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Discussion below the question Does the US National Weather Service use Celsius or Fahrenheit? and correction of my original use of "Centigrade" to the modern Celsius lead me here.

For example, in the merriam-webster.com's entry for centigrade it says:

Did You Know?

The centigrade scale is essentially identical to the Celsius scale, the standard scale by which temperature is measured in most of the world. Anders Celsius of Sweden first devised the centigrade scale in the early 18th century. But in his version, 100° marked the freezing point of water, and 0° its boiling point. Later users found it less confusing to reverse these two. To convert Fahrenheit degrees to centigrade, subtract 32 and multiply by 5/9. To convert centigrade to Fahrenheit, multiply by 9/5 and add 32.

seems to equivocate by using the term "essentially".

Wikipedia's page for Centigrade says:

Centigrade, a historical forerunner to the Celsius temperature scale, synonymous in modern usage

comes closer since synonymous suggests (but doesn't explicitly say) that the two are numerically identical.

If they are both linear scales, and have the same two fixed (and non-identical) points, perhaps there's a mathematical proof that they are identical?

Question: When and how did usage of the term Centigrade give way to Celsius? Are/were they in fact numerically identical?

When did "Later users (find) it less confusing to reverse these two."?

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    $\begingroup$ Anonymous drive-by down voting and silent vtc's can't help users ask better questions. There's probably no more fundamental experimental parameter in thermodynamics than temperature, and the history of how a precise unit and scale was established seems quite on-topic at HSM to me; I'd like to know why someone felt otherwise. Thanks! $\endgroup$ – uhoh Feb 1 at 6:16
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    $\begingroup$ Completely agree. Researchgate had a downvote option and people would downvote an answer, at times, just drive-by downvoting. Finally, this option was eliminated because it is not helpful. $\endgroup$ – M. Farooq Feb 1 at 15:30
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The unabridged Oxford English dictionary clarifies the "when" part of the question. Also consult the paper in Nature (1949) https://www.nature.com/articles/163427a0 for the historic discussion (paper is open access). However, the modern reference point is triple point of water, "The Celsius scale is defined using the T.Pt. = 0.01 °C with 1 °C made identical in size to 1 K." http://www1.lsbu.ac.uk/water/water_properties.html#d

From OED

"Celsius described a scale in which 0 was the boiling point of water and 100 the freezing point ( Observationer om twänne beständiga Grader på en Thermometer (1742)): this is the inverse of the scale subsequently called the Celsius scale. Linnaeus used a thermometer calibrated with 0 as the freezing point and 100 as the boiling point ( Hortus Upsaliensis (1745) 16 Dec.).

Prior to Celsius, a thermometric scale of 100 degrees had been proposed by P. Elvius ( Dissertatio physico-mechanica de thermometris (1710) vii. 35)."

"In scientific use, the term Celsius was formally adopted in place of centigrade in 1948 (see quot. 1949 at sense B.); see the note at centigrade adj. 1a. The Celsius scale was redefined in 1954 in terms of the Kelvin scale, by the relationship °C = °K − 273.15, thereby effectively replacing the freezing point of water at 0°C as a fixed point by the triple point of water at 0.01°C. (see the note at Kelvin n. 4a)."

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    $\begingroup$ We take so many things for granted. Interesting question. $\endgroup$ – M. Farooq Feb 1 at 3:55
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    $\begingroup$ I have online access. The OED is several volumes in print. I pulled out the quote for you. It says "As the scale was originally defined, the temperature interval between two fixed points (the freezing point and boiling point of water) was made to be exactly 100 degrees, so that the value of each point was a matter of experiment (which produced values of about 273° and 373° respectively); in 1954 the scale was redefined in terms of a single fixed point, the triple point of water, to which was assigned the value 273·16° exactly (giving a figure of approx. 273·15° for the ice point)." $\endgroup$ – M. Farooq Feb 1 at 4:06
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    $\begingroup$ As far as I can understand, there are no shifts by these adjustments. Just the reference point has been changed...the triple point of water. $\endgroup$ – M. Farooq Feb 1 at 4:09
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    $\begingroup$ The melting point depends on pressure and so is a bit "soft", whereas the triple point is unambiguous. This says the melting point is 0.002519 ± 0.000002 °C for example en.wikipedia.org/wiki/Melting_point#cite_note-3 $\endgroup$ – uhoh Feb 1 at 4:14
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    $\begingroup$ @uhoh Interestingly this makes any correction from Centigrade to Celsius or the inverse is pedantically wrong because they technically have different definitions of 0 degrees $\endgroup$ – slebetman Feb 1 at 7:41

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