I have a Felix M Arithmometer (shown below) that appears to follow the same design as an Odhner arithmometer.
One thing I noticed about the device is that the turn counter (on the left) does not overflow like the addition register does.
This means if I want to multiply 37 * 49 I must do the following
Procedure A: 1. enter 37 2. rotate + (9 times) 3. shift right 4. rotate + (4 times)
Performing the operation "subtractively" will result in the right answer, but won't display the correct result in the turn counter
Procedure B 1. enter 37 2. rotate - (1 time) (causing underflow) 3. shift right 4. rotate + (5 times)
Procedure C 1. enter 37 2. shift right 3. rotate + (5 times) 4. shift left 5. rotate - (1 time)
If I do procedure B or C, then I see
51 in the turn counter instead of the expected
49 even though the number in the addition register is still
1813 as expected.
There's some logic to this. If I multiply 37 * 48 subtractively, then 52 appears in the turn counter, which can be though of as 5 in the tens place and -2 in the units place. So you can check your work by consulting the turn counter if you remember which digits are supposed to be negative.
I think that a register with overflow is heavier and more expensive to produce than a register without overflow, so it makes sense that the turn counter wouldn't overflow in exactly the same way as the addition register. However, that still doesn't explain why the turn counter counts up then down instead of always counting up.
Were any arithmometers produced anywhere with ordinary overflow behavior in the turn counter?
Is multiplying "subtractively" and remembering which digits are supposed to be negative when interpreting the turn counter an intended mode of operation for an Odhner arithmometer?