During this century, many species of moth, including the the beautiful Luna moth with its crescent-shaped wings and marvelous, intricate antennae, have been driven nearly to extinction by the sodium-vapour lamps prevalent on North American farms. The unfortunate moths fly by night (exclusively or also by day), using the Moon for navigation, as well as the Sun. The basic principle behind the moth's orientation is simple: to fly in a straight line, it needs only to keep constant the angle at which the rays from the brightest object in the sky strike its eyes. During the day, this is no problem, as the Sun is the by far the brightest object which a moth will ever encounter.
The problem occurs at night. Sodium vapour lamps are brighter than the Moon, so the moth tries to navigate by a lamp. The situation is illustrated in the diagram by a moth and a candle which snares moths indoors. It used to be that we believed moths are attracted to flame, but we shall see that they are not attracted to candles and sodium-vapour lamps, only fooled by them.
Heavenly bodies are so far away that they may be considered to be infinitely distant. So, a moth which keeps a constant angle to the rays from the Sun or Moon will not deviate from a straight line, as an infintely distant object does not move with respect to the moth. However, a candle is only a finite distance away, so that any motion by the moth results in a displacement relative to the candle. This means that, for any arbitrary starting angle (80 degrees in the diagram), the angle between the straight flight path and rays of light from the candle changes as the moth moves along the straight path. However, the moth wants to keep this angle constant, so it adjusts its flight path accordingly. The path which the moths traces is a spiral. If the angle is acute to start with (as in the diagram), then the moth follows the spiral inward to its demise. If the angle is obtuse, the moth is lucky and traces the spiral outwards, away from the flame (but it still gets lost). If the angle is right, then the moth flies around and around in a circle.
As it happens, the path taken by the moth is a logarithmic spiral which has
the unique property among geometric figures of having no scale. This means that if a logarithmic spiral
is traced indefinitely outwards and inwards, it looks exactly the same at all magnifications.
However, as the magnification under which it is viewed changes, the spiral appears to rotate.