According to the U.S. Geological Survey's article How much water is there on, in, and above the Earth?,

About 71 percent of the Earth's surface is water-covered

Wikipedia's Earth article also gives ‘about’ 71% (with 29% land) and also cites the perhaps more precise figures of 70.8% / 29.2% found on this University of British Columbia Okanagan page, but none of these sources say when these estimates were first made.

The only estimate with a date I’ve found is in A comprehensive atlas, geographical, historical & commercial [cartographic material], published in 1835, which states that oceans (including inland bays and seas) cover

about three fourths of the surface of the globe.

However, this source does not include Antarctica, the last continent to be discovered, which accounts for 9.2% of earth's land area, and around 2.6% of the earth’s surface.

Antarctica was discovered in the early 1820s, but it was not until in the late 1830s / early 1840s that three expeditions sailed around the continent. Not until several decades later, from the late 1890s, were there many expeditions to Antarctica. The map below, dated 1906, appears to be one of the earliest Antarctica maps in which the continent’s shape is reasonably recognizable (there is also what appears to be a less accurate one from 1897).

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Antarctica 1906 map. Source: A Brief History of Antarctica

What is the earliest mention of an estimate of 71% water (or 70.8%) / 29% land (or 29.2%)? (an answer for either will be acceptable)

Note on the comments below

While useful and informative, the comments unfortunately do not provide a date and focus more on the ‘how’ than the ‘when’. I am not asking ‘how’ (that would almost certainly be off-topic) but about ‘when’. Further, none of the sources cited (USGS, Wkipedia, University of British Columbia Okanagan) mention tides, seasonal cycles or the fractal nature of coastlines as affecting the percentages they cite, nor have I found any sources which give me reason to question the existing narrative (‘about 71% / 29%’ or 70.8% / 29.2%).

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    I'm voting to close this question as off-topic because this belongs on History of Science and Mathematics Stack Exchange or even Earth Science Stack Exchange. – Spencer Dec 20 '18 at 17:16
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    Please demonstrate that the claim "are widely cited on the internet" can be verified as having an appropriate error estimate consistent with the implied precision of plus/minus 0.1%. It is not at all clear to me that these measurements are statically true throughout both the seasonal and tidal cycles of the year at that implied precision. – Pieter Geerkens Dec 20 '18 at 18:20
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    It was revised with the discovery and mapping of every new continent, until all continents were mapped and discovered and we arrived to these modern numbers. The last continent discovered was Antarctida, and it already took some time after that to find out that there is no land under the North Polar Ocean. – Alex Dec 20 '18 at 22:35
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    This question was put on hold because it was deemed off-topic (3 or 4 votes). While this question may fit on another site, this does not make it off-topic here as there is an overlap between many sites on SE. Further, many questions on this site which are tagged science, mathematics or geography require a greater knowledge of those subjects than they do of history, yet they have not been deemed off-topic. The remaining vote, or 2 votes, said this question is too basic. This is clearly not the case. Despite extensive research, I have not found a single link to an answer. – Lars Bosteen Dec 23 '18 at 7:26
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    If you continue to work on this, Maury's "Physical Geography" of 1894 gives fractions of roughly 73-27. – Aaron Brick Dec 23 '18 at 7:33

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