¹'Donovan, John, and Eugene O'Curry. Letters Containing Information Relative to the Antiquities of the County of Clare, Collected during the Progress of the Ordnance Survey in 1839. Ed. Michael O'Flanagan. Bray, 1927.
O'Donovan is here quoting from the 14th-century text Cathreim Thoirdhealbhaigh, or Triumphs of Torlough. See more here. See O'Grady's translation here.
The full text of this poem, as translated by O'Donovan:

Let us give the title of King,
(Which will be of much fame
To the land which has chosen him)
To the valorous griffin [warrior]
The son of the fair-formed Donogh
Of the sealed secrets
Generous heir of generous Blood
The puissant Dermot of fortresses.
he is kind to the Church,
He is head over all,
The heart (centre) of the territories,
A tree under blossom.
Dermot of Dun Mor
The mild, lively, fierce,
Received the hostages
Through his wisdom and sword
His gracious smile and pomp (pride)
He exhibits with grace
And since he has commenced his career
His fame has spread afar
Momonia of Bards
Is his principality
Proclaim we him A King
Of his tribes with great joy.

²Westropp, Thomas J. "Magh Adhair, Co. Clare. The Place of Inauguration of the Dalcassian Kings." Proceedings of the Royal Irish Academy 1889-1901 4.1896 - 1898 (1896): 55-60.
The derivation of "Magh Adhair" from "Adhar's plain," is mentioned in connection with the hero Adar in the legend of Cam Conaill in the 12th-century MS Rawlinson B 502. (FitzPatrick, Elizabeth. Royal Inauguration in Gaelic Ireland C. 1100-1600: A Cultural Landscape Study. Woodbridge, Suffolk, UK: Boydell, 2004. 52-59.)

³O'Donovan, John, and Michael O'Flanagan. Letters Containing Information Relative to the Antiquities of the County of Clare, Collected during the Progress of the Ordnance Survey in 1839. Vol. 4. Bray, 1927. Web. 22 Apr. 2014. <http://www.clarelibrary.ie/eolas/coclare/history/osl/clooney_bunratty2_magh_adhair.htm>.

⁴FitzPatrick, Elizabeth. Royal Inauguration in Gaelic Ireland C. 1100-1600: A Cultural Landscape Study. Woodbridge, Suffolk, UK: Boydell, 2004. 52-59.

⁵O'Brien, John. Focalóir Gaoidhilge-Sax-bhéarla; Or, An Irish-English Dictionary. Dublin: Hodges and Smith, 1832. 311.
This book may be read in its entirety here.

⁶O'Donovan
Here is the full text of O'Donovan's statement, from a letter dated December 4th, 1839:
"What are we then to think of etymological investigators? They can take words asunder as they please, and give to each component part whatever meaning will best answer the historical theory to be established! Nothing amuses me more than the barefaced effontery with which they urge their silly conjectures as valuable truths, and there is no class of men I hold in greater contempt than those who attempt to build a false system of history on their own etymological speculations. I respect O'Brien's learning, but I laugh at his knowledge of Irish history and topography; I despise Vallancey as having no definite knowledge at all, for having published in his own name the MS., productions of others, and for having forged originals and given garbled and false translations of genuine historical documents...
The etymological antiquists of the last century have attempted to erect a visionary fabric of history with materials derived from false derivations of words, and I think it my duty to do my utmost to pull down their foolish systems, convinced that no nation ever derived honor from any history but that which is demonstratively true."

⁷FitzPatrick 52-59.
The author considers the name of the small stream at the edge of Magh Adhair: "The 'Hell River' (Abhann Ifrinn) acts as a natural boundary to it on its west side. There is no available explanation of the origin of the name of this river, but it evokes Otherworld connotations, recalling the portrayal of the 'Cave of Cruachain' as one of the entrances to the Otherworld...The Hell River flows due southeast to join the Boolyree River just south of Hell Bridge." The "Cave of Cruachain," also known as "The Cave of the Cats," or "Hell's Mouth Cave" is explored here in Voices from the Dawn.

⁸Brenneman, Walter L., and Mary G. Brenneman. Crossing the Circle at the Holy Wells of Ireland. Charlottesville: University of Virginia, 1995. 66.

⁹Westropp 56.
Lady Gregory recounts another tale of fairy enchantment at a fort in Co. Clare: "There is a fort in Clare, and two or three men went down it one time and brought rushes and lights with them. And they came to where there was a woman washing at a river, and they heard the crying of young lambs, and it was November; for when we have winter here there is summer there. So they got afraid, and two of the men came back but one of them stopped there and was never heard of after." (Gregory, Augusta. "Legends of the Raths, as Narrated to Lady Gregory." Journal of the Galway Archaeological and Historical Society 2 (1902): 116-17.)

¹⁰Curiously, the 1896 drawing of Cahercalla by Westropp was the sole graphic representation of the fort we could locate on the web, nor were there modern references to the fort, nor could we find it indicated on modern maps. We were about to conclude that it had been destroyed at some point after Westropp's visit. But an April 2014 query to the very capable reference staff at the Clare County Library resulted in locating the fort just where Westropp said it would be, somewhat obscured by vegetation, in a Bing satellite view.

¹¹Westropp 56-58.
Duffy, Seán. Brian Boru and the Battle of Clontarf. Dublin: Gill & Macmillan, 2013. 94-5.

¹²"Proceedings: Fourth Excursion: Magh Adhair." Journal of the Royal Society of Antiquaries of Ireland 10 (1900): 440.
More details may be found here. According to Professor Duffy, the Flan Sunagh chessboard story is likely a later romantic invention with no basis in fact. (Duffy, Seán. "Beal Boru and Magh Adhair on Voices from the Dawn." Message to the author. 1 May 2014. E-mail.)

¹³Westropp 58-59.

¹⁴Newman, Roger Chatterton. Brian Boru, King of Ireland. Dublin: Anvil, 1983. 106-7.
After the insult of the cutting of the sacred tree, Brian marched out into Leinster, and, it was reported, "'All Lynster was preyed and destroyed' by the army."

¹⁵Duffy, Seán. Brian Boru and the Battle of Clontarf. Dublin: Gill & Macmillan, 2013. 94-5.

¹⁶Westropp 60.
Westropp, Thomas J. "County Clare Folk-Tales and Myths: The Danish Wars and King Brian." Clare County Library. Web. 25 Apr. 2014. <http://www.clarelibrary.ie/eolas/coclare/folklore/folk_tales/chapter6.htm>.