# Slide rule manufacture **URL:** \ **Category:** Factual Questions\ **Created:** [July 27, 2021, 8:56pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454 "2021-07-27T20:56:35Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![minor7flat5](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/minor7flat5/32/258_2.png) [@minor7flat5](https://boards.straightdope.com/u/minor7flat5)\ **Post date:** [July 30, 2021, 12:25pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/41 "2021-07-30T12:25:16Z")
> [@ZonexandScout](#): > > I’m surprised that nobody has mentioned the slide rule’s distant cousin, the Vernier caliper, yet. The construction methods are pretty similar, though they serve very different functions. Of course, I’m thinking of a real Vernier and not one of the dial or digital models. I had to learn to read Vernier scales when I was in shop class in junior high and I’m actually a bit shocked that so few people can use one accurately. 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](https://www.penntoolco.com/phase-ii-precision-rotary-table-h220-006-6-horizontal-65-220-006/) 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. ---
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [July 30, 2021, 12:47pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/42 "2021-07-30T12:47:50Z")
> [@DPRK](#): > > …which is why the professor was teaching you about the condition number of a matrix and how to deal with it. All that error analysis stuff would apply to slide rules as well, for that matter. 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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 30, 2021, 1:50pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/43 "2021-07-30T13:50:31Z")
> [@DPRK](#): > > If the parameter is constrained like that, you are supposed to quote a (correctly calculated) confidence interval, which will naturally not include any negative numbers, not merely an uncertainty. > > Example: your variable is Poisson-distributed and you observe 0 events. Then the 95% confidence interval for the mean number of events is [0.00, 3.09] 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. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [July 30, 2021, 2:02pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/44 "2021-07-30T14:02:49Z")
> [@minor7flat5](#): > > 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. 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. ---
**Author:** ![ZonexandScout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zonexandscout/32/544_2.png) [@ZonexandScout](https://boards.straightdope.com/u/ZonexandScout)\ **Post date:** [July 30, 2021, 2:06pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/45 "2021-07-30T14:06:37Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 30, 2021, 3:10pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/46 "2021-07-30T15:10:49Z")
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. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [July 30, 2021, 4:05pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/47 "2021-07-30T16:05:00Z")
And don’t see a hijack at all and love the way the manufaturer has put the notch for **π** inside the symbol to save space. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [July 30, 2021, 5:18pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/48 "2021-07-30T17:18:53Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 30, 2021, 5:21pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/49 "2021-07-30T17:21:48Z")
No, that’d give you a square-root scale. To get a log scale, you’d need to start with an exponential function. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [July 30, 2021, 9:47pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/50 "2021-07-30T21:47:32Z")
> [@Lumpy](#): > > 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. 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: > [@](#): > > In 1791, de Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre. The effort was sanctioned by the French National Assembly, which, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. In particular, his tables were intended for precise land surveys, as part of a greater cadastre effort. The tables were vast, with values calculated to between fourteen and twenty-nine decimal places. > > Inspired by Adam Smith’s _Wealth of Nations,_ de Prony divided up the labor into three levels, bragging that he “could manufacture logarithms as easily as one manufactures pins.” > > The first level consisted of five or six high-ranking mathematicians with sophisticated analytical skills, including Adrien-Marie Legendre and Lazare Carnot. This group chose the analytical formulas most suited to evaluation by numerical methods, and specified the number of decimals and the numerical range the tables were to cover. > > The second group of lesser mathematicians, seven or eight in number, combined analytical and computational skills, and this group calculated the pivotal values using the formulas provided and the sets of starting differences. They also prepared templates for the human computers, and the first worked row of calculations, as well as the instructions for the computers to carry the sequence to completion. > > The third group consisted of sixty to ninety human computers. These had no more than a rudimentary knowledge of arithmetic and carried out the most laborious and repetitive part of the process. Many were out-of-work hairdressers, because, with the guillotining of the aristocracy, the hairdressing trade, which had tended the elaborate hairstyles of the elite, was in recession. ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [July 30, 2021, 11:07pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/51 "2021-07-30T23:07:31Z")
@Napier, seeing your user name in this thread made me wonder. Are you related to [John Napier](https://en.wikipedia.org/wiki/John_Napier)? ---
**Author:** ![E-DUB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/e-dub/32/403_2.png) [@E-DUB](https://boards.straightdope.com/u/E-DUB)\ **Post date:** [July 30, 2021, 11:19pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/52 "2021-07-30T23:19:06Z")
They do make a comeback in the twenty-third century. [https://ratcreature.dreamwidth.org/374430.html?thread=2007198](https://ratcreature.dreamwidth.org/374430.html?thread=2007198) ---
**Author:** ![lobotomyboy63](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lobotomyboy63/32/2900_2.png) [@lobotomyboy63](https://boards.straightdope.com/u/lobotomyboy63)\ **Post date:** [July 30, 2021, 11:21pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/53 "2021-07-30T23:21:32Z")
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. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [July 31, 2021, 2:16am UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/54 "2021-07-31T02:16:25Z")
> [@74westy](#): > > @Napier, seeing your user name in this thread made me wonder. Are you related to [John Napier](https://en.wikipedia.org/wiki/John_Napier)? 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. ---
**Author:** ![Tabco](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tabco/32/7644_2.png) [@Tabco](https://boards.straightdope.com/u/Tabco)\ **Post date:** [July 31, 2021, 3:13am UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/55 "2021-07-31T03:13:33Z")
I forgot to mention that there still might be at least one company producing slides. [https://www.sliderule.tokyo/products/list.php](https://www.sliderule.tokyo/products/list.php) 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. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [July 31, 2021, 4:13am UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/56 "2021-07-31T04:13:08Z")
> [@Chronos](#): > > No, that’d give you a square-root scale. To get a log scale, you’d need to start with an exponential function. 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. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [July 31, 2021, 4:24am UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/57 "2021-07-31T04:24:48Z")
> [@Tabco](#): > > One of the things that fascinates me about slide rules is how quickly they were obsoleted. 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](http://www.projectrho.com/public_html/rocket/astrodeck.php#id--Computing--Edge-notched_card) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 31, 2021, 1:00pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/58 "2021-07-31T13:00:37Z")
> [@Lumpy](#): > > 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. 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. ---
**Author:** ![ZonexandScout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zonexandscout/32/544_2.png) [@ZonexandScout](https://boards.straightdope.com/u/ZonexandScout)\ **Post date:** [July 31, 2021, 1:17pm UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/59 "2021-07-31T13:17:30Z")
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. (End hijack.) ---
**Author:** ![WatchMe](https://avatars.discourse-cdn.com/v4/letter/w/8797f3/32.png) [@WatchMe](https://boards.straightdope.com/u/WatchMe)\ **Post date:** [August 1, 2021, 4:06am UTC](https://boards.straightdope.com/t/slide-rule-manufacture/947454/60 "2021-08-01T04:06:10Z")
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. [Previous page](https://boards.straightdope.com/t/slide-rule-manufacture/947454.md?page=2) [Next page](https://boards.straightdope.com/t/slide-rule-manufacture/947454.md?page=4)