Thank you Rick for this brilliant insight! You have filled in a lot of the gaps that I struggled to research.
I did recently watch some old US Navy videos on fire control computers, explaining how cams, differentials and racks were used to provide the equivilant of operators and functions. It was genuinly fascinating!
I hope you enjoyed the tear down, and if you did, please keep an open eye and ear for a future video (no spolers, however I think you'll like it)!
The [#] key on most all adding machines and accounting machines is typically used as a "Comment". It allows a number to be entered, then the [#] key pressed, and the number is printed with an octothorpe after it to indicate that the number is some kind of comment, perhaps a draft number or some other number for reference that is not included in any calculation. In some later adding machines, the [#] key was replaced by a key that read [NON ADD], to indicate that the number was not added to the accumulator and just printed for reference purposes. Some printing electronic calculators retain this function even today - mostly business-type printing electronic calculators.
In 1937 when the exhibited accounting machine was apparently made, there wasn't much in the way of any kind of digital electronics in existence that would be a part of a device like this. Sophisticated analog electronics in the form of integrators, amplifiers, summers, servos and dividers were used in the extremely complex action of aiming a big gun on a warship at sea. These very sophisticated analog computers had to take into account the roll, yaw, and pitch of the ship as the waves jostled it about, as well as information about the target, things like barometric pressure and humidity, the type of round used in the gun, and countless other factors in real-time in order to insure that the round would come as close to the target as possible. At that time there was no digital computing device of any type that could fit onboard a ship at sea.
The capacitor you found is a motor start capacitor. It dumps a charge into the motor when the motor receives power to overcome the static load of the rotor to get it going, and then normal currents can flow through the windings to keep it spinning. The capacitor should definitely be replaced if there is any attempt to power up the motor. I figure you know that the brushes will likely have to be replaced, and the coils should be ohmed out to make sure that no shorts have developed.
The rubber or leather coupling between the motor and the rest of the mechanism is there for two purposes. One is as you mentioned, to absorb some of the torque pulse that occurs when the motor starts. The other function it provides is a degree of vibration isolation of the operating mechanism from the invariable vibration created by the motor. No motor is perfectly balanced, and the slight imbalances in the motor creates vibrations which can cause undue wear on the mechanisms that it is driving. The isolator helps damp out the vibrations of the motor.
Wanderer Werke never made any truly electronic calculators of their own. The company was purchased by Labor Für Impuslestechnik (now known as Nixdorf) in 1968. Prior to Nixdorf purchasing the business machine division of Wanderer Werke, Nixdorf (I'll use this name because it's a lot easier to type) did all of the electronic design and prototyping of the electronic calculators that were marketed under the Wanderer Werke brand. I believe that Nixdorf also manufactured the electronic calculators, and Wanderer Werke simply marketed, sold, and perhaps serviced them.
All of the mathematical machines that Wanderer Werke built since its founding in 1869 (manufacturing motorcycles initially) were mechanical or electromechanical. Electromechanical refers to a mechanical mechanism that is driven by an electric motor. The only "electronic" components involved were generally capacitors, for sure the motor start capacitor, and sometimes capacitors that were put across switch contacts to reduce arcing from damaging the contact material. All of the calculating in these machines was done by the mechanical gizmos, driven at first by hand with a hand crank, and later with the electric motor to relieve the user's right arm from the burden of pulling on the crank to power the machine's operations.
The machine you uncovered is considered an accounting machine, but it seems very rudimentary. The carriage is designed to take in forms that were pre-printed (like ledger forms), and perform basic math (addition and subtraction only) and print the results where the operator (through the use of a [TAB] like key positioned the carriage. Looking at the mechanism, although i will state here that I am no expert on these old mechanical machines, it appears to be a basic adding machine, with an accumulator that can be added to or subtracted from, with results printed by the printer. Later(1950's) there were vastly more sophisticated electromechanical accounting machines that could actually keep totals in mechanical memory registers, and perform full bookkeeping operations through various means such a plugboard with wire jumpers that "programmed" the operation of the machine, or some that used a table with pegs inserted in various holes to program the machine. These were still mechanical devices, though, with no electronics save capacitors and switches.
Check out this video of a 1958-vintage Ascota 170 Accounting Machine. It is the most advanced all-mechanical accounting machine ever developed. After this, digital electronics began to infiltrate the scene, making these mazes of gears, levers, cams, shafts, and countless other magical mechanism quickly a thing of the past. In this video, it is asked to perform an operation that is something that accounting machines aren't really made to do, but the fact that this machine can do it is a very fitting example of just how advanced this motor-driven mechanical marvel is:
Rick Bensene, The Old Calculator Museum
The "#"character, referred to as the Hashtag symbol, or the "pound sign", or sometimes "number sign" is actually called an octothorpe:
Rick Bensene, The Old Calculator Museum, http://oldcalculatormuseum.com, Beavercreek, Oregon USA
The origin I am familiar with is the children reciting their alphabet, where they would say ".. x, y, z, and per se and".
( If you are interested in the etymology of words then perhaps check out the weekly 'Something Rhymes with Purple' podcast hosted by renowned lexicographer Susie Dent along with Gyles Brandreth.
a531016 - regarding your 'pound sign' explanation...
The use of the # symbol as shorthand for 'pound' would appear to predate ASCII. There are various mentions in printed books from the early 1900's where it suggests its use before a number is to be treated as a 'number sign' and after a number as a 'pound sign' e.g.
(from Google Books
The etymology would appear to trace it all the way back to 'libra pondo', the Latin for 'pound weight'. One theory is that later stylization of the the abbreviation for 'lb' went to the symbol '℔' and then on to the symbol '#'.
I've noticed that on some typewriters from the late 1800's it is depicted more with the two horizontal bars sloping backwards, e.g. Remington:
so two different brands using the same distinct styling.
What would be interesting is what the function is of the # key as used on the accounting machine here. It looks like it is an important key, although on later machines it appears to have been moved to a smaller less used button key.