How do I multiply using this "Addiator"-style calculator?

Question

I've got an old "Addiator"-style calculator (pictured below), but not the instruction manual.

I know how to use it to add (place the stylus next to a digit and pull down, pushing up and looping around to carry if it hits the bottom stop) and subtract (pull up, pushing down and looping to borrow). But this one claims it can also multiply.

Is there a way to multiply using this machine other than either (a) repeated addition, or (b) using a log table to turn multiplication into addition?

Answer 1

The Addiator wikipedia entry does not say much, but as this type of calculator was introduced by the Frenchman Troncet in 1889, the corresponding French entry Calculatrice à crosses gives much more details. Here is a translation of the section on multiplication:

Multiplication and division are possible, but less automatically. To multiply $54$ by $32$, for example, it is possible to add the number $54$ to itself thirty-one times (which is tedious), or to decompose $32$ into $2 + 3*10$: you start by performing the operation $54 + 54$, which gives $108$. Then $540 + 540 + 540$ must be added. The number of additions to be performed is equal to the sum of all the multiplier digits minus one, so multiplying by $99$ requires $17$ additions. We can use the commutativity of multiplication to choose the multiplier factor that requires the fewest operations. For example, rather than multiplying $101$ by $99$ ($101*9 + 1010*9$) in $17$ operations, multiply $99$ by $101$ ($99 + 9900$) in one operation.