Page:Flatland, a Romance of Many Dimensions (1963, fifth edition).djvu/40

 those unhappy countries in which the atmosphere is perfectly dry and transparent. But wherever there is a rich supply of Fog, objects that are at a distance, say of three feet, are appreciably dimmer than those at a distance of two feet eleven inches; and the result is that by careful and constant experimental observation of comparative dimness and clearness, we are enabled to infer with great exactness the configuration of the object observed.

An instance will do more than a volume of generalities to make my meaning clear.

Suppose I see two individuals approaching whose rank I wish to ascertain. They are, we will suppose, a Merchant and a Physician, or in other words, an Equilateral Triangle and a Pentagon: how am I to distinguish them?

It will be obvious, to every child in Spaceland who has touched the threshold of Geometrical Studies, that, if I can bring my eye so that its glance may bisect an angle of the approaching stranger, my view will lie as it were evenly between his two sides that are next to me (viz. and ), so that I shall contemplate the two impartially, and both will appear of the same size.

Now in the case of (1) the Merchant, what shall I see? I shall see a straight line, in which the middle point will be very bright because it is nearest to me; but on either side the line will shade away rapidly into dimness, because the sides and  recede rapidly into the fog and what appear to me as the Merchant’s extremities, viz. and, will be very dim indeed.

On the other hand in the case of (2) the Physician, though