Let us now briefly describe development of science
and some important events during the time when Orffyreus lived i.e. (1681 –1745).
In
his times, Mathematics flourished with geniuses such as: Jacques (Jakob) Bernoulli, Leonhard Euler, Leibnitz, Isaac Newton
and Jean le Rond d'Alembert. Locke, Berkley, and Voltair were eminent philosophers of his time.
In
1681, when Orffyreus was born, around the same time, Newton was busy in quarrelling with Hook to discedit him. Newton
proved that inversesquare gravity did indeed result in elliptical orbits. In the same year, the first clocks with minute
hands appeared, Anton van Leeuwenhoek was elected a Fellow of the Royal Society, "The
Aerial Noctiluca" by Robert Boyle announced the discovery of phosphorus (see
Brand 1669) and "De Motu Animalum" [On the Motions of Animals] by Giovanni Alfosno Borelli was published posthumously. It
dealt with expansion and contractions of muscles, as well as the electric Torpedo Fish (more about which was in a posthumous
sequel the next year) (see Borelli 1664).
In
1682, the Latin scientific journal "Acta Eruditorum" was founded, lasted until 1776, and Leibniz and Orffyreus’ perpetual
motion machines frequently appeared therein as we shall see later. In 1683, "Acta Eruditorum" also published Count Ehrenfried von Tschirnhous (1651?) paper, which described ways to simplify polynomials, and gives new approaches to solving third
and fourthdegree equations. In 1684"Acta Eruditorum" published his article "A
New Method for Maxima and Minima as well as Tangents, which is Impeded by Neither Fractional nor Irrational Quantities, and
a Remarkable Type of Calculus for This". In this work, Leibniz expounded the tenets of differential calculus into six pages,
which practically nobody can comprehend. " Leibniz had to wait for some nine
years after devising his calculus to publish it.
In
1683, the words "insulator" and "conductor" were first used by John Theophile Desaguliers
(12 Mar 16???). He was confirming and extending the work of Stephen Gray.
When
Orffyreus was 2 years old, Edmund Halley saw the Great Comet. When he plotted
its orbit and predicted in writing in 1705 that it would return in 1758, and it did, everybody called it "Halley's Comet"
In 1984, Halley visited Newton, who casually remarked that
he solved that problem long ago. Halley told Newton that he really ought to publish
something about this, and persuaded Newton to eventually publish the most important book of the century, the "Principia."
In
1684, Robert Hooke effusively announced the world, including Edmund Halley and Christopher Wren that he had discovered the
secret laws behind the laws of Kepler. Wren was dubious, and offered a prize
for a correct solution.
In
1687, mathematician La Hire, whose interests in geometry arose from his study of architecture was appointed to the chair of
architecture at the Académie Royale. His interest in geometry arose from his study of perspective and he went on to make important
contributions to conic sections. He considered perpetual motion as a mechanical impossibility.
In
1686, Leibnitz, outlined the Integral Calculus for the first time in print, in
an issue of the journal "Acta Eruditorum." Almost simultaneously with Leibnitz's publication (above), Newton presents to the Royal Society his manuscript of Volume I of the Principia: "De motu
corpru" (The Motions of Bodies)
In
1687, Isaac Newton presented "Philosophiae naturalis principia mathematica" (The
Mathematical Principles of Natural Philosophy), The Principia, which includes his Three Laws of Motion, and his Universal
Law of Gravitation, in September.
In
1689, Isaac Newton, representing Cambridge, became a Member
of the House of Commons. In 1689, Peter the Great became the new Czar of Russia.
As we shall see later he decided to by Orffyreus’ invention.
In
1686, German physicist Otto von Guericke died in Hamburg,
May 11. In 1686, Bernard le Bovier de Fontenelle (11 Feb 16757?) published a
popularization of Descartes in "Entretiens sur la pluralite' des mondes" (Conversations on the Plurality of Worlds), as to
why there are numerous planets in the universe, some bearing life, and some (perhaps) civilizations. An idea that became vital to Science Fiction writers!
In
1690, Philosopher John Locke (29 Aug 16321704) presented his thesis that all human knowledge derives for sensedata and experience
alone, in the remarkable "Essay Concerning Human Understanding." He also praised the new 17^{th} century mathematical
view of the universe.
In
1691, British Chemist/Physicist Robert Boyle died in London,
He believed in capillary perpetual motion. He was the
first to distinguish between an element and a compound. He
defined chemical reaction and analysis. Boyle's Law: "at constant
temperature, the volume of a confined gas decreases in proportion to
the increase in pressure."
On
December 30, 1691, Michel Rolle of France,
published first time what we today call Rolle's Theorem of Calculus, in his book "Methode pour Resoudre les Egalites".
In
1692, Leibnitz introduced the mathematical words "abcissas", "coordinate", and "ordinate".
In 1693, Leibnitz reinvented the idea of Determinants, and explained them in a number of letters to Antoine de L'Hospital,
which were not published until 1850.
In
1693, what we call the calculus was, for the first time, published in a reasonably complete form, by John Wallis in "Opera
Mathematica", Vol.2, citing this as Newton's "Method of Fluxions."
In
1695, Dutch Astronomer/Physicist Christian Huygens died in the Hague
on July 8. Christian Huygens, Mathematician, Physicist, and Astronomer improved the lenses of telescopes, and thereby discovered
the Rings of Saturn and a satellite of Saturn. He was the first to build
clocks with pendulums. His study of systems of weigh led him to conclude that perpetual motion is impossible. Huygens' Principle:
"every point on a wave front of light is a source of new waves."
In
1696, French Astronomer Jean Richer died in Paris. In the
same year "A New Theory of the Earth" by William Whiston, Anton van Leeuwenhoek published "Arcana Naturae" (Mysteries of Nature),
explaining his discovery of microorganisms, specifically what we call Protista, and which he called "animalculaea.", French mathematician Marquis Antoine de L'Hospital (1661?) published "Analyse des
Infiniment Petits" (Analysis of Infinitesimals) which is the first textbook about Differential Calculus. This book, which influenced many mathematicians, included what we call "L'Hospital's Rule"  an intellectual
property which he actually purchased from Jean Bernoulli, who discovered it two years earlier.
In
1697, in an attempt to explain rust and combustion, erroneous concept of "Phlogiston" was put forward by Georg Ernst Stahl
(21 Oct 1660?). He derived it from hypotheses by Johann Joachim Becher, and in vogue for a century until replaced with the
correct theory of oxidation, by Lavoisier. Phlogiston turned out to be the last
vestige of Alchemy.
In
1704, Isaac Newton investigated light mathematically and experimentally and published his results in “Optics". He explained that light is made of tiny particles (which today we call photons), which
create vibrations in the ether. This book was reprinted repeatedly; It became
textbook of the century for experimental physics. It ended with famous set of unasnwered questions, which formed the basis
of sciencefiction later.
In
1705, Edmund Halley's "Synopsis astronomiae cometicae" correctly predicted the 1758 return of the comet last seen in 1682,
which thereafter becomes known as Halley's Comet.
In
1706, William Jones' "Synopsis palmeriarum methesos, or a new introduction to mathematics" became the first book to use the
familiar Greek letter "pi" to represent the ratio of a circle's circumferance to its diameter.
In
1707, Isaac Newton's "Arithmetic universalis" was published; it included an exact description of Descartes' Rule of Signs
In
1713 Isaac Newton's "Principia" appeared in second revised edition, with the new and famous "General scholium", and an introduction
by Roger Cotes.
In
1709, George Berkeley's wrote his "New theory of vision", it was the most important Psychology book of the 18th Century.
In 1710,
George Berkeley's book "Principles of human knowledge" argued that the "being" of objects amounts to their being perceived,
no more, no less.
In
1713, Jacques (Jakob) Bernoulli's published his "Ars conjectandi" (the conjectural arts). It was a posthumously published
treatise on Probability. It includes what we call Bernoulli's Theorem, a version
of the Law of large Numbers, which is the first published application of calculus to Probability Theory.
When
Orffyreus demonstrated his first wheel at Gera, in 1712, about the same time, John Flamsteed published his book "Historia coelestis Brittanica", the first volume of his star catalog, but it was a pirated edition. It cataloged the position of almost 3,000 stars and thus replaced Kepler's catalog;
the official complete edition was published in a posthumous threevolume edition in 1725.
In
1718, Jacques (Jakob) Bernoulli's treatise "Memoirs de L'Academie des Sciences"
was published posthumously. It was the first book to describe what we call the
Calculus of Variations, as a way to find which functions reach a maximum or minimum under various conditions. In
year 1738, Danielle Bernoulli, brother of John Bernoulli derived the famous Bernoulli’s theorem which is a mathematical
statement of the principle of conservation of energy applied to the steady motion of an incomprehensible fluid acted on by
external forces.
In
1721,when Orffyreus was at his creative peak, Willem Jacob van Gravesande published his book
"Mathematical Elements of Natural philosophy confirmed by experiments. It was
an Introduction to Isaac Newton's philosophy. It gave the first major support for Newtonian Physics in continental
Europe. We will see later how the learned professor examined the Orffyreus machine.
In the same year, Christian Wolff's published his work "Allerhand nutzliche versuche, dadurch zu genaur erkenntnis
der natur und kunst der weg gebahned wird" (Generally useful researches for reaching a more exact knowledge of nature and
the arts). He was also involved in the examination of Orffyreus’ wheel.
In
1723, Jacob Leupold published his "Theatrum machinarum generale.” Published in nine volumes, it was
the first systematic analysis of Mechanical Engineering. It included, ahead of its time, a design for a highpressure noncondensing
steam engine, the likes of which were not built until the early 1800s.
In
1725, John Flamsteed's "Historia coelestis Brittanica", in official complete edition, was published in a posthumous threevolume
edition. It cataloged the position of almost 2,884 stars and thus replaced Kepler's
catalog. An incomplete pirated edition appeared in 1712.
In, 1729,
Andrew Motte's produced English translation of Sir Isaac Newton's Latin "Principia"
In
1732, The most popular and translated treatise on Chemistry of its day,
"Elementa Chemiae" was published by Hermann Boerhaave. He rejected Alchemist’s
doctrine and proved that mercury cannot be obtained from lead by transmutation. He
similarly studied the conservation of mass under chemical reactions. He also studied thermal capacity (following a suggestion
by Farenheit) and generally led the way to a quantitative view of the natural world.
In 1734,
Voltaire’s "Lettres Anglaises ou philosophiques" became the first French language book introducing Isaac Newton's mechanics.
A
Swiss contemporary named Johann Bernoulli began to work out the simple and rudimentary concept of energy and the principle
of the conservation of energy. John Bernoulli wrote in 1735:
“If
the quantity of animate forces  the only source of the continuity of motion in nature  could not be conserved, and, consequently,
there were no equality of the acting cause and its result, whole nature would fell into a discovered state.”
In
1735, Carolus Linnaeus' "Systema naturae" presented the system of classification of organisms which is still used in the 21st
century. Carolus Linnaeus was born Rashult, Sweden, 23 May 1707. In 1736, his book “Fundamentica Botanica" organized
the vegetable world, and thus advances the structured modern view of nature.
In
1739, David Hume wrote his “Treatise of Human Nature". In this work, he explained Psychology and Human Nature by the
experimental method. On 26 Apr 1711, David Hume was born in Edinburgh, Scotland.
In
1739, Pierre de Maupertuis wrote his book, ' "Sur la Figure de la Terre". It contained the measurements that he made in lapland,
which confirm that the earth is flattened at the poles (and thus relatively bulges out at the equator).
In
1739, Voltaire’s work “Elements de la philosophie de Newton", coauthored with Madame du Chatelet, brought English
empirical philosophy to the Continental Europe.
Leonhart
Euler was only 11 years old when Orffyreus presented his machine. The elderly,
dying inventor could have had a discussion with Euler in his mature years, in the prime of his power and creative activity,
but unfortunately, they never met.
In
1735, Leonard Euler's "Petersburg Commentaries" introduced the mathematical notation for functions: f(x). Leonhard Euler first used the letter "e" to represent the base of natural logarithms, in correspondence
in 1727. In 1737, He published another book "Mechanica, sive motus scientia analytice
exposita.". It is the first textbook to systematically deal with mechanics by means of Differential Equations. In 1744, Leonhard
Euler wrote his “Theorium motuum planetarium et cometarium". He calculated the orbits of planets and comets, later refined
by Lagrange. In the same year, Leonhard Euler's "Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes"
extended the basic ideas of what we call the Calculus of Variations, and includes
Euler's Equation.
In
1743, Jean le Rond d'Alembert produced his "Traite de dynamique" (Treatise on
Dynamics). He went beyond Newton's laws of motion; d'Alembert's Principle is that actions and reactions in a closed system
of moving bodies are in Equilibrium, and he uses that to solve various problems in Mechanics.
In
1744, d’Alembert’s "Traite de l'equilibre du mouvement des fluides" applied his [1743] principle to describe the
motion of fluids. In 1746, Denis Diderot's wrote his "Pensees philosophique" (Philosophical thoughts). He argued that the
order of nature proves the existence of God. Denis Diderot was born in Langres,
France, 5 Oct 1713.
In
1743 J.D.Alembert (17171783) prominent French scientist philosophers and mathematician enunciated the principle of conservation
of energy in his “Traite de dynamique” and took part in the argument about two measures of motion and considered
it to be “arguments about words unworthy of philosopher’s attention”. He suggested that both measures of
motion formerly equivalent if the animate force is related to the distance traversed and the inanimate force is related to
time. This attempt however was not successful as it did not eliminate the qualitative differences between the forces. When
other forms of motion and their interconvertibility were discovered, their differences are fully realized. D.Alembert, the
philosopher denied that thought is a property of matter and believed that the soul exist independedly of matter.
Works of Euler, D'Alembert , and Larange changed the nature
of mechanical problems into mathematical problems. Owing to the development of differential calculus, they considered the
solution of problem much easier. With the aid of mathematical apparatus, they attempted to turn vague natural philosophical
idea of conservation of motion (force) into an exact law of nature suitable for mathematical processing and experimental demonstration.
In 1752, Euler published another article which introduced Newton’s Second Law in its present form,
i.e. that force equals mass multiplied by acceleration, since Newton himself had identified force with the rate of change
of momentum.
In , 1697, Jean (Johann) Bernoulli (6 Aug 1667?),
Mathematician of Switzerland, presented the problem of the "brachistochrone"
which, involving the determination of the "path of quickest descent", turned out
to be what we call the Cycloid. The problem was productively solved in various
ways, each extending The Calculus, by Bernoulli himself, Leibnitz, L'Hospital, and Newton.
By the end of 18^{th}century, mechanics had already been operating all notions
required to formulate the putative principle of conservation of energy in mechanics.
The expression k + p = constant was derived, where k still stood for the animate force, and p the potential force. At that time scientific scientist did not give much importance to the principle and
it had no other meaning at that time than a formal mathematical one. Unfortunately, it was only later that scientist erroneously
began to view the putative principle as great law of nature forming foundation of science. Similarly the equation of animate
forces Delta mw2/2 = f l also remained vague because of the uncertainty of the right
hand side f l that is notion of work which had been applied intuitively for the first time..
We
can see that by using mathematics scientist of the era changed the character of mechanics and indulged in theoretical speculations
and mathematical work. Nevertheless, perpetual motion was a practical problem that required hard work and experimentation
for its solution. But they could never conceive it as they relied heavily on the knowledge of authorities. They failed to
realize import of perpetual motion, theoretical as well as practical. Without much thought, they simply rejected perpetual
motion because authorities before them had rejected it. It is regrettable that
none of them experimented with perpetual motion. Then, how could we hope them
to have understood a device which was much more complicated than the science of their age (or even our age) could explain?
THE LEVEL OF CRAFT
It
is worth noting that, although today we see Orffyreus more as a practical man rather than as a scholar, nevertheless Ramananda
includes him in his list of the twelve leading thinkers of all time. It was a common practice to hide the secret; craftsman
did it with their inventions when they were filled with fear that their
method would lose its value once divulged. Similarly, Orffyreus never disclosed secret to any one. There is a religious significance
in it, since Orffyreus believed that perpetual motion was a divine craft, the perpetual motion machine was made in heaven’s
image and was therefore perfect. What is more remarkable was Orffyreus' application of the perpetual motion to power production.
Orffyreus father was a mason. In the 17^{th} century the following pattern was followed. First, the candidate took
an obligation on the Bible to preserve the mysteries of the craft. The word and sigh were then communicated and the charges
and legendary history were read. By 1700 a twodegree system, of entered Apprentice and Fellow Craft, was in place, and in
the 1720's a third degree, that of Master Mason, made its appearance. Gradually,
the ceremonies became more elaborate. The obligation, accompanied now by a physical penalty, was followed by the communication
of the sign and word of the degree in question, while in the second part of the ceremony there was a short catechism, using
a simple symbolism based on the stonemason's tools, in which the ceremony and the purpose of the degree were explained. From
the 1770's these explanations began to be expanded, incorporating additional working tools as symbols of particular virtues
and symbolical explanations of the candidate's preparation for each degree, as well as of the lodge furniture and members
regalia. today the basic framework of the craft in England is effectively the same as it has been since a standard for of
ritual was introduced in 1816. It was intended that the craft would become truly universal and open to men of all faiths.
Desagulers played an active role in free masonary.. Many Fellows of the Royal
Society who became Freemasons were influenced by Desaguliers' example. As a result nonChristians could now participate in
Freemasonry without compromising their principles, while Freemasonry itself could demonstrate that, although it supported
religion in general, it was not attempting to replace or challenge any particular denomination. In short, the revisions made
clear that while Freemasonry had an archaic religious basis, it was not in any sense a religion in itself.
.Craft
was becoming part of the fabric of social life. As Britain and neighboring countries were rapidly transformed into a major
industrial power, craft grew on an unprecedented scale. It caused a social upheaval with an explosion of new ideas, especially
in the field of science. What had been regarded as fundamental, inviolate truths now began to be questioned. In the midst
of such social and intellectual ferment craft appeared to many to offer a haven of calm and certainty with its core of unchanging
principles, and within the world of craft men from all sections of society, who might be separated by class and political
ideology in their daily lives, came together as equals
THE
LEVEL OF TECHNOLOGY
Let
us assess the level of technological development in Europe at that time. Indeed,
there was growing interest in scientific investigation and invention as 18^{th} century was marked by enormous volumes
of scientific discovery, and the start of the Industrial Revolution with inventions such as:
Machine Drill for planting seeds (1701), invented by Jethro Tull, Piston Steam Engine (1705), invented by Thomas Newcomen
(England), Piano (1709), invented by Christofori (Italy), Mercury Thermometer
(1714), invented by Farenheit (Germany), Thermometer (1730), invented by Reaumer
(France) precursor by Galileo.
The
clock, air pump, porcelain, and microscope already existed and were gradually improved. Few major inventions, such as iron
and paper manufacturing, house and shipbuilding, windowmaking, and printing all benefited people and made life easier and
more bearable. Printing developed, alchemy gradually transformed into chemistry
and started to provide usable ‘recipes’ for making new materials. The
properties of different elements, types of wood, and types of steel were studied. The
first hot air balloon was designed, and people learnt how to dig tunnels. Nevertheless, the most important technical
invention of the age was the steam engine. In 1698, a steam engine was constructed
by the French scientist Denis Papin (1647 – 1712) in which, for the first time, a piston was moved by steam pressure,
as opposed to the pressure of the atmosphere.
In
1698, an Englishman Thomas Savery (ca.1650?) patented "The Miner's Friend." This
was the first genuinely useful steampowered machine; it pumped water up out of coalmines.
After
the work of Denis Papin and Thomas Savery, Thomas Newcomen developed a steam engine, which was, to a certain extent, appropriate
for use, albeit for pumping water only. It was nearly 100 years later that James Watt developed a better steam engine, which
could actuate moving machines.
Invention is daughter of necessity; therefore, it was necessity that brought about
the revolution, especially in manufacturing. The major advances in technology,
particularly in the use of steam, in the later half of the 18^{th} century has its roots in devices that were invented
earlier in the era. Three big inventions enabled this development and paved the way for the later machines. These were:

John Kay's invention of the flying
shuttle in 1733.

Steam engine as we have described
above.

A frame for spinning cotton thread
with rollers, first set up by Lewis Paul and John Wyatt (1741). However, not
commercially practical, but it was important attempt toward solving the problem of machine spinning. These inventions enormously helped James Hargreaves to invent his spinning jenny 31 years later, which
revolutionized the making of yarn and the weaving of cloth. By 1800, a host of
new and faster processes was in use in manufacturing and transportation.
1.
Mills were also an important part of life in Orffyreus times; in fact, they were the first factories. Gristmill, Sawmill, Iron mill, and Flour Mill were common and they were an important part of the economy
of the cities and towns that grew up around them. They provide lumber for shelter, iron for pots, pans and other implements
and flour for bread. Mills produced manufactured goods for the overseas trade. The
four major types of mills in the 18^{th} century were::
Before
steam became a viable power source, most mills relied upon either water or wind to operate their machinery, forges, and furnaces.
Water was the most reliable source of power, thus people constructed mills near streams and other sources of running water.
Throughout Europe, the towns and cities that grew up around these mills became vital centers of commerce. Of course, water mill, and windmill with their various versions were developed in an empirical way, not
with the help of science.
The
use of machines reduced human labor and enabled goods to be produced in more quantities and cheaper for both producer and
consumer. Before the advent of machines and the factory setting, hand manufactured
goods, in single homes or cottages, where the owner worked side by side with his employees was normal. This changed with the
introduction of machines and mass production.
New
and improved designs of machines and steam engines paved the way for factory system.
New machinery also meant the standardization of products. The industrial
revolution first began in the British textiles' industry. It had its beginnings
in Britain because the English mercantilists were leaders in developing a commercial system that augmented the demand for
more goods. The Industrial Revolution gradually spread in Europe and would soon migrate to America with the opening of Samuel
Slater's cotton mill in Pawtucket, Rhode Island in 1793.
The
expansion in trade resulted into capital growth that was further used to develop industry and efficiency. A cheaper system of production had developed which was largely free from regulation. Besides, growing interest in scientific investigation and invention, there also were new ideas in England
that supported the movement. One of these was the doctrine of laissezfaire,
or leaving business alone. This doctrine had been growing in favor throughout
the 18^{th }century. It was especially popular after the British economist Adam Smith argued strongly for it in his
great work 'The Wealth of Nations' (1776).
Later,
Industrial Revolution lead to several other revolutions as technology became more sophisticated. The Transportation Revolution, Communications Revolution, and the Information Revolution all can trace
their roots in the Industrial Revolution. Each of these revolutions has added
to the betterment of mankind, and each of these has had their own effects on society as a whole.
The
Industrial Revolution has had far more impact on the world than any political revolution, because its influence on society
is longer lasting. For example, today we have automobiles, television, and computers, made possible by this revolution. Without the Industrial Revolution, we would not have these advance technologies.
We
can safely conclude that by denying perpetual motion scientist burst into ignorance and darkness at the time of the presentation
of Orffyreus’ wheel. Instead, both technology and science relied on steam
engine and took a false start. Later, much use of coal and oil polluted the atmosphere. Was it industrial revolution or really an industrial pollution  all at the irreplaceable
price of perpetual motion? Since perpetual motion ensures supply of free energy
to every individual, the pace and shape of the transportation revolution, communications revolution, and the information revolution
that followed after so called industrial revolution would have been different and unimaginable to us, if Orffyreus’
invention was recognized in due course.
Now
it is time to return to Orffyreus and his wonderful machine, to see how Leibniz, one of the greatest German scientists of
his time played a crucial role in dealing with Orffyreus’ amazing invention.

