Researching mid-1880's science magazines was an interesting experience. I discovered that in that era, physics and philosophy (at least, natural philosophy) are still largely overlapping fields (see article 1 cited below). Below are some of the interesting and Flatland-relevant articles I discovered in "The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science" issues of 1884 and 1885.
In 1884, a Dr. Hunt tries to divide up the study of the world into three categories; the "Natural Sciences, Inorganic Nature, and Organic Nature" and each of these studies is divided in a separate dimension (yielding six categories in a 3x2 matrix) into what he calls descriptive and physiological studies. This matrix is approximated below: (easy to see in courier font)
Natural sci. Inorganics Organics Descriptive natural history geography, mineralogy, botany, astronomy zoology
Physiological physio, nat philosophy dynamics (physics), morphology, chemistry biological physiology
Not only does this demonstrate a certain fascination with using dimension to describe the world (one with which I sympathize) but from a social perspective, it belies an urge to classify, to fit into types, that Flatland also demonstrates. Abbott himself may not have the same urge, but his parody flatlanders do.
In November of the same year (1884) in the same journal, a Dr. Mills spends six dense pages of text and two pages of tables in explaining the numerics of the periodic table. He does not explain the material in terms of subatomic particles (in fact, he could not: Rutherford, the discoverer of the atomic nucleus, was merely 14 at the time of Mills' publication). Instead, he presents elaborate mathematical formulae to try to derive their rather unusual weights as a mathematical series. This attempt at derivation demonstrates a fascination with mathematical symmetry approaching that of the Pythagoreans (or even the numerologists). However, Mills is making a good-faith attempt to describe simply what he sees as a complex series of elemental weights. "It is probable, he writes, "that the equation y [the weight] = p (15) - 15 (.9375)**x includes the numerics [the weight, I think] of all known elements excepting hydrogen." p is related to the row number of the periodic table, and x is its position along the row. Quite a strange function.
In June of 1885, however, a Lord Rayleigh published an article, yet again in the same journal: "On the Theory of Illumination in a Fog." Lord Rayleigh assumes, for the purposes of discussion, that the fog is absolutely transparent, and merely considers the reflective properties and what would happen to the brightness of the light. It is clearly a three-dimensional thought experiment, though: " conceive of a small source of radiation... to be surrounded by a spherical cloud, of uniform density, or at any rate symmetrically disposed round the source... the effect of the cloud is to cause diffusion, i.e. to spread the rays passing through any small area of the surface (which in the absence of the cloud would be limited to a small solid angle) more or less uniformly over the complete hemisphere."
Clearly, the issue of fog, and how light travels through it, was one on the minds of the natural scientists of the day; it's not much surprise, then, to find that Abbott fell upon this solution to his dilemma of explaining the flatlanders' vision system.
--Jeremy Kahn