Operating An Odhner Calculator
The Odhner arithmometer was the most produced mechanical calculator.
Although this is an old machine, nevertheless it represents how one operates any basic rotary calculator. Facits have a pinwheel cylinder that shifts internally, instead of a moving carriage, but the principles still hold.
- First, clear the result dials, and then move all setting levers to zero. Position the carriage appropriately. (Use the levers at the front.) The handcrank must be at home position, engaged with its positioning stop.
- To add, enter the number into the setting levers. Pull the crank handle to the right, and then toward you, so that it's going away from you when the handle is at the top. One turn will add the number into the accumulator dials, and the counter register to the left will show .
- Multiplication: If you continue turning, you'll multiply by the number of turns – you're adding repetitively. If you need to multiply by several digits, it's simplest to start with the rightmost multiplier digit, then shift the carriage to the right one position for the next digit.
- To subtract, pull the crank handle to the right, and push it away from you, so the handle is moving toward you when it's at its highest point. If you subtract more than the number in the accumulator dials, you'll get a complement, which you'll need to convert.
- Short-cut multiplication
- It's quite unnecessary to crank six or more times for a multiplier digit. Instead, you can shift the carriage one position to the right, add once, then back up the carriage and subtract, until the counter shows the correct digit. For instance, to multiply by 8, shift, add once, shift back, and subtract twice. (10-2 = 8) Thinking ahead, instead, you can subtract twice before adding; the calculator will keep track for you.
- Clear the machine and enter the dividend into the setting slides, starting at the left. Move the carriage to the right so the leftmost dividend digit aligns with the leftmost setting lever. Add once. Clear the counter. If you're lucky, the machine should have a counter-reverse control that will make the counter increment for subtraction and decrement for addition. (Some later, better machines do this automatically for the first turn after entering the dividend and clearing the counter.)
- So, now you have the dividend in the accumulator, left-justified.
- Change the setting levers to enter the divisor, again to the left.
- Be sure the counter is clear, and start subtracting. If the machine has a bell, you can crank mindlessly until the bell rings, then add once. Otherwise, you'll need to watch the accumulator contents to note (or anticipate) an "overdraft" (subtraction too many times); you have to correct it if it happens, by adding.
- Shift the carriage one position to the left, and resume subtracting.
- Repeat for each quotient digit, until you either reach the machine's limits or have enough digits. The counter cantains your quotient; the accumulator contains the remainder (if any).
- It's of some interest that essentially-automatic division generally appeared before automatic multiplication; as each quotient digit developed, overdraft was allowed to happen, and it triggered a single add cycle followed by a shift.
- Square root is possible, by the "fives method", but the description is rather more complicated. This type of machine, in particular, is quite good for this kind of calculation.
- Short-cut division
- This takes some thought, but can save time. By watching the accumulator, you can anticipate a large quotient digit, and in a fashion similar to short-cut multiplication, you can add and shift, instead of simply subtracting, to save cycles. (The Marchant calculator contains a multi-digit analog magnitude comparator that prevents overdrafts! Changing from subtraction to addition and back is messy and slow in that machine.)
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