While necessity is frequently the mother of invention, annoyance often comes into play as well. This was the case with [Blaise Pascal], who as a teenager was tasked with helping his father calculate the taxes owed by the citizens of Rouen, France. [Pascal] tired of moving the beads back and forth on his abacus and was sure that there was some easier way of counting all those livres, sols, and deniers. In the early 1640s, he devised a mechanical calculator that would come to be known by various names: Pascal’s calculator, arithmetic machine, and eventually, Pascaline.
The instrument is made up of input dials that are connected to output drums through a series of gears. Each digit of a number is entered on its own input dial. This is done by inserting a stylus between two spokes and turning the dial clockwise toward a metal stop, a bit like dialing on a rotary phone. The output is shown in a row of small windows across the top of the machine. Pascal made some fifty different prototypes of the Pascaline before he turned his focus toward philosophy. Some have more dials and corresponding output wheels than others, but the operation and mechanics are largely the same throughout the variations.
Operation of the Pascaline is quite elegant in its simplicity. For example, in order to add 3 and 5, one would insert the stylus between the ‘3’ spokes and turn the dial clockwise until encountering the stop. At this point, the display would read ‘3’. To add five to it, the process is repeated on the same dial by placing the stylus between the ‘5’ spokes and turning clockwise until the stop is reached. This adds five to the accumulator, and the output now reads ‘8’. Before performing a new calculation, the outputs must all be cleared. This is done by setting all of the input wheels to their highest digit, the spokes of which are marked with small slots. Once this is done, entering ‘1’ on the one’s place dial causes all of the accumulators to roll over to zero.
The Pascaline simulator shown in the video has simplified input dials. The actual surviving models show inputs that corresponded with the currency divisions of the time period. The French livre, which equaled one pound of silver, was subdivided into 20 sols. Each sol comprised 12 deniers, the smallest unit. To handle the arithmetic carry operation, each input dial connects to a 10:1 accumulator on the output drum. That is, when input exceeds nine (or in the historical case, 19 sols or 11 deniers), the output drum in the next place advances by one and the input drum resets to zero.
This four-banger in a brass chassis really only performed addition and should probably be called an adding machine. Subtraction is done using nine’s complement arithmetic. Each of the output drums has two sets of digits. Zero through nine appear on the bottom, and the nine’s complement of each digit appears in line above it. For the subtraction operations, a sliding bar is pushed down to reveal the nine’s complement digits on the output drums. Much like the Curta mechanical calculator we covered a few months ago, the Pascaline performs multiplication and division through repeated addition and subtraction operations.
Pascal’s machine was arguably both the first mechanical calculator and the first piece of office technology. It was a remarkable advancement whose carry mechanisms live on in odometers, gas meters, and much more. However, the Pascaline was a fragile creation that was prone to jamming and unintended carry operations. As Pascal himself was the only certified repair technician, it was also somewhat cost-ineffective. A more robust Pascaline could be made out of, say, LEGO.
Retrotechtacular is a weekly column featuring hacks, technology, and kitsch from ages of yore. Help keep it fresh by sending in your ideas for future installments.