Neglecting 'VINTAGE' aspects, so to explain:
Partially a study / speculation of CODE writing dynamics, ALA 1890. Contempory 1890's could potentially include these little (systems) at least physically buildable!
Think about retail plastics, and epoxies available today, down the street. But also, for doing business, where do you go, to hire your people ?
And, don't forget, foisted bribery and organized crime were present, with those 'feet' in your door.
No cozy 'Coding Camps' there, 1898 !
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NOW, info details on large latching ENCODER:
Photo shows one example shaft, for simpler 1 digit latches, very similar. For larger input width, an Encoder uses a reduction and latching process, creating 2 regular sized digits, (00 thru 99).
Try split that 'monster' input into decades, of 10 hoses each, for a 'split and extract' process. You have one 'Pivot shaft', say '4X'.
Using the photo-diagram understand there will be a setting tab on EVERY column, for extraction of any BUS lane (incoming ball). So, you have your high digit, which can later be read out, only that it's much more numerous in managing, still essentially simple.
NEXT, you are free to combine like signal lanes (below the decade capture device). This combining process is going to destroy your BUS signal, considering the 100 lines are now ten lines (low digit) ready for more 'conventional' ten-state latching.
'CONVENTIONAL'
Ha!
Then, the Encoder sub-system has only to latch, say, one of X0, X1, X2, X3, etc up to X9. So that completes the (Row, Column) extraction.
Usually, that's an answer, stored as a table entry. For multiply, 4 X 2 needs an answer; '08'.
Clever readers note: an alternate method would transpose, that ending up as '24' resolved, again, to an answer, '08'. That's simply reversing to use a (Column, Row) transposed method... All simple, really.
The Mechanical Teaching Computer has a student-welcoming feature, named as a ' SCIENCE' micro-instruction... What does it do ? I don't know: That, waits for the student to think up and build !
This ain't rocket science, in a 'pretend' year; 1888