It finds the derivative: The Ott Derivimeter (1930s)
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- Опубліковано 10 лют 2025
- The Ott Derivimeter, an instrument for finding the derivative of a curve drawn on paper. Sold by the Ott company in the early 20th century, though I don't know when mine was made.
This is episode 84 of my video series about old calculating methods.
OTT Hydromet company history video: • OTT HydroMet Celebrate...
Chris Staecker webarea: faculty.fairfi...
#calculus #elsa
I like your dating investigation.
“Found this photo from 1942. So it could be from the 40s, or earlier! Or later too!”
🤣
if it's not from the 40s, could be from earlier, later or neither
It would be a derivative...
@@OGMann Things were changing so rapidly back then. Let's figure out how fast!
He actually said "This one could be from the 40s, or 30s, or even before! Or after, I guess"
The 'after' is referring to the 30s.
I never knew until today that I'd watch a video that included math, antiques, precision measuring equipment, and "Lady, I think you better come back to my place" all in the same video. That's range. Definitely subbed. I didn't even know they were called derivimeters.
I worked in an instrument workshop (hydrography) and serviced Ott chart recorders, beautiful accurate machines
That’s ott.
0:12 "spinny roundy thing" -- that got a huge smile out of me
wait til the gnomon bros hear it…
Clear, concise, accurate
"Look the round things!"
"I love the round things"
"What are the round things...?"
i'd smile if it was "thingy" too :)
Technology connections fr
Great stuff. Old-school bits rooted in reality are great fun. Subscribed. Thanks.
On the topic of Verniers on non-linear scales, there's a really slick trick you can do with a slide rule (source: "Utilizing the Vernier Principle for Precise Readings of Slide Rule Settings" by Roger Wickenden).
The trick is that the log scales on the slide rule are locally linear, so if you line up the right index on the C scale with 9 on the D scale, the C scale can act as a Vernier anywhere else on the D scale (you can do the same for subdividing by 5, 10, 100, etc.).
Makes me think that good ol' Gerb's Variable Scale would be really useful for adapting Vernier readouts to any graduated markings!
Very interesting- I'll look into this. I recall seeing a patent for a Vernier-like trick for use on log scales- maybe it's a similar idea.
I was going to make a pithy comment about the derivimeter's Vernier scale, but yours is far more informative and elegant. Thank you. 🙂
I can imagine using the tangent sum identity to make something that works like this but for tangent, though the identity is more complicated, so it would be less elegant.
Unfortunately the google search turns up an article whose "meat" is behind a $40 paywall.
Well, it's a German instrument from the '30s, so more than likely at least a few calculations related to the angle of London from mainland Europe or perhaps the slope of someone's forehead were made with an instrument like this.
yeah I decided not to get into it, but well said
This remarkable gift for building fine instruments like Curta machines saved Curt Herzstark's life in Buchenwald.
Great to see two commercial derivimeters and great to see somebody demonstrating the prism approach. Concerning your question: The prism derivimeter is described in the paper "Der Prismenderivator und der Differentio-Integraph" von E. von Harbou in "Zeitschrift für angewandte Mathematik und Mechanik", volume 10, number 6, december 1930. As far as I see, this is the published version of the author's doctoral thesis at Königsberg. In the paper, the author in particular makes a series of experiments that supposedly shows that the prism derivimeter is superior to the one with mirror. The author employs the derivimeter in a machine that plots the derivative of a function as a whole. He sees the main application in ballistics and refers to Cranz, Lehrbuch der Ballistik, part 3.
Yes I’ve read the paper (some of it at least- I don’t read German). Can you tell if it was ever a commercial product?
Drawing the perpendcular with a T square after the mirror would introduce error. It'd be better to just use the fact that the perpendicular will have the negative inverse slope. So if the mirror/normal line has slope -5/4, then the tangent will have slope 4/5. But it makes sense that you didn't use that in the video, because it would have been a ..... tangent
Yes- totally right. The indicator on the Gerber actually points perpendicular to the tangent line, but the scale is inverted like you say so it all works out fine.
I'm so glad I found this video channel. As someone who has struggled greatly with maths like Calculus these videos and explanations greatly help.
i love how this works. using the mirror is something i never would have thought of but once it was explained it seems so obvious!
These old precision instruments are outstanding. Wonderful craftmanship. Thanks.
With luck some of them will survive the inevitable demise of humanity and be helpful to whatever species takes over after us. We just have to store them well away from any subduction zones...
You could hand that over to quantum computing and they could build pyramids.
This is why I have notifications turned on for your channel.
This is the first video I got recommended by yt and it is a GEM. Instantly subscribed
@ oh boy you're in for a treat. This isn't even his best. It's like a B+ for him. Go through his catalogue of these videos, there's a playlist. And the freaking documentary he did on the Curta. Bro is a Nerd's Nerd.
@@LeoStaleyMy first time too! Aaaand your comment made me sub lol thanks 😅
This is the ONLY channel I have notifications turned on for. Chris is the best.
Young man, you do nice work. I hope you and yours have a happy, healthy, and successful New Year.
So, in this new year, just a few minutes ago I found your channel in this seemingly endless UA-cam rabbit-hole during my Trigonometry study at home! Subscribed. Loved it from India.
Rivals in their youth but now they're side by side as friends in my basement
Nice. Thanks for doing what you're doing.
I love nerdy gadgets almost as much as I love your delivery when explaining said gadgets. Keep up the ORIGINAL work!
Your explanation of the derivative: "it's a specific way of measuring how fast something is changing"
You can read completely all popular 1000 pages Calculus books and you will never find a better explanation of the derivative.
Your explanation is GENERAL, accurate, intuitive and beautiful.
Most Calculus books tend to explain the derivative by one of its infinite interpretations.
That's still an interpretation though. First and foremost it's the limit of the differential quotient.
Not to say this wasn't the best interpretation one can give.
The slope of the tangent line is really the only problem they were trying to solve. The fact that we model rates with lines is just a happy accident when it comes to that
"most calculus books expect you to do some calculus"
"It's easy bro! Just take lim ( ( f(x+h) - f(x) ) / h ) as h approaches zero! What's a limit? Why, it's just ∀ε ∃δ ∣ |x−c| < δ ⟹ |f(x)−L| < ε man! What the hell does that mean? Just figure it out man!"
The most intuitive way is drawing 3 lines: distance-speed-acceleration (quadratic-linear-constant)... No real math needed, most people just "get it"
A joyful beginning of 2025 with Chris' presentation of the Ott derivimeter! Never saw this one before, really neat and elegant, indeed!
This is such a cool piece of history! Never thought I’d see a device like the Ott Derivimeter. It’s crazy to think about how far technology has come. Sometimes, I wonder what it’d be like to have something like this back when I was struggling with derivatives. Thankfully, tools like SolutionInn have made learning math so much easier!
...ingenious simplicity of mechanical tools like this one never fails to impress me...:D
Computers didn't even really start to exit until sometime in the late '30s. Calculus originated with Newton and Leibniz in the 17th century, so there was a period of several centuries when analog devices like this were required to get the work done in any sort of consistent way.
I'm not sure if anybody would have bothered if they had computers, but then again developing computers required other means of performing the calculations just to design and build one.
@SmallSpoonBrigade ...many amazing things were made with slide rule scale alone. What amazed me about this differentitor is the idea of using mirrors to find the exact angle. So simple, but ingenious...:)
Man, I fucking love metrology.
Right thinking people do. You can tell they are right thinking, because they love metrology. Which is an acceptable definition, because eventually all dictionaries will result in circular definitions.
This is the first time I've seen your channel. I loved it. I never knew derivimeters existed, now I need one, and none are on ebay. Great video.
8:09 Didn't expect trying to woo Elsa with your TWO ~ORIGINAL~ derivimeters 🤣
gotta do somethin with all this game
game is game
Hey, math teachers go clubbing, too. 😎 (I actually gifted a goth math teacher some slide rules she wanted for her students to learn recently.)
@@BrianTRice77 AWWWW that's so sweet of you!!!!!!!!! 😭❤️ Also, I didn't think a goth math teacher would actually exist, I thought I'd be the only person in the world to dare to like both fashion AND math, HAHA
The slope never bothered her anyway. 😂
You gave me a better understanding of geometry in 10 minutes than my 10th grade teacher was able to do in a year.
Chris, your Ott has a serial number, perhaps the company has production records that can more accurately date its manufacture.
I think the rough engraved number I believe you are referring to would have been added and used by the university it came from for inventory and loan tracking purposes.
there's a finely done Number next to the maker's name...
It's German, of course there are records.
The Ott company probably knows when it was made and by who.
In some German and East German camera equipment of that era the year of manufacture is the first two digits of the serial number.
I appreciate the explaining of derivative. I was sick at the very beginning when we started to learn derivatives at school so I struggled with them all the time. On contrary, I understood integrals quite well.
Man, I love your delivery and presentation, so funny! I reckon YT suggested you to me due to all the math content I consume. A win, either way!
I like the prism even more for ensuring precision. Visually determining the smoothness of a curve is somewhat subjective. Line offset is obvious to within a fraction of a μm. So, hurra, prismderivinator!🎉 And hooray, Chris, for bringing us the grooviest gadgets!
This short video explains why I prefer the prism. ua-cam.com/video/ExUV3GOTDqE/v-deo.htmlsi=hVyD-smB0zLnF__3
Another banger mathematical device.
I try to make alot of the Mathematical devices on this channel.
You got me excited for greens theorm
I might 3d print a polar planimeter and attempt to combine it with a 3d printed derivameter and have the full range to do calculus on paper!!!!
A 3d-printed polar planimeter sounds amazing, and probably pretty doable.
This is great. youtube has done a great thing by giving people like you, really into cook, geeky stuff, a platform to educate and entertain. You ott to get more views :)
Cool instrument! I have an OTT pantograph. These guys were serious instrument makers-
Nice! Somebody (I think Ott?) actually made a "differentiograph", which was a pantograph-like thing that traces a curve but draws the derivative curve. Very fancy- I've never actually seen one.
@@ChrisStaecker for the sake of all things good in this world, please find such a device. I can barely begin to imagine how that would work and now that the idea is in my mind, I must see it!
@@ChrisStaecker Just reinvent it. Convert the slope to a linear distance with cams and tiny chains and move the detector and the result plotter across the sheet.
People used to use Teledeltos paper with contours drawn with silver loaded ink to create scalar field representations and then MEASURE the value with an electrical contact to determine the result from an XY input and possible additional input that was used to drive the contour lines.
Nifty. And thanks. I don't think that I've ever seen such a widget as this one. I have heard that there were many such mechanical ideas and devices around hard problems in the past; now we have computers and handheld calculators, some with built-in spreadsheets that might be viewed as gadgets to calculate many hard problems. Slide rules back in their day were also mechanical devices to work out hard problems. And slide rules still can, if you have one, just as the device in this clip demonstrates that it still can do calculus. For those of the 'computer age,' boggle, eh?
That’s a heartwarming narration. Thank you!
It occurred to me while you showed me more about math in 8 min than I learned in my first calculus class, that my teachers in high school were idiots THANK YOU SIR ❤
Please do not auto translate your channel. The experience on youtube is garbage (youtube wont let me see the original title of the video in english, no way to tell what language a video is until i click on it, because youtube gives no indication that the title is translated, auto translated title and description are often bad, cringe, and are always an annoyance when you speak multiple languages because, again, youtube provides no mean to show the original untranslated title and description).
Thanks for letting me know about this- UA-cam recently released some new language features which were default opt-in. I didn't know they would translate my titles & descriptions like that. I'll keep this in mind.
@@ChrisStaeckerY'know, as a native German speaker, I can say the translation is honestly not that bad. It's not perfect, there are some things that could've been worded better and made it sound less formal for a video like this. The auto-generated German audio track (which i've never used in my life until now) is also not bad at all. It does sound robotic and it speeds up and slows down sometimes to accommodate for the length of the original English sentences, but hey, it could've been worse. What irks me though is that these features are apparently opt-in by default and it seems like they put it in your videos without telling you. Like heck, there's apparently even a thing where you can choose from AI-generated responses to reply to comments instead of writing them yourself. Makes me kinda melancholic thinking about what other generative AI features UA-cam will introduce without telling us 🥲
Well they did notify us that it was happening. There was a (one-time) dialog when looking at YT analytics that I had to click on to accept the new defaults. But it was presented only as new features that viewers could use if they wanted- not new features that would become defaults for viewers. And it seems to be all-or nothing: if I disable it, then autotranslations will become unavailable, which seems a shame. Hopefully they’ll change the rules soon-
@@ChrisStaecker"Hopefully they'll change the rules soon." UA-cam has long worked by the logic of "better for us beats better for users" so it's fairly unlikely that it will change. We can hope though.
Wait, so is the audio in German and then Spanish for everyone? I thought I was losing my mind. I can't seem to get any other language in the audio track. The closed-captioning is helping because my Spanish is quite rusty for technical topics.
Mechanical integration is _truly_ fascinating to me for a number of reasons...
Great to see an addition to the pile of devices! 😁
Love a Vernier. Free extra resolution. (Which is accurate because of the mirrors.)
One of my all-time favorite simple ideas.
@@ChrisStaecker same. Key as always is knowing when the extra precision is meaningful. The mirror on the present device I'm guessing is what makes the Vernier worthwhile? How obvious is the kink in the reflection if you intentionally misalign the vernier by just one division?
Guy was great. 10,000 leagues under the sea, Around the World in 80 days... ;)
Thanks, mate. Your channel is a boon to this site.
Another great video. I just love all the mathematical devices that you present.
I was blown away. You taught me something and also made me laugh with your humor, loved it. Happy New Year
I would love to see a video about the von Harbou device but with two videos on slope calculating devices already, I am afraid it could be a bit derivative
Pretty cool video. I worked in metrology for 37 years and also have tuned PID controllers..
Congratulations man, this is a great video and you have been blessed by the algorithm
For anyone whose memory of differential calculus is a little rusty, the tangent to a curve 'C' at a point 'p' can be approximated by taking two points on 'C', 'a' and 'b' (with 'p' between them), and drawing a line 'L' through them. Let 'd' be the distance between 'a' and 'b'. The true tangent to the curve is the limit of 'L' as 'd' goes to 0. That is, as 'd' decreases, the approximation to the tangent becomes more and more accurate.
Using mirrors to reflect the curve is a clever way of getting around the unsolvable technical problem of finding and fixing points that are ever closer together.
From a drafting point of view, this is a very difficult problem to solve and I'm not sure how much a Derivometer would help. I learned to do technical drawing by hand and I'm glad I did, but I say thank goodness for computer graphics and there are many things that I hope I never have to do by hand again.
Couldn’t you mark point p then measure say 3cm left on the chord and mark point a on the curve then measure 3cm right to point b then draw line a to b which should be close enough to the tangent slope for practical purposes? Granted my method would work better on a more regular curve than an abrupt squiggly one.
@@someonespadre No, because in general, you can't measure distances along a curve except by integration, which requires knowing the function and the function being integrable. For the same reason, if you just took two points on the curve and drew a chord, in general, there's no way to tell which point on the curve would be the mid-point between the two points. To find the limit, it doesn't matter what points you start with (provided 'p' lies between them), eventually you will approach 0 distance.
There are only two easy cases, a straight line and a circle. With a straight line, you can find the distance between two points on it by using the Pythagorean theorem and with the circle, the circumference is 2pi times the radius, so the relation between an angle and the length it subtends is the same for all circles. With ellipses, it already becomes difficult. You need elliptical integrals of the second kind to find an arc length.
@@someonespadre Another reason why this wouldn't work is that the rate of change of the radius of curvature along the curve (considered as a function of time) cannot be assumed to be same on either side of a point on the curve. It quite possibly will not be. So, a chord between two points will not, in general, be parallel to the tangent at the point lying between and equidistant to the two points chosen.
Nice device and video and explanation. My chemistry teacher showed us how to use small (capillary) glass tubes intead of the prism to read the reaction speed out of a hand-recorded concentration plot.
I can imagine Capitan Picard proudly displaying an Ott derivometer in his quarters on the Enterprise.
I love your style of narration. You sound like a guy who shows up one day to a classroom full of 5th graders and does a live version of one of your videos to show everyone how cool STEM subjects can be.
You, sir, are awesome. Math comedy done right.
I love this kind of mechanical instruments made for measuring complex functions by its geometric properties, I think there so clever and reminiscent of an era were people use their imagination to do productive things. And now the planimeter could have good and trusted friends
This is super cool! I've never seen a device like this, had no idea they existed. Always interesting to see the brilliant ways that clever people were able to solve problems in the past with limited technology. I have to say, though, watching you punch degree measures into Desmos hurt my soul a little bit. Felt like you were abusing the poor little calculator.
I value extra accurate time measurement. Loved your video, didn't know about these tools.
Very interesting tool. I much enjoyed this.
What a fabulous bit of kit.
In the end you put a smile on my face.
You are having WAY too much fun saying "Ott" and I am now also having WAY too much fun saying it. I don't know if I can match your flawless delivery though xD
When I asked my calculus teacher what the derivative is, he said it's a function. If I had had an Ott derivameter I would have discovered the first day what it took me a quarter to understand. The tangent line is so tangible with this device.
What a gemm of a video.
Brilliant.
So we went from clampin' to Kempten!
Love the content!
This would have been really useful for scientists that collected data from chart plotting machines.
Yes- I think this is the typical way it was used.
This Ott to be in every toolbox!
I love these manual, analog ways of doing things. Absolutely gorgeous. Does it have ten digits of precision? No. Do I care? No. It's a very hand's-on way of doing math, rather than just punching numbers into a calculator.
One thing is missing. The original description of the Ott-Derivimeter mentiones in the last line that a chart is in the wooden box, giving the value of the tangens of an angle found with this gear.
5:43
"Just drawing a tangent" is the hard bit. I wouldn't do it by just eye-balling it like that - even for that "simple" curve. Two points define a line, so I would take two points reasonably close together on either side of that point, and use them to draw the slope to the left and right and take an average. It still won't be very precise but is better than raw dogging a tangent through a single point. Once you have the slope, you already have the derivative. Getting the slope with pen and paper is the hard bit - depends how close your points are together and how thick your pen is.
Muito interessante. Muito mesmo. Obrigado pelo vídeo, pois não conhecia essa ferramenta científica.
I love this piece of equipment!!!
Very cool stuff. Would love to see them be more common
Mechanical differentiators are really fascinating.
"pretty darn good!" is what I say to myself at the end of each of your videos
A treat, as always. I must recommend it to my mathematician friend, Elsa! I'm just slightly disappointed that you didn't use a slide-rule, instead of a digital calculator.
Elsa you say?
@@ChrisStaecker Last initial "H", also dances ballet. You know her, too?
@@cdorcey1735 i was thinking of somebody else 8:15
Okay, the Elsa ship was unexpected.
now we need a lens that actually differentiates the curves it sees
Thoroughly enjoyed as always! 😁
I seen this tool before my science teacher in 7th grade, I don't have any use for it but I want one, I know I'm a tech goof nice video
Doing a bit of digging, there's a short paragraph in A Prismatic Derivator. Nature 129, 126 (1932) that describes it, and lists the parties that produced it. That could give you a lead to track one down. I couldn't find anything else easily though.
Thanks a lot for this- other commenters mentioned papers that I'd already seen, but this one is new to me. And it says it was produced by Askania, which is a great lead. (And I suppose confirms that they really did produce it for sale.) Interesting that the Nature blurb doesn't mention the Ott derivimeter, which I thought was already in production by then. Maybe nott?
I even see mention of it here: www.worldradiohistory.com/Archive-Electronics/30s/Electronics-1933-02.pdf (search prismatic)
Here you can see that it was distributed in America. And then the trail ends again...
Thanks a lot!
One more: a 1931 article DOI 10.1088/0950-7671/8/7/406 has a nicer picture than I'd seen before, with the Askania logo on it.
AWESOME.... I did not know those things even existed. Damn algorithm did it again!
The topic covered here is Metrology. The glass dome is an optical center. An optical center punch is used to mark a point.
I thought that was the science of controlling hurricanes ;)
@michaelbauers8800 The people with too much money from oil production are doing that. I would like to try to make it snow someday. Shoot boiling water into the atmosphere so it instantly evaporated and percipitated down as snow. If would have to be done in a cold climate area at a high elevation.
@@stevepaltzer7605 I have seen people demonstrate instant freeze before. Both the nucleation thing from super cooling, and just tossing boiling water into the air. Both look very "cool"
I demonstrated the prism trick with an prism (as used to fold the optical path in binoculars). Unfortunately, the vertex of the right angle planes was not sharp, so there was always a gap between the lines that limited the accuracy and the localization of the x-coordinate.
I'm swooning over your derivimeters! Be still my beating heart!
Good stuff. Chris Staeker, meet This Old Tony.
Your eBay saved searches list must be incredible
Excellent! Thank you!
not sure if the ladies will fall for it, but i certainly did, well done!
That is neat o. Wonder what the actual use was when the department used it, obviously derivatives but maybe just a guess changes in temperature?
This was so interesting and informative, I would love to own instruments like that ❤, but being married for nearly 50 years I also know that they would be a bone of contention with my wife.
That is indeed one comely original box, though there's an unusual reverberation in there... But what's this? A channel renowned for its comprehensive scrutiny of precision instruments, for the correct identification of obscure apparatuses, their functions and related terminology, yet you settle for the vague and, um, fuzzy 'green billiard fabric' rather than the incomparable and mellifluous 'baize'?!
Man, I really love your videos! To bad there is a finite supply for new stuff 😢
This is exactly why we love the World Wide Web.
The reason they rare is the same reason they are simple and elegant: They are almost completely useless.
It's so much easier to just measure with other tools instead of buying and keeping around this extremely specific instrument. Measuring the slope of a curve is not a procedure that requires a dedicated instrument.
great video man leaving this comment so it gets popular and picked up by the algorithm!
You really want to date the one who says "you had me at derivameter...."
These are the "good old days" people are always talking about
0:38 Start the clonk!
You rarely see this much interest in a derivative outside of mst3k
I remember using a similar (? complimentary?) instrument to integrate areas of ellipses in Celestial Mechanics (Was it called an "ellipsometer"? I can't remember) class way too many years ago. ;-). Ahh, the days of mechanical analog computers! (I don't miss them at all.:)
Wake up hun the math guy has an original case for his derivometer!
"I don't have a little mirror" [polished butcher's knife appears] "maybe get your Mom to help out with this"
Alors je connaissais pas du tout cette ustensile c'est plus précis qu'un rapporteur en effet est équipé d'une loupe d'un miroir je vais tester vos méthodes trigonométrique😊😊😊😊 moi je connais déjà le sinus et le cosinus
I wish you had told me, I had unopened boxes of all three of those devices in the trunk of my Cord.
Mine were beneath the seat of my Tucker but I didn't have the Gerber.
4:42 The fact that the country of manufacture is simply 'Germany' narrows it down a little - any time after 1949 (well, until 1990!) it would have been 'West Germany'...