Back to 1868, Mendeleev's periodic table has not been published yet, but we are quite there. As a scientist, you're still struggling to identify very clearly these elements with limited means. Especially, you feel and observe that there are some kind of cycles, and would like to classify elements highlighting these suspected periods.

Then Meyer, still in 1868 apparently, got the idea to plot atomic volumes of known elements, depending on their relative atomic masses.


As far as I know, relative atomic masses were known (more or less since Dalton), and improved by Stanislao Cannizzaro just before Meyer used them.

But, how did they get the atomic volumes of these elements then ? I suspect something like:

  • In a solid state, if they already knew that atoms were touching each other, we can get the density of elements using for example a standard mold of 1cm3, and then I don't know!
  • In a gaseous state, some computing with the Avogadro constant which was already known, but same, I don't know.

Since some elements are usually gas, some are usually solid, I guess we need to normalize the data so that they are actual atomic volumes and not raw densities. If you can take one or two concrete examples to explain, it'll be appreciated!

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    $\begingroup$ If the question is how Meyer knew the volumes, then this probably is better suited to HSM. If on the other hand the question is just for some idea of how one could measure these things with equipment available to Meyer and his peers then it probably is on topic. $\endgroup$
    – jacob1729
    May 26, 2021 at 13:21
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    $\begingroup$ I’m voting to close this question because this will get more attention if migrated to hsm.stackexchange $\endgroup$ May 26, 2021 at 14:53
  • $\begingroup$ Yes sure, can anyone with the appropriate reputation migrate it please? $\endgroup$ May 26, 2021 at 16:36
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    $\begingroup$ You can't get atomic volume directly from bulk gas state measurements. Atomic volume will reduce the free volume, and thus cause deviations from the ideal gas law, but attractions will also cause deviations, and without knowing the attractive forces you can't separate out the volume effect. As you suspected, and M. Farooq confirmed, this would have instead been done by density measuements on condensed phases (solids and liquids). $\endgroup$
    – theorist
    May 29, 2021 at 21:21

2 Answers 2


Good question. I had to look up his original paper which is freely available on Google Books and Hathi Trust. The paper is "Die Natur der chemischen Elemente als Function ihrer Atomgewichte; von Lothar Meyer." (The nature of chemical elements as a function of their atomic weights)

So you are right atomic weights were well known then. So what is atomic volume? It turns out to be relatively simple. You know very well

Density= Mass / volume;

and then

Atomic volume= Atomic weight/ Density of the (solid) element.

"Eine der Eigenschaften, welche mit dem Atomgewicht ziemlich regelmäßig sich ändert, ist die Raumerfüllung der Elemente, das Atomvolumen. Tafel III. gibt eine graphische Darstellung seiner Änderungen in ihrer Abhängigkeit von den Änderungen der Atomgewichte. Als Abscissen einer Kurve sind den Atomgewichten proportionale Längen, als Ordinaten solche, welche den zugehörigen Atomvoluminibus der Elemente im festen Zustande (nur für das Chlor im flüssigen), also den Quotienten aus Atomgewicht und Dichte proportional sind, aufgetragen. Als Einheiten sind das Atomgewicht des Wasserstoffs und die Dichte des Wassers genommen."

One of the properties which changes rather regularly with the atomic weight is the space filling of the elements, the atomic volume. Table III gives a graphical representation of its changes in their dependence on the changes of the atomic weights. As abscissas of a curve are plotted heights proportional to the atomic weights, as ordinates those which are proportional to the corresponding atomic volumes of the elements in the solid state (only for chlorine in the liquid state), i.e. the quotients of atomic weight and density. The atomic weight of hydrogen and the density of water are taken as units.

Translated with www.DeepL.com/Translator with some manual changes.

So all the comparison is being made, it is relative to hydrogen.

  • $\begingroup$ Here is a direct link, if it helps someone: babel.hathitrust.org/cgi/… Now I am curious to figure out how they were able to get these densities in a solid state, especially for O (mp=54.36 K), N (mp=63.2 K). That will be another question! $\endgroup$ May 29, 2021 at 18:01
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    $\begingroup$ If you have professional Acrobat reader, scan the text using their OCR option with German language as an option. Export it to MS Word and upload this document on DeepL. For free users the limit is 5000 words. You will get a pretty decent English version. That is how I read older papers to get the historical hints. $\endgroup$
    – AChem
    May 29, 2021 at 18:13

Following M. Farooq recommendation, I had a look at the original paper and the extreme left of the table was indeed unknown in the solid state. They apparently got some densities by "transpiration" (ie. in the gaseous state) which should be explained in a previous version of the book (Ann. Chem. Pharm. 1867, Supplem. V, 129 if.). I will try and find the reference later on.

[DE] Da die Atomvolumina von H, N, O, F und Ti in festen Zustande unbekannt sind, so bleibt der Abschnitt I. und die zweite Hälfte von II. vor der Hand unbestimmt. Aus dem durch die Transpiration bestimmten Molecularvolumen der drei ersten dieser Elemente im gasförmigen Zustande (Ann. Chem. Pharm. 1867, Supplem. V, 129 if.) und aus dem der festen Fluor- und Titanverbindungen, verglichen mit dem verwandter Stoffe, läßt sich aber mit ziemlicher Sicherheit folgern, daß die Curve der Atomvolumina der Elemente im festen Zustande im ersten und zweiten Abschnitte ungefähr den auf Taf. III gezeichneten Verlauf haben wird. Aehnliches gilt vom Ende des Abschnittes V. und dem Anfange von VI., zwischen denen die Curve unzweifelhaft im Cs ein Maximum erreichen wird.

[EN] Since the atomic volumes of H, N, O, F and Ti in the solid state are unknown, section I. and the second half of II. remain undetermined before hand. From the molecular volume of the first three of these elements in the gaseous state, determined by transpiration (Ann. Chem. Pharm. 1867, Supplem. V, 129 if.), and from that of the solid fluorine and titanium compounds, compared with that of related substances, it can be concluded with a fair degree of certainty that the curve of the atomic volumes of the elements in the solid state in the first and second sections is approximately the same as that shown in Table I. and Table II. The first and second sections of the curve will have approximately the shape shown in Taf. III. The same applies to the end of section V and the beginning of VI, between which the curve will undoubtedly reach a maximum in Cs.

  • $\begingroup$ The word "transpiration" seems so odd. Did he imply evaporation? $\endgroup$
    – AChem
    Jun 12, 2021 at 15:24
  • $\begingroup$ @M.Farooq I think so, because transpiration and sweating are kind of the same thing in German. $\endgroup$ Jun 12, 2021 at 16:52
  • $\begingroup$ @HolgerFiedler, So should translate that to evaporation? What does the original sentence mean? $\endgroup$
    – AChem
    Jun 12, 2021 at 17:56
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    $\begingroup$ @M.Farooq This is an old text and the language has changed since then. The translation for Transpiration is most likely evaporation. $\endgroup$ Jun 12, 2021 at 19:44

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