Before electronic calculators became affordable in the 1970s, logarithm tables and slide rules were the most common calculation tools used by scientists, engineers, and navigators. However, there was a time in the early 1940s, when a purely mechanical, pocket-sized calculator was engineered. Its use was short-lived – only 30 years or so – but it continues to remain a mechanical marvel.
Curta belonged to the set of mechanical devices that were motivated by the need to reduce frustrating calculations. It has the appearance of a pepper grinder, and a feel of it too because of a crank that has to be rotated to add numbers.
A drum with two sets of teeth is located at the center, and manages the arithmetic. This drum has 37 layers; each layer has a thickness of half a millimeter. It is linked, via a transmission shaft, to a readout numeral wheel, which is located on the top of the Curta, and shows the final result (see image below). The drum is also connected to a setting numeral wheel via a setting shaft. This setting numeral wheel is located on the side of the Curta, and displays the number that is fed into the device:
The ‘carrying’ function of addition is undertaken by a carry pin, a carry lever, a carry gear, and a component called the tens bell. The carry pin extends from the readout wheel and pushes a component called the carry lever whenever the readout numeral wheel crosses ‘9’. This carry lever is responsible for pressing down on the carry gear, which surrounds the shaft corresponding to the subsequent higher place. This positions the gear so that it can communicate with the tens bell, and increment the number by one digit as the bell revolves.
Addition uses one set of teeth of the drum; subtraction uses the other. Multiplication and division are performed using the concepts of addition and subtraction.
Curtas (and most modern computers) carry out subtraction by using the method of complements, i.e., by first computing the nines’ complement of a number. This technique is used to express the difference between two numbers as a sum and therefore rules of addition can be applied to perform subtraction. For example, to find 492-243, the technique can be summarized as:
To clean up all memory of the Curta and start from the beginning, a clearing ring (see image above) can be spun once which sets the results (displayed at the top) as well as the turns counters (located on the side) to zeroes.
To illustrate how a Curta can be used, let us consider two simple examples
Sum of two numbers, 12 and 41
First, the number, 12 is entered using the two setting knobs at the extreme right. The two numbers, ‘1’ and ‘2’ will appear in the two windows. Next, the crank is rotated once; the results register will show the number 12. The second number, 41, is entered similarly, using the numbers, ‘4’, and ‘1’. The crank is turned; this adds up the input, 41, to the previous number on the results register, 12, resulting in the number 53, which appears in the results counter.
It is noted that to subtract two numbers, once again, the first number is introduced using the setting knobs followed by one rotation of the crank. The second number is entered the same way but for it to be subtracted, the crank has to be first lifted to its upper position, followed by one rotation of the crank. The resulting number is displayed in the results register.
Product of two numbers, 3 and 40
A product such as 3 x 40 can be solved by first entering the number 40, followed by three rotations of the crank.
Curtas are no longer in use for computations and are mostly just expensive collectibles for numberphiles. Nevertheless, they are exquisite tokens of a time when cogs and stepped drums were intimately linked to numbers.
Learn more about the Curta
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