An orange-shaped earth is still curved at the poles
The earth itself is shaped like an orange in order to lure some simple astronomer into calling it a globe.
The orange supplies a familiar image of polar flattening: the earth is represented more accurately by an oblate spheroid than by a perfect sphere. But ‘flattening’ does not mean a plane surface at either pole. The period technical account makes the distinction especially clear. The eleventh-edition Encyclopædia Britannica article ‘Earth, Figure of the’ (1911), inspected in Wikisource's transcription, describes eighteenth-century measurements establishing an oblate spheroid and mathematical relations between flattening, rotation and gravity. This is a near-contemporary scientific witness, published three years after Orthodoxy (1908), rather than evidence of Chesterton's source.
The joke therefore compresses different meanings of flatness: departure from perfect spherical symmetry, and the locally level country a traveller might cross. It cannot establish that some parts of the planet escape curvature. Nor was the departure from sphericity incalculable to contemporary science. The useful distinction in Chesterton's example is between an approximately correct description and an inference carried beyond its warrant; his further identification of that mistake with ‘the rationalists’ remains polemical interpretation.
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