Arthur was born to a Limerick family, many members of which had filled municipal offices in that city in early times.
In April 1624, he opened a practice in Dublin, where he spent the greater part of his time, but still attended patients in Limerick during occasional visits.
Among the various cases which he treated the most important one, or at least the one in which he took most pride, was that of Archbishop Usher, ‘pseudo-primas Ardmachanus,’ whose complaint had baffled the English physicians.
His entry-book also contains an exact record of his gradual accumulation of landed property, and also a few pieces in ponderous Latin verse.
Among the latter is an ‘Anagramma physiognomicum in nomen Thomæ Wentworth, Proregis Hiberniæ, truculenti et nefarii hominis.’ But his greatest literary effort is a genealogical account, ‘Edylium genealogicum,’ of the family of Arthur, in Latin elegiacs, in which, besides the glory of his ancestors, he gives some particulars of his own life.