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The recent question Why are leap seconds needed so often? pulled up some interesting details about the definition of the second, and I'd like to have some of them confirmed explicitly.

I'm specifically concerned with the definition of the second between 1956 and 1968, which was linked directly to the astronomical ephemeris time via the definition

the fraction ​1⁄31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.

(see also the Wikipedia section on the history of the second). More specifically, I'd like to have a clear record on this:

  • ​why was the specific fraction 1⁄31,556,925.9747 chosen, and what does it represent?

Metrologically speaking, the reference year was chosen as 1900, but that does not by itself mean that that definition of the second is explicitly fixing the length of that year in seconds: it's definitely saying that some given year lasted exactly 31,556,925.9747 seconds, by definition of the latter, and my question is what year was that? Did the definition fix that to the year 1900? Or to the year 1956, when it was chosen? Or, as was claimed in the previous question to some ill-defined year in the early 19th century?

I would really like answers to provide suitable references, both to modern reviews and to contemporary documents, that support their claims.

And also, while we're here: why as the year 1900 chosen as the metrological golden standard? Why not 1950, say, or 1956? Which scientific and sociological factors went into that choice, and in what proportion?

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  • $\begingroup$ I'm not convinced that any actual year had the specific number of seconds, rather that observations as of 1900 January 0 at 12 hours would be consistent with a year lasting that long should those observations hold true throughout a year. $\endgroup$ – Jon Custer Apr 24 '18 at 20:18
  • $\begingroup$ Would this be more of a History of Science and Mathematics kind of question? I could see it going either way, but it does seem to me to have more of a historical focus. (c.f. the meta post; also, a related question) $\endgroup$ – David Z Apr 24 '18 at 20:27
  • $\begingroup$ @David I'm OK either way. $\endgroup$ – Emilio Pisanty Apr 24 '18 at 20:30
  • $\begingroup$ @EmilioPisanty Ah, well I'm not committed enough to force it one way or another, either. I guess we might as well leave it here. $\endgroup$ – David Z Apr 25 '18 at 21:02
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See the synopsis of the 1952 and 1955 IAU meetings described in Bulletin Horaire, series 4, number 3, 1955 May/June as transcribed at https://www.ucolick.org/~sla/leapsecs/BH1955.html This would be even better with a citation to the text of the 1950 CNRS meeting on Astronomical Constants, but that remains not online.

In the text from the 1950 meeting there is a note added in proof which shows that many astronomers were confused about when the mean solar second was equal to the ephemeris second, but even then there were astronomers who understood that the use of Newcomb's Tables means that the two kinds of seconds were equal roughly around 1820.

Also see Sadler's monograph explaining what Ephemeris Time is, and how it works, and what changes it wrought in Occasional Notices of the RAS, 3, p 103 transcribed online at https://www.ucolick.org/~sla/leapsecs/twokindsoftime.html

Taking Newcomb's polynomial expression for the mean longitude of the sun in the reference frame that he had constructed, the instantaneous velocity of the sun on 1900-01-00.5 would move 360 degrees in that many seconds, where those seconds were expressed in the time scale which was the average rotation of the earth during the interval of the observations Newcomb used to construct that polynomial.

One more reference is Transactions of the IAU B from the 1952 meeting where Commissions 4 and 4a in Recommendation 3 of the French text on page 66 which is the same as Recommendation 2 of the English text on page 88 direct that the empirical term which had been added to Brown's Tables of the Motion of the Moon should no longer be applied. That term had been added to compensate for the fact that the earth had not rotated uniformly during the observations that constructed Brown's theory, so the tabulated position of the moon had needed a fudge factor to agree with observations. Taking out the fudge meant that starting with 1960 the lunar ephemeris would work better so long as the time was interpreted as Ephemeris Time, not Universal Time.

And why 1900? Because Simon Newcomb was God, and everyone had agreed to use his expressions for the fundamental reference frames of everything in astronomy, and nobody dared deviate from the computations that were being made by other astronomers until the precision of the new measurements got good enough that a non-relativistic theory was no longer tolerable.

And, in reference to other questions about why cesium atomic chronometers and 9,192,631,770 cycles is a second, the original measurements by the original teams are in Nature volume 181, page 1054 (12 April 1958) https://www.nature.com/articles/1811054a0 and Phys. Rev. Lett. 1, 105 – 1 August 1958 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.1.105 where the four authors describe how cesium atoms and Ephemeris Time were compared over an interval of 3 years.

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  • $\begingroup$ And in the volumes of the Lick library is even more stuff, including explanation of other unanswered "why are things about time the way they are" questions, but it will take more time to transcribe them. $\endgroup$ – Steve Allen Apr 25 '18 at 20:51

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