Theoretical arms of O'Brien Earl of Thomond with arms of Guy de Bryan, 1st Baron Bryan (d.1390) in 2nd Quarter

Quartered arms of w:Murrough O'Brien, 1st Earl of Thomond, 1st Baron Inchiquin. Quarterly of 4:

• 1&4: Gules, three lions passant guardant in pale per pale or and argent. A difference of the English royal arms of Plantagenet, granted by King Henry VIII at Greenwich in 1543, together with the Earldom of Thomond, to Murrough O'Brien, formerly Prince of Thomond;
• 2: Argent, three piles in point issuing from the chief gules, supposedly a difference of the Anglo-Norman family of de Bryan (Guy de Bryan, 1st Baron Bryan (d.1390)), whose descendant was Sir w:Francis Bryan (1490-1550) a courtier of King Henry VIII and Lord Justice of Ireland during the reign of his son King Edward VI (1547-1553);
• 3: Or, a pheon point down azure, arms of Sir w:Henry Sidney, w:Lord Deputy of Ireland, (1565–71 & 1575–78).

"The vexed question of the pheon" in the O'Brien arms (per Cokayne, G. E. & Geoffrey H. White, eds. (1953). The Complete Peerage, or a history of the House of Lords and all its members from the earliest times, volume XII part 1: Skelmersdale to Towton. Vol. 12.1 (2nd ed.). London: The St. Catherine Press, Thomond, p.716, note (e)) was discussed by G.E.Cockayne (1896) (Joseph Jackson Howard (Ed.), Miscellanea Genealogica et Heraldica, Vol.I, 3rd Series, London, 1896, pp.49-50, G.E.Cockayne, Bookplate of Charles O'Brien[1]). Cockayne suggested that the 2nd and 3rd quarters were originally intended to be the same arms, but due to artistic errors had become two separate coats. The actual undifferenced arms of the Anglo-Norman de Bryan family (Or, three piles in point issuing from the chief azure) are the same tinctures and general shape as the "Sidney pheon" of the 3rd quarter - namely an arrow-head shape azure, point down, on a field or, as reconstructed in this theoretical image.

Text per Cockayne, Bookplate of Charles O'Brien:

It wil be observed that if the pheon (so to call it) in the third quarter reached to the top, the structure of the two last coats would be identical. May we not therefore consider that this pheon (which has always been a "crux" in the coat of O'Brien) is only an (ill-drawn) reduplication of the former coat, it being in one case Argent, three piles conjoined in base gules and in the other the same coat with different tinctures i.e. with the field or and the charge azure as borne in 1370 by Lord Bryan, K.G. The well-known arms of Sidney Or, a pheon azure, are identical with those generally depicted in this third quarter. It is, however, quite clear that the O'Brien family were not entitled according to the laws of heraldry, to quarter the coat of Sydney though It has indeed been suggested that they assumed the same out of respect to Sir Henry Sydney, many times (1567-1578) Lord Deputy of Ireland. That they should thus honour the English Viceroy, by adopting his paternal coat as one of their own quarterings, is, however, a somewhat wild surmise. Mr Vicars, Ulster King of Arms, kindly informs me that the earliest record of this quartering is in the time of Carney, who was Ulster King in the middle of the seventeenth century, that " there are plenty of allusions to this coat as a quartering of Lord Thomond, but no mention of it as that of Sydney until we come to the Lords' entries (i., p. 67), dated 1721, where the quarterings are given as "1st and 4th, O'Bryen or O'Brien  ; 2nd, 0' Bryan  ; 3rd, Sydney". He adds that " in one of the seventeenth century references this coat is given as Azure, a pheon argent. Whether the coat should, or should not, be a pheon is doubtless questionable, but (granting it so to be) it is extremely improbable (pace the "Lords' entries" as above) that it should be the coat of Sydney, and not that of O'Brien or some other Irish family whom the O'Briens represented.