Were the kilogram, the grave, etc. meant to be units of weight, units of mass, or was it ambiguous at the time?

Question

It is sometimes stated that the early metric units of 'weight' really were meant to be exactly that: units of weight (i.e. force), not mass. However, is that really so? In fact, did the people responsible for the creation of these units in the 1790s¹ make a decision on this question one way or the other?

^{1Namely, the Commission of Weights and Measures of the French Academy of Sciences, which was renamed 'temporary commission' in September, 1793.}

As best as I can tell, there are five possibilities:

1. the Commission really did want to define standards of weight (force) and not mass. True, they completely ignored the fact that g varies from place to place, and therefore one can also ask, given the state of metrology at the time, how good or poor job they did; but that's a separate question.

2. The Commission really did want to define standards of mass and not weight.

3. The Commission was aware that there is a difference between specifying standards for weight and mass; however, they decided to leave it open whether the new standards should be understood as standards of weight or of mass (perhaps because they thought—rightly or wrongly—that the variation in g wasn't metrologically important for their purposes).

4. The Commission members didn't clearly distinguish between mass and weight in their own minds (which wouldn't be very surprising in those days).

5. The Commission took it as a matter of course that, even though mass and weight are separate quantities, one can use the same unit to measure both. This is similar to how we have the same unit for inertial mass and gravitational mass: we know that these two are, in principle, separate quantities¹, but since they are always proportional to each other (with the same constant of proportionality for all objects), we may choose to have the same unit for both—or, alternatively, we may say that one may be quantified by the other. Analogously, mass and weight are always proportional to each other (with the same constant of proportionality for all objects²), and so we may choose to have the same unit for both—or, alternatively, we may say that one may be quantified by the other.

^{1If you think that General Relativity eliminated this possibility, imagine this was written sometime between 1901 and 1915.}

^{2We know (from their discussions about using a seconds pendulum to define the standard of length) that the Commission knew that the constant of proportionality, g, does somewhat depend on the latitude. It is not clear what role this fact had on their thinking as far as the unit of 'weight'.}

Perhaps there are other options, but I can't think of any at the moment. My question is, which one of these four is correct (if any?), and based on what historical evidence?

The law of 18 germinal, year 3

I would say that the phrasing of this law is not decisive. The law says that the gram is

the absolute weight (le poids absolu) of a volume of pure water equal to the cube of the hundredth part of the meter, and at the temperature of melting ice.

As I explain in detail in Update 2 below, contemporary texts explain that 'the absolute weight' of an object is the product of the object's volume and the object's specific gravity. According to the same texts, specific gravity is a relative quantity: a ratio of the weight (contemporary texts do clearly mean weight, not mass) of a body of interest to a body of same volume but made of some reference material.

However, it was well understood (and emphasized in the texts) that the ratio of weights is, if all the weighing is done at one and the same location, equal to the ratio of masses. Therefore, specific gravity is also equal to the ratio of mass densities. It is perfectly possible that when people used the concept of specific gravity in the 1790s, they meant two things by it: experimentally, it was a ratio of weights, but conceptually, its meaning was a ratio of mass densities.

If this is so, the definition of the gram may be interpreted as either a unit of weight or a unit of mass.

An example of the claim

What has become of the kilogram, once the unit of weight in the metric system? It has been transformed from the metric unit of weight (force) into the unit of mass (amount of matter), an even more basic role in the world of measurements.
…
The earliest kilogram, then designated as a measure of weight rather than mass, was derived, with difficulty, from the first meter of length.

                                               Herbert A. Klein, The science of measurement : a historical survey
                                                                                                                 (Dover, New York, 1988).
                                               See here and here.

An example of a contrary claim

It was intended that the kilogram should have the same mass as a cubic decimeter of pure water at maximum density, and the experimental determination of that mass was made by finding the difference of weight in air and in water of a hollow brass cylinder whose exterior dimensions at a temperature of 17.6 °C were, height = 2.437672 decimeters, diameter = 2.428368 decimeters, volume = 11.2900054 cubic decimeters.

                                          W. Harkness, "The progress of science as exemplified in the art of
                                                  weighing and measuring." Presidential address delivered before
                                                   the Philosophical Society of Washington, December 10, 1887
                                                   (Bulletin Phil. Soc. vol 10, pp. 39–86). (source)

Confusion between mass and weight

On the other hand, it is well documented that the concepts of weight and mass were embedded in much confusion, so much so that, as late as 1901, the 3rd CGPM felt compelled to pass the following resolution:

Declaration on the unit of mass and on the definition of weight; conventional value of g_n

Taking into account the decision of the Comité International des Poids et Mesures of 15 October 1887, according to which the kilogram has been defined as unit of mass;
Taking into account the decision contained in the sanction of the prototypes of the Metric System, unanimously accepted by the Conférence Générale des Poids et Mesures on 26 September 1889;
Considering the necessity to put an end to the ambiguity which in current practice still exists on the meaning of the word weight, used sometimes for mass, sometimes for mechanical force;

The Conference declares

1. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram;

2. The word “weight” denotes a quantity of the same nature as a “force”: the weight of a body is the product of its mass and the acceleration due to gravity; in particular, the standard weight of a body is the product of its mass and the standard acceleration due to gravity;

3. The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s², value already stated in the laws of some countries.
   

                                                                                                                                                                    (See here, p. 159.)

The question

What evidence is there that can help us understand whether, in the 1790s, the Commission of Weights and Measures of the French Academy of Sciences meant for the grave, the gram, the kilogram, etc. to be the units of weight (force) or the units of mass?

For what it's worth, I wouldn't be surprised if the Commission never seriously thought about the question and would be fine with either interpretation of these units. It is also possible they did think about it, but left it intentionally ambiguous whether these were units of force or of mass.

Note that it will not suffice to point out that e.g. the available texts keep using the word 'weight' rather than 'mass' in connection with these units—unless it can be shown that the relevant author clearly meant to use those as distinct technical terms whose meaning is more or less the same as it is today.

Evidence from some texts from the 1820s and 1830s

Fourier

In Fourier's Analytic Theory of Heat, published in 1822, the author keeps using the construction a mass having a certain weight. For example,

Suppose a mass of ice having a definite weight (a kilogramme) to be at temperature 0
_{On suppose qu'une masse de glace d'un poids determine (un kilogramme) soit a la temperature 0} (§25)

To raise a metallic mass having a certain weight, a kilogramme of iron for example, from the temperature 0 to the temperature 1, a new quantity of heat must be added to that which is already contained in the mass.
_{Pour elever une masse metallique d'un certain poids, par exemple, un kilogramme de fer, depuis la temperature o jusqu'a la temperature 1, il est necessaire d'ajouter une nouvelle quantite de chaleur a celle qui etait deja contenue dans cette masse.} (§26)

The choice of this unit would have been preferable in many respects to that of the quantity of heat required to convert a mass of ice of a given weight, into an equal mass of water at 0, without raising its temperature.
_{Le choix de cette unite serait preferable a plusieurs egards a ceiui de la quantite' de chaleur ne'eessaire pour convertir une masse de glace d'un poids donne, en une masse pareille deau, sans elever la temperature 0.} (§157)

Unfortunately, it is never made clear in the text if 'weight' (poids) is really meant to be understood as a force, or if it is merely a synonym for mass. To my ear, it sounds as if he wants to use weight as a term for force (and thus the kilogram as a unit of force). However, I don't think we can rule out the possibility that it was meant as a unit of mass after all, or that Fourier really didn't give much thought to the distinction and, for his purposes, didn't care which way it was interpreted.

Gauss

As another example, consider Gauss's 'The intensity of the Earth's magnetic force reduced to absolute measurement', published in 1832. On the one hand, the author clearly says that by 'weight' he means a force, and by 'mass', the inertial mass:

Hence the effect of a given amount of magnetic flux on a given amount of either the same or the opposite flux at a given distance is comparable to a given motive force, i.e. with the effect of a given accelerating force on a given mass, and since the magnetic fluxes themselves can be known only through the effects, which they bring forth, the latter must directly serve to measure the former.

In order, however, that we may be able to reduce this measurement to definite concepts, units must above all be established for three kinds of magnitudes, namely, the unit of distance, the unit of ponderable mass, and the unit of acceleration. For the third, the force of gravity at the locus of observation can be assumed.

_{Actio itaque quantitatis datae fluidi magnetici in quantitatem datam vel eiusdem fluidi vel alterius in distantia data comparabilis erit cum vi motrice data, i.e. cum actione vis acceleratricis datae in massam datam, et quum fluida magnetica ipsa non nisi per effectus quos producunt cognoscere liceat, hi ipsi illorum mensurae inseruire debent.}

_{Quo igitur hanc mensuram ad notiones distinctas reuocare possimus, ante omnia circa tria quantitatum genera vnitates stabilire oportet, puta vnitatem distantiarum, vnitatem massarum ponderabilium, vnitatem virium acceleratricium . Pro tertia accipi potest grauitas in loco obseruationis}

… we want to choose A' for the center of gravity, and, denoting by p the weight of the body, i.e. the motive force of gravity on its mass

_{…pro lubitu assumere liceat , pro A' adoptabimus centrum grauitatis , et denotato pondere corporis, i .e . vi motrice quam grauitas massae corporis inducit , per p}

However, he uses the gram as a unit for both weight and mass. Here it is as a unit of weight…

… the thread holds a needle with the usual equipment alone, where the total weight was 496.2 g

_{dum filum portabat acum cum sola supellectile ordinaria, vbi pondus integrum erat 496,2 grammatum}

In experiments I-VIII, in fact, different needles were used, although they had the same weight and the same length (the weight was between 400 g and 440 g)…

_{In experimentis I—VIII adhibitae sunt acus diuersae quidem, sed eiusdem fere ponderis et longitudinis (pondus erat inter 400 et 440 grammata)}

… and here (as a milligram) as a unit of mass:

If we take the second, the millimeter and the milligram for the units of time, distance and mass,…

_{Accipiendo pro vnitatibus temporis, distantiae et massae minutum secundum, millimetrum et milligramma, …}

Based on this admittedly limited evidence, it seems to me that, in the first several decades of the 19th century, it was possible for authors to alternate between using the gram (or the kilogram) as a unit of mass and using it as a unit of weight.

A summary of the question

Fourier and Gauss are important, but my main question is what the members of the Commission of Weights and Measures thought about the issue: did they think they were coming up with a unit of mass or with a unit of weight? Did they care about the distinction? Indeed, one part of my question is whether they thought about that issue at all. Either way, I would like to know what the story was!

Update 1

It has been suggested that the important point is this: since g varies from place to place and the Commission made no mention of that, and since the Commission carried out all comparisons between objects side by side at the same location, the conclusion is that the Commission in fact came up with a standard of mass, not wieght.

While that is a fair point, it does not address what I am asking, which is not about what it turns out that the Commission did, but about what the Commission intended to do, or what it thought it did once it finished its job. As best as I can tell, there are four possibilities:

1. the Commission really did want to define standards of weight (force) and not mass; since they ignored the variation in g, one can then also ask how good or poor job they did, but that's a separate question.

2. The Commission really did want to define standards of mass and not weight.

3. The Commission was aware that there is a difference between specifying standards for weight and mass; however, they decided to leave it open whether the new standards should be understood as standards of weight or of mass (perhaps because they thought—rightly or wrongly—that the variation in g wasn't metrologically important for their purposes).

4. The Commission members didn't clearly distinguish between mass and weight in their own minds.

Perhaps there are other options, but I can't think of any at the moment. My question is, which one of these four is correct, and based on what historical evidence?

(An update of the update: I did think of another possibility. Here it is:

5. The Commission took it as a matter of course that, even though mass and weight are separate quantities, one can use the same unit to measure both—or, one can say that mass 'is quantified by' its weight.)

Update 2

As pointed out in this answer, a law from 18 germinal year 3 (7 Apr 1795) uses the following phrasing (in Article 5):

5. The new measures will henceforth be distinguished by the nickname of republicans; their nomenclature is definitively adopted as follows:

We will call: …
Gram, the absolute weight (le poids absolu) of a volume of pure water equal to the cube of the hundredth part of the meter, and at the temperature of melting ice.

I was able to find two French sources from the second half of the 1700s that explain what le poids absolu means: an encyclopedia from 1774 and a treatise on hydrodynamics from Year 4 of the Republic (23 Sep 1795–22 Sep 1796).

The encyclopedia says that 'absolute weight' is the product of volume and specific gravity (Le poids absolu d'un corps est égal au produit de sa grandeur par sa pesanteur spécfique, see p. 210). And it defines specific gravity just like we still do: 'This term is understood to mean the weight of a body of a certain volume, compared to the weight of another body of the same volume' (L'on entend par ce terme, le poids d'un corps d'un certain volume, comparé au poids d'un autre corps de même volume, p. 205).

The treatise on hydrodynamics has this discussion. I will reproduce a translation (via Google translate, which does an amazing job) of the whole short section:

We must remember that the density of a body (solid or fluid) is the quantity of matter of this body, included in a given volume that we take for unity; or, which comes to the same thing, the quotient of the mass of the body, divided by the number of cubic feet or cubic inches (depending on whether you take the cubic foot or the cubic inch as a unit of measure of volume), which form its total volume. Thus, by naming M the mass, G its volume or its size, D the density, we have D = M / G; and therefore M = G x D, that is, that mass is equal to the product of volume by density. We see that the density of a body is always relative to that of another. Care must be taken to assess the volumes of the two bodies in units of the same species.

Likewise, the specific gravity of a body is the weight of this body under a given volume taken, for unity; or, which comes to the same thing, the quotient of the absolute weight of body, divided by the number of measurements of its volume. If we therefore name P the absolute weight of a body, G its volume, p its specific gravity, we have p = P / G; and therefore P = G x p, that is to say that the absolute weight is equal to the product of the volume by the specific gravity. For example, either the proposed body, fresh water; we know that a cubic foot of fresh water weighs 70 pounds, with very little difference; therefore taking the weight of a cubic foot of water, for the specific gravity of this fluid, we will have p = 70 pounds, and P = G x 70 pounds; if G is 100 cubic feet, it will come P = 7000 pounds; if G = 25 cubic feet, we will have P = 1750 pounds.

In the same place on earth, or at equal latitudes, the masses are proportional to the weights; we must therefore assume that the densities of two bodies are proportional to their specific gravities, since the densities of these two bodies are masses included in the same volume, and that their specific gravities are two weights also included in the same volume.

I am actually not clear where this leaves us.

One thing that seems to be the case (and is consistent with what is often written about the period) is that the scientists of the day considered both mass and weight to be derived quantities, and density and specific gravity as more fundamental.

But it's less clear whether absolute weight is meant to be a measure of weight or a measure of mass; here is why.

As far as what's in the encyclopedia, in today's language, we would say that specific gravity is a dimensionless number (a ratio of weights), and so absolute weight has the dimensions of volume. Now, for the definition to make sense, one has to specify a reference material, but I suppose we may assume that the default reference material is water. This would mean that the specific gravity is exactly 1, so the absolute weight is then numerically exactly equal to the volume, here presumably measured in cm³, so that the gram is then equal to the absolute weight of '1 cm³'. As far as whether this means that the gram is a unit of weight or a unit of mass… let's first consider what the hydrodynamics treatise says, and then come back to it.

The hydrodynamics treatise uses the word 'weight' in an unqualified fashion, which makes it sound as if it is truly a force; this would be consistent with Herbert A. Klein's claim that the standard was designated as a measure of weight rather than mass.

Note also that the text uses the same units, pounds (livres), for both absolute weight and specific gravity. Though I suppose this would tend to favor the interpretation of absolute weight as true weight (force), and so favor Kelin's claim, I confess I don't really know how to make sense of that. What happened to the units of volume??

On the other hand, note the following sentence in the first paragraph of the treatise: We see that the density of a body is always relative to that of another. The paragraph on absolute weight begins with 'likewise', so it looks like what is said about specific gravity should be taken as analogous to what was said about density; and what was said about density is that it is a relative quantity. If that is so, then the treatise is consistent with the encyclopedia after all. (The units that are used are inconsistent, as I've already noted, and are thus of limited help.)

Moreover, in the third paragraph, the treatise says that if all measurements are done at the same location (so that g is constant), then densities are proportional to specific gravities. This suggests that it is density that one really wants, and that measured relationships between specific gravities are merely a convenient route to get at the relationships between densities.

Interpreted that way, not only is the treatise is consistent with the encyclopedia, but also both are then at least not inconsistent with what W. Harkness says: that although the actual measurements compared weights, from those measurements one was meant to deduce relationships between masses; and so the gram was meant as a measure of mass after all.

After all this, I am still not clear whether the Commission meant the gram to be taken as a unit of mass or of weight.

Update 3

The more I read contemporary sources, the more I think Option 5 is correct: that the Commission took it for granted that although weight and mass are separate quantities, at least locally one is always proportional to the other; and so one may be quantified by the other; and so we may use the same units for both. This is much like we continue to use the same units for inertial mass and gravitational mass because they are always proportional to each other, with the same constant of proportionality for all objects. (If you think that General Relativity has shown that these two kinds of mass are in fact one and the same, imagine it's some year between 1901 and 1915.)

A typical example, consider the following text from a 1771 treatise on hydrodynamics, which says literally the following:

The mass of a body …. is the quantity of proper matter of which this body is composed. It is known by weight; therefore if we have, for example, two bodies A & B, the first of which weighs two or three times as much as the second, the first has two or three times as much mass as the second. This proportionality of the weights to the masses is demonstrated by experience which teaches that in the same empty space of air, under the container of the pneumatic machine, all the bodies, whatever difference there is in their figures & in their dimensions, fall with the same speed…
…
By mass measurements, I mean pounds, marcs, ounces, etc., that mass weighs…. in measurements of weight or mass, we can take the ounce as a fundamental unit.

From this perspective, the quotes from Fourier's book above make even more sense. In 1822, Fourier still wrote in a way that suggests that mass is quantified by weight.

And recall that ten years later, Gauss alternated between using the gram as a unit of weight and as a unit of mass.

At the moment, my bets are on Option 5.

Answer 1

It was Jean Richer who demonstrated the fact that, described in a modern conceptual framework, there were variations in the strength of the earth's apparent gravitational field (in the earth-fixed frame) from point to point. His result was published in 1679. However, the interpretation was complicated and led to a controversy between Newton and Cassini as to whether the earth was prolate or oblate. This controversy began in 1720, and the physics was not correctly analyzed for a long time. E.g., John Bernoulli wrote an analysis in 1734 using Descartes' vortices. Further expeditions were organized in 1735 to high and low latitudes in order to do high-precision astronomical observations.

So we need to keep in mind that science didn't move as fast in those days as it does now, and also that there is a general tendency when looking back at the history of science to imagine that scientific confusions were resolved quickly when in fact they took a long time to clear up. The people developing a system of measures in 1790 had probably had their educations and spent their working lives in an environment where the variation of g was exotic cutting-edge science, not something you would learn about in the first chapter of a freshman physics textbook.

Language is conservative, and therefore it's not surprising that people speaking French and English hadn't yet decided to start using two different words for mass and weight. Even today, English lacks a commonly used verb meaning to measure the mass of something -- we have "to weigh," but "to mass" is an uncommon usage. We still use phrases like "Cavendish weighed the earth."

What actually matters is what implicit operational definition the Académie des sciences carried out. Their methods all involved working with objects (distilled water, a hollow brass cylinder, and a solid metallic weight) in Paris (which is, after all, the center of the universe). The standards produced in this way would be duplicated and transported to various places, but because comparisons were always carried out side by side, the different copies would all have the same mass, not the same weight. Therefore the operational definition they implemented was a definition of a unit of mass, regardless of what words were current in scientific usage at the time.

[EDIT] The OP asks in comments whether the state of mind of the academy's committee was #1, #2, #3, or #4. It is clearly not the case that the committee considered this issue, that it came to a consensus, and that this consensus was recorded by history -- for if so, then it would never have been necessary in 1901 for the CGPM to make the clarification quoted by the OP. Most likely the various members of the committee had different states of mind on this issue. It's possible that at least some members of the commission had in mind a possibility #5, which was to forgo conceptual definitions in favor of operational definitions. (Operationalism was explicitly laid out by Bridgman as a broad philosophical stance until 1927, but in the narrower context of defining a system of units it seems pretty obvious to me that it's the only reasonable approach.) In any case I doubt that we will ever know what any member of the committee wanted, thought, or intended as a conceptual definition, unless, e.g., some historical source turns up such as a letter from one member of the committee to another.

The question was very well researched and fleshed out with some interesting quotes from various sources. However, I disagree with the OP's contention that these sources contradict one another. Harkness is just saying that the unit was in operational terms a unit of mass, but that the operationalization of it was carried out by comparing gravitational forces at a given location. Klein is describing the spread of a conceptual shift, not a redefinition.

Answer 2

I would choose #2. The commission reported that Lavoisier and Hauy used a beam scale to determine the mass of the unit volume of water. A beam scale measures mass. As it was the standard weighing device in 1790, there was no need to state that it does not measure the force of weight.

One of the commission members was Laplace. Laplace knew the difference between mass and the force of weight, and he knew that gravity varies on the surface of the earth. He had shown that the measured relation between g and latitude λ (Krafft's formula: g = (1 + 0,0052848 sin²λ) g₀) can be reconciled with the measured oblateness of the earth by assuming that the earth is composed of concentric shells of different density.

The entire commission knew that gravity varies with latitude because in 1790 the initial proposal was to define the metre by the seconds pendulum at 45 degrees latitude. This latititude was specified because gravity varies with latitude.

[EDIT] in reply to the comments:

My source for stating that Lavoisier used a balance in 1793 was Birembaut ("la grande balance de précision que Fortin avait construite pour Lavoisier"). The conclusion that a balance measures mass, not force, was mine.

I think Hutton's dictionary (1815) is a useful source describing what weight meant at the time. Hutton distinguishes weight in physics, and weight in commerce:

• Weight, in physics, .. on different parts of the earth's surface, the weight of the same body is different. ... the weights of the same body, at different distances above the earth, are inversely as the squares of the distances from the centre. ... A body loses so much of its weight, as is equal to the weight of the .. fluid.

• Weight, in commerce, denotes a body of a known weight, appointed to be put into a balance against other bodies, whose weight is required to to be known.

The report of 19 january 1793 shows that, for the french government, a primary purpose of the new weight standard was commercial: it had to be sufficiently reliable for the specification of the silver content of the new coin, the franc.

Answer 3

Whatever the scientists on the committee intended, or even the operational reality of using a standard chunk of metal in different parts of the world, the gram was legislated as a measure of weight, not mass.

Following the citations in the Wikipedia article about the history of the metric system, we find the text of the 1795 law that established the metric system, containing:

5. Les nouvelles mesures seront distinguées dorénavant par le surnom de républicaines; leur nomenclature est définitivement adoptée comme il suit:

...

Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre , et à la température de la glace fondante

or

5. The new measures will henceforth be distinguished by the sobriquet of republicans; their nomenclature is definitively adopted as follows:

...

Gram, the absolute weight of a volume of pure water equal to the cube of the hundredth part of the meter, and to the temperature of melting ice.

-- Décret relatif aux poids et aux mesures du 18 germinal an 3 (7 avril 1795), cited by Wikipedia at https://web.archive.org/web/20160817122340/http://www.metrodiff.org/cmsms/index.php?page=18_germinal_an_3 A live version can be found at https://www.metrodiff.org/wp/metrologie/histoire-de-la-metrologie/18-germinal-an-3/

The original question shows that the French word corresponding to mass is masse and weight is poids, so I don't think there is any ambiguity.

It's quite ironic that they adopted Lavoisier's unit of weight after they chopped his head off.