David Fleischacker, Ph.D.

*[May 26, 2009]*

If Newton’s physics and Dalton’s chemistry are related as a lower to a higher viewpoint, there must be some point of contact, just as numbers and operations were the points of contact between arithmetic and algebra. It seems that this point is mass. Newton and Dalton dealt with masses within the context of “relative weight.” Newton related objects in terms of masses, distances, accelerations, and forces, especially his well-known discovery of the law of gravitation. Dalton discovered patterns in the “relative weights” that lead him to some postulates about atoms and compounds. A significant difference arises though. Newton studied large objects, large meaning what can be seen such as marbles and planets. Dalton studied gases and mixtures of solids and liquids (especially gases), and then made postulates about objects that cannot be seen. The objects that they studied seem very different, so how can they be related as lower and higher viewpoints?

Before drawing some conclusions, a closer examination of Newton and Dalton is in order.

### 1. Isaac Newton: The Law of Gravitation

Newton studied the relation of objects in terms of mass, distances, accelerations, forces, and the gravitational constant. If we specifically examine his equation for universal gravitation, his focus will become clear. The equation requires little space to write,

F = (Gm_{1}m_{2})/d^{2}

Explanation of this formula requires far more than writing it out, and though a full explanation will not be given here (any physics text book will give an explanation and some examples, along with some problems to solve), some identification of each of the terms is in order. In brief, “F” stands for force. “G” for a gravitational constant that is relevant for any mass. “m_{1}” stands for a mass. “m_{2}” stands for a second mass. “d^{2}” is the square of the distance between the masses. The equation relates only two masses. Relating more would be far more complicated. It says nothing about what kind of masses are used, whether they are planets or marbles. Furthermore, it is supposed to be true of any masses whatsoever, hence it received the title of the universal law of gravitation. But, in the concrete, rarely, if ever, are only two masses involved. This law presupposed something similar to the “vacuum” that is presumed in Galileo’s law of falling bodies In that law, without friction a feather and a marble would fall to the earth in the same amount of time. In Newton’s law, without any other masses, presumably, the equation would hold true. However, just as with object falling on earth are effect by friction, so planets are affected by a number of other masses in addition to the earth or sun. So, this law really does not fully explain the motions of any particular planet (In fact, Newton realized it did not explain the data better than Ptolemy’s circular theories, though it was a simpler explanation). Yet, it is an important first step, just as distinguishing acceleration from velocity was an important step toward the law of inertia, the notion of mass, and the law of gravitation.

### 2. John Dalton: The Atomic Theory and Relative Weights

Dalton developed a new atomic theory of mass from their weight relationships. He writes “In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the “simples” which constitute a compound.”^{(1)} He goes on “Now it is one great object of this work, to show the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one or more compound particle. Dalton, like Newton, speaks of “two bodies,” but unlike Newton, Dalton adds the concern with their combination, not their gravitational relation.

“If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple:

1 atom of A + 1 atom of B = 1 atom of C, binary.

1 atom of A + 2 atoms of B = 1 atom of D, ternary.

2 atoms of A + 1 atom of B = 1 atom of E, ternary.

1 atom of A + 3 atoms of B = 1 atom of F, quaternary.

3 atoms of A + 1 atom of B = 1 atom of G, quaternary.” (Page 112)

Then he adds, “etc., etc.”

This is rather similar to what happens when one is discovering algebraic patterns within arithmetic.

Dalton then proceeds to discuss the actual relative weights of different substances that were known. Hydrogen was given a base weight of 1, and to this all the other “simples” or “ultimate particles” can be determined. Carbon is five times the weight of hydrogen, hence it has a relative mass weight of 5. Oxygen is seven times hydrogen, so it has a relative weight of 7. Water is a binary combination of hydrogen and oxygen, so it has a relative mass weight of 8. From this, he then unites the rules for combining bodies with their discovered relative weights to formulate another law which presupposes the law of the conservation of mass. The weights of binary, ternary, and quaternary compounds should be equal to the combined weights of the “simples” that constitute the compounds. Still, analyzing and synthesizing these “simples” and compounds is not an easy matter, and Dalton develops some rules of thumb.^{(2)}

After developing these rules of thumb, Dalton then proceeds to explain which actual weights are combinations of simples, binaries, ternary, etc., and what those simples, binaries, ternaries, etc., might be. For example, he then discussed how one might reason that water is a binary of hydrogen and oxygen.

### 3. The Higher Viewpoint

So, what is the link between Dalton and Newton? The link can be grasped by paying closer attention to the experiments and theories each relied upon and developed. Newton’s law of gravitation applied not only to planets but to any mass object. The gases, solids, and liquids of the chemist are some of those objects. Gases, liquids, and solids have weight, and weight is a combination of a mass and gravitation. Newton was concerned with relationships between any masses, relationships which were defined in terms of their respective distances, and the changes in their velocities (or lack of such changes). So, he described force as a product of mass times acceleration, or force as a product of a gravitational constant multiplied by the two masses, then divided by the distance between them. Dalton does not use Newton’s law of universal gravitation as the lower viewpoint in which he discovers patterns and laws of a higher viewpoint. He only uses the notion of weight, but because he refines it in terms of relative weights, the real difference is due to a difference of mass. When developing “relative weights” what really distinguishes the objects is the mass, because the “gravitational component” is equal.^{(3)} So, what distinguishes Newton’s concern from Dalton’s is that Dalton wanted to discover patterns of different mass relations, Newton wanted an explanation of weight itself. It would be many centuries before the actual formulas of physics could be utilized in the lower viewpoint as a phantasm or image for the higher viewpoint of chemistry.^{(4)} At this point, problems in the combining of weight was the starting point for chemistry just as negative numbers, fractions, and other arithmetic problems were the starting points for algebraic rules.

Dalton’s concerns or horizon form a higher viewpoint because he is developing new principles and laws regarding weights and the combining of weights into compounds.^{(5)} He is not developing a fully elaborate higher viewpoint of all aspects of Newton’s theories and formula’s, but it is a higher viewpoint with regard to one dimension, and that is weight, and implicit in weight, mass. (I will continue to articulate this point in further revisions of these notes because the point of “physics” at which Dalton’s viewpoint arises is much like the initial development of the higher viewpoint of algebra from the problems of negative numbers or of calculus from the power rule, and ignoring all the other areas of arithmetic from which algebra can formulate its new rules, or the other areas of algebra, from which calculus can build its rules).

A further inquiry would bring us to grasp the relationship of Dalton and Mendeleev. Is Mendeleev’s periodic table a higher viewpoint to Dalton’s atomic theory, or is it a homogeneous expansion? That is a further question, which would be worthwhile to investigate.

- John Dalton, “A New System of Chemical Philosophy,” in
__Breakthroughs in Chemistry__, ed. Peter Wolff (New York: A Signet Science Library Book, 1967), 111. - Dalton lists seven rules. “1
^{st}. When only one combination of two bodies can be obtained, it must be presumed to be a binary one, unless some cause appears to the contrary. 2^{nd}. When two combinations are observed, they must be presumed to be a binary and a ternary. 3^{rd}. When three combinations are obtained, we should expect one binary and the other two ternary. 4^{th}. When four combinations are observed, we should expect one binary, two ternary, and one quaternary, etc. 5^{th}. A binary compound should always be specifically heavier than the mere mixture of its two ingredients. 6^{th}. A ternary compound should be specifically heavier than the mixture of a binary and a simple, which would, if combined, constitute it; etc. 7^{th}. The above rules and observations equally apply, when two bodies, such as C and D, D and E, etc. are combined” (115). As a note, Dalton was also one of the first to develop symbols of these “simples” and compounds (recall the need for phantasm to obtain insight). - If the masses of the objects were greater, then they would affect the overall gravitational force, but like most of the objects that Galileo studied, there mass is insignificant (which is why “light” and “heavy” object fall to the earth with the same acceleration, baring any significant friction). These relative masses would hold even if the gases, liquids, and solids were on a different planet, or on the moon, hence the real term that distinguishes is the difference of the masses between the gases, liquids, and solids.
- Gases became important because they, as a matter of fact, were able to be produced from mixing substances, and these gases tended to be divided into what we now call elements. Dalton was one of the first to postulate that these were elements, or as he named them, “simples.”
- Also, notice the similarities to arithmetic and algebra. Arithmetic wanted to get numbers through the operations of addition, subtraction, multiplication, division, powers, and roots. Algebra discovered patterns in adding, subtracting, multiplying, dividing, powering, rooting. Similarly, Newton wanted to related masses through distances, accelerations, gravitational constants, and forces. Dalton discovered some patterns in a particular range of these related weights (that range being limited to the weights of gases, solids, and liquids on earth that can “combine”).