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Let r be the distance of a point P from a fixed origin 0, 0 the angle which OP makes with a fixed direction OZ, il the azimuth of the plane ZOP relative to some fixed plane through OZ.

00The displacements of P due to small variations of these co-ordinates are or along OP, rOO perpendicular to OP in the plane ZOP, and r sinO O~ perpendicular to this plane.

00R is the radial component of force, is the moment about a lilie through 0 perpendicular to the plane ZOP, and 4 is the moment about OZ.

00Instead of it is frequently used the complementary angle ZOP, known as the polar distance of the body.

00After the image of the body is brought into coincidence with the cross threads, the instrument is turned through 180° on the axis, which results in the line of sight of the telescope pointing in a certain direction OQ, determined by the condition QOZ = ZOP. The telescope is then a second time pointed at the object by being moved through the angle QOP. Either of the angles QOZ and ZOP is then one half that through which the telescope has been turned, which may be measured by a graduated circle, and which is the zenith distance of the object measured from the direction of the axis OZ.

00After the image of the body is brought into coincidence with the cross threads, the instrument is turned through 180Ã‚° on the axis, which results in the line of sight of the telescope pointing in a certain direction OQ, determined by the condition QOZ = ZOP. The telescope is then a second time pointed at the object by being moved through the angle QOP. Either of the angles QOZ and ZOP is then one half that through which the telescope has been turned, which may be measured by a graduated circle, and which is the zenith distance of the object measured from the direction of the axis OZ.

00

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