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Looking in Freshman Lab III – Looking into The Constitution of Bodies:
How does the supposition of particles help us to see? 1
LAVOISIER’S PROGRAM FOR GENERATING SEQUENCES OF EXPERIMENTS LEADING TO FACTS AND
IDEAS, BASED ON MEASURING WEIGHTS (1789)
In his “Preliminary Discourse” 2 Lavoisier lays out guidelines for how to arrive at knowledge in
the physical sciences in general and in chemistry in particular. Students should follow the same course
as “nature follows in the formation of a child’s ideas … [T]heir ideas ought to be only the consequence,
the immediate continuation (suite) of an experiment or observation” (0.6). According to Lavoisier the
child’s first ideas, engendered by its sensations of its needs, are of objects appropriate for satisfying
those needs. Insensibly over time, as a result of a sequence (suite) of such sensations and observations
of suitable objects, the child generates a succession “of ideas, all bound to one another.” As with the
child so in chemistry, if one were “an attentive observer,” one “could, up to a certain point, even find
again” in the sequence of sensations, observations, and analyses “the thread and the linking
(enchaînement) of those ideas, bound to one another, which constitute the totality of what we know” in
chemistry (0.5). 3
In accord with this account, we might say that Lavoisier will aim to show us a sequence of
sensations and observations of experiments and a corresponding sequence of ideas, which he generated
from them. In his case following “the course that nature follows” appears to consist: i) in linking “the
facts and the truths of chemistry in the order most appropriate for facilitating the insight (intelligence)
A Wednesday Afternoon Lecture, delivered at St. John’s College, Annapolis, on April 13th, 2022.
For all translations from the first chapters of Lavoisier, Antoine Lavoisier, Oxygen, Acids, and Water, H. Fisher, ed., C. Burke and M. Holtzman,
trls. (Santa Fe: Green Lion Press, 2019) was consulted and often followed word for word. The references in parentheses are to chapter and
paragraph number in that translation.
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Dans notre première enfance nos idées viennent de nos befoins; la sensation de nos besoins fait naître l'idée des objets propres à les satisfaire,
& insenfiblement par une suite de senfations, d'observations & d'analyses, il se forme une génération sucçessive d'idées toutes liées les unes aux
autres, dont un observateur attentif peut même jusqu à un certain point y retrouver le fil & l'enchaînement, & qui constituent l'ensemble de ce
que nous savons.
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�of beginners” and ii) in ensuring that the consequent ideas “derive immediately from the facts” and
“from experiments and observations.” This arrangement would be “the natural linking of experiences
and observations” “from the known to the unknown” (0.5, .6, .8, .10, .11).
As with the child our “sensations give birth to ideas” and ‘’ideas ought to be only what … follows
immediately an experiment or observation” (0.6). Then we are not led “to draw conclusions which by
no means derive immediately from the facts,” (0.8). By presenting the facts and ideas in this way,
Lavoisier will enable us, if we are attentive, to find for ourselves the thread binding those ideas to one
another. In coming to see this connection, we should be in a situation somewhat like that of Goethe’s
reader—mentioned in the first lecture on looking in Freshman Laboratory—who can follow similarity
through its transitions, by holding in her imagination a temporal sequence of appearances, until she can
derive them from one another.
Based upon our experience in the lab up to this point, the interpretation of “derive immediately
from the facts” is that our awareness of an experiment, whether we performed it or read Lavoisier’s
account of it, gives birth to an idea in us. The experiment suddenly “makes sense” to us. But it wouldn’t
have done so absent the foreknowledge we had acquired through experience. In this respect there is an
analogy with Euclid’s sequence of propositions. A given proposition at the place where it is enunciated
appears to derive immediately from the preceding propositions in the sense that given our familiarity
with the earlier ones, in some cases, insight into the truth of the later one may be born in us as we read
it. 4
Following Lavoisier’s course involves, first, describing all the equipment used in each experiment
and telling the step-by-step story of what was done and what occurred throughout. That story includes
both observations and notes of the qualities of the substances involved in the experiment and of the
The analogy could be extended to include Euclid’s postulates. Just as Euclid needs to request that we admit them, if we are to have the
sequence of insights generated by his propositions, so Lavoisier has to ask that we admit his “principle” “that, in every operation, there is an
equal quantity of matter before and after the operation” (see below), as a condition for the possibility of ideas being born in us immediately in
response to his experiments.
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�weights of all of those substances. Other relevant quantities, such as temperature, pressure, and volume
of gases must also be recorded. 5 In addition, one experiment, even if repeated several times, would not
be sufficient:
Chemistry furnishes two means for determining the nature of the constituent parts of bodies: composition and
decomposition. When, for example, water and … alcohol… are combined, creating … eau-de-vie, we are entitled
to conclude therefrom that eau-de-vie is composed of alcohol and water. But the same conclusion can be reached
through decomposition, and we ought to be fully satisfied in chemistry only as far as we have been able to bring
together both kinds of proof (3.3).
Much of Lavoisier’s focus will be on concluding—from experiments in which he observes and
measures especially the weights of the substances before and after the experiment—to a fact that a
particular substance, having weight W, has been composed from two (or more) other substances, having
respective weights w1 and w2. For instance, after his first description of a pair of decompositionrecomposition experiments, Lavoisier writes that it “does not give us exact ideas about the proportion”
of the weights of the component substances (3.14). So, he goes on to perform a further experiment in
the same series, as a result of which one can determine that the one substance “diminishes by an
amount in weight exactly equal to that by which [the other] is increased” (3.25).
In the course of describing the next set of experiments, having noted that “since nothing with
weight passes through the glass,” Lavoisier writes, “we are entitled to conclude from them that the
weight of whatever substance has resulted from this combination … had to be the same as the sum of
the weights” of the substances that were there before the combination (5.7).
He only later 6 states the “principle” upon which he bases this claim: “Nothing is created, …; we may
posit in principle (poser en principe) that, in every” experiment, “there is an equal quantity of matter
before and after” the experiment, “and that there are only changes, modifications” of matter. 7 He is
In their papers at the end of Equilibrium and Measurement, Marotte and Gay-Lussac reported having done this.
Antoine Lavoisier, Oxygen, Acids, and Water, H. Fisher, ed., C. Burke and M. Holtzman, trls. (Santa Fe: Green Lion Press, 2019), p. 57, note to
5.7.
7 Traité Élémentaire de Chimie, T. 1er (Paris : Cuchet, Libraire, 1789), Ch. 13.
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�positing this principle underneath his feet, as it were, like a foundation on which to stand, in order to be
able to investigate. A student 8 put it this way: “you have to find a foundation—which does not shift
around as much as what you are trying to see—on which to discover something new amid what is
shifting.” In this respect Lavoisier seems to be illustrating the following words of Socrates to Glaucon: “a
soul … is forced to seek on the basis of sup-positions (ἐξ ὑποθέσεων)” (Rep 510b). At a minimum
Lavoisier has recognized that such a sup-posit-ion is a necessary condition for being able to learn
anything from chemical experiments by keeping tally of the weights involved in them.
In spite of the support provided by the principle, however, just after having concluded to the
sameness of weights before and after the above experiment, Lavoisier goes on to write that “no matter
how conclusive this experiment may have been, it was not yet sufficiently rigorous,” due to the fact that
it was “not possible to verify the weight” of the resultant compound. “We can only conclude to it by
way of calculation, in supposing it equal to the weights of” the ingredient substances. “But however
evident this conclusion may be, in chemistry and physics it is never allowable to suppose something that
can be determined through direct experiments” (5.9). So, as long as all the weights involved in an
experiment are determinable by some experiment, he does not rely on what he can conclude by
standing on the principle he has posited. For physical scientists have “often supposed instead of
concluding,” and “these suppositions, from one age to the next, … acquire the weight of authority” (0.9).
We might say that when he concludes, Lavoisier encloses together all that he’s observed,
measured, and noted throughout an experiment, in order to come to a fact, which would be the
conclusion, or end, of the experiment. The act of concluding would then be a shift from taking
“composition” as meaning the process of putting (poser) two substances together (com) during an
experiment to viewing it as signifying the qualitative and quantitative make-up, or composition, of the
outcome of an experiment.
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Katherine Bates in Freshman Lab class, 2020.
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�For instance, from having made (ayant fait) a certain weight of white flakes out of a given
weight of oxygen and another of phosphorous, one is entitled to conclude to the fact (fait, factum) that
a certain weight of white flakes is made (est fait) of a given weight of oxygen and another of
phosphorous. A decomposition experiment of unmaking the white flakes would allow concluding to the
fact from an un-making. On this literal understanding of “fact,” it would not be correct to say it’s a fact
that a given substance is elementary, since no making or unmaking has shown that to be the case.
However, in view of the principle, such an enclosing-together is possible only if the “walls” of
the “enclosing room” let nothing come in or out, at least in the course of the experiment. That is, we
would have to suppose something which could not be determined through direct experiments, namely,
that “the great walls of the capacious world” are closed, in the sense that they cannot, “suddenly torn
asunder, have burst apart” 9 and have allowed material substances to pass through them in either
direction.
An example of particular ideas that derive immediately from a sequence of facts, each like the
one in the above example of white flakes, might be the idea that this kind of white flakes, which is found
to have various acidic properties (5.18), is a compound substance, or, to take another case, the idea that
water is a compound substance, composed of hydrogen and oxygen, approximately in the ratio of 1g :
5.2555g (8.12). In Lavoisier’s usage such ideas are “consequences” that we “draw” (0.8). An example of
a general idea would then be compound substance.
Perhaps, in the case of compound substance, it is as if we now not only were looking at these
white flakes and remembering them as the concluding frame of a “film strip” of the just performed
composition experiment, but also were seeing, as such a frame of a generalized film strip, any substance
for which such a sequence of experiments had revealed that instances of it were made of two or more
component substances.
9
Lucretius, De rerum naturae, VI.122-23: divolsa repente maxima dissiluisse capacis moenia mundi.
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�We may take Lavoisier’s figures along with the accompanying text as a musical score in two
different ways. In one way they tell us how to “play” each experiment in our imaginations, picturing the
equipment, the ingredient substances, the sequence of steps and events, and the outcome. We may
write down his numbers for height of mercury, volume of a container, and weights of substances and
then do the calculations. Finally, based upon trust in his report and in his results, we may see that the
burning of phosphorus, which we had considered an alteration of one substance, can be analyzed as the
composition of one substance from two others.
Moreover, we may also see that having kept track of the change in volume and of the weights of
the substances we can conclude to the fact that, for example, 45 gr of phosphorus and 69.375 gr of
oxygen composed to make 114.375 gr of white flakes (5.7). Furthermore, based upon trust that Lavoisier
has done many repetitions of this experiment, we can draw the consequence that such white flakes are
composed of phosphorous and oxygen, roughly in the ratio 1 : 1.54 by weight. So, we now have the idea
of such white flakes as a substance composed of two other substances in this weight ratio.
In the other way of taking the musical score, we “play” Lavoisier’s score in our laboratory, with
equipment similar to his. Here we trust only what we observe, that is, see and measure. Thus—it is
hoped—we arrive at the same conclusion, consequence, and idea, but upon a different basis. In either
way through his “score” Lavoisier has given any human being access to the facts and ideas he has
generated. In that sense these latter are objective.
We also recognize that in addition to the resultant general insight that, in some cases, at least,
apparent alteration might be analyzable as the composition or decomposition of substances, Lavoisier
must have relied, in advance, upon three supplementary insights: 1) that this analysis could be most
productively carried out by keeping track of the weights of the substances involved, 2) that a condition
for the possibility of this keeping-track is the supposition of the principle that, in every operation, there
is an equal quantity of matter before and after the operation, and 3) that another condition for the
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�possibility of this keeping-track is the supposition that the vessels used in the experiments are
impermeable to the passage of the substances involved.
One way to imagine the generation of these insights would be as follows. Suppose we had left a
piece of moistened steel wool in a jar with a top on it. When we return after several days, we notice not
only the rusting of the steel wool but also a sensation of air being sucked into the jar as we unscrew the
top. It would seem as if something had happened to the air, a reduction in amount, simultaneously with
the rusting. Perhaps we could repeat this experience on a larger scale, using a bell jar, inverted over
mercury, weighing some dry steel wool, before and after the period of several days, etc. If when we
calculated we found a significant reduction in the amount of air and a significant increase in the weight
of the steel wool, we might think that the rusting might be a combining of the steel wool with
something in the air. We could then go on to figure out how much of a reduction by weight the air
underwent and compare that with the weight gain of the steel wool (cp. CB 6). 10 We could note along
the way that our calculations would not be valid, unless we had made Lavoisier’s suppositions.
INTERLUDE: GAY-LUSSAC’S RECOLLECTION OF IDEALLY EXACT LIMIT-NUMBERS (1808)
Before returning to Lavoisier, we shall glance at a paper 11 by Gay-Lussac, which is read about a
week after Lavoisier is finished. Gay-Lussac generally proceeds in accord with the course recommended
by Lavoisier, of beginning with observations and experiments, concluding from them to facts, and
deriving ideas immediately from the latter. He did, however, introduce a new feature. The students
sometimes claim that Gay-Lussac introduced mathematics into Lavoisier-style chemistry. What are they
thinking of?
Gay-Lussac began by noting a contrast between the behavior of gases, on the one hand, and, on
the other, that of liquids and solids, which had been revealed by the experimental work of Edme
The Constitution of Bodies (Annapolis, MD: St. John’s College, Printed Spring 2021), p. 6. Future references to this manual will be noted “CB,”
followed by the page number.
11 “Memoire on the Combination of Gaseous Substances with Each Other” (1808), CB 37-42, translation modified in places.
10
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�Mariotte. Mariotte showed that the same reduction in pressure, say, by 2/3, applied to volumes of any
two different gases, say, hydrogen and oxygen, would produce the same expansion of an increase by 2/3
in each of the two volumes, so that for an expansible container of a gas at any given fixed temperature
the product of the pressure-number and the volume-number remains the same, as its pressure and
volume vary. In contrast, as Gay-Lussac noted, “the same compression applied to all solid or liquid
substances would produce a diminution of volume differing in each case” (CB 37).
Thus, while the variations in volume of liquids and solids, with changes in pressure, “have
hitherto presented no regular law,” independent of the nature of the liquid or solid in question, the laws
of the variations in volume of gases are “equal and independent of the nature of each gas.” This
recognition probably led Gay-Lussac to the intuition that he could see something new by simultaneously
narrowing his gaze to experiments involving only ingredient gases and shifting his focus from Lavoisier’s
weight-experiments to volume-experiments. He writes that it is his intention to show thereby that gases
“combine amongst themselves in very simple ratios” (CB 37).
Gay-Lussac thinks that the cause of this key difference between liquids and solids, on the one
hand, and gases, on the other, is that the particles of the former are drawn close to each other by an
attractive force, which is not present in the case of gases (CB 37). Imagining the particular attractions
between particles makes for a complicated picture when we look at volumes of solids and liquids. In
addition, it is a picture which we cannot actually see because we don’t know anything about the smallscale details of the attractions which would allow us to predict any determinate experimental outcome.
So, in effect, Gay-Lussac “hears” attractions between particles as “noise.” That noise is silenced when he
listens only to gases and their volumes. Then, Gay-Lussac “listens” to the regularity Mariotte had found
to be independent of the natures of particular gases.
Gay-Lussac presents the facts from which his idea arose. He performed an experiment with a
colleague in which they found an “exact ratio of 100 of oxygen gas to 200 of hydrogen gas for the
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�[volume] proportion of water.” This result led him to suspect “that the other gases might also combine
in simple ratios” by volume. In the next four experiments he performed, Gay-Lussac found that in two
of them the volume ratios of the combining substances were 100 : 100 and, in the other two, 100 : 200
(CB 38-39).
He goes on to offer “some fresh proofs, after which he states:
Thus it appears evident to me that gases always combine in the simplest proportions when they act on one
another; and we have seen in reality in all the preceding examples that the ratio of combination is 1 to 1, 1 to 2,
or 1 to 3 (CB 41).
He adds that when the result of the combination of two gases is a gas, its volume is also in a very simple
whole-number ratio with that of each of the components (CB 41; cp. Avogadro, CB 43).
Analogous to Archimedes in his first treatise, Gay-Lussac has found a way to see ideal-exact
limit-formations—in his case, to see, in chemical experiments, the unit and assemblages of units
(ἀριθμοί). When he looked at the ingredient and resultant gas volumes in his and others’ experiments,
“the thought occurred to him of another thing”—a unit or two units or three units—a thing not found in
his sensory experience, something as if he knew it “from before.” Socrates would have said that GayLussac “is recollecting that of which he grasped the thought” (Ph 72e-73cd). For instance, Gay-Lussac
saw the volumes of nitrogen gas and oxygen gas that combined to form nitric acid gas as “reaching
after” the One and the Two, respectively, but “in a condition of falling short” of them (Ph 74c-75b; italics
added). Edmund Husserl would have claimed that the unit volumes that Gay-Lussac saw were examples
of ideally exact limit-formations, like those encountered in Lecture II. 12
The last three of Gay-Lussac’s proofs are based upon the results of experiments performed by
Davy, in which the weights of the combining substances and of the resultant substances were given. In
order to “hear” the corresponding volumes, Gay-Lussac must reduce the weight ratios in each case to
volume ratios. He reverses Lavoisier’s procedure (see, for example, Lavoisier 3.25) for translating a
Husserl, op. cit., pp. 22-23; The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological
Philosophy, tr. D. Carr (Northwestern: 1970), pp. 25-26.
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�measured diminution in volume into the corresponding diminution in weight. Gay-Lussac divides the
observed weights by the known densities of the gases in order to determine the volume ratios of the
experiments.
For instance, Gay-Lussac then heard, or, to shift metaphors, saw, the volumes of nitrogen gas
and oxygen gas that combined to form three nitrogen compounds as “reaching after” the One and the
Two, respectively, but “in a condition of falling short” of them (Ph 74c-75b; italics added)—like a chalk
mark reaching after the Straight. For the actual experimental results for these three compounds were
that the nitrogen volume was to the oxygen volume as - 2 : 0.99 and 1 : 1.089 and 1 : 2.047, respectively.
Gay-Lussac comments:
The first and the last of these [ratios] differ only slightly from [2 to 1], and [1 to 2]; it is only the second which
diverges somewhat from [1 to 1]. The difference, however, is not very great, and is such as we might expect in
experiments of this sort; and I have assured myself that it is actually nil (CB40). 13
This assurance suggests that hearing, or seeing, ideal-exact volume-units can allow us to correct
values arrived at by measuring weights. In an application of his new approach—without having to
perform any experiments, but simply by viewing a weight-experiment, through the lens of volume—
Gay-Lussac corrected the accepted density of carbonic acid gas.
Cruickshanks had experimentally determined its value to be 0.9569. When Gay-Lussac looked at
the volume results of an experiment by Berthollet, in which 200 carbonic oxide + 100 oxygen → 200
carbonic acid, he concluded that the relation of the densities is dcoxide = dcacid - ½doxy. Since the latter two
densities had been well established 14 by many experiments as 1.5196 and 1.1036, respectively, GayLussac saw that the density of carbonic oxide gas had to be .9678. The elimination of weight-noise—
“Reducing these proportions to volumes we find—
Nitrogen Oxygen
Nitrous oxide
100
49.5
Nitrous gas
100
108.9
Nitric acid
100
204.7
The first and the last of these proportions differ only slightly from 100 to 50, and 100 to 200; it is only the second which diverges
somewhat from 100 to 100.”
14 CB 41, n. 17.
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�each experiment involving a particular kind of chemical reaction yields slightly different weight
relations—allowed Gay-Lussac to hear the ideal-exact sound of the volume, by which he could correct,
in the second decimal place, the previous value, which depended on weight-experiments.
In his experiments Lavoisier was measuring magnitudes, as dealt with by Euclid in Book V of The
Elements. Now Gay-Lussac is counting numbers, which Euclid treated in Book VII. Gay-Lussac has, thus,
opened the realm of chemistry to include the discrete as well as the continuous. This new seeing of units
and numbers of units in chemistry may be what the students glimpsed when they said that Gay-Lussac
had introduced mathematics into chemistry.
LAVOISIER AND THE ROLE OF IMAGINATION (1789)
We return to Lavoisier in order to consider the role of imagination in chemistry. In accord with
his aim to rely on what we observe and conclude when we perform experiments involving weighing,
Lavoisier wanted to avoid being led astray by the imagination. With respect to the things we want to
come to know, he presents “imagining them” as an alternative to his program of “observing them”
(0.41). Moreover, Lavoisier specifically warns us of the dangers of the imagination, “which constantly
tends to carry us beyond the true … [and] invite[s] us to draw consequences which by no means derive
immediately from the facts” (0.8). Especially “in the case of things that can be neither seen nor felt, it is
of the utmost importance to guard against the deviations of the imagination, which always tends to soar
beyond the true and which has considerable difficulty in confining itself within the narrow circle that the
facts draw around it” (1.10). Thus, what we imagine, in that it leads to consequences not immediately
derivable from the facts, stands squarely opposed to ideas, which do so derive by insight.
For instance, while Lavoisier spoke of particles, he did not go on to imagine what they might be
like in detail. “Lavoisier’s ‘particles’ are simply small portions of a substance, not necessarily either the
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�smallest possible portions or even of uniform size.” 15 He drew no consequences from any suppositions
about the nature of the assumed particulate nature of matter.
Nevertheless, under certain conditions, he does draw tentative consequences, in an interesting
way, from imagining the behavior of particles, namely, their separation by warmth (1.1):
It is understandable that since they are … continually invited (sollicitées) by warmth (chaleur) to separate from one
another, the particles of bodies would have no connection among themselves and that there would be no solid
body if they were not held back by another force that would tend to bring them together and, as it were, to link
them to one another….
And so the particles of bodies can be considered as obeying two forces, one repulsive and one attractive,
between which they are in equilibrium (1.3 & .4; italics added).
This imagined picture—which involves considering-as—does not seem to acquire the status of a
consequence that Lavoisier would or could legitimately draw. On the one hand, he imagines “a real,
material substance, an exceedingly subtle fluid that insinuates itself throughout the particles of bodies
and separates them.” Yet the grounds for speaking of it are that the phenomena of bodies’ changing
state as they are warmed up or cooled down are “difficult to understand … without admitting that they
are the effects” of such an imagined substance. So, that substance would appear to be a supposition of
a different kind than his sup-position of the principle mentioned above as a foundation for the chemist
to stand on. He states: “Even supposing that the existence of this fluid were an hypothesis, we shall see
in what follows that it explains the phenomena of Nature quite felicitously” (1.7). “Explaining” must be
distinguished from concluding or drawing a consequence. The hypothesis of a subtle fluid would help us
to imagine a picture of what might be going on “beneath” or “inside” those things we can actually see
and measure in the lab.
“Since the sensation that we call warmth is the effect of the accumulation of” this imagined
substance, “whatever it may be,” Lavoisier names it, as being the cause of warmth (Lat. calor), “caloric.”
Yet in the same paragraph, he assures us that
15
Lavoisier, Op. cit., p. 13, note to 1.1.
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�rigorously speaking we are not even obliged to suppose that caloric is real matter; it suffices … that it be a
repulsive cause of any sort that separates the particles of matter, and so we may view its effects in an abstract
and mathematical way (1.8).
Lavoisier seems to be inviting us to fantasize anything whatsoever as long as it helps us to imagine what
could be happening when bodies change state with changing temperature. Ultimately, whatever we
imagine will have to agree with any empirically established mathematical functions that express change
of matter as a function of temperature, as well as with the ideal gas law, which we have already
encountered in Ch. VI of Measurement and Equilibrium. 16
While the above account “determines the idea that we ought to attach to the word ‘caloric,’”
Lavoisier wishes to “give correct ideas of the manner in which caloric acts on bodies” (1.10). In the
course of doing that, he reports that caloric “plays in some way the role of solvent” in the case of every
gas, in that it “tends to separate” the particles of all bodies, opposing their attraction (1.28 & 1.30).
Since, in dealing with abstract things, we should not over-rely on the help of sensible
comparisons, Lavoisier offers several ways in which we may form a picture of these opposing
tendencies: “we picture (figure) to ourselves,” now a vessel filled with little lead balls into which a very
fine powder … has been poured,” now pieces of different kinds of wood, submerged in water (1.31-.34).
This use of the imagination to picture sensible comparisons clearly does not risk carrying us beyond
what is true.
These comparisons may call to mind that earlier in the lab Theophrastus, Aristotle, and Harvey
analogized the working of plant parts or animal organs to that of products of art. In those cases, though,
we could actually look at the part in question and see the similarity in it, somewhat as we can see a
particular expression in a face. However, the substance that Lavoisier is looking at in his imagination
bears no visible trace of anything expressive of lead balls or pieces of wood. We are imagining them
alongside or inside the phenomena we are looking at in the lab. Putting it that way is suggestive of the
16
Measurement and Equilibrium (Annapolis: St. John’s College, printed Fall 2020), pp. 128-30.
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�transparencies that Archimedes and Pascal used to bring about an essential seeing in the lab. In the case
of Lavoisier, however, what we fantasize allows us to picture what could be happening below the level
of appearances that could account for them.
Lavoisier’s final discussion of caloric in Ch. I is based on the twin suppositions of the existence of
particles of matter and of particles of caloric. Having stated that caloric is both an elastic fluid and the
cause of the elasticity of bodies, Lavoisier poses the Socratic question, “what is elasticity”? It is the
property that “the particles of a body have of moving away from one another when they have been
forced to draw near,” a “tendency … that manifests itself even at very great distances.” That air can be
highly compressed presupposes that particles of air are already quite far from each other. But we know
from experiments that they tend to move even further away from each other. The only way to explain
that effect is by “supposing that the particles make an effort in every direction to separate” (1.44).
There may, in fact, be such a real repulsion between the particles of elastic fluids, since it would
be consistent with the phenomena, but Lavoisier thinks that such “a repulsive force … is difficult to
conceive” (1.45). Trying out another supposition leads him, finally, to the thought that
the separation of the particles of bodies by caloric is due to a combination of different attractive forces, and it is
the result of these forces that we seek to express … when we say that caloric communicates a repulsive force to
the particles of bodies. (1.46)
At the very least we may say that Lavoisier’s imagining of caloric did not lead him to cling to a
fixed supposition of what is going on “behind” or “inside” the things we can see with our eyes. He is
flexible in the ways in which he imagines the supposed action of caloric. He keeps his eye,
simultaneously, both on the phenomena and on the supposed separation of gas particles with increasing
warmth. He encourages us to play around with different suppositions, without mistaking any of them for
“the true” picture.
14
�DALTON’S SUPPOSITION OF ULTIMATE PARTICLES, OR ATOMS, AND MAKING USE OF THEM (1808)
(NOTE: The terminology used in the discussion of Dalton and his followers will be a translation
into a more modern terminology, established by Cannizzaro, 17 in which “atom” refers to a single
hitherto un-cutable, or in-divisible particle, which may or may not be attached to other particles by
attraction. And “molecule” refers to a separate particle, one not joined to other particles by attraction; it
may consist of one atom or of many.)
Dalton’s first great insight is that “we have hitherto made no use of” the pre-supposition that
each material thing is made up of a great number of atoms. There are two different uses that Dalton has
in mind, first, using experiments to make the particle picture more determinate and, second, using the
particle picture to propose and correct experiments.
First, chemists have not “inferred” from their experimental determination of the relative weights
of the ingredient and resultant substances to “the relative weights of the ultimate particles or atoms of
the [different kinds of] bodies” involved (CB 20-21). If they had done so, they could have seen i) how
many atoms of each kind of elementary substance were in molecules of various compounds, ii) the
relative weights of different elements in those compound molecules, and iii) the relative molecular
weights of the various compounds (CB 21).
The second use that chemists have not made of atoms is dependent on the first. For since the
chemists had no accurate, determinate atomic-molecular picture, they had no way of using particles “to
assist and to guide future investigations, and to correct their results” (CB 21). His claim is analogous to
saying that until he worked out the mathematics of the motions of heavenly bodies, Ptolemy could not
predict the date of a solar eclipse.
17 “The conception of [Avogadro and Ampère] contains nothing contradictory to known facts, provided that we distinguish, as they did,
molecules from atoms; provided that we do not confuse the criteria by which the number and the weight of the former are compared, with the
criteria which serve to deduce the weight of the latter; provided that, finally, we have not fixed in our minds the prejudice that whilst the
molecules of compound substances may consist of different numbers of atoms, the molecules of the various simple substances must all contain
either one atom, or at least an equal number of atoms” (CB 53).
15
�Dalton’s second great insight was that it was impossible to make any use of the presupposition of
atoms as long as chemists were thinking of molecules of, say, water, as being of diverse weights. Just as
Lavoisier could not make any real use of experiments, unless he sup-posed that there is an equal
quantity of matter before and after each experiment, so, too, experiments won’t be able to show
anything about the relative atomic makeup of substances’ molecules, unless we sup-pose 18 that
the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, &c. In other words, every
particle of water is like every other particle of water; every particle of hydrogen is like every other particle of
hydrogen, &c.... (CB 21).
We might say that Dalton has introduced into the world of presupposed, imaginary atoms the
supposition of ideally exact atoms. So, all ingredient and resultant substances will now be seen, at the
same time, in a double vision--both as weights, continuous magnitudes, in the lab and as atom-units of
different kinds, discrete multitudes, in the particle world. In this respect his seeing is like that of Euclid
and of Archimedes’ first treatise. The difference, though, lies in that things—in particular, things in the
material world—are thought of as “reaching for” and “falling short of” (Phdo 75ab) the exact limitformations of Euclid and Archimedes, whereas Dalton thinks of atoms as (tiny, invisible) things that
make up the actual material world. Thus, Dalton is not led to think of his homogeneous particles by what
he sees in the lab, in the way that Cebes might be led to think of Simmias by a picture of him or by a face
glimpsed in a crowd. Dalton isn’t viewing the substance in the lab as an image (εἰκών) of a number of
atom-units. He might, while looking at the particular substance, be supposing a huge number of
identical molecule-units. But the substance could not be said to image them. Moreover, at least so far,
the number of identical molecule-units would also be quite indeterminate.
18 Dalton’s word is “conclude.” The grounds for his conclusion are that “from what is known, we have no reason to apprehend a diversity in
these particulars” and that “it is scarcely possible to conceive how the aggregates of dissimilar particles should be so uniformly the same.” For
it is not conceivable to Dalton that, due to the great number of atoms in any body weighable in the lab, it could be impossible for chemists to
distinguish between the sameness of all atoms of each element and a distribution of the specific gravity of each element that is represented
graphically in the shape of a bell-curve.
16
�How well does Dalton execute his program and use his supposition of homogeneity? He shows
how chemists could go about determining the atomic makeup of molecules and relative atomic weights
of elementary substances and relative molecular weights of compound substances. First, in order to
guide chemists in deducing such “conclusions” from experimental “facts already well ascertained,” he
proposes “general rules” like the following:
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.
2d. When two combinations are observed, they must be presumed to be a binary and a ternary. (CB 22)
The first two pairs of conclusions that he goes on to mention are “1st. That water is a binary
compound of hydrogen and oxygen, and the relative weights of the two elementary atoms are as 1 : 7,
nearly” and “2d. That ammonia is a binary compound of hydrogen and [nitrogen], and the relative
weights of the two [elementary] atoms are as 1 : 5, nearly…” (CB 22). He accompanies his statement of
the conclusions with “arbitrary … signs chosen to represent” the atoms and their composites, as shown
in Figures 1a & b PLATE IV (CB 24-25).
PLATE IV. This plate contains the arbitrary marks or signs chosen to represent the
several chemical elements or ultimate particles.
1
2
3
4
5
6
7
8
9
10
21.
22.
23.
24.
25.
Fig.
Hydrog., its rel. weight 1
Azote, 5
Carbone or charcoal, 5
Oxygen, 7
Phosphorus, 9
Sulphur, 13
Magnesia, 20
Lime, 23
Soda, 28
Potash, 42
11
12
13
14
15
16
17
18
19
20
Fig.
Strontites,46
Barytes, 68
Iron, 38
Zinc, 56
Copper, 56
Lead, 95
Silver, 100
Platina, 100
Gold, 140
Mercury, 67
An atom of water or steam, composed of 1 of oxygen and 1 of
hydrogen, retained in physical contact by a strong affinity, and
supposed to be surrounded by a common atmosphere of heat, its
8
relative weight = ............................................ …………………
An atom of ammonia, composed of 1 of azote and 1 of hydrogen =
6
An atom of nitrous gas, composed of 1 of azote and 1 of oxygen =
12
An atom of olefiant gas, composed of 1 of carbone and 1 of hydrogen = 6
An atom of carbonic oxide composed of 1 of carbone and 1 of oxygen =
12
Figure 1a
17
�Figure 1b
Hence—given Lavoisier’s principle and the results of his and other chemists’ composition and
decomposition experiments, in which the weights of the bodies involved were ascertained—if we
presuppose atoms and suppose them to be homogeneous in Dalton’s sense and apply his heuristic
general rules, then both the relative weights of many atoms and the numbers of them in the molecules
of various compound bodies do follow as “conclusions.” In this way Dalton’s vision resembles that of
Ptolemy. 19
The manual directs our attention to a conclusion that follows directly from Dalton’s supposition,
without any need to apply his “general rules” to particular experiments. There was a debate, 15 years
This is true, provided Ptolemy’s mathematical apparatus be interpreted simultaneously as showing that for which the motions of the
heavenly bodies reach while falling short of it and that which enables the astronomer to say in advance where a given body will be in the sky on
a given date. But there is a difference between the two visions, unless Ptolemy be interpreted as considering his cycles and epicycles to be
invisible material bodies.
19
18
�after Lavoisier’s Treatise, between the chemists Berthollet and Proust as to whether or not substances
react and combine in definite and fixed weight ratios. For example, if 2 gm of substance A reacts with 16
gm of substance B, then 2½ gm of A will react with 20 gm of B, and so on, so that the ratio of the weight
of A to the weight of B is 1 : 8 in every case (CB 33). Lavoisier had pre-supposed that this was so, but
Berthollet claimed to have demonstrated experimentally that compositions of two substances occur “in
all ratios, up to [an] extreme value which … varies with the temperature.” Proust, though, claimed to
have found “fixed ratios” in his experiments (CB 104). 20
On the basis of Dalton’s supposition, Proust must be correct. For if every molecule of water is
made of the same number of homogeneous oxygen atoms and of the same number of homogeneous
hydrogen atoms, then in a given amount of water, say, one million molecules, the weight ratio of oxygen
to hydrogen must be the ratio –
(atomic weight of oxygen)(number of oxygen atoms per water molecule)(1,000,000) :
(atomic weight of hydrogen)(number of hydrogen atoms per water molecule)(1,000,000).
Whether or not Dalton’s “general rules” are “adopted as guides,” the ratios always have to be the same,
on the basis of his supposition. So, in imitation of Gay-Lussac’s correction of Cruikshank’s experimental
determination of the density of carbonic oxide gas (CB 41), Dalton could correct Berthollet’s empirical
claim. This might be like telling an astronomer, who reported having seen an eclipse of the moon
between 10:05 PM and 2:44 AM on a given night, that she must have fallen asleep for an hour and ten
minutes, because it had actually begun earlier, according to our mathematical calculations.
20 The manual adds a second necessary conclusion that follows directly from Dalton’s supposition of homogeneity, without reference to his
general rules, namely, the Law of Multiple Combining Proportions: “From Dalton’s doctrine of atoms it follows that whenever two elements
unite in more than one [ratio] there will be small whole number ratios among the [weights] of the first element that combine with a fixed
[weight] of the second—whole number ratios because the various [weights] of the first element that combine with a fixed [weight] of the
second must always represent whole numbers of atoms; and small because according to Dalton the most prevalent combinations may be
presumed to be those between the least numbers of atoms” (CB 30).
19
�AVOGADRO’S “ONLY ADMISSIBLE” HYPOTHESIS ABOUT SIMPLE GASES (1811)
Avogadro saw that in order to use particles, as Dalton wished to do, chemists needed to
eliminate Dalton’s guesswork, that is, his arbitrary, general rules, as heuristic “guides” (CB 22) to
determine the relative number of particles in compounds (CB 46). Avogadro’s key insight is that it is
necessary to provide “Dalton’s system … with a new means of precision through” connecting it with
Gay-Lussac’s discovery of small whole-number ratios of ideal-exact unit-volumes of gases (CB49). Then,
still looking through the Daltonian lens, Avogadro will be able to see the particles more clearly.
To review where we are at this point: we are supposing that all atoms of any given element are
identical, that all molecules of any given compound are identical, and that at STP all boxes of any given
gas contain the same number of molecules. The density of most gases have been determined by
experiment, as described above. Finally, as Gay-Lussac had shown, gases combine in very simple wholenumber ratios by volume. 21
Avogadro, with all of that in mind, realizes that “viewing” Daltonian particles “through” GayLussacian boxes gives him a way to bring the Daltonian picture into better focus. It makes particles, as it
were, into learnables (μαθήματα), about which one can learn, apart from doing experiments. He sees an
apparent necessity in the relationship between “the relative number of particles which combine and …
the number of composite particles which result,” on the one hand, and, on the other, “the ratios of the
quantities of substances in compounds.” 22 Avogadro believes that introducing a mathematics of
numbers of particles and boxes will enable him “to confirm or rectify” Dalton’s results (CB46).
This insight immediately leads him to another: “It must then be admitted (Il faut donc admettre)
that very simple ratios [or relations] also exist between the volumes of gaseous substances and the
21 “The combinations of gases always form in very simple ratios (rapports) by volume, and that when the result of the combination is a gas, its
volume is also in a very simple ratio with that of [each of] its components” (CB 43).
22
“The ratios of the quantities of substances in compounds would appear to be able to depend only on the relative number of particles which
combine, and on the number of composite particles which result” (CB 43; italics added). Avogadro’s word “quantities” may cover both weights
and volumes. If quantities—weights or volumes—of two gases combine to form a third, the ratios of the first to the second to the resultant
“would seem to be able to depend only on the relative number of particles” in the first, the second, and the resultant volumes, respectively.
20
�numbers of simple or compound particles which form them” (CB 43; italics added). Getting milage out of
the simplicity of the relationship between lab experiments involving boxes of gases and pictures of the
numbers of atoms or molecules composing gases would be easiest if it turned out that, for all gases at
STP, the number of particles per box were identically the same. For then the weight ratio of two boxes,
or equivalently, the densities of two gases, would at once also show the relative weights of the two
gases in the compound molecule. In a way, the boxes would be acting like magnifying glasses, or lenses.
In order to see that, consider Figure 2. Suppose that it turned out that for every gas there were
DALTON’s supposed molecules
1 imagined molecule of oxygen
⃝
1 imagined molecule of hydrogen
AVOGADRO’s lens to ‘see’ weight
of Dalton molecules in Gay-Lussac
boxes
1 box of 100 imagined molecules of
oxygen
GAY-LUSSAC’s unit boxes of gases
weighed in the lab
1 box of 100 imagined molecules of
hydrogen
1 actual box of oxygen
1 actual box of oxygen
ﬦ
Weight of 1 oxygen molecule
-----------------------------------Weight of 1 hydrogen molecule
=
1/100 of weight of 100 oxygen
molecules
-----------------------------------=
1/100 of weight of 100 hydrogen
molecules
Weight of 1 box of oxygen
-----------------------------------Weight of 1 box of hydrogen
Figure 2
exactly 100 molecules of it in one Gay-Lussac box. Then the experimentally determined weight ratio of a
box of oxygen to a box of hydrogen (see left column) would have to be the same as the supposed weight
ratio of one oxygen molecule to one hydrogen molecule (see right column), because the lens shows that
the former ratio is the same as the ratio of the weight of 100 oxygen molecules to 100 hydrogen
molecules.
21
�But could Avogadro learn the relative numbers of particles per box of two different ingredient
gases that result in a compound gas? He claims that the hypothesis just stated in the previous
paragraph, “which presents itself first in this connection,” is not only the first to present itself and the
simplest but also “the hypothesis … which even appears to be the only admissible one” (CB 43).
How could he have learned that no other hypothesis could be admitted? Avogadro devotes
most of the rest of the first paragraph to hypotheses about the possible distances of gas particles from
each other. 23 But he summarizes these speculations by stating that “in our present ignorance of the
manner in which this attraction of the particles … is exerted, there is nothing to decide us a priori” for or
against any one of these hypotheses.
However, he concludes that “the hypothesis we have just proposed relies on that simplicity of
ratio between the volumes of gases in the combinations, which would appear to be unable to be
explained otherwise” (CB 44; italics added). In other words, the necessity of the simple relationship
between experimental boxes and numbers of particles—itself, the necessary result of bringing GayLussac and Dalton together—forces him to reject any hypothesis other than the simplest one. 24
Dalton’s first “object” had been to make “use of” the presupposition of particles, in order to
determine the relative weights of particles and the composition of composite particles (CB 20-21).
Avogadro can claim that relying on his new lens, or hypothesis, he was able to “see,” in all volume
experiments involving gases, the relative numbers of ingredient and resultant molecules involved, and
so, also, their molecular weights. In this way his first hypothesis makes the supposed, invisible realm
distinctly and determinately visible.
23 If you think of gas molecules as floating freely, unattracted by each other, then there is no reason to think that two boxes of different gases
would contain different numbers of particles.
24 In order to see that Avogadro’s hypothesis is the only way to arrive at this simplicity, one would have to work through all the known
experimental results involving gases, while trying out different numbers of molecules per box. For each trial the supposed molecular
composition of each gas would have to remain the same in all reactions. In doing this Avogadro seems to have seen that the simple relations
follow only from one hypothesis about the relation between number of molecules per box, namely, that a box of any gas contains the same
number of molecules.
22
�CANNIZZARO’S DETERMINATION OF A TABLE OF MOLECULAR AND ATOMIC WEIGHTS (1858)
Avogadro’s hypothesis lets us “see” the relative molecular weights of gases, “even before their
composition is known,” since the molecular weights have to be proportional to the experimentally
determined densities of the gases, as we’ve just seen. Cannizzaro’s first insight is that instead of focusing
on particular reactions and particular compounds “it is useful” (giova) to view all the elementary and
compound gases together and, in particular, “to refer” the molecular weights (or, densities) of all gases
to that of the lightest gas (CB 56), namely, hydrogen.
He sets up a ratio scale of relative molecular weights. Since it is a scale of relative, not actual,
weights, the weight-number to assign to the smallest molecule is completely arbitrary. With later
considerations in mind, he assigns to hydrogen the weight-number 2 on the scale, rather, than 1. All
other molecular weights will be determined by their ratios to that of hydrogen = 2. Then looking at unit
volumes through Avogadro’s lens, Cannizzaro can make a table of the molecular weights of all gases,
relative to this unit.
For instance, in order to determine the relative molecular weight of any gas, all he has to do is
look up the density—that is, the weight per box—at the same temperature and pressure, of hydrogen
and of the gas in question. Since
(molecular weight of gas x)/(molecular weight of hydrogen, viz., 2 = (density of gas x)/(density of hydrogen),
he has only to multiply the density of gas x by the density of hydrogen gas and then to multiply that by
2. And he has determined the molecular weight of the gas.
Cannizzaro list the molecular weights of some gases in the right-hand column of Figure 3 (CB
56).
23
�Names of Substances
Hydrogen
Oxygen, ordinary
Oxygen, electrised
Sulphur below 1000°
Sulphur* above 1000°
Chlorine
Bromine
Arsenic
Mercury
Water
Hydrochloric Acid
Acetic Acid
weights of the molecules referred to
the weight of a whole molecule of
Hydrogen taken as unity.
1
16
64
96
32
35.5
80
150
100
9
18.25
30
weights of the molecules referred to the
weight of half a molecule of Hydrogen
taken as unity.
2
32
128
192
64
71
160
300
200
18
36.50†
60
Figure 3
Cannizzaro’s second insight is that we must clearly distinguish between the criteria used just
now to arrive at the weights of all the gas molecules from those that yield the weights of the atoms and
the numbers of them in the molecules (CB 53). Avogadro—in the course of using his “lens” for looking
through equal boxes, at same temperature and pressure, in order to see molecular weights—had been
forced, in considering the composition of water, to recognize that a molecule of elementary oxygen
contains two oxygen atoms.
To see this let’s suppose, again, that there are 100 molecules of any gas in one box. In the
composition experiment, one box of oxygen combined with two boxes of hydrogen to form two boxes,
that is, 200 molecules, of water. If the oxygen molecule consisted of only one oxygen atom, there’d be
only 100 oxygen atoms available for forming 200 water molecules—not enough!
So, Avogadro “supposes” that the molecules “of any simple gas whatever,” like oxygen, are “not
formed of one single” atom, “but result from a certain number of these molecule joined together in a
single one” (CB 45). He also supposed that for instance, if oxygen and hydrogen molecules were,
respectively, O2 and H2, then one atom from each box of oxygen and of hydrogen would have to join to
compose one compound molecule; so, there would be 200 water molecules of the composition H2O,
since there are two boxes (200 molecules, or 400 atoms) of hydrogen and only one box (100 molecules,
or 200 atoms) of oxygen.
24
�But if oxygen and hydrogen molecules were, respectively, O4 and H2, then two atoms of oxygen
would have to join with one hydrogen atom from each box of hydrogen to compose one compound
water molecule. So, there would be 200 water molecules of H2O2. In either case the number of water
molecules “becomes … exactly what is necessary to satisfy the volume of the resulting gas” (CB 45), 25
that is, two boxes of water. Perhaps it is the principle of simplicity, reminiscent of Dalton, that decides
him in favor of H2O.
In order to determine molecular formulas in a more systematic and reliable way, Cannizzaro
considers in one view all of the elements that can be produced in gaseous form. In agreement with the
argument of Proust and the conclusion from Dalton’s supposition, he begins with fixed, determinate,
experimental ratios between the weights of the two component substances in a given compound.
Then the weight of the molecule is divided into parts proportional to the numbers expressing the [experimentally
determined] relative weights of the components, and so we have the [weights] of [the components] contained in
the molecule of the compound, referred to the same unit as that to which we refer the weights of all the molecules
[namely, hydrogen = 2] (CB 57).
This method allows him to construct the following table, shown in Figure 4 (CB 58):
Name of Substance
Hydrogen
Oxygen, ordinary
Oxygen, electrised
Sulphur below 1000°
Sulphur above 1000° (?)
Phosphorus
Chlorine
Bromine
Iodine
Nitrogen
Arsenic
Mercury
Hydrochloric Acid
Hydrobromic Acid
Hydriodic Acid
Water
Ammonia
Arseniuretted Hyd.
Phosphuretted Hyd.
[molecular
wt (H’s = 2)]
2
32
128
192
64
124
71
160
254
28
300
200
36.5
81
128
18
17
78
34
[weights of the molecule’s components]
2
32
128
192
64
124
71
160
254
28
300
200
35.5
80
127
16
14
75
31
Hydrogen
Oxygen
”
Sulphur
”
Phosphorus
Chlorine
Bromine
Iodine
Nitrogen
Arsenic
Mercury
Chlorine
Bromine
Iodine
Oxygen
Nitrogen
Arsenic
Phosphorus
1 Hydrogen
1 ”
1 ”
2 ”
3 ”
3 ”
3 ”
25 “When particles of another substance unite with the former to form a compound particle, the whole [compound] particle which should result
is divided into two or several parts (or separate particles) [each]composed of half, quarter, etc., the number of elementary particles going to
form the constituent particle of the first substance, combined with half, quarter, etc., of the number of constituent particles of the second
substance, which should combine with the whole particle (or, what comes to the same thing, [combined] with a number equal to this [last
number] of half-particles, quarter-particles, etc., of the second substance); so that the number of separate particles of the compound becomes
double, quadruple, etc., what it would have been if there had been no dividing, and exactly what is necessary to satisfy the volume of the
resulting gas” (CB 45).
25
�Calomel
Corrosive Sublimate
Arsenic Trichloride
Protochloride of Phosphorus
Perchloride of Iron
Protoxide of Nitrogen
Binoxide of Nitrogen
235.5
271
181.5
138.5
325
44
30
35.5
71
106.5
106.5
213
16
16
Figure 4
Chlorine
”
”
”
”
Oxygen
”
200 Mercury
200 ”
75 Arsenic
32 Phorphorus
112 Iron
28 Nitrogen
14 ”
In order to understand Cannizzaro’s procedure, let’s suppose that the relative weight ratio for
producing 100g of arseniuretted hydrogen has been found by experiment to be weight of arsenic : weight of hydrogen :: 96.15g : 3.85g.
Cannizzaro would divide the relative molecular weight, 78, of arseniuretted hydrogen into two numbers,
a, representing how much of the 78 is due to arsenic, and h, representing how much of the 78 is due to
hydrogen. So,
78 = a + h.
But also, since the 78 is to be divided in the same proportion as the 100, he knows that
96.15g : 3.85g :: a : h.
Solving these two simultaneously 26 tells him that the breakdown of the molecular weight of
arseniuretted hydrogen into the weights of its component elements has to be 75 parts from arsenic
atoms and 3 from hydrogen atoms.
At this very moment Cannizzaro says the following to his students (CB 59):
‘Compare … the various quantities of the same element contained in the molecule of the free substance and in
those of all its different compounds, and you will not be able to escape the following law: The various quantities
of the same element contained in different molecules are all integral multiples of one and the same quantity, which,
always being integral, ought rightly be called [the atomic weights relative to that of hydrogen as 1] (CB 59,
underlining added). 27
For instance, if we look for chlorine in the right column of Figure 4, we see that the number it
has been found to have is 35.5 or twice that, or triple that. So, 35.5 must be chorine’s relative atomic
weight; and its molecule must be diatomic; and, for instance, there must be three chlorine atoms in
26
27
If a + h = 78 and a/h = 96.15/3.85 = 25, then (78 – h)/h = 25. So, 78 – h = 25h, and 78 = 26h. Or h = 3 and a = 75.
His actual words are: “ought rightly be called atom.”
26
�protochloride of phosphorus (molecular weight = 138.5). A similar search for phosphorus tells us that its
relative atomic weight must be 32 and that there must be one phosphorus atom in a molecule of
protochloride of phosphorus. It is easy to see that we can now “express all chemical reactions by means
of the same numerical values [that is, these relative atomic weights] and integral coefficients” of them
(CB 60). That is, we can write reliable, accurate chemical formulas for such compounds. For the present
example of protochloride of phosphorus, the chemical formula must be PCl3. 28
MENDELEEV’S CONSTRUCTION OF THE PERIODIC TABLE (1870-71)
Mendeleev points to his fundamental insight right at the beginning of the excerpt in the manual.
In order to make the “inadequacy” of current atomic doctrine in chemistry “disappear,” he will “put at
the foundation of the study of the main [physico-chemical] properties of the elements their [relative]
atomic weights,” which Cannizzaro had worked out, less than 10 years before Mendeleev set to work.
Mendeleev’s bringing two previously separate realms into relationship may remind us of Avogadro’s
advancing to a new insight by bringing into relationship Gay-Lussac’s perception of small whole numbers
of boxes of gases and Dalton’s supposed ideal-exact atoms. Mendeleev indicates several steps by which
he came to his insight.
Chemists had long recognized certain “natural groups” of elements based on their physicochemical properties. For instance, lithium, sodium, potassium, rubidium, and cesium had been referred
to as alkali metals; they are good conductors of heat and electricity, are highly malleable and ductile,
have very low boiling and melting points and shiny surfaces, and are distinguished from other metals by
their lower densities and softness. Beryllium, magnesium, calcium, strontium, and barium were known
as alkaline earths; they are solid, hard, dense, and usually shiny, are less reactive than metals, are often
insoluble in water, and are found in the earth crust. Fluorine, chlorine, bromine, and iodine are non-
28
It is, of course, clear to Cannizzaro that the numbers may have to change as future empirical discoveries are made.
27
�metallic, have relatively low melting and boiling points and generate salts (ἅλς) when they react
chemically with metals; they had been grouped together as halogens. Other natural groupings were
“analogues to sulfur,” including oxygen, selenium, and tellurium; as well as analogues to nitrogen,
including phosphorous, arsenic, antimony, and bismuth (CB 81).
Initially the elements were put in groups due to their similarities with respect to these
properties. Then some chemists noticed among pairs or triples of elements of high atomic weight,
analogues to pairs or triples of elements of much lower atomic weights. This noticing of analogues “gave
the first impetus to compare the different properties of the elements with their atomic weights” (CB 81).
For example, the physico-chemical properties of cesium (w 29 = 133) and barium (w = 137) were
analogous to those of potassium (w = 39) and calcium (w = 40). With respect to such properties, they are
proportional, in the sense that
K : Cs (among alkali metals) :: Ca : Ba (among alkaline earths).
In other words, within the natural group of alkali metals, the ways in which K differs from Cs, in its
physico-chemical properties, is analogous to the ways in which Ca differs from Ba, in those properties,
within the group of alkaline earths.
Such analogies led to the insight that the way a given physico-chemical property alters, as we
consider, one after the other, the elements of increasing atomic weight within one natural group, may
often occur in parallel with corresponding changes in other natural groups. That insight, in turn, led to
“thinking of classifying all the elements according to their atomic weights,” as determined by
Cannizzaro, in order to see what might be revealed. Mendeleev reports that when we do this “we find
an astonishing simplicity of relationship” (CB 82).
29
The letter “w” will stand for relative atomic weight, according to Mendeleev’s figures.
28
�His illustration of that simplicity is the arrangement, shown in Figure 5, in two horizontal rows of
all the elements of relative atomic weight between 7 and 36, “in arithmetical order according to their
atomic weights.” He looks in two different ways at these rows.
Li=7
Be=9.4 B=11
C=12 N=14 O=16 F=19.
Na=23 Mg=24 Al=27.3 Si=28 P=31 S=32 Cl=35.5.
Figure 5
First, when he looks at a row by itself and attends, one by one, to the different physical and
chemical properties, he notices “that the character of the elements changes regularly and gradually
with increasing magnitude of the atomic weights” (CB 82; italics added). For instance, the
characteristics—whether qualitative or quantitative—of the elements in the row change from left
to right in the following ways:
i) from being basic to being acidic;
ii) from metals, through semi-metals, to non-metals;
iii) from being good conductors of heat and electricity to being insulators;
iv) from being lustrous and shiny to being dull;
v) from a boiling point of 1330°C rising in the middle and then falling to -188°C;
vi) again rising, from a melting point of -180°C, to a maximum and then falling to -187°C;
vii) density, too, rises to a high point and then falls, as shown in Figure 9;
viii) a graph of the relative atomic volumes [that is, the relative atomic weight (weight per atom)
divided by its density (weight per unit volume) = relative volume per atom] would be U-shaped
ix) and, finally, a graph of the volatility would also be U-shaped (CB 83-84). (See Figure 6 for viii and ix.)
Na
Mg
Al
Si
P
S
Cl
vii) Density:
0.97 1.75 2.67 2.49 1.84
2.06 1.33
viii) At Vol:
24
16
14
10
11
16
27
Figure 6
Second, when we compare the patterns of change, from left to right, along the top row with
29
�those along the bottom row, we find that “the character of the elements changes … in the same
way in both series, so that the corresponding members of them are analogues.” In this example,
the patterns of change are the same for all nine characteristics listed above. Thus, lithium and
sodium, the respective members of each series that are highest in basic character, metallic
character, luster, and conductivity are the leftmost ones, are also at the beginning of rising curves
of the graphs of melting and boiling points and density, and so on (CB 82).
Finally, Mendeleev stresses the importance of the forms of the compounds that are formed—in
order along each of the two rows—with oxygen and with hydrogen. The forms of these compounds
present regularities that are familiar to chemists from their experimental work. As we look from the
beginning of either row, “the corresponding elements in the two series have the same kind of
compounds” with oxygen: That is, two atoms of the given element combine with the following numbers
of oxygen atoms—1, 2, 3, … respectively, a uniformly increasing sequence of whole numbers, as the
atomic weight of the element increases. For instance:
The seven elements of the second series give the following higher oxides capable of forming salts:—
Na2O,
Mg2O2, Al2O3,
or MgO,
Si2O4,
P2O5,
or SiO2,
S2O6, Cl2O7,
or SO3.
Thus, the seven members of the above [second] series correspond in the same sequence to the seven generally
known forms of oxidation (CB 83).
Moreover, beginning with the righthand member in either row and moving left, a similar pairing
of compounds with hydrogen occurs—hydorfluoric acid (HF) and hydrochloric acid (HCl) are 1 : 1; water
(H2O) and hydrogen sulfide (H2S) are 2 : 1, and so on, up to 4 : 1..
Mendeleev states: “This regularity proves that the above comparison of elements presents
natural series in which it is impossible (нельзя) to assume any intermediate members” (CB 82-83;
italics added). The arranging of the elements in the order of increasing relative atomic weight has led
Mendeleev to see a new necessity, or rather impossibility, such as we might find in mathematics.
He goes on to present such pairings for all the elements. That he can do so “indicates a close
30
�dependence of the properties of the elements on their atomic weights.” As we have seen from his
example and as he goes on to show, all the individual relationships of the dependence of physicochemical properties on atomic weight are “periodic.” “First, the properties of elements change with
increasing atomic weight; then, they repeat themselves in a new series of elements, a new period,
with the same regularity as” in the series we just went through in detail (CB 84). Mendeleev is using
“period,” in the sense familiar to us from Ptolemy. Just as a heavenly body has different positions over
time and returns to its starting point, after completing one period, and then begins a repetition, a new
period, so a given physico-chemical property has different values as we consider, in turn, elements of
increasing atomic weight along one row, and returns to a value near its starting value, after completing
one period, and then begins a repetition, a new period, at the first element of the next row.
Once Mendeleev had thought to arrange all the elements in the order determined by their
atomic weights, these repetitive patterns suddenly became visible to him, as a picture of wave-like
motions. His experience might be analogous to suddenly seeing something appear in Figure 7.
Figure 7
31
�Mendeleev next goes on to show how he found the complete periodic dependence of the
physico-chemical properties on the relative atomic weights (CB 85ff). He lined the elements up in rows,
like the ones we’ve considered. Table II, in Figure 8, shows all the elements in eight columns—
Figure 8
the eight natural groups—and twelve rows. Rows 2, and 3 are the two complete series we’ve already
considered. However, the remaining elements revealed their periodicity only when Mendeleev lined
them up below one another in longer rows, in the following way:
Row 4 (group I-VII) + Group VIII + Row 5
above
Row 6 (group I-VII) + Group VIII + Row 7
above
Row 8 (group I-VII) + Group VIII + Row 9
above
Row 10 (group I-VII) + Group VIII + Row 11
Thus, one circuit begins with K and Ca’s properties and ends only with those of Se and Br; a new circuit
begins with Rb and Sr’s properties and ends with those of Te and I. And so on.
32
�Mendeleev concludes by returning to what Dalton saw as the second use that chemists had not
made of particles—using them “to assist and to guide future investigations, and to correct their results”
(CB 21). Perhaps Mendeleev thought that by his time it was not particles, but relative atomic weights
that still had not been made use of. He says that in order for a law, like his periodic law, to acquire
scientific importance its logical consequences have be useful, in the sense that they “explain the as yet
unexplained, give indications of hitherto unknown phenomena, and [allow] one to make predictions
that are accessible to experimental verification” (CB 89).
He does all that in the rest of his article. For instance, the element indium had been discovered
in 1867 and assigned the relative atomic weight of 75.6. Mendeleev saw that there was no open slot in
the periodic table for an element of relative atomic weight 75.6. But by comparing its compounds with
those of other elements, Mendeleev saw that indium would have to be placed in an open slot in in
Group III, row 7, with atomic weight about 113 (CB 91-92).
Moreover, Mendeleev investigated the empty slot in Group IV, row 5. He saw that there had to
exist an element of relative atomic weight “about 72” in that slot. Based on the known physico-chemical
properties of the elements in the slots around the empty one, he predicted the properties that the yetto-be-discovered element would have to possess. About 15 years later the element germanium (Ge), of
relative atomic weight about 72.5 and possessing those properties, was discovered (CB 93-95). Perhaps
chemists experienced this discovery as somewhat like reading a novel, coming away with a very precise
sense of the main character, and then meeting someone at a party who strikes us as perfectly fitting the
fictional portrait. It might seem as if we knew him “from before.” Would Socrates say that we are
“recollecting,” but in some to-be-determined different sense (Ph 72e-73cd)?
What do we make of Dalton’s seeing supposed particles—not actual chalk marks on the
blackboard or lines drawn on paper—as ideal-exact limit-entities, in the realm of μαθήματα, of objects
of study leading to insightful learning? Do they eventually lead to acts of insight into the actual material
33
�world, in the way that Archimedes’ learn-ables about weight or Ptolemy’s about motion do? How does
the way in which they allow us to see more in the world compare with the way Archimedes’
transparencies refine our vision?
Do Mendeleev’s successes in making use of the supposed particles and of their relative atomic
weights show that atoms and molecules are not merely supposed but also actually existing entities in
the material world?
34
�
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Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and for a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>. <br /><br />Click on <strong><a title="Formal Lecture Series" href="http://digitalarchives.sjc.edu/items/browse?collection=5">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://anchor.fm/greenfieldlibrary" title="Anchor.fm">Anchor.fm</a>, <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a>, <a href="https://podcasts.google.com/feed/aHR0cHM6Ly9hbmNob3IuZm0vcy84Yzk5MzdhYy9wb2RjYXN0L3Jzcw" title="Google Podcasts">Google Podcasts</a>, or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe.
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St. John's College Greenfield Library
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St. John's College Formal Lecture Series—Annapolis
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formallectureseriesannapolis
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pdf
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34 pages
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Looking in Freshman Lab III – Looking into The Constitution of Bodies:
How Does the Supposition of Particles Help Us to See?
Description
An account of the resource
Typescript of a lecture delivered on April 13, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series. The lecture is the third in a three-part series on Freshman Lab.
Druecker describes his lecture: "This is a lecture specifically for first-year students. It will tell a story of how the presupposition that particles exist is used and made precise by a succession of chemists, from Lavoisier through Mendeleev. Does it enable us to see anything new in the phenomena we encounter in the laboratory? How does its contribution to seeing compare with that of Archimedes’ and Pascal’s mathematical approaches to weights and fluids?”
Creator
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Druecker, Robert
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St. John's College
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Annapolis, MD
Date
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2022-04-13
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: Make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audiovisual recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online"
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text
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pdf
Subject
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Chemistry--Study and teaching
Lavoisier, Antoine Laurent, 1743-1794
Chemistry--Experiments
Mendeleyev, Dmitry Ivanovich, 1834-1907
Cannizzaro, Stanislao, 1826-1910
Avogadro, Amedeo, 1776-1856
Relation
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<p><a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II (typescript)</a></p>
<p><a href="https://digitalarchives.sjc.edu/items/show/7627">Looking in Freshman Lab part II (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a><br /><br /><br /><br /></p>
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English
Identifier
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Druecker_Robert_2022-04-13
Tutors
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