Tsinger's Method

a method proposed by N. Ia. Tsinger in 1874 for determining the correction to a clock from observations of two stars at equal altitudes. The stars are selected such that at the moments of observations at equal altitudes (zenith distances) the sum of the azimuths of the two stars is close to 360° and such that one star is located in the eastern side of the sky and the other in the western side. Observations are made with a universal instrument or a zenith telescope in the focal plane of whose objectives there is a grid with several horizontal filaments. To fixate small changes in the inclination of the tube, the instrument must have a level that is securely mounted to the horizontal axis of rotation of the tube.

Calculations of the clock correction u can be made using the formula

where α_w α_e T_w, and T_e are the right ascensions and average moments of time of the observations of the western and eastern stars, respectively, r is a correction that depends on the inequality of the declinations of stars that form the pair, δu̇ is a correction that takes into account the change in the inclination of the tube during observations of the pair of stars, and δα is a correction that allows for the influence of diurnal aberrations on the right ascensions.

Because of the simplicity of observations and high accuracy, Tsinger’s method is widely used in astronomical and geodetic work.