People find life entirely too time-consuming.
Stanisław Jerzy Lec

The Swedish-Norwegian engineer Axel Jacob Petersson (1834-1884), was a universal inventor and is famous for several books and articles, and the construction of railways and viaducts, including the famous railway bridge Järnvägsbron i Minnesund, steam engines, a rotating camera for photography, military equipment like a bayonet and a repeating rifle, and other devices, between them two very interesting calculating machines.

First of the machines (called Calculator) Petersson devised in 1871 and presented it in 1873 at the Weltausstellung 1873 Wien (World Exposition 1873 Vienna), while the second was presented in 1876 at the 1876 USA Centennial Exposition in Philadelphia. In several sources is mentioned also a pin-wheel calculating machine, presented in 1866 by one C. Petersson at the Stockholmsutställningen 1866 (Stockholm Art and Industrial Exhibition), but nothing is known about this device, and if it was made by Axel Petersson.

The official report of the United States Centennial Exposition Commission mentioned that:
The most important exhibits of this class [Mechanical Calculation] were the two calculating machines of Mr. George B. Grant, of Cambridge, Massachusetts, the larger one of which is arranged to combine and print functions involving 100 elements. The combination of the several parts is extremely simple; the number of elements can be indefinitely increased, and the machine acts with the greatest certainty. The smaller machine, or arithmometer, is an adding-machine, which successfully rivals the well-known one of ColmarThe adding-machine of Petersson, of Norway, also deserves special mention here.

It seems the machine was in serial production but in small numbers. It is unknown how many devices had been manufactured by Petersson, but to the present time survived four examples, three in Norwegian museums, and one—in the Tekniska museet, Stockholm (see the lower photo).

The construction of the machine is based on the stepped drum of Leibniz, mounted in the center of the machine (it is the first calculating machine to use a single central stepped drum, making it possible to build the machine with a diameter a lot smaller than all previous machines for all four basic arithmetic operations), which can be rotated by a crank. The box is of cylindrical form with a diameter of 9.5 cm and a height of 20 cm and is made of cast iron, copper alloy (brass, copper, and bronze), and wood. The weight of the device is 6.6 kg.

The input mechanism consisted of sliders (five or six in different variants), and the output mechanism consisted of dials (12 or 14 in different variants). In the variant with 14 dials, the tens carry is self-contained and allows “endless” calculation. The computing mechanism was unidirectional and subtraction was done by using complement to 10. The machine has also a revolution counter, which is necessary to be used during multiplication and division.

The result mechanism has two sets of windows, the upper set is used during the addition/multiplication, and the lower (complementary numbers)—during the subtraction/division. Resetting of the result mechanism is driven by a lever (seen in the upper left part of the photo), which should be rotated in a clockwise direction, afterwards the mechanism is restored automatically by a helical spring.

The whole mechanism of Petersson’s Calculator seems to be simple, but very reliable and easy for manufacturing, and as a whole, it is clear that Axel Jacob Peterson was a remarkable constructor. Interestingly, the principle of Petersson’s Calculator will be successfully implemented some 30 years later by Paul Haack (it is unknown if he was a relative to Petersson’s wife Thekla Helene Haak, despite the same surname) and Christel Hamann in Germany in their remarkable machine Gauss.

#### Biography of Axel Jacob Peterson

Axel Jacob (also spelled as Jakob) Petersson was born in Ålem, Kalmar County, Sweden, on 4 March 1834. He was the son of Andreas Petersson (1790-1870) and Catharina Margareta Petersson (nee Selin) (1798-1870). Axel Jacob had two brothers: Johan Alfred (1827-1870) and Karl Andreas (1830-1867), and two sisters: Kristina Sofia (1829-1891) and Amanda Charlotta (1836-1917).

In 1852 Axel Petersson enrolled at Teknologiska Instituten in Stockholm, where he studied civil engineering. He graduated in 1855 and until 1859 he worked in the Sveriges Kanalbygning (Sweden’s Channel Building organization) and in the private Jernbaneanlæg (a Swedish railway construction company). In April 1859, he was hired as an assistant engineer for the construction of the railway Kongsvingerbanen in Norway and moved with his wife Thekla Helene Haak-Petersson (see the nearby photo) to Norway.

Axel Petersson was a brilliant engineer and universal inventor. He was famous for several books and articles, and the construction of railways and viaducts, steam engines, a rotating camera for photography, military equipment like a bayonet and a repeating rifle (see in the lower image Krag–Petersson rifle, developed by Ole Herman Krag and his friend Axel Petersson in the early 1870s, patented in 1872, and adopted by the armed forces of Norway 1876 to 1900), calculating machine, and other devices.

In 1860 Axel Jacob Petersson settled in Kristiania (modern Oslo), where in 1865 he was appointed as an engineering director of the Norway Railway Construction Office. He was responsible for the construction of bridges and viaducts on the Østfold Line and the Dovre Line between Eidsvoll and Hamar. Some of the larger constructions of Petersson were: Minnesund Railway Bridge (Minnesund Jernbanebru), Ljan Viaduct (Ljansbroen), Hølen Viaduct, and Sarp Bridge (Sarpsbroene). Petersson invented the pendulum pillar principle, which was the first in the world applied on Hølen Viaduct.

In Kristiania Axel Jacob Petersson and his wife Thekla Helene Haak-Petersson (born 12 November 1838 in Källdalen Norrbärke, Dalarna, to Peter Theodor Haak (1809-1876) and Carolina Margretha Haak(1807-1879)–died 20 March 1894 in Kristiania) lived in Akershus and had three children—two daughters: Annik (died in infancy), and Elin Margrethe (10 Nov. 1868–23 Sep. 1945); and a son: Axel Tage (1865-1952).

Axel Jacob Petersson’s son—Axel Tage Petersson (see the nearby photo) (8 Apr. 1865–14 Aug. 1952), became a doctor and worked for many years as a district physician in Elverun, a town in Hedmark county, Norway.

Axel Petersson was a co-author of two books on machine design: Rules for Machine Parts Design (1866 and 1877) and Rules for the Design of Waterwheels and Turbines (1868). He also wrote a series of articles in the Polyteknisk tidsskrift journal, mainly concerning railway construction.

Axel Jacob Petersson occupies a prominent place in the Norwegian railway buildings’ history. In particular, he was an ingenious designer of bridges and viaducts with linked spans. Petersson brought contemporary attention far beyond Norway’s borders through his beautiful solutions to difficult technical tasks. His graceful railway bridge Järnvägsbron i Minnesund (see the lower photo), launched in 1879, is still in use.

Axel Jacob Petersson was active until 1881, when as a result of over-strain (which eventually led to mental illness) became seriously ill and never managed to recover until his death on 15 January 1884, in Oslo. In Norway, there was a legendary story that stayed around for a long time that the constructor of the Ljan Viaduct (namely Petersson) had committed suicide before its opening because he did not trust it to stand. The story is fake, as the Ljan Viaduct opened in 1879 (and is still working fine), so Petersson obviously survived it.