In another question, I was asking about the origin of the reduced Planck's constant, $\hbar \equiv \frac{h}{2 \pi} .$ Specifically, I wanted to know why the symbol $`` \hbar "$ was selected for the value $\frac{h}{2 \pi} ,$ where $h$ is Planck's constant.

I found a presentation that claimed it was introduced in a 1926 article:

enter image description here

–Page 17 of "The Planck constant h and the Dirac constant ħ. Their units and their history", by Ian Mills and P. R. Bunker. [PDF]

This seems to make it clear that that article used the symbol, $`` \hbar " .$

However, in checking the cited journal article, it seems to use the symbol $`` h "$ instead.

enter image description here

–Page 1 (printed-page 661) of "On the theory of quantum mechanics", Paul Dirac (1926-10-01). doi:10.1098/rspa.1926.0133.

This would seem to suggest that the presentation claiming that $`` \hbar "$ appeared in the 1926 article was mistaken, if the above screenshot is representative of the 1926 article.

However, as noted in one answer to my question, this article was printed around the time it became possible to use $`` \hbar " .$ So, it seems possible that some printers may've actually used $`` \hbar " ,$ as claimed in the presentation, while the screenshot above shows a different printing that fell back on $`` h " .$

Were such printing variations something that tended to happen in the past? Or, were printings kept more uniform, e.g. done by a single shop in a single go?


  1. Historically, have printings of the same journal article contained minor typographical variations?

  2. Is there an easy way to check if printings of a particular article had a particular variation between printings? For example, is there an easy way to check if the 1926 article discussed above used $`` h "$ in some printings vs. $`` \hbar "$ in other printings?

  • $\begingroup$ Good catch. You should contact the presentation authors and notify them. This $h$ is no different than the normal "h" of the text. $\endgroup$
    – AChem
    Oct 3, 2019 at 19:58
  • $\begingroup$ @M.Farooq - from the second image, it seems clear to me that the $h$ there is not the same font as the rest of the text - the slant is quite apparent. But, while perhaps an italic $h$, it also is not an $\hbar$. $\endgroup$
    – Jon Custer
    Oct 3, 2019 at 20:04
  • $\begingroup$ Yes, sure it is italicized, I meant that it is not h-bar for sure. Did you notice that Dirac did not show the symbol of Planck's constant because he is using the $h$ with a different meaning? $\endgroup$
    – AChem
    Oct 3, 2019 at 20:07
  • 2
    $\begingroup$ I'm not sure how this counts as science, or history of science. Printed materials of all types and flavors have errors. $\endgroup$ Oct 4, 2019 at 13:13
  • $\begingroup$ @CarlWitthoft Since it's about the history of scientific publications, I was thinking it was a history-of-science question. Beyond topicality, my particular interest is largely in understanding the world in which earlier scientists lived; I'm interested in understanding the motivations behind scientific notation as a lens into how they regarded the framing of conceptual frameworks. $\endgroup$
    – Nat
    Oct 4, 2019 at 15:47

1 Answer 1


Having looked through a number of quantum mechanics papers from the era, it is pretty clear that, as @M.Farooq points out, what Dirac is using in the supposed paper-of-origin is just an italic $h$, which he redefines as Plancks' constant (who originally used the $h$) divided by $2\pi$. So, that is for 1926. In 1931, Dirac is still doing the same thing (see, say, Quantised Singularities in the Electromagnetic Field).

In contrast, in 1931, Oppenheimer Note on Light Quanta and the Electromagnetic Field is explicitly using $h/2\pi$ and not $\hbar$ or $h$ as $h/2\pi$.

By February of 1934, On the Theory of the Electron and Positive, W.H. Furry and J. R. Oppenheimer, Physical Review 45 245 (1934) one gets a real $\hbar$:

1934 hbar

By 1937, Dirac seems to have relented (or the editors have insisted) and an $\hbar$ appears in Complex Variables in Quantum Mechanics:

enter image description here

Without spending more time perusing the literature, it is clear that Dirac for some time just preferred to use $h$ instead of an $\hbar$ or $h/2\pi$, thereby redefining $h$ for his purposes. On the American side of the ocean, Oppenheimer shows a change somewhere between 1931 and 1934, moving from $h/2\pi$ to $\hbar$.

Now, all this being said, the answer to the question in the title is a firm No - journal articles were printed and that was that. They would not be reprinted, if at all, for quite some time. Now, Dirac may well have started using $h$ in place of $h/2\pi$, which sets the stage for somebody inventing $\hbar$ to avoid the obvious confusion, but he did not actually use $\hbar$ until later.

  • $\begingroup$ Thanks for the commentary on $`` \hbar " ,$ since as you've correctly picked up on, that's something I'm interested in (and I may end up stealing some of your observations to improve my answer to the other question =P). You also address the more general question in the last paragraph. Could you add in a bit more detail on the last paragraph? In particular, when you say that "journal articles were printed and that was that", would it be correct to interpret this as saying that printing was always done by one shop in one go, without variations in their toolage or later reprints? $\endgroup$
    – Nat
    Oct 4, 2019 at 21:48
  • $\begingroup$ I think what surprises me a bit is that I'd have assumed that a publishing house would accept orders to again print an issue from, say, last year, if for any reason a customer wanted another copy of a popular article, or if a new library was opening up and they needed literature, etc.. Or did they just print a finite number of extras, refusing to print more later? Or, without spamming you with my own guesses, I just mean, how'd they ensure that the printing process wouldn't lack minor variations? $\endgroup$
    – Nat
    Oct 4, 2019 at 21:50
  • $\begingroup$ (To note it, I expect that traditional publishing will continue to disappear, such that information on it will be lost over time. It seems like it could be useful to leave a record of standard practices to help inform history. Despite my own studies in academia, I'm a bit fuzzy on how some of the pre-internet stuff worked.) $\endgroup$
    – Nat
    Oct 4, 2019 at 21:54
  • $\begingroup$ @Nat - When I started grad school in the 1980's, if you wanted reprints of your paper you ordered them when you submitted the final version. They got printed at the same time as the journal itself. If you wanted more later, well, too bad unless you wanted to pay to reset the article. Of course, as the copy machine spread around the world the utility of reprints went way down. One summer job at Yorktown Heights, my boss said he was able to map the spread of copy machines as reprint request postcards stopped coming from those countries... $\endgroup$
    – Jon Custer
    Oct 7, 2019 at 13:05

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