As is not surprising, you can find something about the sources for the name Narnia online; in Professor Downing's essay on names in the Narnia books, one learns, "As to the world in which we meet all these characters, there is an actual place called Narnia. It is best reached, not by climbing into a wardrobe, but by boarding a northbound bus from Rome. Narnia, now called Narni, is a mountain village in the Italian province of Umbria. Lewis would have encountered the name as a passing reference in Tacitus, Livy, and other Latin authors, and he probably liked the sound of the name."
As he had such marvelous libraries available to him for browsing and reading, I'm wondering if he peeped into Johannes M. Watterich's Pontificum Romanorum Vitae (Leipzig, 1862.) Montague Summers describes a matter contained in it this way:
A very extraordinary circumstance is related by Wipert, Archdeacon of the celebrated see of Toul, who wrote the life of Pope S. Leo IX, a Pontiff, who had been for more than twenty years Bishop of Toul, and who died in March, 1054. The historian [Johannes Watterich, I believe he intends here] tells us that some years before the death of S. Leo IX, the citizens of Narni, a little burgh which is picturesquely situated on a lofty rock at the point where the river Nera forces its way through a narrow ravine to join the Tiber, were one day greatly surprised and indeed alarmed to see a mysterious company of persons who appeared to be advancing toward the town. The magistrates, fearing some surprise, gave orders than the gates should be fast closed, whilst the inhabitants incontinently betook themselves to the walls. The procession, however, which was clothed in white and seemed from time to time to vanish among the morning mists and then once again to reappear, was obviously no inimical band. They passed on their way without turning to right or to left, and it is said they seemed to be defiling with measured pace until eventide. All wondered who these persons could be, and at last one of the most prominent citizens, a man of great resolution and courage resolved to address them. To his amazement he saw among them a certain person who had been his host many years before Ascoli, and of whose death he had been recently informed. Calling upon him loudly by his name he asked: "Who are you, and whence cometh this throng?" "I am your old friend," was the reply, "and this multitude is phantom; we have not yet atoned for the sins we committed whilst on earth, and we are not yet deemed worthy to enter the Kingdom of Heaven; therefore are we sent forth as humble penitents, lowly palmers... --Montague Summers, The Vampire: His Kith and Kin (New Hyde Park, NY: University Books, 1960The account goes on from there, as the living friend has a fit from astonishment and is ill for twelve months. Let that me a warning to you not to have truck with ghosts! And it's a reminder to me that 12 days (thus far) is not all that bad...
What strikes me is the "picturesque" little "burgh" on "rock" at the point where one water meets another water--here, it is where the Neva joins the Tiber. What we know as the royal seat of the Narnian world changes a great deal over time, but it fits--at one time or another--this description. Cair refers to walled city or castle. (Paravel most likely stems from tenant paravail, or the feudal concept of tenant-of-a-tenant, but that goes in another direction entirely, with the idea of the ruler as servant to Aslan, who is in turn servant to his father--and also with the idea of ruler as servant to those ruled.) At an unknown time, either in hope of fulfilled prophecy or for use, Cair Paravel was built where one great water meets another; that is, where the Great River, not long after it is joined by the Rush River, flows into the Eastern Ocean. Sometimes in its history, Cair Paravel is surrounded by city, other times not. Sometimes it is sited on a peninsula, and sometimes the sea takes it for an island, and it becomes a palace with protective walls of water. It is, like the "little burgh" of Narni, seated on rock.
Summers' retelling of the story of a ghostly pilgrimage passing by Narni suggests bonds with Narnia and Cair Paravel having to do with "thin places," where one world verges on another. The Narni of Watterich's account is a place on earth where world and the spectral meet and may even converse. It's a "thin place" where our world impinges on the realm of the dead. Likewise Cair Paravel is a border place, sited in the eastern coast and so suggestive of the unknown realm belonging to the Emperor Beyond-the-Sea who is the father of Aslan. The eastern edge is the closest one can come to him in the land of Narnia.
That's why the ruling seat of Narnia is neither at Lantern Waste (where the first human king and queen ruled), nor somewhere central like the spot where the White Witch set her camp. As the Eastern Ocean surrounds what was once a peninsula, Cair Paravel becomes more and more a "between" place that exists on the boundary between earth and water. Even its design reflects this identity. While it may be built stone on stone, the cair has an eastern door that can be flung open onto the Eastern Ocean, where the mermaids sing. As a "thin place" and as a border spot, it mediates between earth and water, between the four human kings and queens and the realm of nature, between civilization and the wild, and between all Narnia and the world beyond ruled by the Emperor Beyond-the-Sea, the King of all Kings.
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As my husband said, you can just imagine Lewis and Tolkien talking this story over in the Bird and Baby (more properly, The Eagle and Child, and less properly, Fowl and Foetus), one nabbing the name and the other daydreaming about an army of wanderers who have to work out their redemption by a particular task--one dayAragorn will hold them to their crime and allegiance.