Divisumma Diary - It Works!

The Divisumma has been sitting on a corner of my desk in full working order for a couple of weeks now. There's a picture of it at the bottom, complete with case and very attentive full-time Divisumma Operator.

Progress since the last posting involved several more variations on the Battle of the Springs, and a lot of lubrication. The problem with springs is that they age, losing some of their strength. Replacing them with new springs is a risky business, because in many cases the exact strength of the spring is important.

I mentioned before the problem that multiplication sometimes gave the wrong answer. At the same time, I noticed that the key that allows you to transfer the result of a multiplication to the multiplier register - for example when computing powers or strings of products like 123 x 456 x 789 - no longer worked.

The Divisumma uses a clever trick to speed up multiplication. If it needs to multiply by 4 or less, it uses repeated addition. For 5 or more, it instead adds an extra one to the next digit, then subtracts. So to multiply by 9, it subtracts once, then adds an extra one to the next digit. If you multiply by 99999, it only performs two actual arithmetic operations, effectively multiplying by 100000 and subtracting 1. The effect is to halve the time to multiply, on average. As you can imagine, the mechanism to do all this, purely mechanically, is frighteningly complex. As ever, I'm lost in admiration for the designer of the machine, Natale Capellaro.

The error in the multiplication could be explained if in certain cases, a value was added instead of being subtracted. To cut a long story short, the problem turned out to be where I had replaced a spring, the long spring 277 from the Battle of the Springs, by a stronger one. It completely solved the problem there, but unfortunately the static end of the spring is not really static, it's a little hook on the end of something that moves. The stronger spring was holding it a fraction of a millimetre away from its correct resting position, and that was enough to block two pieces of the machine: the lever that decides whether to add or subtract, and the lever that causes the multiplication result to be transferred.

So I had to revert to the original spring, and solve my Battle of the Springs problem another way. The service manual says that in certain cases, to get things to work, you should "act upon" various cam followers and the like. So indeed I "acted upon" the little lug 150a, until it stayed out of the way of lug 286n when it was supposed to. It's now twisted quite a lot, I'm sure more than the spirit of "acting upon" would demand, but the machine now works.

Another spring problem caused an equally odd problem. Sometimes, an add or subtract would trigger a total operation, wiping out the value just entered. Curiously, this was related to the length of the number just added. If it had just one digit, the problem didn't happen. If it had 12 digits, it always happened.

The immediate cause of the problem is the mechanism for printing the result of a multiplication or division. This uses the total machinery, and it does it by pulling down the total key at the end of the cycle. It's almost as if a big arm reached out of the machine and pressed the button down. The arrangement for triggering this is amazingly complex, with flimsy levers that run the whole length of the machine. It turned out that the mechanical shock to the machine when the digit carriage was restored, was just enough to trigger one of the pieces of this.

The mechanical stresses in the machine are pretty high. There is very little time to restore the digit carriage within the overall quarter second or so main cycle - maybe 50 milliseconds, to move something quite heavy through 5 centimetres or so. So when it hits the stop, it is moving fast and there is a lot to absorb. Designing these machines to work reliably, considering everything that was going on, was a lot harder than just getting one to work on a bench in the lab.

Anyway, the fix in this case was just to use a new, stronger spring. Problem solved.

Then it was time to put the machine back in its case. The first step was to replace it on the steel base. It hadn't been too hard to get it off - there are just five bolts that hold them together. But getting the holes lined up again was nearly impossible - they have to be correct to within less than a tenth of a millimetre or the bolts just don't engage with the nuts. And two of these bolts are completely inaccessible. Luckily I had just bought these bolt-handling tweezers from Micromark, which were exactly what it took to weave the bolt through the levers and get it to the right place. Even so, for one of them I had to hand-turn the machine to a certain point in a division cycle, to move a lever out of the way and give me access. I can't imagine how they did this assembly in the factory, there must be a trick that I missed.

After that it was just a matter of putting the case back on, cleaning things up, replacing the ribbon, and now I have a perfect piece of retro-computing sitting on my desk. I even use it occasionally, instead of firing up the Windows calculator.

Divisumma Diary: A Little Lubrication

My Divisumma worked, somewhat at least, straight out of the carton. With some very minor attention, it briefly performed all four functions, despite sitting unused in a cupboard somewhere in Italy for probably three decades or more. Not everybody is as lucky. There's an excellent article here (in French) about the restoration of a Tetractys, the Divisumma's big brother (with practically identical internals). The author describes all the lubricants as having gummed up to the point where he had to clean and relubricate it extensively before it would even do basic addition.

I asked a couple of people how best to lubricate the machine, and they both recommended the same thing: AeroKroil. So I sent off for some, and a few other products from the same source while I was at it. Meanwhile, my Divisumma was not working very well at all, culminating of course in the catastrophic jam. There seemed to be no lubricant present, except some dark, dried-out grease in a few places.

When the AeroKroil showed up, I squirted tiny amounts of it into every bearing I could find. What a difference! It was now much easier to turn over by hand, and seemed to run smoothly under power as well, although after The Jam I had become very reluctant to use the motor anyway. I also came across an article in Italian which, after Google translation, said "Lubrication life is entrusted to 4 types of lubricants, each optimized for the kind of friction generated in the appropriate place: dense oil, fat, low viscosity, fat infusions and grease molybdenum disulfide Molykote.". This seemed like a mistranslation - it's hard to imagine them using lard - and indeed it turns out that "grasso" is Italian for both grease and fat. However there's still no indication what the "low viscosity fat" and "fat infusions" actually are. Molykote seemed easier to track down, but there's a bewilderingly huge variety of greases under this name. Also, since it's an industrial product, most suppliers want to sell it to you in 20kg drums or packs of 10 tubes. Luckily I found this supplier. Perusing the list, the BG-20 grease seemed about the best fit, so I sent off for some of that too.

At the same time I was dealing with the machine's various other caprices and dysfunctions, such as The Battle of the Springs. Finally, the Molykote showed up. I spent an hour or two applying tiny beads of it on the end of a nickel spatula (the extremely useful result of the two weeks I spent studying Chemistry at university) to everything that slides - all the cams, the various sliding bearings, and of course the motor and its gearing. That, and plenty of AeroKroil, have made a huge difference to the smoothness of things. One little indication: if you've ever used a Divisumma, you may have noticed that at the end of every operation it makes a gentle "clunk, clunk" noise. That's the one cam that turns directly off the motor output, not through the clutch, bouncing as the motor runs on. When I first got the machine, I barely got three clunks. Now I get eight or nine - an indication of how freely it is now running.

There have been plenty of other little adventures too. For example, for a while when it multiplied, it would sometimes add two to the value of the multiplier - so 9x1 was 11, and 7x1 was 9. I figured it must have been a feature for working with sales forecasts. It's fixed now - it turns out to have been an improbable side effect of The Battle of the Springs. I'm sure you can't wait to read about it.

The Divisumma Diary: The Battle of the Springs

Last time, I had just managed to repair the disastrous jam which tore out a tiny rod deep in the heart of the machine. With much patience and ingenuity, I'd finally got it back in place, and the machine briefly seemed to work. Since then, it has spent a lot more time not working than it has working. Currently, everything is fine except that, like a math-phobic small child, it refuses to do divisions.

I spent a long time dealing with a problem which is really a great illustration of why these machines were so fiendish to service. I'll call it "The Battle of the Springs". The picture shows the two protagonists, and the second picture is a closeup of the actual battlefield, which as so often is far from the comfortable homes of the instigators.

First, a little Divisumma anatomy. Everything that happens in the machine is driven by the main camshaft. In one machine cycle (about a quarter of a second) it turns round once, and drives a single basic operation such as an addition or a subtraction. Exactly what happens depends on which key was pressed to start the cycle. Well, that's almost true. For the total and subtotal functions, there's something called the "extra cycle" which happens prior to a normal machine cycle, to preset various things. It arranges for the printer to leave an extra blank line and print in red, it disconnects the keyboard from the internal operation of the machine, and a few other things. Incidentally, it's the machinery for the extra cycle that causes the "clonk, clonk, clonk" that you hear at the end of every operation.

Another piece of the Divisumma's anatomy is the "memory", the place where quotients are built up during division, where the multiplier is held for multiplication, and which can also be used just to store an intermediate result. This register has a very different physical structure from the normal arithmetic register. It lives at the back of the machine, behind the "executors" which move values between the keyboard, the arithmetic register, and the printer. Some operations need to place a value into the memory, while others need to retrieve a value already there.

And now finally to the battlefield. Operations which need to read the memory value initiate this by releasing the long lever labelled 286 in the picture, so that it can be pulled towards the back of the machine by the spring 277. (The numbers come from the Olivetti service manual). That movement ultimately results in the vertical racks of the memory register being moved into contact with the executors at the right time. Because this is a bit like a total, in this case an extra cycle is performed, and the movement of lever 286 is permitted by the extra cycle machinery, which among many things moves forward the little tab 276m.

With me so far? But there's one problem with all this. This is just a normal operation, so although the result is to be printed, it should not be in red or have double spacing, which the extra cycle would normally do. It's the little tab 150a which, when it drops down, causes these things to happen. 276m moves forward in the extra cycle and 150a drops down. By happy chance, all these things are in the same place. So all that's needed is that when lever 286 moves backwards, the little lug 286n slides under lug 150a, which can no longer drop down, and the value is printed normally. Perfect.

Except that this is actually a race between two springs. The long spring 601 pulls 150 down (gravity could do the trick, but nothing in the Divisumma depends on gravity. It will certainly work on its back, and quite probably upside down too, although I haven't tried it). Meanwhile the short spring 277 pulls 286 backwards.

It's probably about time I told you what problem I was actually having. Sometimes, when I pressed the total key, I got a value of 999999999999, and the current value wasn't cleared. As you can imagine, it took quite a lot of tracking down to figure out what was happening. And as you can guess, I ended up in the Battlefield of the Springs, which is a long way from anything else to do with the total operation. And here's why. When 276m moves backwards, lever 286 has to follow it, and stop 150a dropping down, before 150a makes any movement. If it doesn't, 150a effectively wedges 286n and stops it moving. The result is an impasse - 150a doesn't drop, but also 286n doesn't move backwards. That means that the memory operation doesn't read the memory, but it also stops lever 286 from being fully restored to its normal position. And, via some other complicated linkages, this also means that the total function remains disconnected from the arithmetic register. So the result of this contest of strength is that the machine simply stops working. It just takes one tiny movement of lever 286 to put everything back where it should be, and the machine will work normally again. But for the office worker in 1960, her precious Divisumma was broken. Time to send it to the men in brown coats. You can see why there were so many of them in those days.

Those readers who are following this with the service manual in hand (admittedly improbable) will have noticed that I've diverged slightly from the straight and narrow here. I've commented before on how excellent these manuals are, but in this case Homer nodded. There is no spring 601 in the manual! And lever 150 is really lever 150', and it doesn't have a lug 150a! How can this be? What I think happened is that Olivetti enhanced the original double-spacing mechanism, which was much simpler, but my manual reflects the older design. The web has a surprising number of pictures of the insides of the Divisumma 24, and they all the seem to be the same as mine. This is a problem though, because nothing describes exactly how all these extra pieces are meant to work together, so it's largely guesswork.

Now that I'd finally diagnosed the problem, what could I do about it? The apparent reason was that spring 601 was too strong compared to spring 277, so the obvious thing to do was to put a stronger spring at 277. However I didn't have any suitable springs. I sent off for a pack of 200 small springs (lots of people sell this kit but I'm pretty sure they're all the same one), but while I was waiting I thought, it doesn't actually matter whether the total is printed in red, so why not just stop lever 150 from dropping at all, ever. So with a piece of wire I fixed it to a convenient place at just the right height. That was a real mess! It turned out that the place I fixed it to also moves, and that was enough to mess things up completely. I'd broken one of the Divisumma cardinal rules, which was to forget just how incredibly inter-related everything is in this machine. Lifting lever 150 a bit too far put it in the way of something else, and almost nothing worked correctly.

When my box of springs showed up, I eagerly replaced spring 277 with something stronger. I carefully turned the machine over by hand, and as the extra cycle did its thing and lug 276m slid forward, lever 286 gracefully followed it, preventing the evil tab 150a from dropping down into its path. YES!!! Problem solved, through ingenuity and creativity. How happy I was!

Briefly. Because after that, the total stopped working again, intermittently, but differently - instead of showing all 9s, it would show some apparently random value. That was when I discovered inertia. What happens is this. When the memory read cycle is over, the extra cycle machinery gets put back into its normal position, which means among other things that lug 276m gets pushed forwards and hence lever 286 also. This should restore it to its normal position. Visually, it does. But it just doesn't go quite far enough to latch in place. This leaves it free to move forwards during a total cycle, ultimately resulting in the memory register being engaged. The actual effect of this is that each digit, as printed, is the lower of the value in the memory and the value in the register. It isn't obvious to figure this out!

This time, the problem was that spring 277 was too strong. It turns out there is a tiny gap between the two lugs 276m and 286n. With the original spring, there's enough inertia to move lever A the extra fraction of a millimeter so it engages. But the stronger spring stops this, so the machine doesn't work again, but differently.

To adjust the machine, sometimes the service manual tells you to bend the lugs. So, I thought, the next step would be to tweak the exact position of lug 286n to get things to work properly. I did, and that, I rather think, is why my Divisumma will no longer divide. But that's a story for later.

Divisumma 24

Update August 2020: the person who supplied the manuals has sadly passed away, and they are no longer available from this source. I have placed them online here (Part 1) and here (Part 2). Be aware that they are very big - about 250 MB in total.

It's arrived! My circa 1960 Olivetti Divisumma 24 electromechanical calculator has arrived from Italy. It's in good condition although so far I haven't got it fully working.

First a little background. When I was about 17 (a long time ago!) I worked one summer at an advertising agency doing analysis of some surveys. For this I was equipped with a Divisumma 24. This was, for its time, an amazing machine. It could not only add and subtract, but also multiply and divide, for numbers up to 12 digits. It was very compact, unlike most such machines, and also a very nice piece of industrial design. It fascinated me, and I was especially intrigued as to how it worked. I wrote to Olivetti, and they kindly sent me a green booklet describing in complete detail how one of the simpler machines - just an adding/subtracting machine - worked. A while later I wrote to them again, thanking them profusely and practically begging them for information about the Divisumma. Obviously my letter went to someone else, because this time I got a reply more-or-less accusing me of stealing the book and asserting that Olivetti would never, ever, under any circumstances, give such information. So that was that.
I still have that little green book, and a few weeks ago I took it out of the bookcase and re-read it. I was as intrigued as ever about how the Divisumma worked. A lot has changed in 40 or so years - Olivetti no longer really exists, for one thing, and nobody has used mechanical calculators for three decades. So with Google's help I discovered this source for Olivetti manuals, and a great many others too. A few days later a parcel showed up with seven volumes of green-covered manuals, and I started reading. It's not that hard to understand how it works, but what is truly mind-boggling is that someone was able to design it. Even allowing that it was a process of evolution from simper machines, it is still extremely impressive. Unlike software, which has some structure to it, these are three-dimensional puzzles, where two completely unrelated functions that just happen to need to do something at the same time, can share the machinery. (For example, the mechanism that arranges double line-spacing for totals just happens to be in the right place to reset a lever that controls the way the registers engage for memory operations).
Of course reading these manuals just whetted my appetite again. A bit of searching showed someone in Italy who had one to sell. I paid about $150 for it, but of course the postage - even surface mail - nearly doubled that. And this week it arrived. The seller had done a super job of packaging, including a wooden framework to protect the machine inside the box. It was complete, apart from one minor knob on the keyboard, and the power cord. It even had a roll of yellowing paper.
I rigged up a power cord for it (don't tell the safety nannies about this) and plugged it in. Unfortunately, it didn't work - one of the keys was jammed, and the motor just ran without anything happening. Not really a surprise, but a bit of a disappointment. So then it was off with cover. That comes off surprisingly easy, no screws, just a couple of toggles.
The insides of the machine are in remarkably good condition. There was some fluff around the keyboard, but no rust or damage. All the metal parts seem to be cadmium plated, which means they look the same as the day they were assembled.

I need to say something about the manual, too. The Olivetti technical manuals are also works of art. Every tiny aspect of the machine's operation is described in great detail, with beautiful engineering drawings for every page showing the various levers, bridges, pins, racks, springs and so on - just those relevant to the current description. Once you've digested that, they also include complete instructions for assembling a machine from scratch. The numbering of the parts is consistent through the seven volumes, so once you read in chapter VIII (as befits an Italian product, much use is made or Roman numerals) that lever 73 is key to some particular function, whenever you see lever 73 later on, you know exactly what it does.

So with the help of the manual, I was able to figure out what was jammed, and unjam it. And the machine worked! Well, briefly. For about fifteen glorious minutes it would add, subtract, multiply, divide, and move numbers to and from the "memory" . Even the 30-year old ribbon worked, well enough to read anyway.
But then disaster struck. I started a divide, but instead of the usual kerchunk-kerchunk of the running machine there was just a faint hum, the horrifying noise of the stalled motor. I unplugged it and tried a few things, and eventually it unjammed. Phew! But then I realised things weren't working right, and when I looked, I realised that disaster had struck. Right in the very heart of the machine, a frame had got twisted so badly that it had let a metal rod fall out. This was a totally inaccessible place, without completely dismantling the machine. I was mortified. Just when things had been going so well (I had never really expected the machine to be working), and now, just so much scrap metal. I could almost have wept.
I studied the manuals again, and very carefully, removed the paper roller and associated bits and pieces, saving all the parts in little plastic bags. There was only one problem - a circlip which in the time-honored tradition flew across the room. Luckily I found it easily. That gave me access to the mechanism, from above. Then the real fun started. I found that I could just get a pair of tweezers between the individual elements of the register, and that way I could hold the rod in more or less the right place to insert it. But actually getting it into the holes at either side of the frame was another story. Let's just say it took a long time. Finally the trick was to hold everything in place with wire (actually green garden wire, which gave a certain rusticity to the whole operation). After several hours I had it back in place.
Very carefully I turned the machine over by hand. It seemed to work correctly. But then I discovered how delicate these machines really are. Just like an exceptionally old wine, which is wonderful when opened but undrinkable within ten minutes, so it seems that my early success with the Divisumma was not to last. Every operation revealed some new misalignment or jam, and when that was fixed, another one showed up.
There is really a lost trade and craft here. Back in the day when these machines were commonplace, every town had numerous little back-street workshops, where bent-backed mechanics in brown coats would pore over them when they jammed or refused to work. I'm sure it was a common occurrence. In the few weeks I was using the Divisumma all those years back, it jammed once and had to go for repairs. Probably every machine was in the shop every few weeks. "Oh yes," the brown-coated old guy would say, "looks like the returbitating cam has shifted again, just move it a bit and tighten up the unflurging spring while I'm at it..." and the machine would be as good as new... for a few more weeks.
Anyway, my Divisumma definitely needs some more tender loving care before it will be dividing again. It's a wonderful piece of engineering, and I'm very lucky to have it. It's certainly something to fill those long winter evenings!