Class: Philosophy 221, Dr E. C. Wit
TR January 9 & 11, 1996
9:45 - 11:00, 107 Moore Bldg.
Einstein, A. and Infeld, L., , 1966, The Evolution of Physics, from concepts to relativity quanta, New York: Simon & Schuster
Holton, G. and Brush, S. G., 1973, Introduction to Concepts and Theories in Physical Science, 2nd ed., Reading, Massachusetts: Addison-Wesley Publishing Company,
Kline, M., 1953, Mathematics in Western Culture, New York: Oxford University Press
Levenson, T., 1994, Measure for measure: a musical history of science, New York: Simon & Schuster.
Space, Time and Motion from a historical and philosophical standpoint
The Relationship of the Human Mind to the World of Phenomena
Einstein and Infeld (E&I) start with an almost obligatory statement that they want to give an outline of the human accomplishments in directing the human mind to understand the physical reality. This seems of course to be the intention of all good science. Science could, naively, be said to be the task to let the mind and reality coincide; it is the reproduction of the world of phenomena in the world of ideas. E&I express it as such:
Our intention was rather to sketch in broad outline the attempts of the human mind to find a connection between the world of ideas and the world of phenomena. (E&I, p.xv)
Such relationship is however not directly evident. E&I's eludations seems to suggest that only from the time of Galileo and Newton serious work has been done. They explain the basic idea of this connection between the mind and the world: MATHEMATICS. It might sound strange, but in fact in order to connect to wagons of a train there has to be some kind of link that keeps them together. A Vietnamese and a Dutch cannot talk together if there is nothing that links them together. Only if there is a third language internal to both of them, e.g. english, then they can communicate. A better example, maybe, is that a Dutch and a German can communicate because both dutch and german have certain germanic groundstructure internal to both of them. Now when we want the mind to understand to the world, we should first recognize how different the mind and the world actually are. The mind consists of "immaterial" thoughts, while the world consists of physical events. How can there ever be a connection between the two? E&I neglect to see the importance of that question, or rather, they neglect the long intellectual history that led to the present. They write:
Attempts to read the great mystery story are as old as human thought itself. Only a litttle over three hundred years ago, however, did scienctists begin to understand the language of the story. (E&I, p.5)
We have to recognize however as Newton himself acknowledges that the scientists of 300 years ago were standing oon the shoulders of giants, and that only thus they could see so far. An important contribution to later developments of physics is made by the philosophical and scientific speculations of the Greeks. It were they who made methological attempts to see the intermediate medium of mind and world to be mathematics.
The Greeks developed a geometrically approach to mathematics, partly out of practical reasons -- to deal with new mathematical discoveries, such as the irrational numbers, partly in concordance with the emphasis of Greek philosophy on the eternal forms. The fulfilment of this movement in to its summun was established by Euclid and several Alaxandrian mathematician of the Hellenic area later on. The mathematization proces started with Thales of Milete in the 6th century B.C., was empowered by the Pythagoreans in the subsequent centuries (who proposed rather than a geometrisation of nature, a formulization, i.e. a putting into numbers, of nature -- a more modern approach.) The Pythagoreans were the first group to treat mathematical concepts as abstractions and though Thales and his fellow Ionians had established some theorems deductively, the Pythagoreans employed this process exclusively. Plato was the great philosopher that encorperated in his philosophy several Pythagorean principles. ("Let no one ignorant of geometry enter here.") All that prepared the stage for a large group of mathematicians among his followers and the school he founded.
If we look at when the development of mathematics in the Greek society took of, we can make a direct connection with philosophers like Plato. A lot of Greek mathematicians had been his pupil or came from later generations of students in the Academia founded by him. We can see that in his philosophy both certain new aspects of mathematics as the importance of mathematics prefigure. First of all, the rationalist aspect of Plato's philosophy and the emphasis on Form over Matter can be seen as a model for the new mathematics. Secondly, in his philosophy Plato explicitly stresses the importance of the study of mathematics for a good life.
Brief Grasp of Plato's Philosophy
Plato described the situation of human beings as being imprisoned in a cave. (Draw) This is not so strange as it might appear at the first sight. In our lifes we see thousands of different chairs and still we call them all a "chair." Similarly, we call this painting "beautiful," but also that one. So there must be some Idea of Chair and Beauty that we apply to all of them. From this General Idea we deduce that this particular object is a chair, and that that particular painting is beautiful. Apparently there must be a World of Ideas, from which all that we human beings see are mere shadows. Plato described that world as the world of light, outside the cave. To make the transition from darkness to light, mathematics is the ideal means. On the one hand, it belongs to the world of sense, for mathematical knowledge pertains to object on this Earth. On the other hand, considered solely as idealization, solely as an intellectual persuit, mathematics is indeed distinct from the physical objects it describes. It purifies the mind by drawing it away from the contemplation of the sensible and perishable to the eternal.
For Aristotle and other Greek philosophers the form of an object is the reality to be found in it. Matter as such is primitive and shapeless. This first form of thinking of the essence of reality in mathematical terms has proven to have been a very fruitful means to describe reality. In a way it seems paradoxical. We reject a certain qualitative approach and instead put what we see and feel in numbers, but nonetheless we come to further qualitative conclusions about reality. The only way the paradox could make sense is that we, with modern science, accept that both the mind and the world ‘think' in the language of mathematics. This is not an invention of some scientist in the last centuries, but instead has been prepared for by a long history of philosophy/science.
Nature as a Detective Story
E&I present in their book the history of physics as a detective story, in which the truth about the physical reality is the murder that has to be solved. The story they present is a classic one in which ‘false' clues have to be distinguished from the ‘right' ones. A problem with this whole approach is that the writer of a normal detective story knows ‘who-dunnit.' But even if you are Einstein, you still will never know what the real truth is really about. E&I even admit that. They say:
We are somewhat like a man trying to understand the mechanism of a closed watch. ... He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or meaning of such comparison. (E&I, p.31)
If E&I took their own comparison a little more serious they might have understood that older version of the watch are not so much ‘false' clues, but simply less sophisticated, as most likely their own ‘right' clues, will one day be outdated by new evidence and theories. E&I instead vulminate against Aristotle and the body of the pre-mechanical sciences as being ‘false.'
It seems natural to conclude that the stronger the action exerted on a body, the greater will be its speed. ... It is a familiar fact to readers of detective fiction that a false clew muddles the story and postpones the solution. ... Aristotle's great authority throughout Europe was perhaps the chief reason for the long belief in this intuitive idea. (E&I, p.6)
This misses however a lot of subtleties. For instance, that a renewed interest in the Greek philosophy and sciences was a movement that freed the scientific mind from religious dogmatism and thus eventually opened up the spirit for a secular science. Moreover, a lot of the Hellenic astronomy, for instance, was, scientifically, far superior to what was accepted by the Catholic dogma. Thus marking Galileo as the "real beginning of physics" (E&I, p.6) seems to be arbitrary and rather a play of words, while ascribing to Galileo "the discovery and use of scientific reasoning" (E&I, p.6) seems simply false.
Einstein and Infelt's presentation does have some merrit however. Let's concentrate on the advantages for the rest of this lectures. Most important, it is a fact that the historical discovery of certain scientific path do not present themselves a being the best didactic path. Sometimes it might be better to start with the conclusion of long historic research and judge all the previous material according to the contributions it made to the discovery of the conclusion. This is what E&I are doing. They present us a retrospective picture. They present themselves as the writers of the story of nature and they present us the clues that occured in history to understand this story.
Galileo introduced the notion of an "idealized experiment." This was an experiment that could actually never be carried out in practice, but which revealed an isolated aspect of reality, purified of irrelevant influences. Such approach revealed some fundamental ‘laws' of nature.
The first clue
Thinking about motion it seemed that in experience everything stops after a while. Aristotle had concluded that rest is the natural state of an object and that the objects revealed an ‘habit' to return to their natural state. Galileo turned this idea upside down. In fact, Galileo said, objects in motion stop because of external influences. If we would look at an idealized cart on an ideal frictionless road, there would be nothing that would stop the cart and therefore it is most naturally that objects continue their movement whenever they are moved. This is the law of inertia, that can be formulated as:
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Apparently, the intuitive idea that velocity is an indication of external forces acting on a body, is mistaken. By performing an thought experiment we came to the conclusion that exactly the absences of forces is responsible for a constant velocity. So than what is an indication of force? We saw that the friction force slow the object down. So not velocity itself, but the change of velocity is an indication of force.
This is a peculiar thing. It takes a while to think about it. At first it might seem perfectly ok. You have a change of velocity on the one hand and a force on the other. The peculiarity is that one will never observe a force without a velocity change. Therefore, instead of an explanation of the concept of force, it seems that the second clue rather defines the concept of force.
This is not the full story. Force does mean more than that. This becomes clearer when we look at other phenomena involving motion. The motions that we observed till now were all rectilinear. Of course, this is only a very limited conception of motion. The path of the moon for instance is by approximation a circle but the velocity is constant. If there would be no force working on the moon its path would be a straight line. Thus, there must be some force acting on the moon which makes it change its direction. Force is thus not only connected to the change of velocity, but also of the change of the direction of the motion.
We can understand this in a more general form. We can understand velocity as a vector, its length determining the speed, the coordinates determining the direction. In general, a change of the vector of velocity defines the presence of a force. The clue to an explanation of motion along a straight line was simple: external force is responsible for change in velocity; the force vector has the same direction as the change. And now what is to be regarded as the clue of curvilinear motion? Exactly the same! The vector from the end point of the first to that of the second indicates the direction of the acting force. But it is essential that the velocity vectors should be seperated only by a "very short" time-interval -- making "very short" precise led Newton and Leibniz to the discovery of the differential calculus.
The second clue
A very important example of motion is that of the earth around the sun. It is known that the path is a closed curve, called the ellipse. This can be deduced from Newton's theory of gravitational force but it took a long history from Hellenic scientists from Alexandria, such as Ptolomeny, to Copernicus and Kepler to come to finally come to a quantitative explanation of a long observed fact.
Despite the historical preparation, E&I take the theory of universal gravitation as the second important clue to the detective story. It is Newton's contribution, of course, that he formulated his second law, the law of gravitation, that the attractive force between two bodies depends on the square of the distance between the two bodies.
In fact, these two clues together determine motion. Newton's general law of motion is of a general character and states the connection between force and the change in velocity. Newton's second law, the law of gravitation, is special, and states the exact dependence of the particular kind of force involved on the distance between the bodies. In this way Newton was able to connect the motions of falling stones, of the moon and of planets.
The third clue
One would hardly suspect the existence of an important clue which no one noticed for three hundred years. It concerns the identity of two different concepts of mass. The idea is that we can ‘weight' masses in two different ways, and it is not quite clear initially that these two ways would lead to the same answer. The important clue is that we postulate that such identity does exist. The first way of measuring yield the inertial mass. If we have two identical forces acting on two resting masses and we find that the velocity of the first mass is three times greater than that of the second, then we conclude that the first mass is three times smaller than the second. The gravitational mass is principally a different concept; we do it by weighting on a scale. The first experiment had nothing whatever to do with gravity, the attraction of the earth, while the second is based essentially on its existence. The results appear to be exactly the same, but in classical physics that is just a coincidence. The answer of modern physics (relativity theory!) is that the identity of the two masses is fundamental and forms a new and essential clue leading to a more profound understanding (gravitation º acceleration).
Since this identity of inertial and gravitational mass was fundamental for the formulation of the theory of relativity we are justified in examining it a little more closely here. What experiments prove convincingly that the two masses are the same? The answer lies in Galileo's old experiment in which he dropped different masses from a tower. Informally: the readiness with which a body responds to the call of an external force depends on its inertial mass. If it were true that the earth attracts all bodies with the same force, that of the greatest inertial mass would move more slowly in falling than any other. The "calling" force of the earth depends on the gravitational mass. The "answering" motion of the stone depends on the intertial mass. Sinse the "answering" motion is always the same -- all bodies dropped from the same height fall in the same way -- it must be deduced that the gravitational mass and the inertial mass are equal. This equality is the third clue in uncovering the detective story of nature.
Substance; heat and matter
Substance is a notion that everyone knows and uses in daily life. It often is employed to as referring to ‘chemicals' and in political correct speach it means ‘alchohol and other intoxicating goods.' The more proper use is linked to the concept used by chemistry. Related to the substance as a chemical material,
we think of a substance as something which can be neither created nor destroyed. (E&I, p.41, italics mine.)
A substance is that what reality is made of. If we think about all what we see around us, we know that it might change shape, but that there must be some fine indestructible stuff. If we want to know more about the history and the meaning of the term "substance," chemistry itself is only of partial help. Chemistry has had only a short history on its own. The early figures of the science that called itself chemistry -- Lavoisier, Dalton Berzelius, and Avogadro -- all lived in the period roughly from the second half of the 18th century till the first half of the 19th century. The questions that were answered were, however, from a much older date.
From the early Greek period on, there had been speculations about the internal structure of matter. There had been roughly two answers, as Levenson points out:
- The one says that the world is all of a piece, formed from the same stuff, a single kind of matter than can be rearranged to build all the variety that we see.
- The other holds that the world is made up from many different stuffs, matter that in its simplest state retains the distinct qualities that produce all the varied substances we encounter in the ordinary world of experience.
Before Berzelius made in his "Transaction of Physics, Chemistry & Mineralogy" of 1818 the choice for the latter, a long history of speculation and research on the matter had shaped many intuitions and conflicting concepts.
The First Atom
As early as the 6th century BD, Thales of Milete had answered the question about the inner structure of matter according to the first option: Everything is Water. The choice was not random or absurd, and one could give several reason why he made this choice. The distinction between form (eidos, idea, essence!) and matter (body, Christian contempt for the body as the inessential) is the distinction between that what is essential and that what is accidental. It is the form that really matters. Now if the form or the shape of a thing is that what really matters and we want to think of what that form actually is, then we could think of a substance that is flexible and able to take all possible shapes: Water!
However, this theory was soon challenged, and one century later Democritus formulated another theory, which can be called the first atomic theory. He also wanted to answer the question of the inner structure of matter. He reasoned that it is impossible to divide a physical object infinitely, because infinite division would create "cosmic mush, formless and ultimately nonexistent." The infinite divided stuff, being formless, would be unable to reconstitute itself. Infinite division is taking away the form, i.e., the essence of the physical object, which is impossible. Therefore, division has to stop somewhere on something indivisible -- a-tomos.
According to the atomists, atoms were invisible and made of the same stuff, but they differed in size and shape. But it was still a miracle how the atoms could be responsible for the diversity of the world, if they were all made of the same stuff. The atomists used a beautiful metaphor to explain that mystery. There exist another area, in which limited number of units -- only differing in size and shape -- construct a diverse reality: letters put together create a wor(l)d with meaning! The atomist argued that the atoms were like letters: if they were put together in a specific way, they would make a molecule (Epicures) which was another substance -- This suggests that they might have know something about chemical reactions.
Lucretius, a Roman writer, summarized the atomist theory in his "De rerum natura":
Obviously it makes a great difference in these verses of mine in what context and order the letters are arranged. If they are not all alike, yet the most are so; but differences in their position marks the difference in what results [the words]. So it is when we turn to real things; when the combination, motion, order, position, shapes of matter [the atoms] change, so does the thing composed [out of these atoms].
Democritus' reasoning came in certain instances very close to certain positions that we hold today:
- Brownian motion, discovered in 19th century, later explained by Einstein.
- Democritus' account of certain macroscopic properties of certain physical objects (hardness of certain metals, gas-like property of gases, etc.) on the basis of the microscopic structure.
However, the Greek atomist were philosophers and not experimental scientists. They never tried to find experimental evidence for their conjectures.
Nonetheless, in the Greek concept of the atom lay the seeds of a renewed atomic theory more than 2,000 years later. The Greek theory had made several important assumptions:
- the possibility of simple particles beyond the reach of the human senses,
- the possibility to reason from what we can see to what we cannot, to build an inferential chain to bridge the gap between experience and the hidden essence of matter,
- the existence of a void between the atoms,
- the conservation law of atoms: no atom can be created or destroyed.
The Greek atomic theory was quickly pushed aside and in the Medieval times the 4-elements theory (water, fire, earth and air) was adopted. It was not until the end of the 16th century that Bruno took up the atomic theory again -- for which (and other things) he paid with his life: burned in 1600 by the Inquisition.
Re-emergence of the Atom
In retrospect it is clear that the model of the atom re-emerged out of several distinct questions:
- What is the physical structure of matter? What is the nature of heat?
- What is the nature of fire? (The Phlogiston Theory)
- What is the basis of chemical phenomena?
ad 1. What is the physical structure of matter? What is the nature of heat?
In Newton's theory of physics the universal law of gravitation postulates that particles of matter are the agencies of mutual attraction. Newton speaks of point-masses and his theory only works for those ideal entities. This methodological requirement could, however, be translated into a certain view of matter. Rather than seeing matter as a kind of homogeneous tissue, which was not uncommon at that time, Newton suggested that on a sub-human, microscopic level matter consisted of "solid, massy, hard, impenetrable moveable particles" (1704, Opticks) This conception of matter is beautifully consistent with his theoretical "point-masses."
In the 17th century people like Torricelli and Boyle developed a Gas Theory. They found that there existed a certain relationship between Pressure P, Temperature T (in K) and Volume V of a gas, the Gas Law:
P*V/ T = constant
When Boyle tried to explain this relationship, he suggested two different atomic gas-models:
- static model
- kinetic model
The Static Model
A gas consists of particles at rest, and, therefore, they must be comprised out of compressible material to explain the fact that a gas can expand. Some suggested things like little springs or, as Torricelli had proposed, like little pieces of wool. This explained part of the expandable nature of a gas, but, according to the theory, it is possible for a gas to expand infinitely -- a thing for which the idea of a spring did not seem to fit. Newton had shown that bodies could act on a distance, but that was an attractive force. Therefore, some suggested that on the atomic level there existed a repulsive force -- N.B. to be able to explain expansion. It was Newton himself who showed that if we assumed that the repulsive force was inversely proportional with the distance between the two centers, it explained the pressure-increase, when the volume would decrease.
In this model heat was viewed as a special kind of substance, caloric, surrounding the atom. When we heat something, we would in fact add more caloric to the object. This static atomic theory pictured the atoms as balls with some caloric stuff around them, and very often the atoms were contiguously positioned in the material -- depending on whether or not one accepted the repulsive force working at a distance. The static theory was widely accepted until mid-nineteenth century.
The Kinetic Model
Already in 1738 the Swiss physicist/statistician Daniel Bernoulli worked out several implications that Boyle had called the kinetic theory. Many of his notions were extremely revolutionary; so revolutionary, that his work on the atomic theory was soon forgotten. Boyle had thought of the kinetic model of gases as describing the atoms in constant agitation, moving around in some kind of "imponderable fluid." This fluid, also called ether, has been one of the most recalcitrant notions in the history of science. For a long time people have tried to prove that there exist something like ether, but all endeavors have been in vain. Bernoulli, on the other hand, discarded this notion and followed the original Greek idea: atoms are moving around in a void. The elements are perfectly elastic and in the void they moved according to Newton's laws of motion. His theory was a form of Impact-Theory, which is still accepted until this day. The pressure exerted by the gas is nothing but the result of the impact of the collisions of the many, fully elastic particles. This would explain the Gas Law: if we decrease V, then the particles have lesser space to move around, and, therefore, more impacts occur per square inch: i.e., increase of P.
Bernoulli had also a substantially different answer to the question of the nature of heat. Instead of considering it to be another element, it was his hypothesis that heat is nothing but the motion of particles. This is the contemporary notion of heat. It had taken a long time before science was able to make a proper distinction between heat and temperature. The two notions were often confused. Especially in the static model temperature and heat were identified: heat, or caloric, was taken to be like a substance which was responsible for the temperature of the object.
Whereas retrospectively we see that Bernoulli had a much more advanced notion of the atom, his theory was difficult to accept for his contemporaries because of two of his hypotheses:
- The equivalence of heat and internal molecular motion. This notion of heat completely ignored the very fashionable concepts of ether and caloric.
- The idea that a well-defined numerical relationship, such as the above described Gas Law, could be deduced from a chaotic picture of randomly moving particles. Is was an old idea that no order could result from chaotic events. It was only with the development of statistics in the 19th century (the invention of "averages" and stochastic laws) that people started to understand that some order could result from chaos: for instance, social science discovered that the number of crimes and suicides exhibited ordered yearly averages.
ad 2. What is the nature of fire? (The Phlogiston Theory)
Besides the concepts of ether, the concept of the phlogiston hunted the history of science for centuries and let to many fruitless research. It was finally Lavoisier who after 250 years solved the mystery, by which he triggered the first developments of what can now be called chemistry. In 1772 the French Academy of Sciences put together a committee to investigate how it could be possible that diamonds are consumed by fire. In that time fire was still a mysterious phenomena. For a long time, during the Middle Ages, fire had been considered a separate element, but since the development of the sciences in the 16th and 17th century it became clear that such an explanation was not tenable. Thus, instead, the phlogiston theory had been presented. A phlogiston was thought as an insensible, undetectable fluid that left the material, when the material was burning. Fire was nothing but phlogistons leaving the object. This explained the loss of weight and bulk of a burning object. However, by careful measurement, it had been shown, that certain metals gained weight when they were roasted over high heat. Scientist had suggested that some phlogistons possessed a negative weight -- somewhat like Aristotle's concept of "lightness."
Lavoisier, member of the committee, re-installed an old Greek atomist assumption: Matter is Conserved. This meant that he rejected the idea of negative matter, and, thus, he rejected the phlogiston theory. In a series of carefully controlled experiments, he found out air consisted of two parts. One part makes a burning candle lit up, while the other extinguishes it. He also saw that the inflammable part reduced with a burning object in a closed environment, leaving the nonflammable part behind. Instead of introducing a mysterious particle that left the burning object, he found out that fire is nothing but a "chemical reaction" between the inflammable part, which he called "oxygen," and the material. This destroyed the phlogiston theory and opened up a way to study other "chemical reactions."
ad 3. What is the basis of chemical phenomena?
Rather than postulating the existence of the atom, Lavoisier's work necessitated its existence. The hypothetical approach was initiated by Newton, who had asked: "If atoms exist, how would they behave?" Although Lavoisier didn't "believe" in the existence of atoms, his theory enabled his successors to accomplish to prove it. Nonetheless, people were far away from the "right" atomic theory. That only came by a further investigation into the nature of other chemical phenomena.
In the 17th and 18th century slowly the concept of a chemical element developed. It was operationally defined as a substance which cannot be separated into different components by any known methods. It meant the shift from the question "What is an atom?" to a more pragmatic view that helped to bring about new developments. Even Dalton's postulate of the wrong, "static theory" gave falsifiable predictions that initiated new theories.
Dalton accepted the "static theory" of atoms, because he believed that Newton had actually demonstrated it to be right. Together with this theory he accepted the caloric view of heat. He thought of atoms as centers around which a layer of caloric lay. The edge of every caloric layer touched the adjacent caloric layer (Dalton didn't believe in the repulsive force between atoms working at a distance). Moreover, atoms were unchangeable, compounds are made of molecules, all atoms or molecules of a pure substance are identically alike, and in chemical reactions atoms are only rearranged, not created or destroyed. But the most important assumption he made was the following: in forming molecules during chemical reactions, the number of combining atoms of the different elements form simple, definite ratios. Even though the assumption is false, it sparked a lot of fruitful researched. Dalton set out, for instance, to determine the relative weight of the atoms, because he "knew" in what ratio the different atoms reacted. He assumed, for instance, that water was the product of the reaction of 1 Hydrogen and 1 Oxygen atom -- the simplest ratio. Of course, in the subsequent determination of the relative weights of many atoms, several inconsistencies came up, which led Berzelius to make corrections to Dalton's work.
It was finally, in 1811, an Italian, Avogadro, who saw the inherent restrictions and contradictions of the "static theory." The "static theory" could not explain how it was possible that two volumes of Hydrogen and 1 volume of Oxygen would become two volumes of water-vapor. Avogadro took two important steps to overcome the deadlock into which chemistry was about to get:
- He rejected the static theory and accepted a form of kinetic theory instead.
- He formulated a postulate, which today is known as Avogadro's Law, i.e., Equal volumes of all gases, whether elements or compounds, or even mixtures, contain equal number of elements.
This finally solved the problem how two volumes of Hydrogen and 1 volume of Oxygen could become two volumes of water-vapor, namely by assuming that water consisted of 2 Hydrogen and 1 Oxygen element [2 H2 + O2 --> 2 H2O]. Nonetheless, in the next 50 years Avogadro was forgotten and chemistry continued in Dalton's steps. Slight amendments were made, but always on the assumption that the atoms in a gas are contiguous. This led to constant contradictions, which, in the 1840s, almost led to the loss of faith in the entire atomic theory. At that point Avogadro's work was rediscovered, which necessitated the acceptance of the kinetic concept of the atom. Thus, in a century the foundations of chemistry had been layed out, by determining certain basic qualities of the atom. The concept of the atom has been expanded to accommodate quantum theory, and it has undergone some dramatic corrections in recent years, but this goes, unfortunately, beyond the scope of this class.