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Pausanias states that the end of the First Messenian War was the first year of the 14th Olympiad.
The date must have been 724 / 723 BC if the first year of the first Olympiad was 776 / 775 BC.
Kings Polydorus of the Agiads and Theopompus of the Eurypontids were reigning at that time, roughly in mid-reign.
The end of the war must be 379 years from the return of the Heraclids.
According to Isaac Newton, also a classical scholar, the ten kings reigned an average of 38 years each, which can be used as an estimator of the dates.
Eurysthenes would have ruled in 1104 – 1066 BC, with an unknown margin of error, as much of the data is relatively uncertain.

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