Progress is made by lazy men looking for easier ways to do things.
The German engineer and master builder—Johann Helfrich Müller (1746-1830) is a very interesting figure in the world of mechanic calculators, not only for his small calculator, essentially an improved version of the machine of Philipp Matthäus Hahn, which he created, but for his plans to build a difference engine almost 40 years before Charles Babbage. He also wanted to built a machine, that was capable of being configured to use Leibnitz’s arithmetica dyadica.
Johann Müller was a creative mind and started to make inventions from the beginning of 1770s. Firstly he created a theater, equipped with optical and mechanical effects for the children of his boss—Prince Georg Wilhelm, later on he designed a large and powerful burning mirror, as well as other devices.
In the beginning of 1780s Müller was asked by the local superintendent’s office to check and recalculate some tables relating to the volumes of trees. To shorten this task he had come up with the idea of a machine for the purpose. Soon he realized however that with a few small changes, he could get the machine to perform subtraction, division and multiplication as well. Most probably, at that time he came across an article (probably that in the magazine Teutschen Merkur) about the calculating machine of his compatriot, Philipp Hahn, which he decided to use as a prototype, and to try to improve somehow. Interestingly, later in middle 1780s Müller was accused by Hahn for stealing his design, but flatly denied accusations, although comparing the machines of Hahn and Müller (they are as like as two peas), it is hard to believe, that Müller didn’t use at least the basic design of Hahn. Moreover, the German author and critic Johann Heinrich Merck, who visited Hahn in 1778, was a friend of Müller.
After about three months of designing, in June, 1782, the project was ready and Müller gave the drawings to a local clock-maker in Darmstadt, with the order to make the machine in metal. The work was taken over by a pair of journeymen in the same trade and on the 20 June 1784, the machine was ready. On 24 June 1784, the 14-digit calculator (see the upper image) was demonstrated in the Göttingen Academy of Sciences, which appointed Müller as a correspondent. In July 1784 the device was described in the journal Göttingische Anzeigen von gelehrten Sachen (p. 1201-1206, see the description), and later in other editions.
Müller’s calculating machine is very similar to the machine of Hahn and was based on the Stepped Drum of Leibniz, but it is larger (285 mm diameter, 95 mm height, weight 15.5 kg). It was in the form of a round box with a handle placed centrally and the number wheels concentrically arranged around the handle. It could calculate with 14 figures and its number and gear wheels could be altered to enable it to operate with non-decimal number systems.
An adding operation can be done as follows:
1. Using the buttons (marked with h), we set the first addend in the windows of dials (f), using the black digits.
2. Set the other addend using the side dials (g).
3. Make one revolution of the crank (K). The sum can be read using the black digits in the windows of dials (f).
4. Third, fourth, … addends can be entered at the side circles (g) and each adding operation is performed using one revolution of the crank.
The subtraction can be performed in similar way, but the minuend is set according to the red digits in the windows of dials (f), while the subtrahend is set in the side dials (g). After the rotating of the handle to one revolution the result can be seen using red digits in the windows of dials (f).
The multiplication can be done by performing successive additions, while the division is done in the way, similar to the multiplication, but are used the red digits of the dials and is based on successive subtractions (just like using the machine oh Hahn).
Compared with Hanh’s machine, Müller’s had three important improvements:
1. The axes of stepped drums from the Hahn’s machine, which are used for entering of the numbers, are not anymore set by pulling upwards (which requires a great precision), but by means of rotating dials, with inscribed digits from 0 to 9 over their periphery.
2. The axes, along with mounted on them pinion-wheels, can be easily changed with pinion-wheels with different number of teeth, which provides a possibility of calculations in different numeral systems.
3. In the mechanism of the machine is included a bell, which rings in case of overflow during the adding or negative result during the subtraction (if the operator tried to subtract a larger number from a smaller one).
While still working on his machine, on 22 May 1783, Müller wrote a letter to his schoolmate and friend, the German physicist Georg Christoph Lichtenberg (1742-1799), in which he described his invention and set forth his plans. He intended to make a profit from the machine and informed Lichtenberg about his intention to make another copy of it, as soon as the first one was ready. He also wanted to build a couple of simpler calculating machines for addition and subtraction only and hoped to sell his machines in England and Russia. Later on however the Grand Duke of Hesse-Darmstadt Ludwig I, bought the first machine for 4000 Gulden, and incorporated it in his collection of scientific instruments.
Müller intended also to use his machine for calculating of tables. He wrote: How easy it would be, by this means, to correct and extend the tables of logarithms. Later on Müller in fact used the machine to calculate a set of tables—”Tafeln des Kubischen Gehalts des Bauholzes”, which was published in Frankfurt in 1788 (see the lower image). In another letter to Lichtenberg from 9 September, 1784, Müller recorded a new thought in a postscript for a printing tabulating machine, as follows:
P. S. If the calculating machine sells well, I would in the future make a machine, which would simultaneously print in printer’s ink on paper any arbitrary arithmetical progression in natural numbers or the units, together with the numbers of the terms and the lines in between and which would halt of its own accord, when the side of the paper was full up. After setting the first figures, all one has to do is to turn a handle and after stopping to turn over the paper or to put another sheet in its place. In this way, a sequence of 60 terms can be delivered in a minute.
Admittedly Müller never built a machine of this kind. Instead the idea was further perfected and presented together with his universal calculating machine in a book published in Frankfurt and Mainz in 1786. This 50 page booklet was edited by Müller’s friend Philipp Engel Klipstein. It contained, besides an exhaustive description of the mode of operation and design of the constructed machine, also a discussion about its advantages over manual computation and a detailed account of the special security (correction) mechanisms incorporated.
Finally, under the heading “Further inventions of superior calculating machines and an arithmetical printing machine” the new machine was presented. In these passages, it is made clear that Müller, perhaps at an even earlier date, had invented a difference engine (capable to operate to the third order of difference) for the rapid production of error-free tables, by means of “whole series of numbers” and by using “difference-numbers” (Differenzzahlen). A description similar to that in the postscript to Lichtenberg is given of the printing part, which was supposed to print directly onto paper, rather than produce matrices for stereotypes.
No mention is made of how the necessary mechanisms to accomplish this were to be designed. Nonetheless it is clear from this document that Johann Müller had conceived the idea of a difference engine by the year 1786. Müller indicates that if someone were willing to finance its construction, he was willing to make the machine. He estimated that a table of x3 (1 ≤ x ≤ 100000) could be produced in just over ten days of effort, even if the operator only worked for eight hours per day.
Such a machine will be proposed almost 40 years later by Charles Babbage. It is known that several chapters of the book have been translated for Charles Babbage by his friend John Hershel. However, the date of this translation is unknown and the question remains whether some of Müller’s ideas have been used for Babbage’s machines.
Biography of Johann Helfrich Müller
Johann Helfrich von Müller was born in Cleve (a town in the northwest of North Rhine-Westphalia in Germany), on 16 January 1746, in the family of Lorenz Friedrich Müller (1715-1796), a colonel of the artillery, who worked as an architect and chief engineer in Giessen, and Maria Magdalena Josepha Hambloch (1726-1800). Johann had a brother, Franz, who later became a lieutenant colonel in the British Army. The German writer and journalist Helfrich Peter Sturz (1736-1779) was their cousin.
In 1753 the family moved to Darmstadt, where Johann received his initial education at small private schools, getting private lessons in languages and drawing. Later he was sent to study at the Darmstadt Grammar School. In the spring of 1762, he became a cadet in the Artillery Corps of the Hessian army at Giessen, where his family had moved, and began to attend lectures in mathematics and physics at the University of Giessen (Interestingly, at the same university some 20 years before lectured as a professor of mathematics one of the creators of early calculating machine—Christian Ludwig Gersten). However, Johann he never got an academic degree, because at his father’s request, he left the University and started self-study.
Johann’s father, Lorenz, who was in the building trade (architect and engineer), and was a son of the architect and civil engineer Helfrich Müller (1686–1759), wanted his son to carry on the family tradition, but Johann appears to have found certain other careers equally tempting. While still at the grammar school, he wanted to become a painter; at the university he hoped to be a professor of mathematics and physics. Soon however he discovered that the profession of an engineer was the most interesting of all and he devoted much time to reading books on statistics, hydraulics and mechanics.
In 1769, the Artillery Corps was reduced in strength and Müller was forced to look for work elsewhere. Shortly afterwards, he was employed as an engineer by Prince Georg Wilhelm, the Governor in Giessen—a man with wide interests in both civil and military engineering and architecture. In 1769/1770 Müller made an extensive educational travel to Italy (Rome, Naples, and Venice) and Austria (Vienna). In April 1772, Prince Wilhelm took Müller with him on a five month trip to Paris, where they visited and studied many of the marvelous buildings and machines in the city and at St. Cloud, Versailles and Marly. On his return from the trip, Müller devoted most of his time to architectural and mechanical design and various financial calculations for his master.
In February 1774, Müller became building inspector in Darmstadt and three years later master builder with the responsibility for designing and maintaining buildings (Ingenieur Hauptman). He also was expected to act as an adviser in case of emergencies such as floods. In 1778 he returned to the military service as a Captain in Artillery Corps, to be raised as a Lieutenant-Colonel in 1797, and a Colonel in 1800.
In 1770s Müller took part in the design of several public buildings in Darmstadt. The fountain in the Market Square in the front of the old Rathaus (Town hall) of Darmstadt, built by design by Johann Müller in 1780, is still preserved (see the upper photo from 1900).
Johann Müller was a person of a very creative mind and started to make inventions from the beginning of 1770s. First he created, by an order from the Prince, a theater, equipped with optical and mechanical effects for the children of the Prince. Later on he designed a large and powerful burning mirror, sun clock, air pump, air gun, barometer, range finder, and even a perpetuum mobile, but the most interesting for us invention was certainly his calculating device in 1780s.
In the period 1776-1790 Müller was the state architect of Giessen. From 1792 until his retirement in 1820 Müller served as a Hofmeister and Major in Darmstadt. For his efforts and contribution he was knighted (together with his brother) by the Grand Duke of Hesse on 23 June, 1810 (i. e. he became von Müller).
On 19 August 1781, Müller married to Catherine Fabrice Johanetta von Westerfeld (1761-1830), a daughter of Esaias Fabrice von Westerfeld (1709–1779) and Elisabeth Katharine Schröder (1724–1765). The family had five children—two daughters and three sons, but unfortunately all died young, except for one of the daughters—Friederike (1784-1841). Friederike’s daughter is the German novelist and social critic Johanna Udalrike Louise Gerhardine Schücking (1815-1855).
Johann Helfrich von Müller died on 12 June 1830, in Darmstadt.