*The Non-Euclidean World*. ... [p. 65] Suppose, for example, a world enclosed in a large sphere and subject to the following laws:-The temperature is not uniform; it is greatest at the centre, and gradually decreases as we move towards the circumference of the sphere ... If *R* be the radius of the sphere, and *r* the distance of the point considered from the centre, the absolute temperature will be proportional to *R^2-r^2*. Further, ... the linear dilatation of any body is proportional to its absolute temperature. Finally, I shall assume that a body transported from one point to another of different temperatures is instantaneously in thermal equilibrium with its new environment. There is nothing in these hypotheses either contradictory or unimaginable. A moving object will become smaller and smaller as it approaches the circumference of the sphere. ... to its inhabitants [the world] will appear infinite. ... [p. 68] If they construct a geometry, it will not be like ours
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Published before 1923