Higher
Viewpoints: Part Four
From Newton to Dalton: Physics to Chemistry
by David Fleischacker
Draft Version 1
Copyright © 1997. All rights reserved
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 (actually Dalton used
"weights"-and this is linked to mass). 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 these objects 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 = (Gm1m2)/d2
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. "m1" stands for a
mass. "m2" stands for a second mass. "d2"
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 (Without friction a
feather and a marble would fall to the earth in the same amount
of time). In the gravitational law, planets are affected by a
number of other masses in addition to the 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. He goes on to discuss the possibilities
of two bodies which might combine with each other.
"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."
Notice the similarity to algebra?
Dalton then proceeds to discuss the actual relative weights of
different substances that were known. Hydrogen was given a based
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
arithmatic 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 homogeous
expansion? That is a further question, which would be worthwhile
to investigate.
1. John Dalton, "A New System of
Chemical Philosophy," in Breakthroughs in Chemistry,
ed. Peter Wolff (New York: A Signet Science Library Book, 1967),
111.
2. Dalton lists seven rules. "1st.
When only one combination of two bodies can be obtained, it must
be presumed to be a binary one, unless some cause appear to the
contrary. 2nd. When two combinations are observed,
they must be presumed to be a binary and a ternary. 3rd.
When three combinations are obtained, we should expect one binary
and the other two ternary. 4th. When four combinations
are observed, we should expect one binary, two ternary, and one
quaternary, etc. 5th. A binary compound should always
be specifically heavier than the mere mixture of its two
ingredients. 6th. A ternary compound should be
specifically heavier than the mixture of a binary and a simple,
which would, if combined, constitute it; etc. 7th. 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).
3. 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.
4. 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."
5. 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").
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