# Circle Definitions for Land Surveyors

circle—The circular disc of a surveying instrument which is perpendicular to and centered about an axis of rotation and on the perimeter of which graduations have been etched to accurately represent the magnitude of rotation. The horizontal and vertical circle intersection of the graduations of theodolites and transits with an index mark or vernier represents the angle measure when the coincidence of a sighting on one point is subtracted from the coincidence of a sighting on another point.

circle, diurnal—The apparent daily path of a celestial body, approximating a parallel of declination.

circle, small-1 The intersection of a sphere with a plane not passing through the center of the sphere. The formulae of spherical trigonometry generally do not apply to arcs of small circles but only to arcs of great circles. Circles of latitude are small circles. 2 The intersection of a sphere representing the Earth with a plane that does not pass through the center of the sphere.

circle of position—A small circle on the globe (Earth) at every point of which, at the instant of observation, the observed celestial body (sun, star, or planet) has the same altitude and, therefore, the same zenith distance. At the instant of observation, the observed body is in the zenith of the center of the circle of position, and the point of observation is somewhere on that circle. A second observation on the same object at a different time or on a different object at the same time will determine a second and different circle of position, and, if the point of observation has not been moved, it will be at an intersection of these circles. If the point of observation has moved, as can occur when on a moving ship, allowance is made for the direction and amount of the movement, and a position obtained for either point of observation. In navigation, a short part of a circle of position is plotted as a straight line and called “Sumner line” or “line of position.”

circles of declination—See hour circle.

Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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