I must forewarn you that this lecture will deal only with very elementary mathematics. Its subject is what may be termed the preparatory school stage in the education of the navigator. Nevertheless, it is a subject of particular interest and importance because it is in the field of navigation that we first meet with mathematics quite outside learned academic circles. It was among sailors that the process was begun (and it is not yet complete) of transforming the craftsman—whose skill rests on tradition and experience—into the technician—who works on established scientific principles. For the scholar, mathematics is like poetry—an end in itself.