurate, but good enough.
I’ve seen some in a lab that could measure to a fiftieth of a millimeter. It’s astounding to me that you can get that kind of precision by just sliding a couple of pieces of metal against each other and looking at them by eye.
But yeah, you can’t count on students knowing how to use one. Whenever I’ve taught a lab that involved using them, I’ve always led off with a mini lesson on how to read one.
As to how you get a logarithmic scale rather than a linear scale, it’s probably true that slide rule manufacturers just looked up the logarithm from a table and marked the scales that way. But another way is to plot a graph with the squares of numbers (x=1 y=2; x=2, y=4; x=3, y=9; etc.) and then draw down the x value from the y value, so you mark at what point of x that y equals 3, 4, 5, etc. Any parabolic function should give you a logarithmic scale.
In one of the photos of the weird dividing engine I posted above you can see straight lines inscribed on one of the cams, so it is plausible that someone consulted a table of logarithms at some point, although there is obviously a bit more to it than mere low-res eyeballing.
It is an interesting exercise to try to work out by hand the logarithms of (let’s say) 1, 2, 3, 4, 5, 6, 7, 8, 9 out to a few places— you start to figure out some tricks. But, from the Wikipedia article on Gaspard de Prony:
Sorry if I missed it upthread, but IIRC when I was growing up in the Midwest, there was a commercial on TV that mentioned one. I think the message was that kids should stay in school. A guy from the electric company is talking to teens and mentions a slide rule. One teen asks, “What’s that?” He replies, “If you’d stayed in school, you’d know.”
I kinda wish I’d learned to use one…they’re like secret decoder rings to me. I suppose that the miraculous TI-30 made them obsolete.
I wish I was! But I’m not related by any line I can trace, and Napier isn’t my real name.
I have to admire somebody who invented logarithms and got almost all the way to inventing slide rules, but made a bigger name for himself writing pamphlets claiming the Pope was the Antichrist. My kinda guy.
I have a couple of Concise circular rules and while perhaps not having the same sense of luxury as a bamboo slide rule from Hemmi, they’re still decent. I’ve not tried to order directly from the company itself so I don’t know what would happen if people from outside of Japan tried to buy one.
At least until a few years a go, Faber Castell still had unsold stock on hand and you could buy them. I think they either finally ran out or just got tired of hanging on to them.
One of the things that fascinates me about slide rules is how quickly they were obsoleted. Keuffel & Esser celebrated their 100th anniversary in 1967 with a press release stating the following:
We are proud to have shared this exciting century with all members of the technical professions we serve–a working partnership we hope continues for another 100 years.
They stopped making slide rules within a decade and hung on selling paper products for another decade before they were bought out.
My mistake, I thought that was an exponential function. But same principle, plot the curve and then mark the axis corresponding to the logarithmic scale.
Something fascinating that become obsolete even faster and more completely than slide rules: Edge-notched cards, a way of doing basic sorting and database search functions completely mechanically using index cards. Made utterly obsolete by the introduction of digitized databases. http://www.projectrho.com/public_html/rocket/astrodeck.php#id--Computing--Edge-notched_card
A common mistake. A power law is x to some power: x^2, x^3, etc. An exponential has some other number to the power of x, such as 2^x, e^x, or 10^x. Exponentials grow much faster than power laws: If you take any power law at all, even one with a very large exponent, and any exponential with a base bigger than 1, the exponential will eventually overtake the power law.
That’s a long-lost memory! I had to use those types of cards as an undergraduate in the 70s. Our ethnology library used those and they actually came as part of a subscription service, so we got new, pre-notched cards to add every few months. Depending on how loosely the cards were packed, you could sort on up to six criteria at once. Putting them back was a bitch.
While slide rules may be hard to find, there are quite a few watches that have circular slide rules incorporated into the dial. But, of course, while the idea of being able to calculate things with the turn of a dial on the wrist may seem useful, in the days of everyone carrying around powerful computers in our pockets, the slide rules on watches usually end up getting about as much use as a real slide rule would.