Rømer's Discovery

In the year of 1672 the astronomer Jean Picard invited Ole Rømer to work with him in Paris. As Ole Rømer went to Paris he brought along Tycho Brahe’s complete observations– and soon he was occupied in studying Jupiter and the eclipses of Jupiter’s four moons.

Rømer found that the moons did not appear to revolve regularly – sometimes a moon seamed to revolve faster and sometimes slower. The only explanation he could find was, that light is not instant. He called his discovery: The Hesitation of Light. In November 1676 Rømer issued a small article in Journal des Sçavans about his revolutionary discovery.
The value Rømer calculated for the finite velocity of light was very close to the value we acknowledge nowadays.
Rømer constructed this Jupiter-moon-calculator in 1677. With this machine he could explain the phenomenon to other scientists.

References:
H-U. Fuchs: Messung der Lichtgeschwindigkeit nach Ole Rømer.
Orion 33.Jg.(1995)No.148.
Kristen Rohlfes: Olaf Römer und die Lichtgeschwindigkeit.
Sterne und Weltraum 1974/10 p.311.
Poul Darnell: The Planetary Machines at Rosenborg.
Translated form an article in " Seks beretninger
fra teknikkens historie". ISBN 87-872-0053-8.
Henry C. King in cooperation with John R. Millburn: Geared to the Stars.
University of Toronto Press, Torento 1978. ISBN 0-8020-2312-6. P.107 & 113.