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I'm currently looking at a graph (figure 5 of Ede (1967), "Advances in Free Convection", in Hartnett and Irvine (eds.), Advances in Heat Transfer vol. 4, New York: Academic Press), in which the tic-mark labels on the vertical axis are of the form $\overline{1}.4$, $\overline{1}.5$, $\overline{1}.6$, etc.. It's fairly clear that the overline is intended to mean a negative sign. However, comparing the curve on the graph with the equation for that curve given in the text, it looks to me like the negative sign might apply only to the digit on which the overline appears, so that the digit after the decimal point represents positive tenths, i.e $\overline{1}.4$ means $-0.6$, $\overline{1}.8$ means $-0.2$, etc.. Does that sound remotely plausible to anyone?

ETA: I found this Wikipedia article which confirms ('Most of the other early sources used a bar over a digit to indicate a negative sign for a it') that such a notation exists. However, my question still stands, in the form "Does it sound remotely plausible to anyone that someone might have used that notation to label a graph in a book on heat transfer in 1967?"

Daniel Hatton
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    You is need one integer transition to tell which sequence they're using. – Transistor Feb 09 '21 at 23:19
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    This was standard notation back in the days when everyone knew how to use log tables and pocket calculators didn't exist. The table gave $\log_{10} 2 = 0.3010$, so if you wanted to use $\log_{10} 0.2$ you wrote $\bar 1.3010$, not $-1+0.3010$ or $-0.6990$. Log tables were still "standard" calculation tools in UK secondary schools in 1967 (source, I was there at the time!) – alephzero Feb 10 '21 at 12:59
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    ... so for example to multiply $0.002 \times 30$ using a log table, you look up the logs of $2$ and $3$, calculate $\bar 3.3010 + 1.4771 = \bar 2.7781$, look up $0.7781 = 0.5999$ in the antilog table, and the answer was $0.05999$ (approximately!). That was much easier than using "normal notation" for the negative numbers. – alephzero Feb 10 '21 at 13:10
  • @alephzero Thanks, that makes sense, particularly since the quantity on the relevant axis is indeed the base-10 logarithm of a standard characteristic number. – Daniel Hatton Feb 10 '21 at 13:21
  • @Transistor Thanks for that tip. I just looked again, and the top end of the axis goes $\overline{1}.8$, $\overline{1}.9$, $\overline{2}.0$, suggesting that the negative sign is being applied to both digits. That's awkward, because the hypothesis that it's only applied to one digit really does give better consistency between the graph and the text. – Daniel Hatton Feb 10 '21 at 13:25
  • BTW, I've just edited the question to link to the Google Books preview of the graph, in case that's useful. – Daniel Hatton Feb 10 '21 at 15:24

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