Brunsviga Dupla, s/n 109710
This machine has the questionable honour of being the machine in my collection that took the longest time to purchase.
A friend in France emailed me a link to a picture on Facebook (reproduced here) - clearly showing a Brunsviga Dupla
This machine is of course very rare, with only 146 being produced from autumn 1927 to 1930, and stock remaining to be sold until 1940 according to the “Haase list”.
Since the picture was posted by a second hand shop, I assumed that if they advertised it on their social media, it would be for sale - I wanted to know at what price, and was getting ready to drive to Bremerhaven.
Unfortunately, when the reply arrived, it said the machine was not for sale, as it was needed for decorative purposes. I did not push, but let them know that if this should ever change, they definitely should let me know. I kept emailing every three or so months, to signal my interest, very often receiving no reply at all.
Finally, it seemed that something changed, and the machine was no longer needed for decoration - they would however, like to see whether any museums would be interested. I gave them a few tips where to inquire, but most museums interested in calculators would already have a Dupla ... and the other question would be whether they’d like to pay for it. As a donation, sure - but I’d also like it as a donation!
After nothing more happened for a few more months, I sent another email. The shop supervisor would then pose the question to the board of directors, which could then decide. Their meeting would be next week. But could I perhaps give a suggestion with regard to an offer I would be prepared to make? Which I duly did, of course, with a bracket of figures from “disaster” to “normal used, blocked, with a few repairs to make” to “mint as new condition”.
After which, of course, I didn’t hear anything at all, and also no longer received any reply. (this was in April 2024)
The next thing that happened was that the board of directors contacted me directly (no pun intended) - to ask me what my offer would be. I repeated my offer from before - and predictably, heard nothing. The pace at this second hand shop is glacial. After a week or two I sent another message to ask whether the offer was perhaps not to expectation? No reply.
However, last week (end of July 2024) I received a message from the shop supervisor - “We can now sell the machine!”. Well, excellent, we agreed on a date, I drove to Bremerhaven, we established together that the state of the machine corresponded to “good used with some issues”, and I paid the agreed upon price.
The Brunsvige Dupla is the spiritual successor to the Brunsviga G of 1908. That machine, which is even rarer, has an extra counter register in addition to the two result registers, one of which can be switched to complements, just like in this machine.
The Dupla only has one counter register, but it has the advantage that switching to negative is not a manual operation, but instead it happens automatically at the initial turn of the crank. A quirk that the Brunsviga G had, that has not disappeared in the Dupla, is that when register 2 is switched to complements, this can only be done with the carriage in the leftmost position, after which the first turn of the crank (in this position) must be negative. This is so that an extra 1 can be added to the rightmost result wheel to correctly show complements. But we’ll get back to that.
So, first some repair information. When I got to the machine, everything was blocked. This was however easy to fix - the backtransfer crank was not in its zero position, blocking the entire machine. Apart from being dirty, the lever for switching register 2 to complements was missing, and the hole where it ought to be sticking up had chewed-up edges. I expected this to be an easy fix, and luckily, I was right. There were only a few pitfalls.
When I got to my hotel room, and unloaded the machine from the car, this is what it looked like.
It didn’t change appreciably when arriving home.
The feet were thick (and crumbling) orange rubber vacuum hose glued to wooden spacers. That obviously had to go, and be replaced with something more in keeping with how the machine should look.
The nickel plating didn’t look great, but should clean up.
This was of course the crux of the matter - the missing lever for switching to complements. Apart from the register being filthy, you can see here that the lever was simply bent up from the flat bar, and has broken off. The other nasty suprie was that the two screws which hold this sliding bar in place have domed slotted heads, which have then been ground down until barely anything is left from the slit. By using a very thin screwdriver made from leaves of spring steel, I did manage to get both screws loose though. That was a bit of a hair-raising moment.
That break is nothing that a bit of heat and silver solder can’t fix ...
Luckily, the register cleaned right up.
... like so.
reinstalled, with the ground screw head plainly visible.
Since the pinwheel cylinder needs to engage with two registers, it is absolutely huge. That also means there is ample opportunity for tens carry, and also for offsetting the digits with respect to one another, so that the effort in turning the crank is spread over a certain angle, because otherwise all digits would engage at the same time, causing very unequal effort along a crank turn. Smart thinking!
Everything reinstalled, counter register cleaned as well.
One of the comma sliders was missing its little pin at the end, and the spring had partially unwound. I sourced a new spring, turned a new ...eh, nipple ? and reinstalled the lot.
Here is the finished machine.
Some details - this is the slider for locking the clearing on register 2. Locked ...
...and free.
Push button for releasing the retainers on register 1, so it can be set manually with the thumbwheels. One button on each side.
The backtransfer lever. Pulling it forward to the stop will let you backtransfer the contents of register 1 to the input, on the condition that a) the carriage is on the left; b) the input has been cleared and c) the zeroing lever for register 1 is pulled 180° forward. If you pull out the handle, you can go past the stop, and you can backtransfer the content from register 2 to the input, on fulfilling all conditions above, as well as d) register 2 being engaged with the pinwheel cylinder.
Speaking of which, this is the lever that does that. To the front is engaged, to the back is disengaged. A green stripe will show below the top plate to show register 2 is “safe” (but not in this picture, since the register is engaged). However, you can see the green stripe here:
The final trick is the little nubbin on the top left of the register, which we now know used to be a bent piece of steel plate, part of that thin bar under the cover of the top register in the carriage. It is spring loaded, but pushed to the left will shift the blind over the result wheels to the left, yielding us a register prepared for showing complements.
Why prepared? Because of course the complement of 00000 is not 99999 but 00000. If we subtract 1 from white 00000, we get 99999. The complement of that should be red 00001, not red 00000 - so there is an extra red 1 missing at this point that needs to be added - and that is done on the first turn of the crank, which it is mandatory to make in the negative direction.
The above is what happens with a single negative turn, with the input register completely at zero
This also highlights the automatic direction selection of the counter register - which will also switch to complements and do the exact same trick, so the number of negative turns is now counted positively, with the register in red.
Before moving on to the videos and applications, I will show you some pictures, which have been done before by Hans-Jürgen Denker, if you know where to look. By simply looking at pictures, you have no idea how comically large the Brunsviga Dupla really is. Here is a comparison with the “normal” Brunsviga ZK (which was the second pinwheel calculator I ever bought). THe Brunsviga Dupla weighs 21.1kg. Still some way away from the 37kg of the Brunsviga G, but still, it is a hefty little bugger!
Now, coming back to applications - here is a video of an 8% discount calculation on 3572 RM, the same example we did on the Brunsvige G. The Brunsviga Dupla allows to find the discounted total, the original figure, the percentage subtracted, and the discount itself.
Another claim to fame for the Brunsviga Dupla was its discussion by Comrie, in the Monthly Notes of the Royal Astronomical Society. You can find this article in Vol 88, of March 1928, on page 447-459. There is a follow-up article by E. Chappell, in Vol. 91, p. 817-819 (May 1931) in which an alternative approach to the calculation is suggested. Comrie is having none of it though, and suggests that you actually don’t even need a Brunsviga Dupla for it. Honestly, although he clearly knows what he’s talking about, he doesn’t seem like someone I’d invite for a barbecue :-p
Now, what is this talk of difference engines? We all know that Charles Babbage tried to build one in the 1840s, and was never successful. Some others, like Wiberg’s and Scheutz’s, have been built and were successful for calculating tables. So how does a Brunsviga Dupla emulate a difference engine then ? Any function with a sufficiently small value can be approximated by a 2nd order polynome. If the function is a second order polynome, then the approximation is of course exact. Analytical derivation will get you the second difference easily - i.e., ax² + bx + c - the first derivative equals 2ax +b, the second derivative equals 2a. So the constant second difference is two times the quadratic coefficient a.
It also works for higher order functions, as long as they change slowly enough, but then of course the second difference will not be exactly constant. The point is that the first first difference, and all second differences can be calculated easily by analytical derivation for any function.
Comrie then describes a procedure in which nothing needs to be written down to come up with a projected series of function values.
He starts by putting the first value of the function in the setting levers of the machine, and cranks it into register 2. Register 1 is cleared, and the first second difference is set into it with the thumbwheels Then the first difference is cranked into both registers. This yields the next value for the function in (1), and the second first difference in (2). The input is cleared and the second first difference in (2) is backtransfered to the input; Now the same sequence is always repeated - set the second difference in the thumbwheels of 1, and crank the nth first difference into both registers - yielding the function value in (2) and the (n+1)th first difference in (1). Repeat ad infinitum. The current argument of the function can be found in the counter register.
The big disadvantage that this method has is that the second differences always need to be set with the thumbwheels on register 1. This gets old after a while, and painful on the fingertips. It would be nice if the second differences could be set with the setting pins instead. Still your fingertips become painful, but only after a longer time. The next method (E. Chappell’s) provides for that in a way. How is it different ? Set up the machine with the function value in (2), (1) empty, and the first difference in the setting pins, and crank once. Now the secodn value of the function is in (2), and the first difference in (1). Clear th setting register, set the second difference. Disengage 2, crank. The second first difference is now in 1. Clear setting register, backtransfer this to the seting register. Engage (2), crank. Function value 3 is now in (2), and the 2nd first difference in the (1). Set the econd difference in the setting register, and continue. In the 1928 article, there are more interesting things to do with a Dupla, such as interpolation, calculating full series of differences, as well as correlation cross terms and squares in the least squares method, three at a time by using the 15 digit register efficiently. Refer to the article for details - it can be found here. Chappell’s article and Comries reply are here
There is a nice diagram in the article (provided by Brunsviga) outlining the controls of the machine in English.
You trade the ease of setting the setting register instead of the result for having to crank twice, and always having to remember to switch off and back on register 2 with the function value. So that’s the Brunsviga Dupla!
What are some other serial numbers “out there” ?
In Comrie’s article, the GNC provided sketch has s/n
104371 - we’ll assume this was a real, early machine - does it still exist?
106483 is in the Deutsches Museum in München
106487 is in the Science Museum in London
106491 occurs in the literature in an Italian observatory. We don’t know whether this machine still exists
107302 is in the Braunschweigisches Landesmuseum in Braunschweig
109710 is this machine
115005 is in the hands of a private collector
115006 id.
115014 is in the Arithmeum, Bonn
115906 is in the Musea di Prato in Italy
116076 still exists and is in Buenos Aires.