The Swedish born, American civil engineer, inventor, and author John William Nystrom (1825–1885) (born as *Johan Vilhelm Nyström*) is known as the author of many books and inventions, among them, an interesting calculating device (a slide rule, a type of mechanical analog computer), invented in 1848 and patented on 3 March 1851. Nystrom was a Swedish engineer, who emigrated to the New World in the middle 1840s and settled in Philadelphia, embarking on a career primarily focused on nautical engineering and steam vessels. The complicated and repetitive calculations required for propeller and propulsion designs evolved into the development of his *calculating machine*.

The calculating device of Nystrom (see the nearby drawing from patent US7961) was a circular slide rule/calculator, based on logarithms, and was promoted for use not only in addition and subtraction, but also in multiplication and division. The device was presented and received a *First Premium* at the *Franklin Institute Exhibition* of 1849.

Nystrom promoted the device as *the merchant will find this calculating machine to be all they desire* and solicited a manufacturer in the 17 May 1851, issue of Scientific American, hailing it as *the most important one ever brought before the public*. By 1852, Nystrom offered the device at three prices—$10.00, $15.00, and $20.00 (a huge sum at that time), and initially he was likely making the instrument himself. Later in the 1850s it was manufactured and sold in Philadelphia by James W. Queen, and by George Thorsted in New York, and from 1864 to 1887 by William J. Young, one of the most prolific American instrument makers in the 19th century (totally about one hundred devices sold).

Let’s see how the inventor himself describes the device in his popular *Pocket Book of Mechanics and Engineering* (first published in 1854, this book had 27 editions published between 1854 and 2012 in English):

*The device consists of a silvered brass plate of about nine inches in diameter, on which are fixed two movable arms, extending from the centre to the periphery. On the plate are engraved a number of curved lines in such form and divisions that with their intersection with the arms, the most complicated calculations can be performed almost instantly.
The arrangement for trigonometrical calculations is such that it is not necessary to notice the functions sine, cosine, tangent, etc., operating only by the angle expressed in degrees and minutes, and without any tables, which makes it so easy that anyone who can read figures, will be able to solve trigonometrical questions. Any kind of calculations can be performed on this instrument, no matter how complicated it may be, whilst there is nothing intricate in its use. The author, who is the inventor of the calculator, has thoroughly tested its practical utility. All the calculations in Nystrom’s Pocket Book of Mechanics and Engineering have been computed by this instrument…*

There is also a detailed description of the device in a 42-pages book from 1854 (see description of Nystrom’s Calculator).

The patent model of Nystrom’s Calculator is still preserved in the collection of the National Museum of American History in Washington, D.C. (see the nearby image).

The surface of the device is a brass disc that rests on three wooden feet. It has two graduated brass arms, pivoted about a central spindle, which may be clamped to any desired angular separation and rotated together. Glass magnifiers are attached to both arms. A small dial on the top of the central knob can be moved to record rotations of more than one full circle.

There are four unlabeled circles on the calculating rule, called *a*, *b*, *c*, and *d*. They go from the outer rim inward. Circle *b* is divided into 20 equal parts. Subdivisions of these parts are represented by a series of parallel curves extending between the outer rim and circle *b*. These, in combination with scales marked on the rim of the arms, allow one to measure subdivisions of the distance between equal parts. The outermost circle *a* is a logarithmic scale ranging from 1 to 10 twice. A series of lines between the two outer circles give intermediate values, which are read from the rotating arms. The circle *c*, just inside *b*, is divided from 0 to 90 degrees so that the sine of an angle indicated is given on the outer circle *a*. The parts of the scale are unequal, with the tens value of degrees from 10 to 49 indicated by large digits. The innermost circle *d* is divided for finding cosines.

#### Biography of John Nystrom

John William Nystrom was born in 1824 in Småland province, Sweden, as Johan Vilhelm Nyström. After receiving his engineering degree from *Kungliga Tekniska Högskolan* (Royal Technological Institute) in Stockholm, in the middle 1840s, he emigrated to America (he became a US citizen in 1854) and settled in Philadelphia, embarking on a career primarily focused on nautical engineering and steam vessels.

In 1859 Nystrom proposed a hexadecimal (base 16) system of notation, arithmetic, and metrology called the *Tonal System*. The system was described in a book from 1862 and in addition to new weights and measures, his proposal included a new calendar with sixteen months, a new system of coinage, and a hexadecimal clock with sixteen hours in a day. In 1875, Nystrom proposed a new duodecimal (base 12) system of notation, arithmetic, and metrology called the *Duodenal System*.

While in Philadelphia, Nystrom became a protégé of William Sellers (1824-1905) (see the nearby photo), a mechanical engineer, manufacturer, businessman, and inventor who filed more than 90 patents, president of the Franklin Institute, and for many years, head of the machine tool firm of William Sellers & Co., which was a very influential machine tool builder during the latter half of the 19th century.

Nystrom became an Assistant Secretary and Chief Engineer of the US Navy during the Civil War. He also spent a number of years abroad, advising both Russian (in the end of 1850s he was appointed as engineer in chief to the Volga-Don Railway and Don-Azoph Steam Navigation Company, Consulting Engineer to the Russian Steam Navigation and Trading, and designed a hydraulic pontoon-doc in Sankt-Peterburg), and Peruvian governments on their operation and deployment of steamships. Later on, he returned to the USA and spent his remaining years in Philadelphia, being quite active in the affairs of Franklin Institute, as a member of the board and chairman.

Nystrom was the author of many other books and inventions besides the above-mentioned, such as: steam engines, refrigerator, hydraulic pontoon-dock, centripetal propeller, eye-pieces for telescopes, and others.

John William Nystrom died in Philadelphia, Pennsylvania, on 11 May 1885, at the age of 61.