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In the System of the World (Book III of Principia), Newton clearly
indicates that there are two tides per day and draws an ellipse that
represents a cross section of the Earth (showing bulges on both sides).
He goes so far as to explain some unusual occurrences that had been noted
by sailors in Batshaw and the kingdom of Tunquin that, on the day
following the moon's transition from one side of the equator to the
other, there is only one tide per day.
In my quick perusal of this passage, however, I cannot find where he
explains why there must be bulges on opposite sides of the Earth.