06 January 2020

Arithmographe: The First Portable Calculator

Somewhere between 1666 and 1675, a Parisian doctor of medicine, Claude Perrault, designed a device which could perform many arithmetic operations. He named it as Abaque Rhabdologique. Later, many mathematicians and inventors improved and re-shaped this ingenious machine. But it never became so popular. Later in 1889, J. L. Troncet of France created an improvised version of the above and he called it the Arithmographe.
Troncet’s invention became enormously popular. It became a market hit by the end of 19th and continued to be popular till the beginning of the 20th century. Initially, they were sold as a small notebook with a set of multiplication tables, a manual about how to operate it and a stylus. The dimensions of the Arithmographe were: 10 x 13.5 x 0.5 cm. He used flat metal bands with notched edges to represent digits. These bands were moved with the stylus to enter numbers. In the earlier machines there was no possibility to "carry ovedr". But that was rectified.
Troncet's Arithmographe used the technique of moving the stylus up to and around the top, to "carry over" when the sum of two digits was greater than 9, but there was no zeroing (reset) mechanism, which was introduced later by others.
One of the most popular versions of the Troncet-type calculator was the Addiator, which was created in Germany by Addiator Gesellschaft. Introduced in 1920, over 100,000 units were sold in the first year, and versions of this device remained in production as late as 1982. The Addiator could be used to add or subtract. In the early versions of these devices, two panels were provided by having the addition function on the front and the subtraction function on the back. Later models had two separate panels on the front, one for addition and one for subtraction.

These machines are operated with a metal stylus provided with the machine.
Arithmographe and the Addiator have become a collector's item now. But you can make one easily by following the instructions below.

Make an Arithmographe
As part of your School Project

Things required:
  • Cardboard,
  • Three plastic scales of 12 inches scale with a width of 3 cm.
  • A hacksaw blade
  • Gum, cutter etc.
Preparing the base:
  • Take a card board 37 cm X 25 cm
  • Draw vertical line at 4 -1-1-3-1-1-3-1-1-3-1-1-4 cms apart.
  • Bend it as shown in picture 1. 
  • Apply gum inside the bends and stick them.
  • Take another card board of 37 cm X 17 cm and paste it below the first one. Picture-2
  • Cut 9 pieces (picture3) of 37 cm X 3 cm and paste 3 each in each slot as shown in picture 3. 
  • Close the bottom with another small card board piece as shown in picture 4. 
Preparing the scale:

  • Take a scale and from 1 cm to 10.5 cm make 20 cuts at every 0.5 cm with a hacksaw blade as shown in the picture.
  • The scale is kept with the flat side up
  • Take the second one and make such 10 cuts on the right side and 20 cuts on the left side starting from 1.cm
  • Take the third scale and make 10 cuts on the right side with a gap of 0.5 cm as shown above.

Preparing the 4 strips: 

  • Cut 4 card board strips of 13 X 3 cm size bend both end at 1 cm (picture 6)
  • Paste the first strip at 7.5 cm from the bottom. Picture-9.
  • Paste the second strip above it at 8.5 cm after leaving 1 cm gap. Picture-9.
  • Place the first scale in the first slot and align to the bottom. Picture-9.
  • Mark where the 10th cut from top is appearing. Paste the third strip just below the 10th cut. Picture-9.
  • Paste the fourth strip just 0.5 cm above the first cut. Picture-9.
Adding Numbers to the scale:
  • Make three strips like this on the three scales just 2.5 cm from the bottom. Picture 8
  • While pasting, align the scale to the bottom and paste this number strip on it so that the arrow should be visible between the two bottom strips. Picture 10

Preparing the cutout:
  • Take a 11 X 11 cardboard and make a cutout out shown in picture 7, with the same measurement.
  • Paste this on top of the third and fourth strips. While pasting, the number should align to the first 1 to 10 cuts on the scale. Picture 10.

The Final Touch.
  • Insert each scale in the respective slots.
  • Align the scales properly so that  
  • "0" will appear between the first and second cardboard strips.
  • On the first scale, the 11th cut will align to "9" and the 20th cut will align to "0" of the cutout.
  • On the second scale, 10th cut on the right will align to 9, and on the left side, the 11th cut will align to "9" and the 20th cut will align to "0" of the cutout.
  • On the third scale, 10th cut on the right will align to 9.
How to do the calculation:
Example1: 2+2=4
Take a pen. Insert the point on the cut against 2 in the first scale and slide it downward till the pen touches the bottom. The bottom "0" will change to "2" to add 2 to this, insert the pen again in the cut against the number "2" and slide down. The bottom two will become "4".
Example2: 4+8=12
To add "8" to this number, insert the pen in the gap against the number 8 and slide down. You may not be able to slide the scale down to make the pen touch the bottom. At this point you will see an Upward Arrow in the result box. Then without lifting the pen, slide the scale up till the pen touches the top. Once it touches the top lift the pen and insert it in the small column next on the right side of the second scale.. Now slide that scale one step down. Now the answer will be: 12.
This is how the calculation is done.