File:Bowditch 1943 Figure 77 Circles of Equal Altitude.jpg

English: Circles of Equal Altitude. Figure 77 from Bowditch American Practical Navigator (1943). Explanatory text reads:

Equal altitude circles. In figure 77, if EE'E' represents the earth projected upon the horizon of a point A, and if it be assumed that, at some particular instant of time a celestial body is in the zenith of that point, then the true altitude of the body as observed at A will be 90°. In such a case the great circle EE'E' , which forms the horizon of A, will divide the earth into two hemispheres, and from any point on the surface of one of these hemispheres the body will be visible, while over the whole of the other hemisphere it will be invisible. The great circle EE'E' , from the fact of its marking the limit of illumination of the body, is termed the circle of illumination, and from any point on its circumference the true altitude of the center of the body will be zero . On any small circle of the sphere BB'B', CC'C', DD'D', whose plane is parallel to the plane of the circle of illumination and which lies within the hemisphere throughout which the body is visible, it will be apparent that the true altitude of the body at any point of the circumference of one of these circles is equal to its true altitude at any other point of the same circumference; thus the altitude of the body at B is equal to its altitude at B' or B', and its altitude at D is the same as at D'or D' . It follows that at any instant of time there is a series of positions on the earth at which a celestial body appears at the same given altitude, and these positions lie in the circumference of a circle described upon the earth's surface whose center is at that position which has the body in the zenith, and whose radius depends upon the zenith distance, or what is the same thing upon the altitude. Such circles are termed circles of equal altitude. It is important to note that an observer making an instantaneous transit through the latitudes and longitudes passed over by any rhumb line drawn within the hemisphere of illumination, through the point A , will experience no astronomical difference with reference to the observed body in the zenith of A,

save an altitude difference.