about the vane at the top of the boat's mast shifted a little, as if there had been a slight change in the direction of the wind. He observed this three or four times without speaking; at last he mentioned it to the sailors, and expressed his surprise that the wind should shift so regularly every time they put about. The sailors told him that the wind had not shifted, but that the apparent change was owing to the change in the direction of the boat, and assured him that the same thing invariably happened in all cases. This accidental observation led him to conclude that the phenomenon which had puzzled him so much was owing to the combined motion of light and of the earth. To explain exactly what is meant we must again have recourse to a diagram; and we may also make use of an illustration which has become classical. [Illustration: FIG. 5.] [Sidenote: Analogy of rain.] If rain is falling vertically, as represented by the direction A B; and if a pedestrian is walking horizontally in the direction C D, the rain will appear to him to be coming in an inclined direction, E F, and he will find it better to tilt his umbrella forwards. The quicker his pace the more he will find it advisable to tilt the umbrella. This analogy was stated by Lalande before the days of umbrellas in the following words: "Je suppose que, dans un temps calme, la pluie tombe perpendiculairement, et qu'on soit dans une voiture ouverte sur le devant; si la voiture est en repos, on ne reçoit pas la moindre goutte de pluie; si la voiture avance avec rapidité, la pluie entre sensiblement, comme si elle avoit pris une direction oblique." Lalande's example, modified to suit modern conditions, has been generally adopted by teachers, and in examinations candidates produce graphic pictures of the stationary, the moderate-paced, and the flying, possessors of umbrellas. [Sidenote: Aberration.]