Readers interested in this subject should also refer to the page on this site, titled "Mathematically breaking down the Equation"


Showing how the Equation of Time can be generated by one gear rotating around another.

Kurt Descovich - 2016 - Schwartenau Heliochronometer : Ref NASS Compendium 23:1 Mar 2016  : see also page on Moving Hour Lines Sundials.  See left image, the Left end of the blue slider is fixed (except when adjusting for Daylight Savings time, The Right end is connected to the rotatable equatorial ring, See right image, the knob at the bottom adjusts for the year in the leap year cycle. The little pointer in the middle of the picture allows the tiny adjustment of the movement of perihelion towards the vernal equinox.
Mark Frank - 2014 - Astro Skeleton Clock. Short speeded-up video showing how the differential drive outboard wheel dips and rises throughout the year controlled by a equation kidney cam. This action is one year compressed into only a few seconds.


Jens Olsen 1872 - 1945

Almost certainly, the most significant Equation modelling has been accomplished by the famous Jens Olsen clock that can be seen in the town hall in Copenhagen. The clock - comprising more than 15,000 parts, was completed after the death of Jens Olsen in 1955.

The Front of the Jens Olsen Clock. The top right face shows the Equation of Time, local time and Solar Time

Detail of Equation Clock Face. TOP - (A) Equation of Time & (B) EoT longitude corrected (these hands are fixed 9 mins 47 second apart ; the longitude difference between CET's 15° East and Copenhagen.  LEFT Local Mean Time.  RIGHT True Solar Time. The clock was not running when this photo was taken (see the vast difference between local and true solar time).

The Rear of the Jens Olsen Clock. The rectangular section (bottom centre) generated the 5 sine components of the lunar motion and, at the right , the 2 main & 1 small sine components of the Equation of Time. The connection between the signal generation and the Dial (now top right) is via a steel ribbon.

Note that the black & white illustrations, following, were taken from Otto Mortensen's book "Jens Olsen's Clock" - 1957 - Copenhagen Technological Institute. No longer in print. Otto Mortensen was Olsen's  friend and collaborator. He was the chief clockmaker who completed the clock, following Olsen's death.
Details of Equation Mechanism,

Behind the Tusi Couples, is the gear work to generate the anomalistic and tropical year

Jan Olsen's own diagram showing the generation of Tropical and Anomalistic year rotations

Detail of the 2 Tusi Couples and the 3rd order correction

The two Tusi couples, having been summed by a pulley system are connected via a steel ribbon to the Equation face, seen below.
Click to enlarge : Detail of Rear of Equation Face : LEFT : Whole works - top left is the quarter-round sector with steel ribbon from Equation mechanism and to left centre, the connection rod to main pendulum mean time mechanism RIGHT details.
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